```  ---------------------------------
-
-  geom.h
-    header file for geometric routines
-
-   see qh-geom.htm and geom.c
-
-   copyright (c) 1993-2002 The Geometry Center
-*/
-
-#ifndef qhDEFgeom
-#define qhDEFgeom 1
-
-/* ============ -macros- ======================== */
-
-/*----------------------------------
-
-  fabs_(a)
-    returns the absolute value of a
-*/
-#define fabs_( a ) ((( a ) < 0 ) ? -( a ):( a ))
-
-/*----------------------------------
-
-  fmax_(a,b)
-    returns the maximum value of a and b
-*/
-#define fmax_( a,b )  ( ( a ) < ( b ) ? ( b ) : ( a ) )
-
-/*----------------------------------
-
-  fmin_(a,b)
-    returns the minimum value of a and b
-*/
-#define fmin_( a,b )  ( ( a ) > ( b ) ? ( b ) : ( a ) )
-
-/*----------------------------------
-
-  maximize_(maxval, val)
-    set maxval to val if val is greater than maxval
-*/
-#define maximize_( maxval, val ) {if (( maxval ) < ( val )) ( maxval )= ( val );}
-
-/*----------------------------------
-
-  minimize_(minval, val)
-    set minval to val if val is less than minval
-*/
-#define minimize_( minval, val ) {if (( minval ) > ( val )) ( minval )= ( val );}
-
-/*----------------------------------
-
-  det2_(a1, a2,
-        b1, b2)
-
-    compute a 2-d determinate
-*/
-#define det2_( a1,a2,b1,b2 ) (( a1 )*( b2 ) - ( a2 )*( b1 ))
-
-/*----------------------------------
-
-  det3_(a1, a2, a3,
-       b1, b2, b3,
-       c1, c2, c3)
-
-    compute a 3-d determinate
-*/
-#define det3_( a1,a2,a3,b1,b2,b3,c1,c2,c3 ) ( ( a1 )*det2_( b2,b3,c2,c3 ) \
-                - ( b1 )*det2_( a2,a3,c2,c3 ) + ( c1 )*det2_( a2,a3,b2,b3 ) )
-
-/*----------------------------------
-
-  dX( p1, p2 )
-  dY( p1, p2 )
-  dZ( p1, p2 )
-
-    given two indices into rows[],
-
-    compute the difference between X, Y, or Z coordinates
-*/
-#define dX( p1,p2 )  ( *( rows[p1] ) - *( rows[p2] ))
-#define dY( p1,p2 )  ( *( rows[p1]+1 ) - *( rows[p2]+1 ))
-#define dZ( p1,p2 )  ( *( rows[p1]+2 ) - *( rows[p2]+2 ))
-#define dW( p1,p2 )  ( *( rows[p1]+3 ) - *( rows[p2]+3 ))
-
-/*============= prototypes in alphabetical order, infrequent at end ======= */
-
-void    qh_backnormal (realT **rows, int numrow, int numcol, boolT sign, coordT *normal, boolT *nearzero);
-void	qh_distplane (pointT *point, facetT *facet, realT *dist);
-facetT *qh_findbest (pointT *point, facetT *startfacet,
-		     boolT bestoutside, boolT isnewfacets, boolT noupper,
-		     realT *dist, boolT *isoutside, int *numpart);
-facetT *qh_findbesthorizon (boolT ischeckmax, pointT *point,
-	             facetT *startfacet, boolT noupper, realT *bestdist, int *numpart);
-facetT *qh_findbestnew (pointT *point, facetT *startfacet, realT *dist,
-		     boolT bestoutside, boolT *isoutside, int *numpart);
-void 	qh_gausselim(realT **rows, int numrow, int numcol, boolT *sign, boolT *nearzero);
-realT   qh_getangle(pointT *vect1, pointT *vect2);
-pointT *qh_getcenter(setT *vertices);
-pointT *qh_getcentrum(facetT *facet);
-realT   qh_getdistance(facetT *facet, facetT *neighbor, realT *mindist, realT *maxdist);
-void    qh_normalize (coordT *normal, int dim, boolT toporient);
-void    qh_normalize2 (coordT *normal, int dim, boolT toporient,
-            realT *minnorm, boolT *ismin);
-pointT *qh_projectpoint(pointT *point, facetT *facet, realT dist);
-
-void    qh_setfacetplane(facetT *newfacets);
-void 	qh_sethyperplane_det (int dim, coordT **rows, coordT *point0,
-              boolT toporient, coordT *normal, realT *offset, boolT *nearzero);
-void 	qh_sethyperplane_gauss (int dim, coordT **rows, pointT *point0,
-	     boolT toporient, coordT *normal, coordT *offset, boolT *nearzero);
-boolT   qh_sharpnewfacets (void);
-
-/*========= infrequently used code in geom2.c =============*/
-
-
-coordT *qh_copypoints (coordT *points, int numpoints, int dimension);
-void    qh_crossproduct (int dim, realT vecA[3], realT vecB[3], realT vecC[3]);
-realT 	qh_determinant (realT **rows, int dim, boolT *nearzero);
-realT   qh_detjoggle (pointT *points, int numpoints, int dimension);
-void    qh_detroundoff (void);
-realT   qh_detsimplex(pointT *apex, setT *points, int dim, boolT *nearzero);
-realT   qh_distnorm (int dim, pointT *point, pointT *normal, realT *offsetp);
-realT   qh_distround (int dimension, realT maxabs, realT maxsumabs);
-realT   qh_divzero(realT numer, realT denom, realT mindenom1, boolT *zerodiv);
-realT   qh_facetarea (facetT *facet);
-realT   qh_facetarea_simplex (int dim, coordT *apex, setT *vertices,
-          vertexT *notvertex,  boolT toporient, coordT *normal, realT *offset);
-pointT *qh_facetcenter (setT *vertices);
-facetT *qh_findgooddist (pointT *point, facetT *facetA, realT *distp, facetT **facetlist);
-void    qh_getarea (facetT *facetlist);
-boolT   qh_gram_schmidt(int dim, realT **rows);
-boolT   qh_inthresholds (coordT *normal, realT *angle);
-void    qh_joggleinput (void);
-realT  *qh_maxabsval (realT *normal, int dim);
-setT   *qh_maxmin(pointT *points, int numpoints, int dimension);
-realT   qh_maxouter (void);
-void    qh_maxsimplex (int dim, setT *maxpoints, pointT *points, int numpoints, setT **simplex);
-realT   qh_minabsval (realT *normal, int dim);
-int     qh_mindiff (realT *vecA, realT *vecB, int dim);
-boolT   qh_orientoutside (facetT *facet);
-void    qh_outerinner (facetT *facet, realT *outerplane, realT *innerplane);
-coordT  qh_pointdist(pointT *point1, pointT *point2, int dim);
-void    qh_printmatrix (FILE *fp, char *string, realT **rows, int numrow, int numcol);
-void    qh_printpoints (FILE *fp, char *string, setT *points);
-void    qh_projectinput (void);
-void 	qh_projectpoints (signed char *project, int n, realT *points,
-             int numpoints, int dim, realT *newpoints, int newdim);
-int     qh_rand( void);
-void    qh_srand( int seed);
-realT   qh_randomfactor (void);
-void    qh_randommatrix (realT *buffer, int dim, realT **row);
-void    qh_rotateinput (realT **rows);
-void    qh_rotatepoints (realT *points, int numpoints, int dim, realT **rows);
-void    qh_scaleinput (void);
-void    qh_scalelast (coordT *points, int numpoints, int dim, coordT low,
-		   coordT high, coordT newhigh);
-void 	qh_scalepoints (pointT *points, int numpoints, int dim,
-  		realT *newlows, realT *newhighs);
-boolT   qh_sethalfspace (int dim, coordT *coords, coordT **nextp,
-              coordT *normal, coordT *offset, coordT *feasible);
-coordT *qh_sethalfspace_all (int dim, int count, coordT *halfspaces, pointT *feasible);
-pointT *qh_voronoi_center (int dim, setT *points);
-
-#endif /* qhDEFgeom */
-
-
-
diff --git a/extern/qhull/include/qhull/io.h b/extern/qhull/include/qhull/io.h
deleted file mode 100644
index 351d56b3708..00000000000
--- a/extern/qhull/include/qhull/io.h
+++ /dev/null
@@ -1,149 +0,0 @@
-/*  ---------------------------------
-
-   io.h
-   declarations of Input/Output functions
-
-   see README, qhull.h and io.c
-
-   copyright (c) 1993-2002, The Geometry Center
-*/
-
-#ifndef qhDEFio
-#define qhDEFio 1
-
-/*============ constants and flags ==================*/
-
-/*----------------------------------
-
-  qh_MAXfirst
-    maximum length of first two lines of stdin
-*/
-#define qh_MAXfirst  200
-
-/*----------------------------------
-
-    min radius for Gp and Gv, fraction of maxcoord
-*/
-
-/*----------------------------------
-
-  qh_GEOMepsilon
-    adjust outer planes for 'lines closer' and geomview roundoff.
-    This prevents bleed through.
-*/
-#define qh_GEOMepsilon 2e-3
-
-/*----------------------------------
-
-  qh_WHITESPACE
-    possible values of white space
-*/
-#define qh_WHITESPACE " \n\t\v\r\f"
-
-
-/*----------------------------------
-
-  qh_RIDGE
-    to select which ridges to print in qh_eachvoronoi
-*/
-typedef enum
-{
-    qh_RIDGEall = 0, qh_RIDGEinner, qh_RIDGEouter
-}
-qh_RIDGE;
-
-/*----------------------------------
-
-  printvridgeT
-    prints results of qh_printvdiagram
-
-  see:
-    qh_printvridge for an example
-*/
-typedef void (*printvridgeT)(FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
-
-/*============== -prototypes in alphabetical order =========*/
-
-void    dfacet( unsigned id);
-void    dvertex( unsigned id);
-void    qh_countfacets (facetT *facetlist, setT *facets, boolT printall,
-              int *numfacetsp, int *numsimplicialp, int *totneighborsp,
-              int *numridgesp, int *numcoplanarsp, int *numnumtricoplanarsp);
-pointT *qh_detvnorm (vertexT *vertex, vertexT *vertexA, setT *centers, realT *offsetp);
-setT   *qh_detvridge (vertexT *vertex);
-setT   *qh_detvridge3 (vertexT *atvertex, vertexT *vertex);
-int     qh_eachvoronoi (FILE *fp, printvridgeT printvridge, vertexT *atvertex, boolT visitall, qh_RIDGE innerouter, boolT inorder);
-int     qh_eachvoronoi_all (FILE *fp, printvridgeT printvridge, boolT isupper, qh_RIDGE innerouter, boolT inorder);
-void	qh_facet2point(facetT *facet, pointT **point0, pointT **point1, realT *mindist);
-setT   *qh_facetvertices (facetT *facetlist, setT *facets, boolT allfacets);
-void    qh_geomplanes (facetT *facet, realT *outerplane, realT *innerplane);
-void    qh_markkeep (facetT *facetlist);
-setT   *qh_markvoronoi (facetT *facetlist, setT *facets, boolT printall, boolT *islowerp, int *numcentersp);
-void    qh_order_vertexneighbors(vertexT *vertex);
-void	qh_printafacet(FILE *fp, int format, facetT *facet, boolT printall);
-void    qh_printbegin (FILE *fp, int format, facetT *facetlist, setT *facets, boolT printall);
-void 	qh_printcenter (FILE *fp, int format, char *string, facetT *facet);
-void    qh_printcentrum (FILE *fp, facetT *facet, realT radius);
-void    qh_printend (FILE *fp, int format, facetT *facetlist, setT *facets, boolT printall);
-void    qh_printend4geom (FILE *fp, facetT *facet, int *num, boolT printall);
-void    qh_printextremes (FILE *fp, facetT *facetlist, setT *facets, int printall);
-void    qh_printextremes_2d (FILE *fp, facetT *facetlist, setT *facets, int printall);
-void    qh_printextremes_d (FILE *fp, facetT *facetlist, setT *facets, int printall);
-void	qh_printfacet(FILE *fp, facetT *facet);
-void	qh_printfacet2math(FILE *fp, facetT *facet, int notfirst);
-void	qh_printfacet2geom(FILE *fp, facetT *facet, realT color[3]);
-void    qh_printfacet2geom_points(FILE *fp, pointT *point1, pointT *point2,
-			       facetT *facet, realT offset, realT color[3]);
-void	qh_printfacet3math (FILE *fp, facetT *facet, int notfirst);
-void	qh_printfacet3geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]);
-void	qh_printfacet3geom_points(FILE *fp, setT *points, facetT *facet, realT offset, realT color[3]);
-void	qh_printfacet3geom_simplicial(FILE *fp, facetT *facet, realT color[3]);
-void	qh_printfacet3vertex(FILE *fp, facetT *facet, int format);
-void	qh_printfacet4geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]);
-void	qh_printfacet4geom_simplicial(FILE *fp, facetT *facet, realT color[3]);
-void	qh_printfacetNvertex_nonsimplicial(FILE *fp, facetT *facet, int id, int format);
-void	qh_printfacetNvertex_simplicial(FILE *fp, facetT *facet, int format);
-void    qh_printfacetridges(FILE *fp, facetT *facet);
-void	qh_printfacets(FILE *fp, int format, facetT *facetlist, setT *facets, boolT printall);
-void	qh_printhelp_degenerate(FILE *fp);
-void	qh_printhelp_singular(FILE *fp);
-void	qh_printhyperplaneintersection(FILE *fp, facetT *facet1, facetT *facet2,
-  		   setT *vertices, realT color[3]);
-void	qh_printneighborhood (FILE *fp, int format, facetT *facetA, facetT *facetB, boolT printall);
-void    qh_printline3geom (FILE *fp, pointT *pointA, pointT *pointB, realT color[3]);
-void	qh_printpoint(FILE *fp, char *string, pointT *point);
-void	qh_printpointid(FILE *fp, char *string, int dim, pointT *point, int id);
-void    qh_printpoint3 (FILE *fp, pointT *point);
-void    qh_printpoints_out (FILE *fp, facetT *facetlist, setT *facets, int printall);
-void    qh_printpointvect (FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius, realT color[3]);
-void    qh_printpointvect2 (FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius);
-void	qh_printridge(FILE *fp, ridgeT *ridge);
-void    qh_printspheres(FILE *fp, setT *vertices, realT radius);
-void    qh_printvdiagram (FILE *fp, int format, facetT *facetlist, setT *facets, boolT printall);
-int     qh_printvdiagram2 (FILE *fp, printvridgeT printvridge, setT *vertices, qh_RIDGE innerouter, boolT inorder);
-void	qh_printvertex(FILE *fp, vertexT *vertex);
-void	qh_printvertexlist (FILE *fp, char* string, facetT *facetlist,
-                         setT *facets, boolT printall);
-void	qh_printvertices (FILE *fp, char* string, setT *vertices);
-void    qh_printvneighbors (FILE *fp, facetT* facetlist, setT *facets, boolT printall);
-void    qh_printvoronoi (FILE *fp, int format, facetT *facetlist, setT *facets, boolT printall);
-void    qh_printvnorm (FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
-void    qh_printvridge (FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
-void	qh_produce_output(void);
-void    qh_projectdim3 (pointT *source, pointT *destination);
-int     qh_readfeasible (int dim, char *remainder);
-coordT *qh_readpoints(int *numpoints, int *dimension, boolT *ismalloc);
-void    qh_setfeasible (int dim);
-boolT	qh_skipfacet(facetT *facet);
-
-#endif /* qhDEFio */
diff --git a/extern/qhull/include/qhull/mem.h b/extern/qhull/include/qhull/mem.h
deleted file mode 100644
index e9ebd1bb9bc..00000000000
--- a/extern/qhull/include/qhull/mem.h
+++ /dev/null
@@ -1,174 +0,0 @@
-/*  ---------------------------------
-
-   mem.h
-     prototypes for memory management functions
-
-   see qh-mem.htm, mem.c and qset.h
-
-   for error handling, writes message and calls
-     qh_errexit (qhmem_ERRmem, NULL, NULL) if insufficient memory
-       and
-     qh_errexit (qhmem_ERRqhull, NULL, NULL) otherwise
-
-   copyright (c) 1993-2002, The Geometry Center
-*/
-
-#ifndef qhDEFmem
-#define qhDEFmem
-
-/*---------------------------------
-
-  qh_NOmem
-    turn off quick-fit memory allocation
-
-  notes:
-    mem.c implements Quickfit memory allocation for about 20% time
-    savings.  If it fails on your machine, try to locate the
-    problem, and send the answer to qhull@geom.umn.edu.  If this can
-    not be done, define qh_NOmem to use malloc/free instead.
-
-   #define qh_NOmem
-*/
-
-/*-------------------------------------------
-    to avoid bus errors, memory allocation must consider alignment requirements.
-    malloc() automatically takes care of alignment.   Since mem.c manages
-    its own memory, we need to explicitly specify alignment in
-    qh_meminitbuffers().
-
-    A safe choice is sizeof(double).  sizeof(float) may be used if doubles
-    do not occur in data structures and pointers are the same size.  Be careful
-    of machines (e.g., DEC Alpha) with large pointers.  If gcc is available,
-    use __alignof__(double) or fmax_(__alignof__(float), __alignof__(void *)).
-
-   see qh_MEMalign in user.h for qhull's alignment
-*/
-
-#define qhmem_ERRmem 4    /* matches qh_ERRmem in qhull.h */
-#define qhmem_ERRqhull 5  /* matches qh_ERRqhull in qhull.h */
-
-/*----------------------------------
-
-  ptr_intT
-    for casting a void* to an integer-type
-
-  notes:
-    On 64-bit machines, a pointer may be larger than an 'int'.
-    qh_meminit() checks that 'long' holds a 'void*'
-*/
-typedef unsigned long ptr_intT;
-
-/*----------------------------------
-
-  qhmemT
-    global memory structure for mem.c
-
- notes:
-   users should ignore qhmem except for writing extensions
-   qhmem is allocated in mem.c
-
-   qhmem could be swapable like qh and qhstat, but then
-   multiple qh's and qhmem's would need to keep in synch.
-   A swapable qhmem would also waste memory buffers.  As long
-   as memory operations are atomic, there is no problem with
-   multiple qh structures being active at the same time.
-   If you need separate address spaces, you can swap the
-   contents of qhmem.
-*/
-typedef struct qhmemT qhmemT;
-extern qhmemT qhmem;
-
-struct qhmemT {               /* global memory management variables */
-  int      BUFsize;	      /* size of memory allocation buffer */
-  int      BUFinit;	      /* initial size of memory allocation buffer */
-  int      TABLEsize;         /* actual number of sizes in free list table */
-  int      NUMsizes;          /* maximum number of sizes in free list table */
-  int      LASTsize;          /* last size in free list table */
-  int      ALIGNmask;         /* worst-case alignment, must be 2^n-1 */
-  void	 **freelists;          /* free list table, linked by offset 0 */
-  int     *sizetable;         /* size of each freelist */
-  int     *indextable;        /* size->index table */
-  void    *curbuffer;         /* current buffer, linked by offset 0 */
-  void    *freemem;           /*   free memory in curbuffer */
-  int 	   freesize;          /*   size of free memory in bytes */
-  void 	  *tempstack;         /* stack of temporary memory, managed by users */
-  FILE    *ferr;              /* file for reporting errors */
-  int      IStracing;         /* =5 if tracing memory allocations */
-  int      cntquick;          /* count of quick allocations */
-                              /* remove statistics doesn't effect speed */
-  int      cntshort;          /* count of short allocations */
-  int      cntlong;           /* count of long allocations */
-  int      curlong;           /* current count of inuse, long allocations */
-  int      freeshort;	      /* count of short memfrees */
-  int      freelong;	      /* count of long memfrees */
-  int      totshort;          /* total size of short allocations */
-  int      totlong;           /* total size of long allocations */
-  int      maxlong;           /* maximum totlong */
-  int      cntlarger;         /* count of setlarger's */
-  int      totlarger;         /* total copied by setlarger */
-};
-
-
-/*==================== -macros ====================*/
-
-/*----------------------------------
-
-  qh_memalloc_(size, object, type)
-    returns object of size bytes
-	assumes size<=qhmem.LASTsize and void **freelistp is a temp
-*/
-
-#ifdef qh_NOmem
-#define qh_memalloc_(size, freelistp, object, type) {\
-  object= (type*)qh_memalloc (size); }
-#else /* !qh_NOmem */
-
-#define qh_memalloc_(size, freelistp, object, type) {\
-  freelistp= qhmem.freelists + qhmem.indextable[size];\
-  if ((object= (type*)*freelistp)) {\
-    qhmem.cntquick++;  \
-    *freelistp= *((void **)*freelistp);\
-  }else object= (type*)qh_memalloc (size);}
-#endif
-
-/*----------------------------------
-
-  qh_memfree_(object, size)
-    free up an object
-
-  notes:
-    object may be NULL
-    assumes size<=qhmem.LASTsize and void **freelistp is a temp
-*/
-#ifdef qh_NOmem
-#define qh_memfree_(object, size, freelistp) {\
-  qh_memfree (object, size); }
-#else /* !qh_NOmem */
-
-#define qh_memfree_(object, size, freelistp) {\
-  if (object) { \
-    qhmem .freeshort++;\
-    freelistp= qhmem.freelists + qhmem.indextable[size];\
-    *((void **)object)= *freelistp;\
-    *freelistp= object;}}
-#endif
-
-/*=============== prototypes in alphabetical order ============*/
-
-void *qh_memalloc(int insize);
-void qh_memfree (void *object, int size);
-void qh_memfreeshort (int *curlong, int *totlong);
-void qh_meminit (FILE *ferr);
-void qh_meminitbuffers (int tracelevel, int alignment, int numsizes,
-			int bufsize, int bufinit);
-void qh_memsetup (void);
-void qh_memsize(int size);
-void qh_memstatistics (FILE *fp);
-
-#endif /* qhDEFmem */
diff --git a/extern/qhull/include/qhull/merge.h b/extern/qhull/include/qhull/merge.h
deleted file mode 100644
index 7fc2afa5967..00000000000
--- a/extern/qhull/include/qhull/merge.h
+++ /dev/null
@@ -1,171 +0,0 @@
-/*  ---------------------------------
-
-   merge.h
-
-   see qh-merge.htm and merge.c
-
-   copyright (c) 1993-2002, The Geometry Center
-*/
-
-#ifndef qhDEFmerge
-#define qhDEFmerge 1
-
-
-/*============ -constants- ==============*/
-
-/*----------------------------------
-
-  qh_ANGLEredundant
-    indicates redundant merge in mergeT->angle
-*/
-#define qh_ANGLEredundant 6.0
-
-/*----------------------------------
-
-  qh_ANGLEdegen
-    indicates degenerate facet in mergeT->angle
-*/
-#define qh_ANGLEdegen     5.0
-
-/*----------------------------------
-
-  qh_ANGLEconcave
-    offset to indicate concave facets in mergeT->angle
-
-  notes:
-    concave facets are assigned the range of [2,4] in mergeT->angle
-    roundoff error may make the angle less than 2
-*/
-#define qh_ANGLEconcave  1.5
-
-/*----------------------------------
-
-  MRG... (mergeType)
-    indicates the type of a merge (mergeT->type)
-*/
-typedef enum {	/* in sort order for facet_mergeset */
-  MRGnone= 0,
-  MRGcoplanar,		/* centrum coplanar */
-  MRGanglecoplanar,	/* angle coplanar */
-  			/* could detect half concave ridges */
-  MRGconcave,		/* concave ridge */
-  MRGflip,		/* flipped facet. facet1 == facet2 */
-  MRGridge,		/* duplicate ridge (qh_MERGEridge) */
-                        /* degen and redundant go onto degen_mergeset */
-  MRGdegen,		/* degenerate facet (not enough neighbors) facet1 == facet2 */
-  MRGredundant,		/* redundant facet (vertex subset) */
-  			/* merge_degenredundant assumes degen < redundant */
-  MRGmirror,	        /* mirror facet from qh_triangulate */
-  ENDmrg
-} mergeType;
-
-/*----------------------------------
-
-  qh_MERGEapex
-    flag for qh_mergefacet() to indicate an apex merge
-*/
-#define qh_MERGEapex     True
-
-/*============ -structures- ====================*/
-
-/*----------------------------------
-
-  mergeT
-    structure used to merge facets
-*/
-
-typedef struct mergeT mergeT;
-struct mergeT {		/* initialize in qh_appendmergeset */
-  realT   angle;        /* angle between normals of facet1 and facet2 */
-  facetT *facet1; 	/* will merge facet1 into facet2 */
-  facetT *facet2;
-  mergeType type;
-};
-
-
-/*=========== -macros- =========================*/
-
-/*----------------------------------
-
-  FOREACHmerge_( merges ) {...}
-    assign 'merge' to each merge in merges
-
-  notes:
-    uses 'mergeT *merge, **mergep;'
-    if qh_mergefacet(),
-      restart since qh.facet_mergeset may change
-    see FOREACHsetelement_
-*/
-#define FOREACHmerge_( merges ) FOREACHsetelement_(mergeT, merges, merge)
-
-/*============ prototypes in alphabetical order after pre/postmerge =======*/
-
-void    qh_premerge (vertexT *apex, realT maxcentrum, realT maxangle);
-void    qh_postmerge (char *reason, realT maxcentrum, realT maxangle,
-             boolT vneighbors);
-void    qh_all_merges (boolT othermerge, boolT vneighbors);
-void    qh_appendmergeset(facetT *facet, facetT *neighbor, mergeType mergetype, realT *angle);
-setT   *qh_basevertices( facetT *samecycle);
-void    qh_checkconnect (void /* qh new_facets */);
-boolT   qh_checkzero (boolT testall);
-void    qh_copynonconvex (ridgeT *atridge);
-void    qh_degen_redundant_facet (facetT *facet);
-void   	qh_degen_redundant_neighbors (facetT *facet, facetT *delfacet);
-vertexT *qh_find_newvertex (vertexT *oldvertex, setT *vertices, setT *ridges);
-void    qh_findbest_test (boolT testcentrum, facetT *facet, facetT *neighbor,
-           facetT **bestfacet, realT *distp, realT *mindistp, realT *maxdistp);
-facetT *qh_findbestneighbor(facetT *facet, realT *distp, realT *mindistp, realT *maxdistp);
-void 	qh_flippedmerges(facetT *facetlist, boolT *wasmerge);
-void 	qh_forcedmerges( boolT *wasmerge);
-void	qh_getmergeset(facetT *facetlist);
-void 	qh_getmergeset_initial (facetT *facetlist);
-void    qh_hashridge (setT *hashtable, int hashsize, ridgeT *ridge, vertexT *oldvertex);
-ridgeT *qh_hashridge_find (setT *hashtable, int hashsize, ridgeT *ridge,
-              vertexT *vertex, vertexT *oldvertex, int *hashslot);
-void 	qh_makeridges(facetT *facet);
-void    qh_mark_dupridges(facetT *facetlist);
-void    qh_maydropneighbor (facetT *facet);
-int     qh_merge_degenredundant (void);
-void    qh_merge_nonconvex( facetT *facet1, facetT *facet2, mergeType mergetype);
-void    qh_mergecycle (facetT *samecycle, facetT *newfacet);
-void    qh_mergecycle_all (facetT *facetlist, boolT *wasmerge);
-void    qh_mergecycle_facets( facetT *samecycle, facetT *newfacet);
-void    qh_mergecycle_neighbors(facetT *samecycle, facetT *newfacet);
-void    qh_mergecycle_ridges(facetT *samecycle, facetT *newfacet);
-void    qh_mergecycle_vneighbors( facetT *samecycle, facetT *newfacet);
-void 	qh_mergefacet(facetT *facet1, facetT *facet2, realT *mindist, realT *maxdist, boolT mergeapex);
-void    qh_mergefacet2d (facetT *facet1, facetT *facet2);
-void 	qh_mergeneighbors(facetT *facet1, facetT *facet2);
-void 	qh_mergeridges(facetT *facet1, facetT *facet2);
-void    qh_mergesimplex(facetT *facet1, facetT *facet2, boolT mergeapex);
-void    qh_mergevertex_del (vertexT *vertex, facetT *facet1, facetT *facet2);
-void    qh_mergevertex_neighbors(facetT *facet1, facetT *facet2);
-void	qh_mergevertices(setT *vertices1, setT **vertices);
-setT   *qh_neighbor_intersections (vertexT *vertex);
-void    qh_newvertices (setT *vertices);
-boolT   qh_reducevertices (void);
-vertexT *qh_redundant_vertex (vertexT *vertex);
-boolT   qh_remove_extravertices (facetT *facet);
-vertexT *qh_rename_sharedvertex (vertexT *vertex, facetT *facet);
-void	qh_renameridgevertex(ridgeT *ridge, vertexT *oldvertex, vertexT *newvertex);
-void    qh_renamevertex(vertexT *oldvertex, vertexT *newvertex, setT *ridges,
-			facetT *oldfacet, facetT *neighborA);
-boolT 	qh_test_appendmerge (facetT *facet, facetT *neighbor);
-boolT   qh_test_vneighbors (void /* qh newfacet_list */);
-void    qh_tracemerge (facetT *facet1, facetT *facet2);
-void    qh_tracemerging (void);
-void    qh_updatetested( facetT *facet1, facetT *facet2);
-setT   *qh_vertexridges (vertexT *vertex);
-void    qh_vertexridges_facet (vertexT *vertex, facetT *facet, setT **ridges);
-void    qh_willdelete (facetT *facet, facetT *replace);
-
-#endif /* qhDEFmerge */
diff --git a/extern/qhull/include/qhull/poly.h b/extern/qhull/include/qhull/poly.h
deleted file mode 100644
index 294ec9527fc..00000000000
--- a/extern/qhull/include/qhull/poly.h
+++ /dev/null
@@ -1,290 +0,0 @@
-/*  ---------------------------------
-
-   poly.h
-   header file for poly.c and poly2.c
-
-   see qh-poly.htm, qhull.h and poly.c
-
-   copyright (c) 1993-2002, The Geometry Center
-*/
-
-#ifndef qhDEFpoly
-#define qhDEFpoly 1
-
-/*===============   constants ========================== */
-
-/*----------------------------------
-
-  ALGORITHMfault
-*/
-#define qh_ALGORITHMfault 0
-
-/*----------------------------------
-
-  DATAfault
-*/
-#define qh_DATAfault 1
-
-/*----------------------------------
-
-  DUPLICATEridge
-    special value for facet->neighbor to indicate a duplicate ridge
-
-  notes:
-    set by matchneighbor, used by matchmatch and mark_dupridge
-*/
-#define qh_DUPLICATEridge ( facetT * ) 1L
-
-/*----------------------------------
-
-  MERGEridge       flag in facet
-    special value for facet->neighbor to indicate a merged ridge
-
-  notes:
-    set by matchneighbor, used by matchmatch and mark_dupridge
-*/
-#define qh_MERGEridge ( facetT * ) 2L
-
-
-/*============ -structures- ====================*/
-
-/*=========== -macros- =========================*/
-
-/*----------------------------------
-
-  FORALLfacet_( facetlist ) { ... }
-    assign 'facet' to each facet in facetlist
-
-  notes:
-    uses 'facetT *facet;'
-    assumes last facet is a sentinel
-
-  see:
-    FORALLfacets
-*/
-#define FORALLfacet_( facetlist ) if ( facetlist ) for( facet=( facetlist );facet && facet->next;facet=facet->next )
-
-/*----------------------------------
-
-  FORALLnew_facets { ... }
-    assign 'newfacet' to each facet in qh.newfacet_list
-
-  notes:
-    uses 'facetT *newfacet;'
-    at exit, newfacet==NULL
-*/
-#define FORALLnew_facets for( newfacet=qh newfacet_list;newfacet && newfacet->next;newfacet=newfacet->next )
-
-/*----------------------------------
-
-  FORALLvertex_( vertexlist ) { ... }
-    assign 'vertex' to each vertex in vertexlist
-
-  notes:
-    uses 'vertexT *vertex;'
-    at exit, vertex==NULL
-*/
-#define FORALLvertex_( vertexlist ) for ( vertex=( vertexlist );vertex && vertex->next;vertex= vertex->next )
-
-/*----------------------------------
-
-  FORALLvisible_facets { ... }
-    assign 'visible' to each visible facet in qh.visible_list
-
-  notes:
-    uses 'vacetT *visible;'
-    at exit, visible==NULL
-*/
-#define FORALLvisible_facets for (visible=qh visible_list; visible && visible->visible; visible= visible->next)
-
-/*----------------------------------
-
-  FORALLsame_( newfacet ) { ... }
-    assign 'same' to each facet in newfacet->f.samecycle
-
-  notes:
-    uses 'facetT *same;'
-    stops when it returns to newfacet
-*/
-#define FORALLsame_(newfacet) for (same= newfacet->f.samecycle; same != newfacet; same= same->f.samecycle)
-
-/*----------------------------------
-
-  FORALLsame_cycle_( newfacet ) { ... }
-    assign 'same' to each facet in newfacet->f.samecycle
-
-  notes:
-    uses 'facetT *same;'
-    at exit, same == NULL
-*/
-#define FORALLsame_cycle_(newfacet) \
-     for (same= newfacet->f.samecycle; \
-         same; same= (same == newfacet ?  NULL : same->f.samecycle))
-
-/*----------------------------------
-
-  FOREACHneighborA_( facet ) { ... }
-    assign 'neighborA' to each neighbor in facet->neighbors
-
-  FOREACHneighborA_( vertex ) { ... }
-    assign 'neighborA' to each neighbor in vertex->neighbors
-
-  declare:
-    facetT *neighborA, **neighborAp;
-
-  see:
-    FOREACHsetelement_
-*/
-#define FOREACHneighborA_(facet)  FOREACHsetelement_(facetT, facet->neighbors, neighborA)
-
-/*----------------------------------
-
-  FOREACHvisible_( facets ) { ... }
-    assign 'visible' to each facet in facets
-
-  notes:
-    uses 'facetT *facet, *facetp;'
-    see FOREACHsetelement_
-*/
-#define FOREACHvisible_(facets) FOREACHsetelement_(facetT, facets, visible)
-
-/*----------------------------------
-
-  FOREACHnewfacet_( facets ) { ... }
-    assign 'newfacet' to each facet in facets
-
-  notes:
-    uses 'facetT *newfacet, *newfacetp;'
-    see FOREACHsetelement_
-*/
-#define FOREACHnewfacet_(facets) FOREACHsetelement_(facetT, facets, newfacet)
-
-/*----------------------------------
-
-  FOREACHvertexA_( vertices ) { ... }
-    assign 'vertexA' to each vertex in vertices
-
-  notes:
-    uses 'vertexT *vertexA, *vertexAp;'
-    see FOREACHsetelement_
-*/
-#define FOREACHvertexA_(vertices) FOREACHsetelement_(vertexT, vertices, vertexA)
-
-/*----------------------------------
-
-  FOREACHvertexreverse12_( vertices ) { ... }
-    assign 'vertex' to each vertex in vertices
-    reverse order of first two vertices
-
-  notes:
-    uses 'vertexT *vertex, *vertexp;'
-    see FOREACHsetelement_
-*/
-#define FOREACHvertexreverse12_(vertices) FOREACHsetelementreverse12_(vertexT, vertices, vertex)
-
-
-/*=============== prototypes poly.c in alphabetical order ================*/
-
-void    qh_appendfacet(facetT *facet);
-void    qh_appendvertex(vertexT *vertex);
-void 	qh_attachnewfacets (void);
-boolT   qh_checkflipped (facetT *facet, realT *dist, boolT allerror);
-void	qh_delfacet(facetT *facet);
-void 	qh_deletevisible(void /*qh visible_list, qh horizon_list*/);
-setT   *qh_facetintersect (facetT *facetA, facetT *facetB, int *skipAp,int *skipBp, int extra);
-unsigned qh_gethash (int hashsize, setT *set, int size, int firstindex, void *skipelem);
-facetT *qh_makenewfacet(setT *vertices, boolT toporient, facetT *facet);
-void    qh_makenewplanes ( void /* newfacet_list */);
-facetT *qh_makenew_nonsimplicial (facetT *visible, vertexT *apex, int *numnew);
-facetT *qh_makenew_simplicial (facetT *visible, vertexT *apex, int *numnew);
-void    qh_matchneighbor (facetT *newfacet, int newskip, int hashsize,
-			  int *hashcount);
-void	qh_matchnewfacets (void);
-boolT   qh_matchvertices (int firstindex, setT *verticesA, int skipA,
-			  setT *verticesB, int *skipB, boolT *same);
-facetT *qh_newfacet(void);
-ridgeT *qh_newridge(void);
-int     qh_pointid (pointT *point);
-void 	qh_removefacet(facetT *facet);
-void 	qh_removevertex(vertexT *vertex);
-void    qh_updatevertices (void);
-
-
-/*========== -prototypes poly2.c in alphabetical order ===========*/
-
-void    qh_addhash (void* newelem, setT *hashtable, int hashsize, unsigned hash);
-void 	qh_check_bestdist (void);
-void    qh_check_maxout (void);
-void    qh_check_output (void);
-void    qh_check_point (pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2);
-void   	qh_check_points(void);
-void 	qh_checkconvex(facetT *facetlist, int fault);
-void    qh_checkfacet(facetT *facet, boolT newmerge, boolT *waserrorp);
-void 	qh_checkflipped_all (facetT *facetlist);
-void 	qh_checkpolygon(facetT *facetlist);
-void    qh_checkvertex (vertexT *vertex);
-void 	qh_clearcenters (qh_CENTER type);
-void 	qh_createsimplex(setT *vertices);
-void 	qh_delridge(ridgeT *ridge);
-void    qh_delvertex (vertexT *vertex);
-setT   *qh_facet3vertex (facetT *facet);
-facetT *qh_findbestfacet (pointT *point, boolT bestoutside,
-           realT *bestdist, boolT *isoutside);
-facetT *qh_findfacet_all (pointT *point, realT *bestdist, boolT *isoutside,
-			  int *numpart);
-int 	qh_findgood (facetT *facetlist, int goodhorizon);
-void 	qh_findgood_all (facetT *facetlist);
-void    qh_furthestnext (void /* qh facet_list */);
-void    qh_furthestout (facetT *facet);
-void    qh_infiniteloop (facetT *facet);
-void 	qh_initbuild(void);
-void 	qh_initialhull(setT *vertices);
-setT   *qh_initialvertices(int dim, setT *maxpoints, pointT *points, int numpoints);
-vertexT *qh_isvertex (pointT *point, setT *vertices);
-vertexT *qh_makenewfacets (pointT *point /*horizon_list, visible_list*/);
-void    qh_matchduplicates (facetT *atfacet, int atskip, int hashsize, int *hashcount);
-void    qh_nearcoplanar ( void /* qh.facet_list */);
-vertexT *qh_nearvertex (facetT *facet, pointT *point, realT *bestdistp);
-int 	qh_newhashtable(int newsize);
-vertexT *qh_newvertex(pointT *point);
-ridgeT *qh_nextridge3d (ridgeT *atridge, facetT *facet, vertexT **vertexp);
-void    qh_outcoplanar (void /* facet_list */);
-pointT *qh_point (int id);
-void 	qh_point_add (setT *set, pointT *point, void *elem);
-setT   *qh_pointfacet (void /*qh facet_list*/);
-setT   *qh_pointvertex (void /*qh facet_list*/);
-void 	qh_prependfacet(facetT *facet, facetT **facetlist);
-void	qh_printhashtable(FILE *fp);
-void    qh_printlists (void);
-void    qh_resetlists (boolT stats, boolT resetVisible /*qh newvertex_list newfacet_list visible_list*/);
-void    qh_setvoronoi_all (void);
-void	qh_triangulate (void /*qh facet_list*/);
-void    qh_triangulate_facet (facetT *facetA, vertexT **first_vertex);
-void    qh_triangulate_link (facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB);
-void	qh_triangulate_mirror (facetT *facetA, facetT *facetB);
-void    qh_triangulate_null (facetT *facetA);
-void    qh_vertexintersect(setT **vertexsetA,setT *vertexsetB);
-setT   *qh_vertexintersect_new(setT *vertexsetA,setT *vertexsetB);
-void    qh_vertexneighbors (void /*qh facet_list*/);
-boolT 	qh_vertexsubset(setT *vertexsetA, setT *vertexsetB);
-
-
-#endif /* qhDEFpoly */
diff --git a/extern/qhull/include/qhull/qhull.h b/extern/qhull/include/qhull/qhull.h
deleted file mode 100644
index 896ec1e9c18..00000000000
--- a/extern/qhull/include/qhull/qhull.h
+++ /dev/null
@@ -1,1048 +0,0 @@
-/*  ---------------------------------
-
-   qhull.h
-   user-level header file for using qhull.a library
-
-   see qh-qhull.htm, qhull_a.h
-
-   copyright (c) 1993-2002, The Geometry Center
-
-   NOTE: access to qh_qh is via the 'qh' macro.  This allows
-   qh_qh to be either a pointer or a structure.  An example
-   of using qh is "qh DROPdim" which accesses the DROPdim
-   the 'qhstat' macro.
-
-   includes function prototypes for qhull.c, geom.c, global.c, io.c, user.c
-
-   use mem.h for mem.c
-   use qset.h for qset.c
-
-   see unix.c for an example of using qhull.h
-
-   recompile qhull if you change this file
-*/
-
-#ifndef qhDEFqhull
-#define qhDEFqhull 1
-
-/*=========================== -included files ==============*/
-
-#include
-#include
-#include
-
-#if __MWERKS__ && __POWERPC__
-#include
-#include
-#include
-#endif
-
-#ifndef __STDC__
-#ifndef __cplusplus
-#if     !_MSC_VER
-#error  Neither __STDC__ nor __cplusplus is defined.  Please use strict ANSI C or C++ to compile
-#error  Qhull.  You may need to turn off compiler extensions in your project configuration.  If
-#error  your compiler is a standard C compiler, you can delete this warning from qhull.h
-#endif
-#endif
-#endif
-
-#include "user.h"      /* user defineable constants */
-
-/*============ constants and basic types ====================*/
-
-/*----------------------------------
-
-  qh_VERSION
-    version string by year and date
-
-    the revision increases on code changes only
-
-  notes:
-    change date:    Changes.txt, Announce.txt, README.txt, qhull.man
-                    qhull-news.html, Eudora signatures,
-    change version: README.txt, qhull.html, file_id.diz, Makefile
-    change year:    Copying.txt
-    recompile user_eg.c, rbox.c, qhull.c, qconvex.c, qdelaun.c qvoronoi.c, qhalf.c
-    make copy of qhull-news.html as qh-news.htm
-*/
-
-#define qh_VERSION "2002.1 2002/8/20"
-
-/*----------------------------------
-
-  coordT
-    coordinates and coefficients are stored as realT (i.e., double)
-
-  notes:
-    could use 'float' for data and 'double' for calculations (realT vs. coordT)
-      This requires many type casts, and adjusted error bounds.
-      Also C compilers may do expressions in double anyway.
-*/
-#define coordT realT
-
-/*----------------------------------
-
-  pointT
-    a point is an array of DIM3 coordinates
-*/
-#define pointT coordT
-
-/*----------------------------------
-
-  flagT
-    Boolean flag as a bit
-*/
-#define flagT unsigned int
-
-/*----------------------------------
-
-  boolT
-    boolean value, either True or False
-
-  notes:
-    needed for portability
-*/
-#define boolT unsigned int
-#ifdef False
-#undef False
-#endif
-#ifdef True
-#undef True
-#endif
-#define False 0
-#define True 1
-
-/*----------------------------------
-
-  qh_CENTER
-    to distinguish facet->center
-*/
-typedef enum
-{
-    qh_ASnone = 0, qh_ASvoronoi, qh_AScentrum
-}
-qh_CENTER;
-
-/*----------------------------------
-
-  qh_PRINT
-    output formats for printing (qh.PRINTout).
-    'Fa' 'FV' 'Fc' 'FC'
-
-
-   notes:
-   some of these names are similar to qh names.  The similar names are only
-   used in switch statements in qh_printbegin() etc.
-*/
-typedef enum {qh_PRINTnone= 0,
-  qh_PRINTarea, qh_PRINTaverage,           /* 'Fa' 'FV' 'Fc' 'FC' */
-  qh_PRINTcoplanars, qh_PRINTcentrums,
-  qh_PRINTfacets, qh_PRINTfacets_xridge,   /* 'f' 'FF' 'G' 'FI' 'Fi' 'Fn' */
-  qh_PRINTgeom, qh_PRINTids, qh_PRINTinner, qh_PRINTneighbors,
-  qh_PRINTnormals, qh_PRINTouter,          /* 'n' 'Fo' 'i' 'm' 'Fm' 'o' */
-  qh_PRINTincidences, qh_PRINTmathematica, qh_PRINTmerges, qh_PRINToff,
-  qh_PRINToptions, qh_PRINTpointintersect, /* 'FO' 'Fp' 'FP' 'p' 'FQ' 'FS' */
-  qh_PRINTpointnearest, qh_PRINTpoints, qh_PRINTqhull, qh_PRINTsize,
-  qh_PRINTsummary, qh_PRINTtriangles,      /* 'Fs' 'Ft' 'Fv' 'FN' 'Fx' */
-  qh_PRINTvertices, qh_PRINTvneighbors, qh_PRINTextremes,
-  qh_PRINTEND} qh_PRINT;
-
-/*----------------------------------
-
-  qh_ALL
-    argument flag for selecting everything
-*/
-#define qh_ALL      True
-#define qh_NOupper  True     /* argument for qh_findbest */
-#define qh_IScheckmax  True     /* argument for qh_findbesthorizon */
-#define qh_ISnewfacets  True     /* argument for qh_findbest */
-#define qh_RESETvisible  True     /* argument for qh_resetlists */
-
-/*----------------------------------
-
-  qh_ERR
-    Qhull exit codes, for indicating errors
-*/
-#define qh_ERRnone  0    /* no error occurred during qhull */
-#define qh_ERRinput 1    /* input inconsistency */
-#define qh_ERRsingular 2 /* singular input data */
-#define qh_ERRprec  3    /* precision error */
-#define qh_ERRmem   4    /* insufficient memory, matches mem.h */
-#define qh_ERRqhull 5    /* internal error detected, matches mem.h */
-
-/* ============ -structures- ====================
-   each of the following structures is defined by a typedef
-   all realT and coordT fields occur at the beginning of a structure
-        (otherwise space may be wasted due to alignment)
-   define all flags together and pack into 32-bit number
-*/
-
-typedef struct vertexT vertexT;
-typedef struct ridgeT ridgeT;
-typedef struct facetT facetT;
-#ifndef DEFsetT
-#define DEFsetT 1
-typedef struct setT setT;          /* defined in qset.h */
-#endif
-
-/*----------------------------------
-
-  facetT
-    defines a facet
-
-  notes:
-   qhull() generates the hull as a list of facets.
-
-  topological information:
-    f.previous,next     doubly-linked list of facets
-    f.vertices          set of vertices
-    f.ridges            set of ridges
-    f.neighbors         set of neighbors
-    f.toporient         True if facet has top-orientation (else bottom)
-
-  geometric information:
-    f.offset,normal     hyperplane equation
-    f.maxoutside        offset to outer plane -- all points inside
-    f.center            centrum for testing convexity
-    f.simplicial        True if facet is simplicial
-    f.flipped           True if facet does not include qh.interior_point
-
-  for constructing hull:
-    f.visible           True if facet on list of visible facets (will be deleted)
-    f.newfacet          True if facet on list of newly created facets
-    f.coplanarset       set of points coplanar with this facet
-                        (includes near-inside points for later testing)
-    f.outsideset        set of points outside of this facet
-    f.furthestdist      distance to furthest point of outside set
-    f.visitid           marks visited facets during a loop
-    f.replace           replacement facet for to-be-deleted, visible facets
-    f.samecycle,newcycle cycle of facets for merging into horizon facet
-
-  see below for other flags and fields
-*/
-struct facetT {
-#if !qh_COMPUTEfurthest
-  coordT   furthestdist;/* distance to furthest point of outsideset */
-#endif
-#if qh_MAXoutside
-  coordT   maxoutside;  /* max computed distance of point to facet
-  			Before QHULLfinished this is an approximation
-  			since maxdist not always set for mergefacet
-			Actual outer plane is +DISTround and
-			computed outer plane is +2*DISTround */
-#endif
-  coordT   offset;      /* exact offset of hyperplane from origin */
-  coordT  *normal;      /* normal of hyperplane, hull_dim coefficients */
-			/*   if tricoplanar, shared with a neighbor */
-  union {               /* in order of testing */
-   realT   area;        /* area of facet, only in io.c if  ->isarea */
-   facetT *replace;	/*  replacement facet if ->visible and NEWfacets
-  			     is NULL only if qh_mergedegen_redundant or interior */
-   facetT *samecycle;   /*  cycle of facets from the same visible/horizon intersection,
-   			     if ->newfacet */
-   facetT *newcycle;    /*  in horizon facet, current samecycle of new facets */
-   facetT *trivisible;  /* visible facet for ->tricoplanar facets during qh_triangulate() */
-   facetT *triowner;    /* owner facet for ->tricoplanar, !isarea facets w/ ->keepcentrum */
-  }f;
-  coordT  *center;      /*  centrum for convexity, qh CENTERtype == qh_AScentrum */
-      			/*  Voronoi center, qh CENTERtype == qh_ASvoronoi */
-			/*   if tricoplanar, shared with a neighbor */
-  facetT  *previous;    /* previous facet in the facet_list */
-  facetT  *next;        /* next facet in the facet_list */
-  setT    *vertices;    /* vertices for this facet, inverse sorted by ID
-                           if simplicial, 1st vertex was apex/furthest */
-  setT    *ridges;      /* explicit ridges for nonsimplicial facets.
-  			   for simplicial facets, neighbors defines ridge */
-  setT    *neighbors;   /* neighbors of the facet.  If simplicial, the kth
-			   neighbor is opposite the kth vertex, and the first
-			   neighbor is the horizon facet for the first vertex*/
-  setT    *outsideset;  /* set of points outside this facet
-		           if non-empty, last point is furthest
-			   if NARROWhull, includes coplanars for partitioning*/
-  setT    *coplanarset; /* set of points coplanar with this facet
-  			   > qh.min_vertex and <= facet->max_outside
-                           a point is assigned to the furthest facet
-		           if non-empty, last point is furthest away */
-  unsigned visitid;     /* visit_id, for visiting all neighbors,
-			   all uses are independent */
-  unsigned id;	        /* unique identifier from qh facet_id */
-  unsigned nummerge:9;  /* number of merges */
-#define qh_MAXnummerge 511 /*     2^9-1, 32 flags total, see "flags:" in io.c */
-  flagT    tricoplanar:1; /* True if TRIangulate and simplicial and coplanar with a neighbor */
-			  /*   all tricoplanars share the same ->center, ->normal, ->offset, ->maxoutside */
-			  /*   all tricoplanars share the same apex */
-                          /*   if ->degenerate, does not span facet (one logical ridge) */
-                          /*   one tricoplanar has ->keepcentrum and ->coplanarset */
-                          /*   during qh_triangulate, f.trivisible points to original facet */
-  flagT	   newfacet:1;  /* True if facet on qh newfacet_list (new or merged) */
-  flagT	   visible:1;   /* True if visible facet (will be deleted) */
-  flagT    toporient:1; /* True if created with top orientation
-			   after merging, use ridge orientation */
-  flagT    simplicial:1;/* True if simplicial facet, ->ridges may be implicit */
-  flagT    seen:1;      /* used to perform operations only once, like visitid */
-  flagT    seen2:1;     /* used to perform operations only once, like visitid */
-  flagT	   flipped:1;   /* True if facet is flipped */
-  flagT    upperdelaunay:1; /* True if facet is upper envelope of Delaunay triangulation */
-  flagT    notfurthest:1; /* True if last point of outsideset is not furthest*/
-
-/*-------- flags primarily for output ---------*/
-  flagT	   good:1;      /* True if a facet marked good for output */
-  flagT    isarea:1;    /* True if facet->f.area is defined */
-
-/*-------- flags for merging ------------------*/
-  flagT    dupridge:1;  /* True if duplicate ridge in facet */
-  flagT    mergeridge:1; /* True if facet or neighbor contains a qh_MERGEridge
-                            ->normal defined (also defined for mergeridge2) */
-  flagT    mergeridge2:1; /* True if neighbor contains a qh_MERGEridge (mark_dupridges */
-  flagT    coplanar:1;  /* True if horizon facet is coplanar at last use */
-  flagT     mergehorizon:1; /* True if will merge into horizon (->coplanar) */
-  flagT	    cycledone:1;/* True if mergecycle_all already done */
-  flagT    tested:1;    /* True if facet convexity has been tested (false after merge */
-  flagT    keepcentrum:1; /* True if keep old centrum after a merge, or marks owner for ->tricoplanar */
-  flagT	   newmerge:1;  /* True if facet is newly merged for reducevertices */
-  flagT	   degenerate:1; /* True if facet is degenerate (degen_mergeset or ->tricoplanar) */
-  flagT	   redundant:1;  /* True if facet is redundant (degen_mergeset) */
-};
-
-
-/*----------------------------------
-
-  ridgeT
-    defines a ridge
-
-  notes:
-  a ridge is DIM3-1 simplex between two neighboring facets.  If the
-  facets are non-simplicial, there may be more than one ridge between
-  two facets.  E.G. a 4-d hypercube has two triangles between each pair
-  of neighboring facets.
-
-  topological information:
-    vertices            a set of vertices
-    top,bottom          neighboring facets with orientation
-
-  geometric information:
-    tested              True if ridge is clearly convex
-    nonconvex           True if ridge is non-convex
-*/
-struct ridgeT {
-  setT    *vertices;    /* vertices belonging to this ridge, inverse sorted by ID
-                           NULL if a degen ridge (matchsame) */
-  facetT  *top;         /* top facet this ridge is part of */
-  facetT  *bottom;      /* bottom facet this ridge is part of */
-  unsigned id:24;       /* unique identifier, =>room for 8 flags */
-  flagT    seen:1;      /* used to perform operations only once */
-  flagT    tested:1;    /* True when ridge is tested for convexity */
-  flagT    nonconvex:1; /* True if getmergeset detected a non-convex neighbor
-			   only one ridge between neighbors may have nonconvex */
-};
-
-/*----------------------------------
-
-  vertexT
-     defines a vertex
-
-  topological information:
-    next,previous       doubly-linked list of all vertices
-    neighbors           set of adjacent facets (only if qh.VERTEXneighbors)
-
-  geometric information:
-    point               array of DIM3 coordinates
-*/
-struct vertexT {
-  vertexT *next;        /* next vertex in vertex_list */
-  vertexT *previous;    /* previous vertex in vertex_list */
-  pointT  *point;       /* hull_dim coordinates (coordT) */
-  setT    *neighbors;   /* neighboring facets of vertex, qh_vertexneighbors()
-			   inits in io.c or after first merge */
-  unsigned visitid; /* for use with qh vertex_visit */
-  unsigned id:24;   /* unique identifier, =>room for 8 flags */
-  flagT    seen:1;      /* used to perform operations only once */
-  flagT    seen2:1;     /* another seen flag */
-  flagT    delridge:1;  /* vertex was part of a deleted ridge */
-  flagT	   deleted:1;   /* true if vertex on qh del_vertices */
-  flagT    newlist:1;   /* true if vertex on qh newvertex_list */
-};
-
-/*======= -global variables -qh ============================*/
-
-/*----------------------------------
-
-  qh
-   all global variables for qhull are in qh, qhmem, and qhstat
-
-  notes:
-   qhmem is defined in mem.h and qhstat is defined in stat.h
-   access to qh_qh is via the "qh" macro.  See qh_QHpointer in user.h
-*/
-typedef struct qhT qhT;
-#if qh_QHpointer
-#define qh qh_qh->
-extern qhT *qh_qh;     /* allocated in global.c */
-#else
-#define qh qh_qh.
-extern qhT qh_qh;
-#endif
-
-struct qhT {
-
-/*----------------------------------
-
-  qh constants
-    configuration flags and constants for Qhull
-
-  notes:
-    The user configures Qhull by defining flags.  They are
-    copied into qh by qh_setflags().  qh-quick.htm#options defines the flags.
-*/
-  boolT ALLpoints;        /* true 'Qs' if search all points for initial simplex */
-  boolT ANGLEmerge;	  /* true 'Qa' if sort potential merges by angle */
-  boolT APPROXhull;       /* true 'Wn' if MINoutside set */
-  realT MINoutside;       /*   'Wn' min. distance for an outside point */
-  boolT ATinfinity;       /* true 'Qz' if point num_points-1 is "at-infinity"
-                             for improving precision in Delaunay triangulations */
-  boolT AVOIDold;         /* true 'Q4' if avoid old->new merges */
-  boolT BESToutside;      /* true 'Qf' if partition points into best outsideset */
-  boolT CDDinput;         /* true 'Pc' if input uses CDD format (1.0/offset first) */
-  boolT CDDoutput;        /* true 'PC' if print normals in CDD format (offset first) */
-  boolT CHECKfrequently;  /* true 'Tc' if checking frequently */
-  realT premerge_cos;     /*   'A-n'   cos_max when pre merging */
-  realT postmerge_cos;    /*   'An'    cos_max when post merging */
-  boolT DELAUNAY;         /* true 'd' if computing DELAUNAY triangulation */
-  boolT DOintersections;  /* true 'Gh' if print hyperplane intersections */
-  int   DROPdim;          /* drops dim 'GDn' for 4-d -> 3-d output */
-  boolT FORCEoutput;      /* true 'Po' if forcing output despite degeneracies */
-  int   GOODpoint;        /* 1+n for 'QGn', good facet if visible/not(-) from point n*/
-  pointT *GOODpointp;     /*   the actual point */
-  boolT GOODthreshold;    /* true if qh lower_threshold/upper_threshold defined
-  			     false if qh SPLITthreshold */
-  int   GOODvertex;       /* 1+n, good facet if vertex for point n */
-  pointT *GOODvertexp;     /*   the actual point */
-  boolT HALFspace;        /* true 'Hn,n,n' if halfspace intersection */
-  int   IStracing;        /* trace execution, 0=none, 1=least, 4=most, -1=events */
-  int   KEEParea;         /* 'PAn' number of largest facets to keep */
-  boolT KEEPcoplanar;     /* true 'Qc' if keeping nearest facet for coplanar points */
-  boolT KEEPinside;       /* true 'Qi' if keeping nearest facet for inside points
-			      set automatically if 'd Qc' */
-  int   KEEPmerge;        /* 'PMn' number of facets to keep with most merges */
-  realT KEEPminArea;      /* 'PFn' minimum facet area to keep */
-  realT MAXcoplanar;      /* 'Un' max distance below a facet to be coplanar*/
-  boolT MERGEexact;	  /* true 'Qx' if exact merges (coplanar, degen, dupridge, flipped) */
-  boolT MERGEindependent; /* true 'Q2' if merging independent sets */
-  boolT MERGING;          /* true if exact-, pre- or post-merging, with angle and centrum tests */
-  realT   premerge_centrum;  /*   'C-n' centrum_radius when pre merging.  Default is round-off */
-  realT   postmerge_centrum; /*   'Cn' centrum_radius when post merging.  Default is round-off */
-  boolT MERGEvertices;	  /* true 'Q3' if merging redundant vertices */
-  realT MINvisible;       /* 'Vn' min. distance for a facet to be visible */
-  boolT NOnarrow;         /* true 'Q10' if no special processing for narrow distributions */
-  boolT NOnearinside;     /* true 'Q8' if ignore near-inside points when partitioning */
-  boolT NOpremerge;       /* true 'Q0' if no defaults for C-0 or Qx */
-  boolT ONLYgood; 	  /* true 'Qg' if process points with good visible or horizon facets */
-  boolT ONLYmax; 	  /* true 'Qm' if only process points that increase max_outside */
-  boolT PICKfurthest;     /* true 'Q9' if process furthest of furthest points*/
-  boolT POSTmerge;        /* true if merging after buildhull (Cn or An) */
-  boolT PREmerge;         /* true if merging during buildhull (C-n or A-n) */
-  			/* NOTE: some of these names are similar to qh_PRINT names */
-  boolT PRINTcentrums;	  /* true 'Gc' if printing centrums */
-  boolT PRINTcoplanar;    /* true 'Gp' if printing coplanar points */
-  int	PRINTdim;      	  /* print dimension for Geomview output */
-  boolT PRINTdots;        /* true 'Ga' if printing all points as dots */
-  boolT PRINTgood;        /* true 'Pg' if printing good facets */
-  boolT PRINTinner;	  /* true 'Gi' if printing inner planes */
-  boolT PRINTneighbors;	  /* true 'PG' if printing neighbors of good facets */
-  boolT PRINTnoplanes;	  /* true 'Gn' if printing no planes */
-  boolT PRINToptions1st;  /* true 'FO' if printing options to stderr */
-  boolT PRINTouter;	  /* true 'Go' if printing outer planes */
-  boolT PRINTprecision;   /* false 'Pp' if not reporting precision problems */
-  qh_PRINT PRINTout[qh_PRINTEND]; /* list of output formats to print */
-  boolT PRINTridges;      /* true 'Gr' if print ridges */
-  boolT PRINTspheres;     /* true 'Gv' if print vertices as spheres */
-  boolT PRINTstatistics;  /* true 'Ts' if printing statistics to stderr */
-  boolT PRINTsummary;     /* true 's' if printing summary to stderr */
-  boolT PRINTtransparent; /* true 'Gt' if print transparent outer ridges */
-  boolT PROJECTdelaunay;  /* true if DELAUNAY, no readpoints() and
-			     need projectinput() for Delaunay in qh_init_B */
-  int   PROJECTinput;     /* number of projected dimensions 'bn:0Bn:0' */
-  boolT QUICKhelp;	  /* true if quick help message for degen input */
-  boolT RANDOMdist;       /* true if randomly change distplane and setfacetplane */
-  realT RANDOMfactor;     /*    maximum random perturbation */
-  realT RANDOMa;         /*  qh_randomfactor is randr * RANDOMa + RANDOMb */
-  realT RANDOMb;
-  boolT RANDOMoutside;    /* true if select a random outside point */
-  int	REPORTfreq;       /* buildtracing reports every n facets */
-  int   REPORTfreq2;	  /* tracemerging reports every REPORTfreq/2 facets */
-  int	RERUN;            /* 'TRn' rerun qhull n times (qh.build_cnt) */
-  int	ROTATErandom;	  /* 'QRn' seed, 0 time, >= rotate input */
-  boolT SCALEinput;       /* true 'Qbk' if scaling input */
-  boolT SCALElast;        /* true 'Qbb' if scale last coord to max prev coord */
-  boolT SETroundoff;      /* true 'E' if qh DISTround is predefined */
-  boolT SKIPcheckmax;	  /* true 'Q5' if skip qh_check_maxout */
-  boolT SKIPconvex;       /* true 'Q6' if skip convexity testing during pre-merge */
-  boolT SPLITthresholds;  /* true if upper_/lower_threshold defines a region
-                               used only for printing (not for qh ONLYgood) */
-  int	STOPcone;         /* 'TCn' 1+n for stopping after cone for point n*/
-			  /*       also used by qh_build_withresart for err exit*/
-  int	STOPpoint;        /* 'TVn' 'TV-n' 1+n for stopping after/before(-)
-  int	TESTpoints;	  /* 'QTn' num of test points after qh.num_points.  Test points always coplanar. */
-  boolT TESTvneighbors;   /*  true 'Qv' if test vertex neighbors at end */
-  int   TRACElevel;       /* 'Tn' conditional IStracing level */
-  int	TRACElastrun;	  /*  qh.TRACElevel applies to last qh.RERUN */
-  int   TRACEpoint;       /* 'TPn' start tracing when point n is a vertex */
-  realT TRACEdist;        /* 'TWn' start tracing when merge distance too big */
-  int   TRACEmerge;       /* 'TMn' start tracing before this merge */
-  boolT TRIangulate;	  /* true 'Qt' if triangulate non-simplicial facets */
-  boolT TRInormals;	  /* true 'Q11' if triangulate duplicates normals (sets Qt) */
-  boolT UPPERdelaunay;    /* true 'Qu' if computing furthest-site Delaunay */
-  boolT VERIFYoutput;     /* true 'Tv' if verify output at end of qhull */
-  boolT VIRTUALmemory;    /* true 'Q7' if depth-first processing in buildhull */
-  boolT VORONOI;	  /* true 'v' if computing Voronoi diagram */
-
-  /*--------input constants ---------*/
-  realT AREAfactor;       /* 1/(hull_dim-1)! for converting det's to area */
-  boolT DOcheckmax;       /* true if calling qh_check_maxout (qh_initqhull_globals) */
-  char	*feasible_string;  /* feasible point 'Hn,n,n' for halfspace intersection */
-  coordT *feasible_point;  /*    as coordinates, both malloc'd */
-  boolT GETarea;          /* true 'Fa', 'FA', 'FS', 'PAn', 'PFn' if compute facet area/Voronoi volume in io.c */
-  boolT KEEPnearinside;   /* true if near-inside points in coplanarset */
-  int 	hull_dim;         /* dimension of hull, set by initbuffers */
-  int 	input_dim;	  /* dimension of input, set by initbuffers */
-  int 	num_points;       /* number of input points */
-  pointT *first_point;    /* array of input points, see POINTSmalloc */
-  boolT POINTSmalloc;     /*   true if qh first_point/num_points allocated */
-  pointT *input_points;   /* copy of original qh.first_point for input points for qh_joggleinput */
-  boolT input_malloc;     /* true if qh input_points malloc'd */
-  char 	qhull_command[256];/* command line that invoked this program */
-  char 	rbox_command[256]; /* command line that produced the input points */
-  char  qhull_options[512];/* descriptive list of options */
-  int   qhull_optionlen;  /*    length of last line */
-  int   qhull_optionsiz;  /*     size of qhull_options before qh_initbuild */
-  boolT VERTEXneighbors;  /* true if maintaining vertex neighbors */
-  boolT ZEROcentrum;      /* true if 'C-0' or 'C-0 Qx'.  sets ZEROall_ok */
-  realT *upper_threshold; /* don't print if facet->normal[k]>=upper_threshold[k]
-                             must set either GOODthreshold or SPLITthreshold
-  			     if Delaunay, default is 0.0 for upper envelope */
-  realT *lower_threshold; /* don't print if facet->normal[k] <=lower_threshold[k] */
-  realT *upper_bound;     /* scale point[k] to new upper bound */
-  realT *lower_bound;     /* scale point[k] to new lower bound
-  			     project if both upper_ and lower_bound == 0 */
-
-/*----------------------------------
-
-  qh precision constants
-    precision constants for Qhull
-
-  notes:
-    qh_detroundoff() computes the maximum roundoff error for distance
-    and other computations.  It also sets default values for the
-    qh constants above.
-*/
-  realT ANGLEround;       /* max round off error for angles */
-  realT cos_max;	  /* max cosine for convexity (roundoff added) */
-  realT DISTround;        /* max round off error for distances, 'E' overrides */
-  realT MAXabs_coord;     /* max absolute coordinate */
-  realT MAXlastcoord;     /* max last coordinate for qh_scalelast */
-  realT MAXsumcoord;      /* max sum of coordinates */
-  realT MAXwidth;         /* max rectilinear width of point coordinates */
-  realT MINdenom_1;       /* min. abs. value for 1/x */
-  realT MINdenom;         /*    use divzero if denominator < MINdenom */
-  realT MINdenom_1_2;     /* min. abs. val for 1/x that allows normalization */
-  realT MINdenom_2;       /*    use divzero if denominator < MINdenom_2 */
-  realT MINlastcoord;     /* min. last coordinate for qh_scalelast */
-  boolT NARROWhull;       /* set in qh_initialhull if angle < qh_MAXnarrow */
-  realT *NEARzero;        /* hull_dim array for near zero in gausselim */
-  realT NEARinside;       /* keep points for qh_check_maxout if close to facet */
-  realT ONEmerge;         /* max distance for merging simplicial facets */
-  realT outside_err;      /* application's epsilon for coplanar points
-                             qh_check_bestdist() qh_check_points() reports error if point outside */
-  realT WIDEfacet;        /* size of wide facet for skipping ridge in
-			     area computation and locking centrum */
-
-/*----------------------------------
-
-  qh internal constants
-    internal constants for Qhull
-*/
-  char qhull[sizeof("qhull")]; /* for checking ownership */
-  void *old_stat;         /* pointer to saved qh_qhstat, qh_save_qhull */
-  jmp_buf errexit;        /* exit label for qh_errexit, defined by setjmp() */
-  char jmpXtra[40];       /* extra bytes in case jmp_buf is defined wrong by compiler */
-  jmp_buf restartexit;    /* restart label for qh_errexit, defined by setjmp() */
-  char jmpXtra2[40];      /* extra bytes in case jmp_buf is defined wrong by compiler*/
-  FILE *fin;              /* pointer to input file, init by qh_meminit */
-  FILE *fout;             /* pointer to output file */
-  FILE *ferr;             /* pointer to error file */
-  pointT *interior_point; /* center point of the initial simplex*/
-  int   normal_size;      /* size in bytes for facet normals and point coords*/
-  int   center_size;      /* size in bytes for Voronoi centers */
-  int   TEMPsize;         /* size for small, temporary sets (in quick mem) */
-
-/*----------------------------------
-
-  qh facet and vertex lists
-    defines lists of facets, new facets, visible facets, vertices, and
-    new vertices.  Includes counts, next ids, and trace ids.
-  see:
-    qh_resetlists()
-*/
-  facetT *facet_list;     /* first facet */
-  facetT  *facet_tail;     /* end of facet_list (dummy facet) */
-  facetT *facet_next;     /* next facet for buildhull()
-    			     previous facets do not have outside sets
-                             NARROWhull: previous facets may have coplanar outside sets for qh_outcoplanar */
-  facetT *newfacet_list;  /* list of new facets to end of facet_list */
-  facetT *visible_list;   /* list of visible facets preceeding newfacet_list,
-                             facet->visible set */
-  int       num_visible;  /* current number of visible facets */
-  unsigned tracefacet_id;  /* set at init, then can print whenever */
-  facetT *tracefacet;     /*   set in newfacet/mergefacet, undone in delfacet*/
-  unsigned tracevertex_id;  /* set at buildtracing, can print whenever */
-  vertexT *tracevertex;     /*   set in newvertex, undone in delvertex*/
-  vertexT *vertex_list;     /* list of all vertices, to vertex_tail */
-  vertexT  *vertex_tail;    /*      end of vertex_list (dummy vertex) */
-  vertexT *newvertex_list; /* list of vertices in newfacet_list, to vertex_tail
-                             all vertices have 'newlist' set */
-  int 	num_facets;	  /* number of facets in facet_list
-			     includes visble faces (num_visible) */
-  int 	num_vertices;     /* number of vertices in facet_list */
-  int   num_outside;      /* number of points in outsidesets (for tracing and RANDOMoutside)
-                               includes coplanar outsideset points for NARROWhull/qh_outcoplanar() */
-  int   num_good;         /* number of good facets (after findgood_all) */
-  unsigned facet_id;      /* ID of next, new facet from newfacet() */
-  unsigned ridge_id;      /* ID of next, new ridge from newridge() */
-  unsigned vertex_id;     /* ID of next, new vertex from newvertex() */
-
-/*----------------------------------
-
-  qh global variables
-    defines minimum and maximum distances, next visit ids, several flags,
-    and other global variables.
-    initialize in qh_initbuild or qh_maxmin if used in qh_buildhull
-*/
-  unsigned long hulltime; /* ignore time to set up input and randomize */
-                          /*   use unsigned to avoid wrap-around errors */
-  boolT ALLOWrestart;     /* true if qh_precision can use qh.restartexit */
-  int   build_cnt;        /* number of calls to qh_initbuild */
-  qh_CENTER CENTERtype;   /* current type of facet->center, qh_CENTER */
-  int 	furthest_id;      /* pointid of furthest point, for tracing */
-  facetT *GOODclosest;    /* closest facet to GOODthreshold in qh_findgood */
-  realT JOGGLEmax;        /* set 'QJn' if randomly joggle input */
-  boolT maxoutdone;       /* set qh_check_maxout(), cleared by qh_addpoint() */
-  realT max_outside;      /* maximum distance from a point to a facet,
-			       before roundoff, not simplicial vertices
-			       actual outer plane is +DISTround and
-			       computed outer plane is +2*DISTround */
-  realT max_vertex;       /* maximum distance (>0) from vertex to a facet,
-			       before roundoff, due to a merge */
-  realT min_vertex;       /* minimum distance (<0) from vertex to a facet,
-			       before roundoff, due to a merge
-			       if qh.JOGGLEmax, qh_makenewplanes sets it
-  			       recomputed if qh.DOcheckmax, default -qh.DISTround */
-  boolT NEWfacets;        /* true while visible facets invalid due to new or merge
-			      from makecone/attachnewfacets to deletevisible */
-  boolT findbestnew;	  /* true if partitioning calls qh_findbestnew */
-  boolT findbest_notsharp; /* true if new facets are at least 90 degrees */
-  boolT NOerrexit;        /* true if qh.errexit is not available */
-  realT PRINTradius;      /* radius for printing vertex spheres and points */
-  boolT POSTmerging;      /* true when post merging */
-  int 	printoutvar;	  /* temporary variable for qh_printbegin, etc. */
-  int 	printoutnum;	  /* number of facets printed */
-  boolT QHULLfinished;    /* True after qhull() is finished */
-  realT totarea;          /* 'FA': total facet area computed by qh_getarea */
-  realT totvol;           /* 'FA': total volume computed by qh_getarea */
-  unsigned int visit_id;  /* unique ID for searching neighborhoods, */
-  unsigned int vertex_visit; /* unique ID for searching vertices */
-  boolT ZEROall_ok;       /* True if qh_checkzero always succeeds */
-  boolT WAScoplanar;      /* True if qh_partitioncoplanar (qh_check_maxout) */
-
-/*----------------------------------
-
-  qh global sets
-    defines sets for merging, initial simplex, hashing, extra input points,
-    and deleted vertices
-*/
-  setT *facet_mergeset;   /* temporary set of merges to be done */
-  setT *degen_mergeset;   /* temporary set of degenerate and redundant merges */
-  setT *hash_table;	  /* hash table for matching ridges in qh_matchfacets
-                             size is setsize() */
-  setT *other_points;     /* additional points (first is qh interior_point) */
-  setT *del_vertices;     /* vertices to partition and delete with visible
-                             facets.  Have deleted set for checkfacet */
-
-/*----------------------------------
-
-  qh global buffers
-    defines buffers for maxtrix operations, input, and error messages
-*/
-  coordT *gm_matrix;      /* (dim+1)Xdim matrix for geom.c */
-  coordT **gm_row;        /* array of gm_matrix rows */
-  char* line;             /* malloc'd input line of maxline+1 chars */
-  int maxline;
-  coordT *half_space;     /* malloc'd input array for halfspace (qh normal_size+coordT) */
-  coordT *temp_malloc;    /* malloc'd input array for points */
-
-/*----------------------------------
-
-  qh static variables
-    defines static variables for individual functions
-
-  notes:
-    do not use 'static' within a function.  Multiple instances of qhull
-    may exist.
-
-    do not assume zero initialization, 'QPn' may cause a restart
-*/
-  boolT ERREXITcalled;    /* true during errexit (prevents duplicate calls */
-  boolT firstcentrum; 	  /* for qh_printcentrum */
-  realT last_low;         /* qh_scalelast parameters for qh_setdelaunay */
-  realT last_high;
-  realT last_newhigh;
-  unsigned lastreport;    /* for qh_buildtracing */
-  int mergereport;        /* for qh_tracemerging */
-  boolT old_randomdist;   /* save RANDOMdist when io, tracing, or statistics */
-  int   ridgeoutnum;      /* number of ridges in 4OFF output */
-  void *old_qhstat;       /* for saving qh_qhstat in save_qhull() */
-  setT *old_tempstack;     /* for saving qhmem.tempstack in save_qhull */
-  setT *coplanarset;      /* set of coplanar facets for searching qh_findbesthorizon() */
-};
-
-/*=========== -macros- =========================*/
-
-/*----------------------------------
-
-  otherfacet_(ridge, facet)
-    return neighboring facet for a ridge in facet
-*/
-#define otherfacet_(ridge, facet) \
-                        (((ridge)->top == (facet)) ? (ridge)->bottom : (ridge)->top)
-
-/*----------------------------------
-
-  getid_(p)
-    return ID for facet, ridge, or vertex
-    return MAXINT if NULL (-1 causes type conversion error )
-*/
-#define getid_(p)       ((p) ? (p)->id : -1)
-
-/*============== FORALL macros ===================*/
-
-/*----------------------------------
-
-  FORALLfacets { ... }
-    assign 'facet' to each facet in qh.facet_list
-
-  notes:
-    uses 'facetT *facet;'
-    assumes last facet is a sentinel
-
-  see:
-    FORALLfacet_( facetlist )
-*/
-#define FORALLfacets for (facet=qh facet_list;facet && facet->next;facet=facet->next)
-
-/*----------------------------------
-
-  FORALLpoints { ... }
-    assign 'point' to each point in qh.first_point, qh.num_points
-
-  declare:
-    coordT *point, *pointtemp;
-*/
-#define FORALLpoints FORALLpoint_(qh first_point, qh num_points)
-
-/*----------------------------------
-
-  FORALLpoint_( points, num) { ... }
-    assign 'point' to each point in points array of num points
-
-  declare:
-    coordT *point, *pointtemp;
-*/
-#define FORALLpoint_(points, num) for(point= (points), \
-      pointtemp= (points)+qh hull_dim*(num); point < pointtemp; point += qh hull_dim)
-
-/*----------------------------------
-
-  FORALLvertices { ... }
-    assign 'vertex' to each vertex in qh.vertex_list
-
-  declare:
-    vertexT *vertex;
-
-  notes:
-    assumes qh.vertex_list terminated with a sentinel
-*/
-#define FORALLvertices for (vertex=qh vertex_list;vertex && vertex->next;vertex= vertex->next)
-
-/*----------------------------------
-
-  FOREACHfacet_( facets ) { ... }
-    assign 'facet' to each facet in facets
-
-  declare:
-    facetT *facet, **facetp;
-
-  see:
-    FOREACHsetelement_
-*/
-#define FOREACHfacet_(facets)    FOREACHsetelement_(facetT, facets, facet)
-
-/*----------------------------------
-
-  FOREACHneighbor_( facet ) { ... }
-    assign 'neighbor' to each neighbor in facet->neighbors
-
-  FOREACHneighbor_( vertex ) { ... }
-    assign 'neighbor' to each neighbor in vertex->neighbors
-
-  declare:
-    facetT *neighbor, **neighborp;
-
-  see:
-    FOREACHsetelement_
-*/
-#define FOREACHneighbor_(facet)  FOREACHsetelement_(facetT, facet->neighbors, neighbor)
-
-/*----------------------------------
-
-  FOREACHpoint_( points ) { ... }
-    assign 'point' to each point in points set
-
-  declare:
-    pointT *point, **pointp;
-
-  see:
-    FOREACHsetelement_
-*/
-#define FOREACHpoint_(points)    FOREACHsetelement_(pointT, points, point)
-
-/*----------------------------------
-
-  FOREACHridge_( ridges ) { ... }
-    assign 'ridge' to each ridge in ridges set
-
-  declare:
-    ridgeT *ridge, **ridgep;
-
-  see:
-    FOREACHsetelement_
-*/
-#define FOREACHridge_(ridges)    FOREACHsetelement_(ridgeT, ridges, ridge)
-
-/*----------------------------------
-
-  FOREACHvertex_( vertices ) { ... }
-    assign 'vertex' to each vertex in vertices set
-
-  declare:
-    vertexT *vertex, **vertexp;
-
-  see:
-    FOREACHsetelement_
-*/
-#define FOREACHvertex_(vertices) FOREACHsetelement_(vertexT, vertices,vertex)
-
-/*----------------------------------
-
-  FOREACHfacet_i_( facets ) { ... }
-    assign 'facet' and 'facet_i' for each facet in facets set
-
-  declare:
-    facetT *facet;
-    int     facet_n, facet_i;
-
-  see:
-    FOREACHsetelement_i_
-*/
-#define FOREACHfacet_i_(facets)    FOREACHsetelement_i_(facetT, facets, facet)
-
-/*----------------------------------
-
-  FOREACHneighbor_i_( facet ) { ... }
-    assign 'neighbor' and 'neighbor_i' for each neighbor in facet->neighbors
-
-  FOREACHneighbor_i_( vertex ) { ... }
-    assign 'neighbor' and 'neighbor_i' for each neighbor in vertex->neighbors
-
-  declare:
-    facetT *neighbor;
-    int     neighbor_n, neighbor_i;
-
-  see:
-    FOREACHsetelement_i_
-*/
-#define FOREACHneighbor_i_(facet)  FOREACHsetelement_i_(facetT, facet->neighbors, neighbor)
-
-/*----------------------------------
-
-  FOREACHpoint_i_( points ) { ... }
-    assign 'point' and 'point_i' for each point in points set
-
-  declare:
-    pointT *point;
-    int     point_n, point_i;
-
-  see:
-    FOREACHsetelement_i_
-*/
-#define FOREACHpoint_i_(points)    FOREACHsetelement_i_(pointT, points, point)
-
-/*----------------------------------
-
-  FOREACHridge_i_( ridges ) { ... }
-    assign 'ridge' and 'ridge_i' for each ridge in ridges set
-
-  declare:
-    ridgeT *ridge;
-    int     ridge_n, ridge_i;
-
-  see:
-    FOREACHsetelement_i_
-*/
-#define FOREACHridge_i_(ridges)    FOREACHsetelement_i_(ridgeT, ridges, ridge)
-
-/*----------------------------------
-
-  FOREACHvertex_i_( vertices ) { ... }
-    assign 'vertex' and 'vertex_i' for each vertex in vertices set
-
-  declare:
-    vertexT *vertex;
-    int     vertex_n, vertex_i;
-
-  see:
-    FOREACHsetelement_i_
- */
-#define FOREACHvertex_i_(vertices) FOREACHsetelement_i_(vertexT, vertices,vertex)
-
-/********* -qhull.c prototypes (duplicated from qhull_a.h) **********************/
-
-void    qh_qhull (void);
-boolT   qh_addpoint (pointT *furthest, facetT *facet, boolT checkdist);
-void	qh_printsummary(FILE *fp);
-
-/********* -user.c prototypes (alphabetical) **********************/
-
-void 	qh_errexit(int exitcode, facetT *facet, ridgeT *ridge);
-void 	qh_errprint(char* string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex);
-int     qh_new_qhull (int dim, int numpoints, coordT *points, boolT ismalloc,
-		char *qhull_cmd, FILE *outfile, FILE *errfile);
-void    qh_printfacetlist(facetT *facetlist, setT *facets, boolT printall);
-void 	qh_user_memsizes (void);
-
-/***** -geom.c/geom2.c prototypes (duplicated from geom.h) ****************/
-
-facetT *qh_findbest (pointT *point, facetT *startfacet,
-		     boolT bestoutside, boolT newfacets, boolT noupper,
-		     realT *dist, boolT *isoutside, int *numpart);
-facetT *qh_findbestnew (pointT *point, facetT *startfacet,
-                     realT *dist, boolT bestoutside, boolT *isoutside, int *numpart);
-boolT   qh_gram_schmidt(int dim, realT **rows);
-void    qh_outerinner (facetT *facet, realT *outerplane, realT *innerplane);
-void	qh_printsummary(FILE *fp);
-void    qh_projectinput (void);
-void    qh_randommatrix (realT *buffer, int dim, realT **row);
-void    qh_rotateinput (realT **rows);
-void    qh_scaleinput (void);
-void    qh_setdelaunay (int dim, int count, pointT *points);
-coordT  *qh_sethalfspace_all (int dim, int count, coordT *halfspaces, pointT *feasible);
-
-/***** -global.c prototypes (alphabetical) ***********************/
-
-unsigned long qh_clock (void);
-void 	qh_checkflags (char *command, char *hiddenflags);
-void 	qh_freebuffers (void);
-void    qh_freeqhull (boolT allmem);
-void    qh_init_A (FILE *infile, FILE *outfile, FILE *errfile, int argc, char *argv[]);
-void    qh_init_B (coordT *points, int numpoints, int dim, boolT ismalloc);
-void 	qh_init_qhull_command (int argc, char *argv[]);
-void    qh_initbuffers (coordT *points, int numpoints, int dim, boolT ismalloc);
-void 	qh_initflags (char *command);
-void 	qh_initqhull_buffers (void);
-void 	qh_initqhull_globals (coordT *points, int numpoints, int dim, boolT ismalloc);
-void    qh_initqhull_mem (void);
-void 	qh_initqhull_start (FILE *infile, FILE *outfile, FILE *errfile);
-void 	qh_initthresholds (char *command);
-void    qh_option (char *option, int *i, realT *r);
-#if qh_QHpointer
-void 	qh_restore_qhull (qhT **oldqh);
-qhT    *qh_save_qhull (void);
-#endif
-
-/***** -io.c prototypes (duplicated from io.h) ***********************/
-
-void    dfacet( unsigned id);
-void    dvertex( unsigned id);
-void	qh_printneighborhood (FILE *fp, int format, facetT *facetA, facetT *facetB, boolT printall);
-void	qh_produce_output(void);
-coordT *qh_readpoints(int *numpoints, int *dimension, boolT *ismalloc);
-
-
-/********* -mem.c prototypes (duplicated from mem.h) **********************/
-
-void qh_meminit (FILE *ferr);
-void qh_memfreeshort (int *curlong, int *totlong);
-
-/********* -poly.c/poly2.c prototypes (duplicated from poly.h) **********************/
-
-void    qh_check_output (void);
-void    qh_check_points (void);
-setT   *qh_facetvertices (facetT *facetlist, setT *facets, boolT allfacets);
-facetT *qh_findbestfacet (pointT *point, boolT bestoutside,
-           realT *bestdist, boolT *isoutside);
-vertexT *qh_nearvertex (facetT *facet, pointT *point, realT *bestdistp);
-pointT *qh_point (int id);
-setT   *qh_pointfacet (void /*qh.facet_list*/);
-int     qh_pointid (pointT *point);
-setT   *qh_pointvertex (void /*qh.facet_list*/);
-void    qh_setvoronoi_all (void);
-void	qh_triangulate (void /*qh facet_list*/);
-
-/********* -stat.c prototypes (duplicated from stat.h) **********************/
-
-void    qh_collectstatistics (void);
-void    qh_printallstatistics (FILE *fp, char *string);
-
-#endif /* qhDEFqhull */
diff --git a/extern/qhull/include/qhull/qhull_a.h b/extern/qhull/include/qhull/qhull_a.h
deleted file mode 100644
index d4e69b071be..00000000000
--- a/extern/qhull/include/qhull/qhull_a.h
+++ /dev/null
@@ -1,127 +0,0 @@
-/*  ---------------------------------
-
-   qhull_a.h
-   all header files for compiling qhull
-
-   see qh-qhull.htm
-
-   see qhull.h for user-level definitions
-
-   see user.h for user-defineable constants
-
-   defines internal functions for qhull.c global.c
-
-   copyright (c) 1993-2002, The Geometry Center
-
-   Notes:  grep for ((" and (" to catch fprintf("lkasdjf");
-           full parens around (x?y:z)
-	   use '#include qhull/qhull_a.h' to avoid name clashes
-*/
-
-#ifndef qhDEFqhulla
-#define qhDEFqhulla
-
-#include
-#include
-#include
-#include
-#include
-#include     /* some compilers will not need float.h */
-#include
-#include
-#include
-/*** uncomment here and qset.c
-     if string.h does not define memcpy()
-#include
-*/
-#include "qhull.h"
-#include "mem.h"
-#include "qset.h"
-#include "geom.h"
-#include "merge.h"
-#include "poly.h"
-#include "io.h"
-#include "stat.h"
-
-#if qh_CLOCKtype == 2  /* defined in user.h from qhull.h */
-#include
-#include
-#include
-#endif
-
-#ifdef _MSC_VER  /* Microsoft Visual C++ */
-#pragma warning( disable : 4056)  /* float constant expression.  Looks like a compiler bug */
-#pragma warning( disable : 4146)  /* unary minus applied to unsigned type */
-#pragma warning( disable : 4244)  /* conversion from 'unsigned long' to 'real' */
-#pragma warning( disable : 4305)  /* conversion from 'const double' to 'float' */
-#endif
-
-/* ======= -macros- =========== */
-
-/*----------------------------------
-
-  traceN((fp.ferr, "format\n", vars));
-    calls fprintf if qh.IStracing >= N
-
-  notes:
-    removing tracing reduces code size but doesn't change execution speed
-*/
-#ifndef qh_NOtrace
-#define trace0(args) {if (qh IStracing) fprintf args;}
-#define trace1(args) {if (qh IStracing >= 1) fprintf args;}
-#define trace2(args) {if (qh IStracing >= 2) fprintf args;}
-#define trace3(args) {if (qh IStracing >= 3) fprintf args;}
-#define trace4(args) {if (qh IStracing >= 4) fprintf args;}
-#define trace5(args) {if (qh IStracing >= 5) fprintf args;}
-#else /* qh_NOtrace */
-#define trace0(args) {}
-#define trace1(args) {}
-#define trace2(args) {}
-#define trace3(args) {}
-#define trace4(args) {}
-#define trace5(args) {}
-#endif /* qh_NOtrace */
-
-/***** -qhull.c prototypes (alphabetical after qhull) ********************/
-
-void 	qh_qhull (void);
-boolT   qh_addpoint (pointT *furthest, facetT *facet, boolT checkdist);
-void 	qh_buildhull(void);
-void    qh_buildtracing (pointT *furthest, facetT *facet);
-void    qh_build_withrestart (void);
-void 	qh_errexit2(int exitcode, facetT *facet, facetT *otherfacet);
-void    qh_findhorizon(pointT *point, facetT *facet, int *goodvisible,int *goodhorizon);
-pointT *qh_nextfurthest (facetT **visible);
-void 	qh_partitionall(setT *vertices, pointT *points,int npoints);
-void    qh_partitioncoplanar (pointT *point, facetT *facet, realT *dist);
-void    qh_partitionpoint (pointT *point, facetT *facet);
-void 	qh_partitionvisible(boolT allpoints, int *numpoints);
-void    qh_precision (char *reason);
-void	qh_printsummary(FILE *fp);
-
-/***** -global.c internal prototypes (alphabetical) ***********************/
-
-void    qh_appendprint (qh_PRINT format);
-void 	qh_freebuild (boolT allmem);
-void 	qh_freebuffers (void);
-void    qh_initbuffers (coordT *points, int numpoints, int dim, boolT ismalloc);
-int     qh_strtol (const char *s, char **endp);
-double  qh_strtod (const char *s, char **endp);
-
-/***** -stat.c internal prototypes (alphabetical) ***********************/
-
-void	qh_allstatA (void);
-void	qh_allstatB (void);
-void	qh_allstatC (void);
-void	qh_allstatD (void);
-void	qh_allstatE (void);
-void	qh_allstatE2 (void);
-void	qh_allstatF (void);
-void	qh_allstatG (void);
-void	qh_allstatH (void);
-void 	qh_freebuffers (void);
-void    qh_initbuffers (coordT *points, int numpoints, int dim, boolT ismalloc);
-
-#endif /* qhDEFqhulla */
diff --git a/extern/qhull/include/qhull/qset.h b/extern/qhull/include/qhull/qset.h
deleted file mode 100644
index 6c0ff758de4..00000000000
--- a/extern/qhull/include/qhull/qset.h
+++ /dev/null
@@ -1,468 +0,0 @@
-/*  ---------------------------------
-
-   qset.h
-     header file for qset.c that implements set
-
-   see qh-set.htm and qset.c
-
-   only uses mem.c, malloc/free
-
-   for error handling, writes message and calls
-      qh_errexit (qhmem_ERRqhull, NULL, NULL);
-
-   set operations satisfy the following properties:
-    - sets have a max size, the actual size (if different) is stored at the end
-    - every set is NULL terminated
-    - sets may be sorted or unsorted, the caller must distinguish this
-
-   copyright (c) 1993-2002, The Geometry Center
-*/
-
-#ifndef qhDEFset
-#define qhDEFset 1
-
-/*================= -structures- ===============*/
-
-#ifndef DEFsetT
-#define DEFsetT 1
-typedef struct setT setT;   /* a set is a sorted or unsorted array of pointers */
-#endif
-
-/*------------------------------------------
-
-setT
-  a set or list of pointers with maximum size and actual size.
-
-variations:
-  unsorted, unique   -- a list of unique pointers with NULL terminator
-  			   user guarantees uniqueness
-  sorted	     -- a sorted list of unique pointers with NULL terminator
-  			   qset.c guarantees uniqueness
-  unsorted           -- a list of pointers terminated with NULL
-  indexed  	     -- an array of pointers with NULL elements
-
-structure for set of n elements:
-
-	--------------
-	|  maxsize
-	--------------
-	|  e[0] - a pointer, may be NULL for indexed sets
-	--------------
-	|  e[1]
-
-	--------------
-	|  ...
-	--------------
-	|  e[n-1]
-	--------------
-	|  e[n] = NULL
-	--------------
-	|  ...
-	--------------
-	|  e[maxsize] - n+1 or NULL (determines actual size of set)
-	--------------
-
-*/
-
-/*-- setelemT -- internal type to allow both pointers and indices
-*/
-typedef union setelemT setelemT;
-union setelemT {
-  void    *p;
-  int      i;         /* integer used for e[maxSize] */
-};
-
-struct setT {
-  int maxsize;          /* maximum number of elements (except NULL) */
-  setelemT e[1];        /* array of pointers, tail is NULL */
-                        /* last slot (unless NULL) is actual size+1
-                           e[maxsize]==NULL or e[e[maxsize]-1]==NULL */
-                        /* this may generate a warning since e[] contains
-			   maxsize elements */
-};
-
-/*=========== -constants- =========================*/
-
-/*-------------------------------------
-
-  SETelemsize
-    size of a set element in bytes
-*/
-#define SETelemsize sizeof(setelemT)
-
-
-/*=========== -macros- =========================*/
-
-/*-------------------------------------
-
-   FOREACHsetelement_(type, set, variable)
-     define FOREACH iterator
-
-   declare:
-     assumes *variable and **variablep are declared
-     no space in "variable)" [DEC Alpha cc compiler]
-
-   each iteration:
-     variable is set element
-     variablep is one beyond variable.
-
-   to repeat an element:
-     variablep--; / *repeat* /
-
-   at exit:
-     variable is NULL at end of loop
-
-   example:
-     #define FOREACHfacet_( facets ) FOREACHsetelement_( facetT, facets, facet )
-
-   notes:
-     use FOREACHsetelement_i_() if need index or include NULLs
-
-   WARNING:
-     nested loops can't use the same variable (define another FOREACH)
-
-     needs braces if nested inside another FOREACH
-     this includes intervening blocks, e.g. FOREACH...{ if () FOREACH...} )
-*/
-#define FOREACHsetelement_(type, set, variable) \
-        if (((variable= NULL), set)) for(\
-          variable##p= (type **)&((set)->e[0].p); \
-	  (variable= *variable##p++);)
-
-/*------------------------------------------
-
-   FOREACHsetelement_i_(type, set, variable)
-     define indexed FOREACH iterator
-
-   declare:
-     type *variable, variable_n, variable_i;
-
-   each iteration:
-     variable is set element, may be NULL
-     variable_i is index, variable_n is qh_setsize()
-
-   to repeat an element:
-     variable_i--; variable_n-- repeats for deleted element
-
-   at exit:
-     variable==NULL and variable_i==variable_n
-
-   example:
-     #define FOREACHfacet_i_( facets ) FOREACHsetelement_i_( facetT, facets, facet )
-
-   WARNING:
-     nested loops can't use the same variable (define another FOREACH)
-
-     needs braces if nested inside another FOREACH
-     this includes intervening blocks, e.g. FOREACH...{ if () FOREACH...} )
-*/
-#define FOREACHsetelement_i_(type, set, variable) \
-        if (((variable= NULL), set)) for (\
-          variable##_i= 0, variable= (type *)((set)->e[0].p), \
-                   variable##_n= qh_setsize(set);\
-          variable##_i < variable##_n;\
-          variable= (type *)((set)->e[++variable##_i].p) )
-
-/*----------------------------------------
-
-   FOREACHsetelementreverse_(type, set, variable)-
-     define FOREACH iterator in reverse order
-
-   declare:
-     assumes *variable and **variablep are declared
-     also declare 'int variabletemp'
-
-   each iteration:
-     variable is set element
-
-   to repeat an element:
-     variabletemp++; / *repeat* /
-
-   at exit:
-     variable is NULL
-
-   example:
-     #define FOREACHvertexreverse_( vertices ) FOREACHsetelementreverse_( vertexT, vertices, vertex )
-
-   notes:
-     use FOREACHsetelementreverse12_() to reverse first two elements
-     WARNING: needs braces if nested inside another FOREACH
-*/
-#define FOREACHsetelementreverse_(type, set, variable) \
-        if (((variable= NULL), set)) for(\
-	   variable##temp= qh_setsize(set)-1, variable= qh_setlast(set);\
-	   variable; variable= \
-	   ((--variable##temp >= 0) ? SETelemt_(set, variable##temp, type) : NULL))
-
-/*-------------------------------------
-
-   FOREACHsetelementreverse12_(type, set, variable)-
-     define FOREACH iterator with e[1] and e[0] reversed
-
-   declare:
-     assumes *variable and **variablep are declared
-
-   each iteration:
-     variable is set element
-     variablep is one after variable.
-
-   to repeat an element:
-     variablep--; / *repeat* /
-
-   at exit:
-     variable is NULL at end of loop
-
-   example
-     #define FOREACHvertexreverse12_( vertices ) FOREACHsetelementreverse12_( vertexT, vertices, vertex )
-
-   notes:
-     WARNING: needs braces if nested inside another FOREACH
-*/
-#define FOREACHsetelementreverse12_(type, set, variable) \
-        if (((variable= NULL), set)) for(\
-          variable##p= (type **)&((set)->e[1].p); \
-	  (variable= *variable##p); \
-          variable##p == ((type **)&((set)->e[0].p))?variable##p += 2: \
-	      (variable##p == ((type **)&((set)->e[1].p))?variable##p--:variable##p++))
-
-/*-------------------------------------
-
-   FOREACHelem_( set )-
-     iterate elements in a set
-
-   declare:
-     void *elem, *elemp;
-
-   each iteration:
-     elem is set element
-     elemp is one beyond
-
-   to repeat an element:
-     elemp--; / *repeat* /
-
-   at exit:
-     elem == NULL at end of loop
-
-   example:
-     FOREACHelem_(set) {
-
-   notes:
-     WARNING: needs braces if nested inside another FOREACH
-*/
-#define FOREACHelem_(set) FOREACHsetelement_(void, set, elem)
-
-/*-------------------------------------
-
-   FOREACHset_( set )-
-     iterate a set of sets
-
-   declare:
-     setT *set, **setp;
-
-   each iteration:
-     set is set element
-     setp is one beyond
-
-   to repeat an element:
-     setp--; / *repeat* /
-
-   at exit:
-     set == NULL at end of loop
-
-   example
-     FOREACHset_(sets) {
-
-   notes:
-     WARNING: needs braces if nested inside another FOREACH
-*/
-#define FOREACHset_(sets) FOREACHsetelement_(setT, sets, set)
-
-/*-------------------------------------------
-
-   SETindex_( set, elem )
-     return index of elem in set
-
-   notes:
-     for use with FOREACH iteration
-
-   example:
-     i= SETindex_(ridges, ridge)
-*/
-#define SETindex_(set, elem) ((void **)elem##p - (void **)&(set)->e[1].p)
-
-/*-----------------------------------------
-
-   SETref_( elem )
-     l.h.s. for modifying the current element in a FOREACH iteration
-
-   example:
-     SETref_(ridge)= anotherridge;
-*/
-#define SETref_(elem) (elem##p[-1])
-
-/*-----------------------------------------
-
-   SETelem_(set, n)
-     return the n'th element of set
-
-   notes:
-      assumes that n is valid [0..size] and that set is defined
-      use SETelemt_() for type cast
-*/
-#define SETelem_(set, n)           ((set)->e[n].p)
-
-/*-----------------------------------------
-
-   SETelemt_(set, n, type)
-     return the n'th element of set as a type
-
-   notes:
-      assumes that n is valid [0..size] and that set is defined
-*/
-#define SETelemt_(set, n, type)    ((type*)((set)->e[n].p))
-
-/*-----------------------------------------
-
-     return address of the n'th element of a set
-
-   notes:
-      assumes that n is valid [0..size] and set is defined
-*/
-#define SETelemaddr_(set, n, type) ((type **)(&((set)->e[n].p)))
-
-/*-----------------------------------------
-
-   SETfirst_(set)
-     return first element of set
-
-*/
-#define SETfirst_(set)             ((set)->e[0].p)
-
-/*-----------------------------------------
-
-   SETfirstt_(set, type)
-     return first element of set as a type
-
-*/
-#define SETfirstt_(set, type)      ((type*)((set)->e[0].p))
-
-/*-----------------------------------------
-
-   SETsecond_(set)
-     return second element of set
-
-*/
-#define SETsecond_(set)            ((set)->e[1].p)
-
-/*-----------------------------------------
-
-   SETsecondt_(set, type)
-     return second element of set as a type
-*/
-#define SETsecondt_(set, type)     ((type*)((set)->e[1].p))
-
-/*-----------------------------------------
-
-       return address of set's elements
-*/
-
-/*-----------------------------------------
-
-   SETreturnsize_(set, size)
-     return size of a set
-
-   notes:
-      set must be defined
-      use qh_setsize(set) unless speed is critical
-*/
-#define SETreturnsize_(set, size) (((size)= ((set)->e[(set)->maxsize].i))?(--(size)):((size)= (set)->maxsize))
-
-/*-----------------------------------------
-
-   SETempty_(set)
-     return true (1) if set is empty
-
-   notes:
-      set may be NULL
-*/
-#define SETempty_(set) 	          (!set || (SETfirst_(set) ? 0:1))
-
-/*-----------------------------------------
-
-   SETtruncate_(set)
-     return first element of set
-
-   see:
-     qh_settruncate()
-
-*/
-#define SETtruncate_(set, size) {set->e[set->maxsize].i= size+1; /* maybe overwritten */ \
-      set->e[size].p= NULL;}
-
-/*======= prototypes in alphabetical order ============*/
-
-void  qh_setaddnth(setT **setp, int nth, void *newelem);
-void  qh_setappend(setT **setp, void *elem);
-void  qh_setappend_set(setT **setp, setT *setA);
-void  qh_setappend2ndlast(setT **setp, void *elem);
-void  qh_setcheck(setT *set, char *tname, int id);
-void  qh_setcompact(setT *set);
-setT *qh_setcopy(setT *set, int extra);
-void *qh_setdel(setT *set, void *elem);
-void *qh_setdellast(setT *set);
-void *qh_setdelnth(setT *set, int nth);
-void *qh_setdelnthsorted(setT *set, int nth);
-void *qh_setdelsorted(setT *set, void *newelem);
-setT *qh_setduplicate( setT *set, int elemsize);
-int   qh_setequal(setT *setA, setT *setB);
-int   qh_setequal_except (setT *setA, void *skipelemA, setT *setB, void *skipelemB);
-int   qh_setequal_skip (setT *setA, int skipA, setT *setB, int skipB);
-void  qh_setfree(setT **set);
-void  qh_setfree2( setT **setp, int elemsize);
-void  qh_setfreelong(setT **set);
-int   qh_setin(setT *set, void *setelem);
-int   qh_setindex(setT *set, void *setelem);
-void  qh_setlarger(setT **setp);
-void *qh_setlast(setT *set);
-setT *qh_setnew(int size);
-setT *qh_setnew_delnthsorted(setT *set, int size, int nth, int prepend);
-void  qh_setprint(FILE *fp, char* string, setT *set);
-void  qh_setreplace(setT *set, void *oldelem, void *newelem);
-int   qh_setsize(setT *set);
-setT *qh_settemp(int setsize);
-void  qh_settempfree(setT **set);
-void  qh_settempfree_all(void);
-setT *qh_settemppop(void);
-void  qh_settemppush(setT *set);
-void  qh_settruncate (setT *set, int size);
-int   qh_setunique (setT **set, void *elem);
-void  qh_setzero (setT *set, int index, int size);
-
-
-#endif /* qhDEFset */
diff --git a/extern/qhull/include/qhull/stat.h b/extern/qhull/include/qhull/stat.h
deleted file mode 100644
index 1dae54ed21d..00000000000
--- a/extern/qhull/include/qhull/stat.h
+++ /dev/null
@@ -1,520 +0,0 @@
-  /*  ---------------------------------
-
-   stat.h
-     contains all statistics that are collected for qhull
-
-   see qh-stat.htm and stat.c
-
-   copyright (c) 1993-2002, The Geometry Center
-
-   recompile qhull if you change this file
-
-   Integer statistics are Z* while real statistics are W*.
-
-   define maydebugx to call a routine at every statistic event
-
-*/
-
-#ifndef qhDEFstat
-#define qhDEFstat 1
-
-
-/*---------------------------------
-
-  qh_KEEPstatistics
-    0 turns off statistic gathering (except zzdef/zzinc/zzadd/zzval/wwval)
-*/
-#ifndef qh_KEEPstatistics
-#define qh_KEEPstatistics 1
-#endif
-
-/*---------------------------------
-
-  Zxxx for integers, Wxxx for reals
-
-  notes:
-    be sure that all statistics are defined in stat.c
-      otherwise initialization may core dump
-    can pick up all statistics by:
-      grep '[zw].*_[(][ZW]' *.c >z.x
-    remove trailers with query">-
-    remove leaders with  query-replace-regexp [ ^I]+  (
-*/
-#if qh_KEEPstatistics
-enum statistics {     /* alphabetical after Z/W */
-    Zacoplanar,
-    Wacoplanarmax,
-    Wacoplanartot,
-    Zangle,
-    Wangle,
-    Wanglemax,
-    Wanglemin,
-    Zangletests,
-    Wareatot,
-    Wareamax,
-    Wareamin,
-    Zavoidold,
-    Wavoidoldmax,
-    Wavoidoldtot,
-    Zback0,
-    Zbestcentrum,
-    Zbestdist,
-    Zcentrumtests,
-    Zcheckpart,
-    Zcomputefurthest,
-    Zconcave,
-    Wconcavemax,
-    Wconcavetot,
-    Zconcaveridges,
-    Zconcaveridge,
-    Zcoplanar,
-    Wcoplanarmax,
-    Wcoplanartot,
-    Zcoplanarangle,
-    Zcoplanarcentrum,
-    Zcoplanarhorizon,
-    Zcoplanarinside,
-    Zcoplanarpart,
-    Zcoplanarridges,
-    Wcpu,
-    Zcyclefacetmax,
-    Zcyclefacettot,
-    Zcyclehorizon,
-    Zcyclevertex,
-    Zdegen,
-    Wdegenmax,
-    Wdegentot,
-    Zdegenvertex,
-    Zdelfacetdup,
-    Zdelridge,
-    Zdelvertextot,
-    Zdelvertexmax,
-    Zdetsimplex,
-    Zdistcheck,
-    Zdistconvex,
-    Zdistgood,
-    Zdistio,
-    Zdistplane,
-    Zdiststat,
-    Zdistvertex,
-    Zdistzero,
-    Zdoc1,
-    Zdoc2,
-    Zdoc3,
-    Zdoc4,
-    Zdoc5,
-    Zdoc6,
-    Zdoc7,
-    Zdoc8,
-    Zdoc9,
-    Zdoc10,
-    Zdoc11,
-    Zdoc12,
-    Zdropdegen,
-    Zdropneighbor,
-    Zdupflip,
-    Zduplicate,
-    Wduplicatemax,
-    Wduplicatetot,
-    Zdupridge,
-    Zdupsame,
-    Zflipped,
-    Wflippedmax,
-    Wflippedtot,
-    Zflippedfacets,
-    Zfindbest,
-    Zfindbestmax,
-    Zfindbesttot,
-    Zfindcoplanar,
-    Zfindfail,
-    Zfindhorizon,
-    Zfindhorizonmax,
-    Zfindhorizontot,
-    Zfindjump,
-    Zfindnew,
-    Zfindnewmax,
-    Zfindnewtot,
-    Zfindnewjump,
-    Zfindnewsharp,
-    Zgauss0,
-    Zgoodfacet,
-    Zhashlookup,
-    Zhashridge,
-    Zhashridgetest,
-    Zhashtests,
-    Zinsidevisible,
-    Zintersect,
-    Zintersectfail,
-    Zintersectmax,
-    Zintersectnum,
-    Zintersecttot,
-    Zmaxneighbors,
-    Wmaxout,
-    Wmaxoutside,
-    Zmaxridges,
-    Zmaxvertex,
-    Zmaxvertices,
-    Zmaxvneighbors,
-    Zmemfacets,
-    Zmempoints,
-    Zmemridges,
-    Zmemvertices,
-    Zmergeflipdup,
-    Zmergehorizon,
-    Zmergeinittot,
-    Zmergeinitmax,
-    Zmergeinittot2,
-    Zmergeintohorizon,
-    Zmergenew,
-    Zmergesettot,
-    Zmergesetmax,
-    Zmergesettot2,
-    Zmergesimplex,
-    Zmergevertex,
-    Wmindenom,
-    Wminvertex,
-    Zminnorm,
-    Zmultiridge,
-    Znearlysingular,
-    Zneighbor,
-    Wnewbalance,
-    Wnewbalance2,
-    Znewfacettot,
-    Znewfacetmax,
-    Znewvertex,
-    Wnewvertex,
-    Wnewvertexmax,
-    Znoarea,
-    Znonsimplicial,
-    Znowsimplicial,
-    Znotgood,
-    Znotgoodnew,
-    Znotmax,
-    Znumfacets,
-    Znummergemax,
-    Znummergetot,
-    Znumneighbors,
-    Znumridges,
-    Znumvertices,
-    Znumvisibility,
-    Znumvneighbors,
-    Zonehorizon,
-    Zpartangle,
-    Zpartcoplanar,
-    Zpartflip,
-    Zparthorizon,
-    Zpartinside,
-    Zpartition,
-    Zpartitionall,
-    Zpartnear,
-    Zpbalance,
-    Wpbalance,
-    Wpbalance2,
-    Zpostfacets,
-    Zpremergetot,
-    Zprocessed,
-    Zremvertex,
-    Zremvertexdel,
-    Zrenameall,
-    Zrenamepinch,
-    Zrenameshare,
-    Zretry,
-    Wretrymax,
-    Zridge,
-    Wridge,
-    Wridgemax,
-    Zridge0,
-    Wridge0,
-    Wridge0max,
-    Zridgemid,
-    Wridgemid,
-    Wridgemidmax,
-    Zridgeok,
-    Wridgeok,
-    Wridgeokmax,
-    Zsearchpoints,
-    Zsetplane,
-    Ztestvneighbor,
-    Ztotcheck,
-    Ztothorizon,
-    Ztotmerge,
-    Ztotpartcoplanar,
-    Ztotpartition,
-    Ztotridges,
-    Ztotvertices,
-    Ztotvisible,
-    Ztricoplanar,
-    Ztricoplanarmax,
-    Ztricoplanartot,
-    Ztridegen,
-    Ztrimirror,
-    Ztrinull,
-    Wvertexmax,
-    Wvertexmin,
-    Zvertexridge,
-    Zvertexridgetot,
-    Zvertexridgemax,
-    Zvertices,
-    Zvisfacettot,
-    Zvisfacetmax,
-    Zvisvertextot,
-    Zvisvertexmax,
-    Zwidefacet,
-    Zwidevertices,
-    ZEND};
-
-/*---------------------------------
-
-  Zxxx/Wxxx statistics that remain defined if qh_KEEPstatistics=0
-
-  notes:
-    be sure to use zzdef, zzinc, etc. with these statistics (no double checking!)
-*/
-#else
-enum statistics {     /* for zzdef etc. macros */
-  Zback0,
-  Zbestdist,
-  Zcentrumtests,
-  Zcheckpart,
-  Zconcaveridges,
-  Zcoplanarhorizon,
-  Zcoplanarpart,
-  Zcoplanarridges,
-  Zcyclefacettot,
-  Zcyclehorizon,
-  Zdelvertextot,
-  Zdistcheck,
-  Zdistconvex,
-  Zdistzero,
-  Zdoc1,
-  Zdoc2,
-  Zdoc3,
-  Zdoc11,
-  Zflippedfacets,
-  Zgauss0,
-  Zminnorm,
-  Zmultiridge,
-  Znearlysingular,
-  Wnewvertexmax,
-  Znumvisibility,
-  Zpartcoplanar,
-  Zpartition,
-  Zpartitionall,
-  Zprocessed,
-  Zretry,
-  Zridge,
-  Wridge,
-  Wridgemax,
-  Zridge0,
-  Wridge0,
-  Wridge0max,
-  Zridgemid,
-  Wridgemid,
-  Wridgemidmax,
-  Zridgeok,
-  Wridgeok,
-  Wridgeokmax,
-  Zsetplane,
-  Ztotmerge,
-    ZEND};
-#endif
-
-/*---------------------------------
-
-  ztype
-    the type of a statistic sets its initial value.
-
-  notes:
-    The type should be the same as the macro for collecting the statistic
-*/
-
-/*========== macros and constants =============*/
-
-/*----------------------------------
-
-  MAYdebugx
-    define as maydebug() to be called frequently for error trapping
-*/
-#define MAYdebugx
-
-/*----------------------------------
-
-  zzdef_, zdef_( type, name, doc, -1)
-    define a statistic (assumes 'qhstat.next= 0;')
-
-  zdef_( type, name, doc, count)
-    define an averaged statistic
-    printed as name/count
-*/
-#define zzdef_(stype,name,string,cnt) qhstat id[qhstat next++]=name; \
-   qhstat doc[name]= string; qhstat count[name]= cnt; qhstat type[name]= stype
-#if qh_KEEPstatistics
-#define zdef_(stype,name,string,cnt) qhstat id[qhstat next++]=name; \
-   qhstat doc[name]= string; qhstat count[name]= cnt; qhstat type[name]= stype
-#else
-#define zdef_(type,name,doc,count)
-#endif
-
-/*----------------------------------
-
-  zzinc_( name ), zinc_( name)
-    increment an integer statistic
-*/
-#define zzinc_(id) {MAYdebugx; qhstat stats[id].i++;}
-#if qh_KEEPstatistics
-#define zinc_(id) {MAYdebugx; qhstat stats[id].i++;}
-#else
-#define zinc_(id) {}
-#endif
-
-/*----------------------------------
-
-    add value to an integer or real statistic
-*/
-#define zzadd_(id, val) {MAYdebugx; qhstat stats[id].i += (val);}
-#define wwadd_(id, val) {MAYdebugx; qhstat stats[id].r += (val);}
-#if qh_KEEPstatistics
-#define zadd_(id, val) {MAYdebugx; qhstat stats[id].i += (val);}
-#define wadd_(id, val) {MAYdebugx; qhstat stats[id].r += (val);}
-#else
-#endif
-
-/*----------------------------------
-
-  zzval_( name ), zval_( name ), wwval_( name )
-    set or return value of a statistic
-*/
-#define zzval_(id) ((qhstat stats[id]).i)
-#define wwval_(id) ((qhstat stats[id]).r)
-#if qh_KEEPstatistics
-#define zval_(id) ((qhstat stats[id]).i)
-#define wval_(id) ((qhstat stats[id]).r)
-#else
-#define zval_(id) qhstat tempi
-#define wval_(id) qhstat tempr
-#endif
-
-/*----------------------------------
-
-  zmax_( id, val ), wmax_( id, value )
-    maximize id with val
-*/
-#define wwmax_(id, val) {MAYdebugx; maximize_(qhstat stats[id].r,(val));}
-#if qh_KEEPstatistics
-#define zmax_(id, val) {MAYdebugx; maximize_(qhstat stats[id].i,(val));}
-#define wmax_(id, val) {MAYdebugx; maximize_(qhstat stats[id].r,(val));}
-#else
-#define zmax_(id, val) {}
-#define wmax_(id, val) {}
-#endif
-
-/*----------------------------------
-
-  zmin_( id, val ), wmin_( id, value )
-    minimize id with val
-*/
-#if qh_KEEPstatistics
-#define zmin_(id, val) {MAYdebugx; minimize_(qhstat stats[id].i,(val));}
-#define wmin_(id, val) {MAYdebugx; minimize_(qhstat stats[id].r,(val));}
-#else
-#define zmin_(id, val) {}
-#define wmin_(id, val) {}
-#endif
-
-/*================== stat.h types ==============*/
-
-
-/*----------------------------------
-
-  intrealT
-    union of integer and real, used for statistics
-*/
-typedef union intrealT intrealT;    /* union of int and realT */
-union intrealT {
-    int i;
-    realT r;
-};
-
-/*----------------------------------
-
-  qhstat
-    global data structure for statistics
-
-  notes:
-   access to qh_qhstat is via the "qhstat" macro.  There are two choices
-   qh_QHpointer = 1     access globals via a pointer
-                        enables qh_saveqhull() and qh_restoreqhull()
-		= 0     qh_qhstat is a static data structure
-		        only one instance of qhull() can be active at a time
-			default value
-   qh_QHpointer is defined in qhull.h
-
-   allocated in stat.c
-*/
-typedef struct qhstatT qhstatT;
-#if qh_QHpointer
-#define qhstat qh_qhstat->
-extern qhstatT *qh_qhstat;
-#else
-#define qhstat qh_qhstat.
-extern qhstatT qh_qhstat;
-#endif
-struct qhstatT {
-  intrealT   stats[ZEND];     /* integer and real statistics */
-  unsigned   char id[ZEND+10]; /* id's in print order */
-  char      *doc[ZEND];       /* array of documentation strings */
-  short int  count[ZEND];     /* -1 if none, else index of count to use */
-  char       type[ZEND];      /* type, see ztypes above */
-  char       printed[ZEND];   /* true, if statistic has been printed */
-  intrealT   init[ZTYPEend];  /* initial values by types, set initstatistics */
-
-  int        next;            /* next index for zdef_ */
-  int        precision;       /* index for precision problems */
-  int        vridges;         /* index for Voronoi ridges */
-  int        tempi;
-  realT      tempr;
-};
-
-/*========== function prototypes ===========*/
-
-void    qh_allstatA(void);
-void    qh_allstatB(void);
-void    qh_allstatC(void);
-void    qh_allstatD(void);
-void    qh_allstatE(void);
-void    qh_allstatE2(void);
-void    qh_allstatF(void);
-void    qh_allstatG(void);
-void    qh_allstatH(void);
-void    qh_allstatI(void);
-void    qh_allstatistics (void);
-void    qh_collectstatistics (void);
-void	qh_freestatistics (void);
-void    qh_initstatistics (void);
-boolT 	qh_newstats (int index, int *nextindex);
-boolT 	qh_nostatistic (int i);
-void    qh_printallstatistics (FILE *fp, char *string);
-void    qh_printstatistics (FILE *fp, char *string);
-void  	qh_printstatlevel (FILE *fp, int id, int start);
-void  	qh_printstats (FILE *fp, int index, int *nextindex);
-realT   qh_stddev (int num, realT tot, realT tot2, realT *ave);
-
-#endif   /* qhDEFstat */
diff --git a/extern/qhull/include/qhull/user.h b/extern/qhull/include/qhull/user.h
deleted file mode 100644
index 79558967a52..00000000000
--- a/extern/qhull/include/qhull/user.h
+++ /dev/null
@@ -1,762 +0,0 @@
-/*  ---------------------------------
-
-   user.h
-   user redefinable constants
-
-   see qh-user.htm.  see COPYING for copyright information.
-
-   before reading any code, review qhull.h for data structure definitions and
-   the "qh" macro.
-*/
-
-#ifndef qhDEFuser
-#define qhDEFuser 1
-
-/*============= data types and configuration macros ==========*/
-
-/*----------------------------------
-
-  realT
-    set the size of floating point numbers
-
-  qh_REALdigits
-    maximimum number of significant digits
-
-  qh_REAL_1, qh_REAL_2n, qh_REAL_3n
-    format strings for printf
-
-  qh_REALmax, qh_REALmin
-    maximum and minimum (near zero) values
-
-  qh_REALepsilon
-    machine roundoff.  Maximum roundoff error for addition and multiplication.
-
-  notes:
-   Select whether to store floating point numbers in single precision (float)
-   or double precision (double).
-
-   Use 'float' to save about 8% in time and 25% in space.  This is particularly
-   help if high-d where convex hulls are space limited.  Using 'float' also
-   reduces the printed size of Qhull's output since numbers have 8 digits of
-   precision.
-
-   Use 'double' when greater arithmetic precision is needed.  This is needed
-   for Delaunay triangulations and Voronoi diagrams when you are not merging
-   facets.
-
-   If 'double' gives insufficient precision, your data probably includes
-   degeneracies.  If so you should use facet merging (done by default)
-   or exact arithmetic (see imprecision section of manual, qh-impre.htm).
-   You may also use option 'Po' to force output despite precision errors.
-
-   You may use 'long double', but many format statements need to be changed
-   and you may need a 'long double' square root routine.  S. Grundmann
-   (sg@eeiwzb.et.tu-dresden.de) has done this.  He reports that the code runs
-   much slower with little gain in precision.
-
-   WARNING: on some machines,    int f(){realT a= REALmax;return (a == REALmax);}
-      returns False.  Use (a > REALmax/2) instead of (a == REALmax).
-
-   REALfloat =   1      all numbers are 'float' type
-             =   0      all numbers are 'double' type
-*/
-#define REALfloat 0
-
-#if (REALfloat == 1)
-#define realT float
-#define REALmax FLT_MAX
-#define REALmin FLT_MIN
-#define REALepsilon FLT_EPSILON
-#define qh_REALdigits 8   /* maximum number of significant digits */
-#define qh_REAL_1 "%6.8g "
-#define qh_REAL_2n "%6.8g %6.8g\n"
-#define qh_REAL_3n "%6.8g %6.8g %6.8g\n"
-
-#elif (REALfloat == 0)
-#define realT double
-#define REALmax DBL_MAX
-#define REALmin DBL_MIN
-#define REALepsilon DBL_EPSILON
-#define qh_REALdigits 16    /* maximum number of significant digits */
-#define qh_REAL_1 "%6.16g "
-#define qh_REAL_2n "%6.16g %6.16g\n"
-#define qh_REAL_3n "%6.16g %6.16g %6.16g\n"
-
-#else
-#error unknown float option
-#endif
-
-/*----------------------------------
-
-  qh_CPUclock
-    define the clock() function for reporting the total time spent by Qhull
-    returns CPU ticks as a 'long int'
-    qh_CPUclock is only used for reporting the total time spent by Qhull
-
-  qh_SECticks
-    the number of clock ticks per second
-
-  notes:
-    looks for CLOCKS_PER_SEC, CLOCKS_PER_SECOND, or assumes microseconds
-    to define a custom clock, set qh_CLOCKtype to 0
-
-    if your system does not use clock() to return CPU ticks, replace
-    qh_CPUclock with the corresponding function.  It is converted
-    to unsigned long to prevent wrap-around during long runs.
-
-
-   Set qh_CLOCKtype to
-
-     1	   	for CLOCKS_PER_SEC, CLOCKS_PER_SECOND, or microsecond
-                Note:  may fail if more than 1 hour elapsed time
-
-     2	   	use qh_clock() with POSIX times() (see global.c)
-*/
-#define qh_CLOCKtype 1  /* change to the desired number */
-
-#if (qh_CLOCKtype == 1)
-
-#if defined (CLOCKS_PER_SECOND)
-#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
-#define qh_SECticks CLOCKS_PER_SECOND
-
-#elif defined (CLOCKS_PER_SEC)
-#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
-#define qh_SECticks CLOCKS_PER_SEC
-
-#elif defined (CLK_TCK)
-#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
-#define qh_SECticks CLK_TCK
-
-#else
-#define qh_CPUclock    ((unsigned long)clock())  /* return CPU clock */
-#define qh_SECticks 1E6
-#endif
-
-#elif (qh_CLOCKtype == 2)
-#define qh_CPUclock    qh_clock()  /* return CPU clock */
-#define qh_SECticks 100
-
-#else /* qh_CLOCKtype == ? */
-#error unknown clock option
-#endif
-
-/*----------------------------------
-
-  qh_RANDOMtype, qh_RANDOMmax, qh_RANDOMseed
-    define random number generator
-
-    qh_RANDOMint generates a random integer between 0 and qh_RANDOMmax.
-    qh_RANDOMseed sets the random number seed for qh_RANDOMint
-
-  Set qh_RANDOMtype (default 5) to:
-    1       for random() with 31 bits (UCB)
-    2       for rand() with RAND_MAX or 15 bits (system 5)
-    3       for rand() with 31 bits (Sun)
-    4       for lrand48() with 31 bits (Solaris)
-    5       for qh_rand() with 31 bits (included with Qhull)
-
-  notes:
-    Random numbers are used by rbox to generate point sets.  Random
-    numbers are used by Qhull to rotate the input ('QRn' option),
-    simulate a randomized algorithm ('Qr' option), and to simulate
-    roundoff errors ('Rn' option).
-
-    Random number generators differ between systems.  Most systems provide
-    rand() but the period varies.  The period of rand() is not critical
-    since qhull does not normally use random numbers.
-
-    The default generator is Park & Miller's minimal standard random
-    number generator [CACM 31:1195 '88].  It is included with Qhull.
-
-    If qh_RANDOMmax is wrong, qhull will report a warning and Geomview
-    output will likely be invisible.
-*/
-#define qh_RANDOMtype 5   /* *** change to the desired number *** */
-
-#if (qh_RANDOMtype == 1)
-#define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, random()/MAX */
-#define qh_RANDOMint random()
-#define qh_RANDOMseed_(seed) srandom(seed);
-
-#elif (qh_RANDOMtype == 2)
-#ifdef RAND_MAX
-#define qh_RANDOMmax ((realT)RAND_MAX)
-#else
-#define qh_RANDOMmax ((realT)32767)   /* 15 bits (System 5) */
-#endif
-#define qh_RANDOMint  rand()
-#define qh_RANDOMseed_(seed) srand((unsigned)seed);
-
-#elif (qh_RANDOMtype == 3)
-#define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, Sun */
-#define qh_RANDOMint  rand()
-#define qh_RANDOMseed_(seed) srand((unsigned)seed);
-
-#elif (qh_RANDOMtype == 4)
-#define qh_RANDOMmax ((realT)0x7fffffffUL)  /* 31 bits, lrand38()/MAX */
-#define qh_RANDOMint lrand48()
-#define qh_RANDOMseed_(seed) srand48(seed);
-
-#elif (qh_RANDOMtype == 5)
-#define qh_RANDOMmax ((realT)2147483646UL)  /* 31 bits, qh_rand/MAX */
-#define qh_RANDOMint qh_rand()
-#define qh_RANDOMseed_(seed) qh_srand(seed);
-/* unlike rand(), never returns 0 */
-
-#else
-#error: unknown random option
-#endif
-
-/*----------------------------------
-
-  qh_ORIENTclock
-    0 for inward pointing normals by Geomview convention
-*/
-#define qh_ORIENTclock 0
-
-
-/*========= performance related constants =========*/
-
-/*----------------------------------
-
-  qh_HASHfactor
-    total hash slots / used hash slots.  Must be at least 1.1.
-
-  notes:
-    =2 for at worst 50% occupancy for qh hash_table and normally 25% occupancy
-*/
-#define qh_HASHfactor 2
-
-/*----------------------------------
-
-  qh_VERIFYdirect
-    with 'Tv' verify all points against all facets if op count is smaller
-
-  notes:
-    if greater, calls qh_check_bestdist() instead
-*/
-#define qh_VERIFYdirect 1000000
-
-/*----------------------------------
-
-  qh_INITIALsearch
-     if qh_INITIALmax, search points up to this dimension
-*/
-#define qh_INITIALsearch 6
-
-/*----------------------------------
-
-  qh_INITIALmax
-    if dim >= qh_INITIALmax, use min/max coordinate points for initial simplex
-
-  notes:
-    from points with non-zero determinants
-    use option 'Qs' to override (much slower)
-*/
-#define qh_INITIALmax 8
-
-/*----------------------------------
-
-  qh_JOGGLEdefault
-    default qh.JOGGLEmax is qh.DISTround * qh_JOGGLEdefault
-
-  notes:
-    rbox s r 100 | qhull QJ1e-15 QR0 generates 90% faults at distround 7e-16
-    rbox s r 100 | qhull QJ1e-14 QR0 generates 70% faults
-    rbox s r 100 | qhull QJ1e-13 QR0 generates 35% faults
-    rbox s r 100 | qhull QJ1e-12 QR0 generates 8% faults
-    rbox s r 100 | qhull QJ1e-11 QR0 generates 1% faults
-    rbox s r 100 | qhull QJ1e-10 QR0 generates 0% faults
-    rbox 1000 W0 | qhull QJ1e-12 QR0 generates 86% faults
-    rbox 1000 W0 | qhull QJ1e-11 QR0 generates 20% faults
-    rbox 1000 W0 | qhull QJ1e-10 QR0 generates 2% faults
-    the later have about 20 points per facet, each of which may interfere
-
-    pick a value large enough to avoid retries on most inputs
-*/
-#define qh_JOGGLEdefault 30000.0
-
-/*----------------------------------
-
-  qh_JOGGLEincrease
-    factor to increase qh.JOGGLEmax on qh_JOGGLEretry or qh_JOGGLEagain
-*/
-#define qh_JOGGLEincrease 10.0
-
-/*----------------------------------
-
-  qh_JOGGLEretry
-    if ZZretry = qh_JOGGLEretry, increase qh.JOGGLEmax
-
-  notes:
-    try twice at the original value in case of bad luck the first time
-*/
-#define qh_JOGGLEretry 2
-
-/*----------------------------------
-
-  qh_JOGGLEagain
-    every following qh_JOGGLEagain, increase qh.JOGGLEmax
-
-  notes:
-    1 is OK since it's already failed qh_JOGGLEretry times
-*/
-#define qh_JOGGLEagain 1
-
-/*----------------------------------
-
-  qh_JOGGLEmaxincrease
-    maximum qh.JOGGLEmax due to qh_JOGGLEincrease
-    relative to qh.MAXwidth
-
-  notes:
-    qh.joggleinput will retry at this value until qh_JOGGLEmaxretry
-*/
-#define qh_JOGGLEmaxincrease 1e-2
-
-/*----------------------------------
-
-  qh_JOGGLEmaxretry
-    stop after qh_JOGGLEmaxretry attempts
-*/
-#define qh_JOGGLEmaxretry 100
-
-/*========= memory constants =========*/
-
-/*----------------------------------
-
-  qh_MEMalign
-    memory alignment for qh_meminitbuffers() in global.c
-
-  notes:
-    to avoid bus errors, memory allocation must consider alignment requirements.
-    malloc() automatically takes care of alignment.   Since mem.c manages
-    its own memory, we need to explicitly specify alignment in
-    qh_meminitbuffers().
-
-    A safe choice is sizeof(double).  sizeof(float) may be used if doubles
-    do not occur in data structures and pointers are the same size.  Be careful
-    of machines (e.g., DEC Alpha) with large pointers.
-
-    If using gcc, best alignment is
-              #define qh_MEMalign fmax_(__alignof__(realT),__alignof__(void *))
-*/
-#define qh_MEMalign fmax_(sizeof(realT), sizeof(void *))
-
-/*----------------------------------
-
-  qh_MEMbufsize
-    size of additional memory buffers
-
-  notes:
-    used for qh_meminitbuffers() in global.c
-*/
-#define qh_MEMbufsize 0x10000       /* allocate 64K memory buffers */
-
-/*----------------------------------
-
-  qh_MEMinitbuf
-    size of initial memory buffer
-
-  notes:
-    use for qh_meminitbuffers() in global.c
-*/
-#define qh_MEMinitbuf 0x20000      /* initially allocate 128K buffer */
-
-/*----------------------------------
-
-  qh_INFINITE
-    on output, indicates Voronoi center at infinity
-*/
-#define qh_INFINITE  -10.101
-
-/*----------------------------------
-
-  qh_DEFAULTbox
-    default box size (Geomview expects 0.5)
-*/
-#define qh_DEFAULTbox 0.5
-
-/*======= conditional compilation ============================*/
-
-/*----------------------------------
-
-  __cplusplus
-    defined by C++ compilers
-
-  __MSC_VER
-    defined by Microsoft Visual C++
-
-  __MWERKS__ && __POWERPC__
-    defined by Metrowerks when compiling for the Power Macintosh
-
-  __STDC__
-    defined for strict ANSI C
-*/
-
-/*----------------------------------
-
-  qh_COMPUTEfurthest
-    compute furthest distance to an outside point instead of storing it with the facet
-    =1 to compute furthest
-
-  notes:
-    computing furthest saves memory but costs time
-      about 40% more distance tests for partitioning
-      removes facet->furthestdist
-*/
-#define qh_COMPUTEfurthest 0
-
-/*----------------------------------
-
-  qh_KEEPstatistics
-    =0 removes most of statistic gathering and reporting
-
-  notes:
-    if 0, code size is reduced by about 4%.
-*/
-#define qh_KEEPstatistics 1
-
-/*----------------------------------
-
-  qh_MAXoutside
-    record outer plane for each facet
-    =1 to record facet->maxoutside
-
-  notes:
-    this takes a realT per facet and slightly slows down qhull
-    it produces better outer planes for geomview output
-*/
-#define qh_MAXoutside 1
-
-/*----------------------------------
-
-  qh_NOmerge
-    disables facet merging if defined
-
-  notes:
-    This saves about 10% space.
-
-    Unless 'Q0'
-      qh_NOmerge sets 'QJ' to avoid precision errors
-
-    #define qh_NOmerge
-
-  see:
-    qh_NOmem in mem.c
-
-    see user.c/user_eg.c for removing io.o
-*/
-
-/*----------------------------------
-
-  qh_NOtrace
-    no tracing if defined
-
-  notes:
-    This saves about 5% space.
-
-    #define qh_NOtrace
-*/
-
-/*----------------------------------
-
-  qh_QHpointer
-    access global data with pointer or static structure
-
-  qh_QHpointer  = 1     access globals via a pointer to allocated memory
-                        enables qh_saveqhull() and qh_restoreqhull()
-			costs about 8% in time and 2% in space
-
-		= 0     qh_qh and qh_qhstat are static data structures
-		        only one instance of qhull() can be active at a time
-			default value
-
-  notes:
-    all global variables for qhull are in qh, qhmem, and qhstat
-    qh is defined in qhull.h
-    qhmem is defined in mem.h
-    qhstat is defined in stat.h
-
-  see:
-    user_eg.c for an example
-*/
-#define qh_QHpointer 0
-#if 0  /* sample code */
-    qhT *oldqhA, *oldqhB;
-
-    exitcode= qh_new_qhull (dim, numpoints, points, ismalloc,
-                      flags, outfile, errfile);
-    /* use results from first call to qh_new_qhull */
-    oldqhA= qh_save_qhull();
-    exitcode= qh_new_qhull (dimB, numpointsB, pointsB, ismalloc,
-                      flags, outfile, errfile);
-    /* use results from second call to qh_new_qhull */
-    oldqhB= qh_save_qhull();
-    qh_restore_qhull (&oldqhA);
-    /* use results from first call to qh_new_qhull */
-    qh_freeqhull (qh_ALL);  /* frees all memory used by first call */
-    qh_restore_qhull (&oldqhB);
-    /* use results from second call to qh_new_qhull */
-    qh_freeqhull (!qh_ALL); /* frees long memory used by second call */
-    qh_memfreeshort (&curlong, &totlong);  /* frees short memory and memory allocator */
-#endif
-
-/*----------------------------------
-
-  qh_QUICKhelp
-    =1 to use abbreviated help messages, e.g., for degenerate inputs
-*/
-#define qh_QUICKhelp    0
-
-/* ============ -merge constants- ====================
-
-   These constants effect facet merging.  You probably will not need
-   to modify these.  They effect the performance of facet merging.
-*/
-
-/*----------------------------------
-
-  qh_DIMmergeVertex
-    max dimension for vertex merging (it is not effective in high-d)
-*/
-#define qh_DIMmergeVertex 6
-
-/*----------------------------------
-
-  qh_DIMreduceBuild
-     max dimension for vertex reduction during build (slow in high-d)
-*/
-#define qh_DIMreduceBuild 5
-
-/*----------------------------------
-
-  qh_BESTcentrum
-     if > 2*dim+n vertices, qh_findbestneighbor() tests centrums (faster)
-     else, qh_findbestneighbor() tests all vertices (much better merges)
-
-  qh_BESTcentrum2
-     if qh_BESTcentrum2 * DIM3 + BESTcentrum < #vertices tests centrums
-*/
-#define qh_BESTcentrum 20
-#define qh_BESTcentrum2 2
-
-/*----------------------------------
-
-  qh_BESTnonconvex
-    if > dim+n neighbors, qh_findbestneighbor() tests nonconvex ridges.
-
-  notes:
-    It is needed because qh_findbestneighbor is slow for large facets
-*/
-#define qh_BESTnonconvex 15
-
-/*----------------------------------
-
-  qh_MAXnewmerges
-    if >n newmerges, qh_merge_nonconvex() calls qh_reducevertices_centrums.
-
-  notes:
-    It is needed because postmerge can merge many facets at once
-*/
-#define qh_MAXnewmerges 2
-
-/*----------------------------------
-
-  qh_MAXnewcentrum
-    if <= dim+n vertices (n approximates the number of merges),
-      reset the centrum in qh_updatetested() and qh_mergecycle_facets()
-
-  notes:
-    needed to reduce cost and because centrums may move too much if
-    many vertices in high-d
-*/
-#define qh_MAXnewcentrum 5
-
-/*----------------------------------
-
-  qh_COPLANARratio
-    for 3-d+ merging, qh.MINvisible is n*premerge_centrum
-
-  notes:
-    for non-merging, it's DISTround
-*/
-#define qh_COPLANARratio 3
-
-/*----------------------------------
-
-  qh_DISToutside
-    When is a point clearly outside of a facet?
-    Stops search in qh_findbestnew or qh_partitionall
-    qh_findbest uses qh.MINoutside since since it is only called if no merges.
-
-  notes:
-    'Qf' always searches for best facet
-    if !qh.MERGING, same as qh.MINoutside.
-    if qh_USEfindbestnew, increase value since neighboring facets may be ill-behaved
-      [Note: Zdelvertextot occurs normally with interior points]
-            RBOX 1000 s Z1 G1e-13 t1001188774 | QHULL Tv
-    When there is a sharp edge, need to move points to a
-    clearly good facet; otherwise may be lost in another partitioning.
-    if too big then O(n^2) behavior for partitioning in cone
-    if very small then important points not processed
-    Needed in qh_partitionall for
-      RBOX 1000 s Z1 G1e-13 t1001032651 | QHULL Tv
-    Needed in qh_findbestnew for many instances of
-      RBOX 1000 s Z1 G1e-13 t | QHULL Tv
-
-  See:
-    qh_DISToutside -- when is a point clearly outside of a facet
-    qh_SEARCHdist -- when is facet coplanar with the best facet?
-    qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
-*/
-#define qh_DISToutside ((qh_USEfindbestnew ? 2 : 1) * \
-     fmax_((qh MERGING ? 2 : 1)*qh MINoutside, qh max_outside))
-
-/*----------------------------------
-
-  qh_RATIOnearinside
-    ratio of qh.NEARinside to qh.ONEmerge for retaining inside points for
-    qh_check_maxout().
-
-  notes:
-    This is overkill since do not know the correct value.
-    It effects whether 'Qc' reports all coplanar points
-    Not used for 'd' since non-extreme points are coplanar
-*/
-#define qh_RATIOnearinside 5
-
-/*----------------------------------
-
-  qh_SEARCHdist
-    When is a facet coplanar with the best facet?
-    qh_findbesthorizon: all coplanar facets of the best facet need to be searched.
-
-  See:
-    qh_DISToutside -- when is a point clearly outside of a facet
-    qh_SEARCHdist -- when is facet coplanar with the best facet?
-    qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
-*/
-#define qh_SEARCHdist ((qh_USEfindbestnew ? 2 : 1) * \
-      (qh max_outside + 2 * qh DISTround + fmax_( qh MINvisible, qh MAXcoplanar)));
-
-/*----------------------------------
-
-  qh_USEfindbestnew
-     Always use qh_findbestnew for qh_partitionpoint, otherwise use
-     qh_findbestnew if merged new facet or sharpnewfacets.
-
-  See:
-    qh_DISToutside -- when is a point clearly outside of a facet
-    qh_SEARCHdist -- when is facet coplanar with the best facet?
-    qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
-*/
-#define qh_USEfindbestnew (zzval_(Ztotmerge) > 50)
-
-/*----------------------------------
-
-  qh_WIDEcoplanar
-    n*MAXcoplanar or n*MINvisible for a WIDEfacet
-
-    if vertex is further than qh.WIDEfacet from the hyperplane
-    then its ridges are not counted in computing the area, and
-    the facet's centrum is frozen.
-
-  notes:
-   qh.WIDEfacet= max(qh.MAXoutside,qh_WIDEcoplanar*qh.MAXcoplanar,
-      qh_WIDEcoplanar * qh.MINvisible);
-*/
-#define qh_WIDEcoplanar 6
-
-/*----------------------------------
-
-  qh_MAXnarrow
-    max. cosine in initial hull that sets qh.NARROWhull
-
-  notes:
-    If qh.NARROWhull, the initial partition does not make
-    coplanar points.  If narrow, a coplanar point can be
-    coplanar to two facets of opposite orientations and
-    distant from the exact convex hull.
-
-    Conservative estimate.  Don't actually see problems until it is -1.0
-*/
-#define qh_MAXnarrow -0.99999999
-
-/*----------------------------------
-
-  qh_WARNnarrow
-    max. cosine in initial hull to warn about qh.NARROWhull
-
-  notes:
-    this is a conservative estimate.
-    Don't actually see problems until it is -1.0.  See qh-impre.htm
-*/
-#define qh_WARNnarrow -0.999999999999999
-
-/*----------------------------------
-
-  qh_ZEROdelaunay
-    a zero Delaunay facet occurs for input sites coplanar with their convex hull
-    the last normal coefficient of a zero Delaunay facet is within
-        qh_ZEROdelaunay * qh.ANGLEround of 0
-
-  notes:
-    qh_ZEROdelaunay does not allow for joggled input ('QJ').
-
-    You can avoid zero Delaunay facets by surrounding the input with a box.
-
-    Use option 'PDk:-n' to explicitly define zero Delaunay facets
-      k= dimension of input sites (e.g., 3 for 3-d Delaunay triangulation)
-      n= the cutoff for zero Delaunay facets (e.g., 'PD3:-1e-12')
-*/
-#define qh_ZEROdelaunay 2
-
-#endif /* qh_DEFuser */
-
-
-
diff --git a/extern/qhull/make/msvc_7_0/qhull.vcproj b/extern/qhull/make/msvc_7_0/qhull.vcproj
deleted file mode 100644
index 1b754d8e076..00000000000
--- a/extern/qhull/make/msvc_7_0/qhull.vcproj
+++ /dev/null
@@ -1,677 +0,0 @@
-
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diff --git a/extern/qhull/make/msvc_9_0/qhull.vcproj b/extern/qhull/make/msvc_9_0/qhull.vcproj
deleted file mode 100644
index fe5b3e806b6..00000000000
--- a/extern/qhull/make/msvc_9_0/qhull.vcproj
+++ /dev/null
@@ -1,877 +0,0 @@
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diff --git a/extern/qhull/src/Make-config.sh b/extern/qhull/src/Make-config.sh
deleted file mode 100755
index 90bbb958599..00000000000
--- a/extern/qhull/src/Make-config.sh
+++ /dev/null
@@ -1,285 +0,0 @@
-#!/bin/sh -e
-#
-# Make-config.sh
-#
-#     Setup for Debian build
-#
-#     Writes configure.in and Makefile.am files
-#     and runs automake and autoconfig
-#
-#     Use 'make dist' to build Unix distribution.
-#     Use 'configure; make' to build Qhull
-#
-#note:
-#     'configure; make' does not work under cygwin.
-#	src/unix.c:354: variable 'qh_qh' can't be auto-imported.
-
-###################################################
-###########  ../configure.in ######################
-###################################################
-
-echo Create ../configure.in
-cat >../configure.in <<\HERE-CONFIGURE
-dnl configure.in for the qhull package
-dnl Author: Rafael Laboissiere
-dnl Created: Mon Dec  3 21:36:21 CET 2001
-
-AC_INIT(src/qhull.c)
-AM_INIT_AUTOMAKE(qhull, 2002.1)
-
-AC_PROG_CC
-AC_PROG_LIBTOOL
-
-AC_OUTPUT([Makefile src/Makefile html/Makefile eg/Makefile])
-
-HERE-CONFIGURE
-
-###################################################
-###########  ../Makefile.am #######################
-###################################################
-
-echo Create ../Makefile.am
-cat >../Makefile.am <<\HERE-TOP
-### Makefile.am for the qhull package (main)
-### Author: Rafael Laboissiere
-### Created: Mon Dec  3 21:36:21 CET 2001
-
-### Documentation files
-
-# to:
-docdir = \$(prefix)/share/doc/\$(PACKAGE)
-
-# which:
-doc_DATA = \
-  Announce.txt \
-  COPYING.txt \
-  REGISTER.txt
-
-### Extra files to be included in the tarball
-
-EXTRA_DIST = \
-  \$(doc_DATA) \
-  File_id.diz \
-  QHULL-GO.pif
-
-### Subdirectories for Automaking
-
-SUBDIRS = src html eg
-
-HERE-TOP
-
-###################################################
-###########  ../eg/Makefile.am ####################
-###################################################
-
-echo Create ../eg/Makefile.am
-cat >../eg/Makefile.am <<\HERE-AM
-### Makefile.am for the qhull package (eg)
-### Author: Rafael Laboissiere
-### Created: Mon Dec  3 21:36:21 CET 2001
-
-### Documentation files
-
-# to:
-docdir = \$(prefix)/share/doc/\$(PACKAGE)
-examplesdir = \$(docdir)/examples
-
-# which:
-examples_DATA = \
-  q_eg \
-  q_egtest \
-  q_test \
-  Qhull-go.bat \
-  q_test.bat
-
-### Extra files to be included in the tarball
-
-EXTRA_DIST = \$(examples_DATA)
-
-HERE-AM
-
-###################################################
-###########  ../html/Makefile.am ##################
-###################################################
-
-echo Create ../html/Makefile.am
-cat >../html/Makefile.am <<\HERE-HTML
-### Makefile.am for the qhull package (html)
-### Author: Rafael Laboissiere
-### Created: Mon Dec  3 21:36:21 CET 2001
-
-### Man pages (trick to get around .man extension)
-
-%.1: %.man
-	cp \$< \$@
-CLEANFILES = *.1
-man_MANS = rbox.1 qhull.1
-
-### Documentation files
-
-# to:
-docdir = \$(prefix)/share/doc/\$(PACKAGE)
-htmldir = \$(docdir)/html
-
-# which:
-html_DATA = \
-  index.htm \
-  qconvex.htm \
-  qdelau_f.htm \
-  qdelaun.htm \
-  qh--4d.gif \
-  qh--cone.gif \
-  qh--dt.gif \
-  qh--geom.gif \
-  qh--half.gif \
-  qh--rand.gif \
-  qh-eg.htm \
-  qh-faq.htm \
-  qh-get.htm \
-  qh-home.htm \
-  qh-impre.htm \
-  qh-in.htm \
-  qh-optc.htm \
-  qh-optf.htm \
-  qh-optg.htm \
-  qh-opto.htm \
-  qh-optp.htm \
-  qh-optq.htm \
-  qh-optt.htm \
-  qh-quick.htm \
-  qhalf.htm \
-  qhull.htm \
-  qvoron_f.htm \
-  qvoronoi.htm \
-  rbox.htm
-
-### Extra files to be included in the tarball
-
-EXTRA_DIST = \
-  \$(html_DATA) \
-  qhull.man \
-  qhull.txt \
-  rbox.man \
-  rbox.txt
-
-HERE-HTML
-
-###################################################
-###########  ../src/Makefile.am ###################
-###################################################
-
-echo Create ../src/Makefile.am
-cat >../src/Makefile.am <<\HERE-SRC
-### Makefile.am for the qhull package (src)
-### Author: Rafael Laboissiere
-### Created: Mon Dec  3 21:36:21 CET 2001
-
-### Shared Library
-
-# to:
-lib_LTLIBRARIES = libqhull.la
-
-# from:
-libqhull_la_SOURCES = \
-  user.c \
-  global.c \
-  stat.c \
-  io.c \
-  geom2.c \
-  poly2.c \
-  merge.c \
-  qhull.c \
-  geom.c \
-  poly.c \
-  qset.c \
-  mem.c
-
-# how:
-libqhull_la_LDFLAGS = -version-info 0:0:0 -lm
-
-### Utility programs
-
-# to:
-bin_PROGRAMS = qhull rbox qconvex qdelaunay qvoronoi qhalf
-
-# from:
-qhull_SOURCES = unix.c
-rbox_SOURCES = rbox.c
-qconvex_SOURCES = qconvex.c
-qdelaunay_SOURCES = qdelaun.c
-qvoronoi_SOURCES = qvoronoi.c
-qhalf_SOURCES = qhalf.c
-
-# how:
-
-### Include files
-
-  geom.h \
-  mem.h \
-  poly.h \
-  qhull_a.h \
-  stat.h \
-  io.h \
-  merge.h \
-  qhull.h  \
-  qset.h \
-  user.h
-
-
-### Example programs
-
-# to:
-docdir = \$(prefix)/share/doc/\$(PACKAGE)
-examplesdir = \$(docdir)/examples
-
-# which:
-examples_DATA = \
-  user_eg.c \
-  user_eg2.c \
-  qhull_interface.cpp \
-  Makefile.txt \
-  Make-config.sh \
-  MBorland
-
-doc_DATA = Changes.txt \
-    index.htm \
-    qh-geom.htm \
-    qh-globa.htm \
-    qh-io.htm \
-    qh-mem.htm \
-    qh-merge.htm \
-    qh-poly.htm \
-    qh-qhull.htm \
-    qh-set.htm \
-    qh-stat.htm \
-    qh-user.htm
-
-
-### Extra files to be included in the tarball
-
-EXTRA_DIST = \
-  \$(doc_DATA) \
-  \$(examples_DATA)
-
-HERE-SRC
-
-###################################################
-###########  run automake autoconf ################
-###################################################
-
-
-echo Run automake, libtoolize, and autoconf
-cd ..; aclocal &&\
-  automake --foreign --add-missing --force-missing && \
-  libtoolize --force && \
-  autoconf
-
diff --git a/extern/qhull/src/Makefile b/extern/qhull/src/Makefile
deleted file mode 100644
index 81c06758cbb..00000000000
--- a/extern/qhull/src/Makefile
+++ /dev/null
@@ -1,55 +0,0 @@
-# -*- mode: gnumakefile; tab-width: 8; indent-tabs-mode: t; -*-
-# vim: tabstop=8
-#
-# \$Id\$
-#
-# ***** BEGIN GPL LICENSE BLOCK *****
-#
-# This program is free software; you can redistribute it and/or
-# modify it under the terms of the GNU General Public License
-#
-# This program is distributed in the hope that it will be useful,
-# but WITHOUT ANY WARRANTY; without even the implied warranty of
-# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-# GNU General Public License for more details.
-#
-# You should have received a copy of the GNU General Public License
-# along with this program; if not, write to the Free Software Foundation,
-# Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
-#
-# The Original Code is Copyright (C) 2001-2002 by NaN Holding BV.
-#
-# The Original Code is: all of this file.
-#
-# Contributor(s): GSR
-#
-# ***** END GPL LICENSE BLOCK *****
-#
-#
-
-LIBNAME = qhull
-DIR = \$(OCGDIR)/extern/\$(LIBNAME)
-
-CCFLAGS += \$(LEVEL_1_CPP_WARNINGS)
-
-CPPFLAGS += -I../include
-
-CSRCS = user.c global.c stat.c io.c geom2.c poly2.c \
-       merge.c qhull.c geom.c poly.c qset.c mem.c
-CCSRCS =
-include nan_compile.mk
-
-install: \$(ALL_OR_DEBUG)
-	@[ -d \$(NAN_QHULL) ] || mkdir -p \$(NAN_QHULL)
-	@[ -d \$(NAN_QHULL)/include/qhull ] || mkdir -p \$(NAN_QHULL)/include/qhull
-	@[ -d \$(NAN_QHULL)/lib/\$(DEBUG_DIR) ] || mkdir -p \$(NAN_QHULL)/lib/\$(DEBUG_DIR)
-	@\$(NANBLENDERHOME)/intern/tools/cpifdiff.sh \$(DIR)/\$(DEBUG_DIR)lib\$(LIBNAME).a \$(NAN_QHULL)/lib/\$(DEBUG_DIR)
-ifeq (\$(OS),darwin)
-	ranlib \$(NAN_QHULL)/lib/\$(DEBUG_DIR)lib\$(LIBNAME).a
-endif
-	@\$(NANBLENDERHOME)/intern/tools/cpifdiff.sh ../include/qhull/*.h \$(NAN_QHULL)/include/qhull
-
-
diff --git a/extern/qhull/src/Makefile.txt b/extern/qhull/src/Makefile.txt
deleted file mode 100644
index e87b66b49bc..00000000000
--- a/extern/qhull/src/Makefile.txt
+++ /dev/null
@@ -1,190 +0,0 @@
-# Unix Makefile for qhull and rbox
-#
-#
-#       make           to produce qhull qconvex qdelaunay qhalf qvoronoi rbox
-#       make qvoronoi  to produce qvoronoi (etc.)
-#       make qhullx    to produce qhull qconvex etc.  w/o using libqhull.a
-#       make doc       to print documentation
-#       make install   to copy qhull, rbox, qhull.1, rbox.1 to BINDIR, MANDIR
-#       make new       to rebuild qhull and rbox from source
-#
-#       make printall  to print all files
-#       make user_eg   to produce user_eg
-#       make user_eg2  to produce user_eg2
-#       make clean     to remove object files and core
-#       make cleanall  to remove all generated files
-#
-#       PRINTMAN --  command for printing manual pages
-#       PRINTC --  command for printing C files
-#       BINDIR -- directory where to copy executables
-#       MANDIR -- directory where to copy manual pages
-#       CC --     ANSI C or C++ compiler
-#       CCOPTS1 - options used to compile .c files
-#       CCOPTS2 -- options used to link .o files
-#
-#       CFILES -- .c files for printing
-#       HFILES -- .h files for printing
-#       DFILES -- documentation files
-#       MFILES -- man pages and html files
-#       TFILES -- .txt versions of html html files
-#       FILES -- all other files
-#       OBJS -- specifies the object files of libqhull.a
-#
-BINDIR  = /usr/local/bin
-MANDIR  = /usr/local/man/man1
-
-# if you do not have enscript, try a2ps or just use lpr.  The files are text.
-PRINTMAN = enscript -2rl
-PRINTC = enscript -2r
-# PRINTMAN = lpr
-# PRINTC = lpr
-
-#for Gnu's gcc compiler -O2 for optimization, -g for debugging, -Wall for check
-#
-CC     = gcc
-CCOPTS1 = -O2 -ansi
-
-# for Sun's cc compiler, -fast or O2 for optimization, -g for debugging, -Xc for ANSI
-#CC = cc
-#CCOPTS1 = -Xc -v -fast
-
-# for Silicon Graphics cc compiler, -O2 for optimization, -g for debugging
-#CC = cc
-#CCOPTS1 = -ansi -O2
-
-# for Next cc compiler with fat executable
-#CC = cc
-#CCOPTS1 = -ansi -O2 -arch m68k -arch i386 -arch hppa
-
-CCOPTS2 = \$(CCOPTS1)
-
-# OBJS in execution frequency order.  CFILES after qhull.c are alphabetical
-OBJS = user.o global.o stat.o io.o geom2.o poly2.o \
-       merge.o qhull.o geom.o poly.o qset.o mem.o
-
-CFILES= unix.c qhull.c geom.c geom2.c global.c io.c mem.c merge.c poly.c \
-        poly2.c qset.c stat.c user.c qconvex.c qdelaun.c qhalf.c qvoronoi.c
-HFILES= user.h qhull.h qhull_a.h geom.h io.h mem.h merge.h poly.h qset.h stat.h
-TXTFILES= ../Announce.txt ../REGISTER.txt ../COPYING.txt ../README.txt Changes.txt
-DOCFILES= ../html/rbox.txt ../html/qhull.txt
-FILES=  Makefile rbox.c user_eg.c ../eg/q_test ../eg/q_egtest ../eg/q_eg
-HTMFILES= qhull.man rbox.man qh-in.htm qh-optg.htm qh-optt.htm qh-optp.htm \
-        index.htm qh-quick.htm qh-impre.htm qh-eg.htm \
-        qh-optc.htm qh-opto.htm qh-optf.htm qh-optq.htm \
-	    qh-c.htm qh-faq.htm qhull.htm qconvex.htm qdelaun.htm \
-		qh-geom.htm qh-globa.htm qh-io.htm qh-mem.htm qh-merge.htm \
-		qh-poly.htm qh-qhull.htm qh-set.htm qh-stat.htm qh-user.htm \
-		qdelau_f.htm qhalf.htm qvoronoi.htm qvoron_f.htm rbox.htm
-
-all: rbox qconvex qdelaunay qhalf qvoronoi qhull
-
-unix.o:   qhull.h user.h mem.h
-qconvex.o:   qhull.h user.h mem.h
-qdelaun.o:   qhull.h user.h mem.h
-qhalf.o:   qhull.h user.h mem.h
-qvoronoi.o:   qhull.h user.h mem.h
-qhull.o:  \$(HFILES)
-geom.o:   \$(HFILES)
-geom2.o:  \$(HFILES)
-global.o: \$(HFILES)
-io.o:     \$(HFILES)
-mem.o:    mem.h
-merge.o:  \$(HFILES)
-poly.o:   \$(HFILES)
-poly2.o:  \$(HFILES)
-qset.o:   qset.h mem.h
-stat.o:   \$(HFILES)
-user.o:   \$(HFILES)
-
-.c.o:
-	\$(CC) -c \$(CCOPTS1) \$<
-
-clean:
-	rm -f *.o ../core qconvex qdelaunay qhalf qvoronoi qhull libqhull.a \
-	    *.exe
-
-cleanall: clean
-	rm -f *~ ../rbox ../qhull ../qhalf ../qconvex ../qdelaunay ../qhalf\
-	   ../qvoronoi ../user_eg ../user_eg2 ../*.exe >/dev/null
-
-doc:
-	\$(PRINTMAN) \$(TXTFILES) \$(DOCFILES)
-
-install: all
-	cp ../qconvex \$(BINDIR)/qconvex
-	cp ../qdelaunay \$(BINDIR)/qdelaunay
-	cp ../qhalf \$(BINDIR)/qhalf
-	cp ../qhull \$(BINDIR)/qhull
-	cp ../qvoronoi \$(BINDIR)/qvoronoi
-	cp ../rbox \$(BINDIR)/rbox
-	cp ../html/qhull.man \$(MANDIR)/qhull.1
-	cp ../html/rbox.man \$(MANDIR)/rbox.1
-
-new:    cleanall all
-
-printall: doc printh printc printf
-
-printh:
-	\$(PRINTC) \$(HFILES)
-
-printc:
-	\$(PRINTC) \$(CFILES)
-
-printf:
-	\$(PRINTC) \$(FILES)
-
-libqhull.a: \$(OBJS)
-	@echo if 'ar' or 'ranlib' fails, try 'make qhullx'
-	ar r libqhull.a \$(OBJS)
-	@echo the next line may need to be removed.
-	-test -x /bin/ranlib -o -x /usr/bin/ranlib && ranlib libqhull.a
-
-# don't use ../qconvex.  Does not work on Red Hat Linux
-qconvex: qconvex.o libqhull.a
-	\$(CC) -o qconvex \$(CCOPTS2) qconvex.o -L. -lqhull -lm
-	cp qconvex ..
-
-qdelaunay: qdelaun.o libqhull.a
-	\$(CC) -o qdelaunay \$(CCOPTS2) qdelaun.o -L. -lqhull -lm
-	cp qdelaunay ..
-
-qhalf: qhalf.o libqhull.a
-	\$(CC) -o qhalf \$(CCOPTS2) qhalf.o -L. -lqhull -lm
-	cp qhalf ..
-
-qvoronoi: qvoronoi.o libqhull.a
-	\$(CC) -o qvoronoi \$(CCOPTS2) qvoronoi.o -L. -lqhull -lm
-	cp qvoronoi ..
-
-qhull: unix.o libqhull.a
-	\$(CC) -o qhull \$(CCOPTS2) unix.o -L. -lqhull -lm
-	cp qhull ..
-	-chmod +x ../eg/q_test ../eg/q_eg ../eg/q_egtest
-	-cd ..; ./rbox D4 | ./qhull
-
-# compile qhull without using libqhull.a
-qhullx: qconvex.o qdelaun.o qhalf.o qvoronoi.o unix.o \$(OBJS)
-	\$(CC) -o qconvex \$(CCOPTS2) qconvex.o \$(OBJS) -lm
-	\$(CC) -o qdelaunay \$(CCOPTS2) qdelaun.o \$(OBJS) -lm
-	\$(CC) -o qhalf \$(CCOPTS2) qhalf.o \$(OBJS) -lm
-	\$(CC) -o qvoronoi \$(CCOPTS2) qvoronoi.o \$(OBJS) -lm
-	\$(CC) -o qhull \$(CCOPTS2) unix.o \$(OBJS) -lm
-	cp qconvex qdelaunay qhalf qvoronoi qhull ..
-	-chmod +x ../eg/q_test ../eg/q_eg ../eg/q_egtest
-	-cd ..; ./rbox D4 | ./qhull
-
-rbox: rbox.o
-	\$(CC) -o rbox rbox.o \$(CCOPTS2) -lm
-	cp rbox ..
-
-user_eg: user_eg.o libqhull.a
-	\$(CC)  -o user_eg \$(CCOPTS2) user_eg.o  -L. -lqhull -lm
-	cp user_eg ..
-
-user_eg2: user_eg2.o libqhull.a
-	\$(CC)  -o user_eg2 \$(CCOPTS2) user_eg2.o  -L. -lqhull -lm
-	cp user_eg2 ..
-
-# end of Makefile
diff --git a/extern/qhull/src/geom.c b/extern/qhull/src/geom.c
deleted file mode 100644
index ca4bcaf2541..00000000000
--- a/extern/qhull/src/geom.c
+++ /dev/null
@@ -1,1230 +0,0 @@
-/*  ---------------------------------
-
-   geom.c
-   geometric routines of qhull
-
-   see qh-geom.htm and geom.h
-
-   copyright (c) 1993-2002 The Geometry Center
-
-   infrequent code goes into geom2.c
-*/
-
-#include "qhull_a.h"
-
-/*---------------------------------
-
-  qh_distplane( point, facet, dist )
-    return distance from point to facet
-
-  returns:
-    dist
-    if qh.RANDOMdist, joggles result
-
-  notes:
-    dist > 0 if point is above facet (i.e., outside)
-    does not error (for sortfacets)
-
-  see:
-    qh_distnorm in geom2.c
-*/
-void qh_distplane (pointT *point, facetT *facet, realT *dist) {
-  coordT *normal= facet->normal, *coordp, randr;
-  int k;
-
-  switch(qh hull_dim){
-  case 2:
-    *dist= facet->offset + point[0] * normal[0] + point[1] * normal[1];
-    break;
-  case 3:
-    *dist= facet->offset + point[0] * normal[0] + point[1] * normal[1] + point[2] * normal[2];
-    break;
-  case 4:
-    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3];
-    break;
-  case 5:
-    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4];
-    break;
-  case 6:
-    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5];
-    break;
-  case 7:
-    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6];
-    break;
-  case 8:
-    *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6]+point[7]*normal[7];
-    break;
-  default:
-    *dist= facet->offset;
-    coordp= point;
-    for (k= qh hull_dim; k--; )
-      *dist += *coordp++ * *normal++;
-    break;
-  }
-  zinc_(Zdistplane);
-  if (!qh RANDOMdist && qh IStracing < 4)
-    return;
-  if (qh RANDOMdist) {
-    randr= qh_RANDOMint;
-    *dist += (2.0 * randr / qh_RANDOMmax - 1.0) *
-      qh RANDOMfactor * qh MAXabs_coord;
-  }
-  if (qh IStracing >= 4) {
-    fprintf (qh ferr, "qh_distplane: ");
-    fprintf (qh ferr, qh_REAL_1, *dist);
-    fprintf (qh ferr, "from p%d to f%d\n", qh_pointid(point), facet->id);
-  }
-  return;
-} /* distplane */
-
-
-/*---------------------------------
-
-  qh_findbest( point, startfacet, bestoutside, qh_ISnewfacets, qh_NOupper, dist, isoutside, numpart )
-    find facet that is furthest below a point
-    for upperDelaunay facets
-      returns facet only if !qh_NOupper and clearly above
-
-  input:
-    starts search at 'startfacet' (can not be flipped)
-    if !bestoutside (qh_ALL), stops at qh.MINoutside
-
-  returns:
-    best facet (reports error if NULL)
-    early out if isoutside defined and bestdist > qh.MINoutside
-    dist is distance to facet
-    isoutside is true if point is outside of facet
-    numpart counts the number of distance tests
-
-    qh_findbestnew()
-
-  notes:
-    If merging (testhorizon), searches horizon facets of coplanar best facets because
-    after qh_distplane, this and qh_partitionpoint are the most expensive in 3-d
-      avoid calls to distplane, function calls, and real number operations.
-    caller traces result
-    Optimized for outside points.   Tried recording a search set for qh_findhorizon.
-
-  when called by qh_partitionvisible():
-    indicated by qh_ISnewfacets
-    qh.newfacet_list is list of simplicial, new facets
-    qh_findbestnew set if qh_sharpnewfacets returns True (to use qh_findbestnew)
-    qh.bestfacet_notsharp set if qh_sharpnewfacets returns False
-
-  when called by qh_findfacet(), qh_partitionpoint(), qh_partitioncoplanar(),
-    indicated by !qh_ISnewfacets
-    returns best facet in neighborhood of given facet
-      this is best facet overall if dist > -   qh.MAXcoplanar
-        or hull has at least a "spherical" curvature
-
-  design:
-    initialize and test for early exit
-    repeat while there are better facets
-      for each neighbor of facet
-        exit if outside facet found
-	test for better facet
-    if point is inside and partitioning
-      test for new facets with a "sharp" intersection
-      if so, future calls go to qh_findbestnew()
-    test horizon facets
-*/
-facetT *qh_findbest (pointT *point, facetT *startfacet,
-		     boolT bestoutside, boolT isnewfacets, boolT noupper,
-		     realT *dist, boolT *isoutside, int *numpart) {
-  realT bestdist= -REALmax/2 /* avoid underflow */;
-  facetT *facet, *neighbor, **neighborp, *bestfacet= NULL;
- /* facetT *bestfacet_all= startfacet; */
-  int oldtrace= qh IStracing;
-  unsigned int visitid= ++qh visit_id;
-  int numpartnew=0;
-  boolT testhorizon = True; /* needed if precise, e.g., rbox c D6 | qhull Q0 Tv */
-
-  zinc_(Zfindbest);
-  if (qh IStracing >= 3 || (qh TRACElevel && qh TRACEpoint >= 0 && qh TRACEpoint == qh_pointid (point))) {
-    if (qh TRACElevel > qh IStracing)
-      qh IStracing= qh TRACElevel;
-    fprintf (qh ferr, "qh_findbest: point p%d starting at f%d isnewfacets? %d, unless %d exit if > %2.2g\n",
-	     qh_pointid(point), startfacet->id, isnewfacets, bestoutside, qh MINoutside);
-    fprintf(qh ferr, "  testhorizon? %d noupper? %d", testhorizon, noupper);
-    fprintf (qh ferr, "  Last point added was p%d.", qh furthest_id);
-    fprintf(qh ferr, "  Last merge was #%d.  max_outside %2.2g\n", zzval_(Ztotmerge), qh max_outside);
-  }
-  if (isoutside)
-    *isoutside= True;
-  if (!startfacet->flipped) {  /* test startfacet */
-    *numpart= 1;
-    qh_distplane (point, startfacet, dist);  /* this code is duplicated below */
-    if (!bestoutside && *dist >= qh MINoutside
-    && (!startfacet->upperdelaunay || !noupper)) {
-      bestfacet= startfacet;
-      goto LABELreturn_best;
-    }
-    bestdist= *dist;
-    if (!startfacet->upperdelaunay) {
-      bestfacet= startfacet;
-    }
-  }else
-    *numpart= 0;
-  startfacet->visitid= visitid;
-  facet= startfacet;
-  while (facet) {
-    trace4((qh ferr, "qh_findbest: neighbors of f%d, bestdist %2.2g f%d\n",
-                facet->id, bestdist, getid_(bestfacet)));
-    FOREACHneighbor_(facet) {
-      if (!neighbor->newfacet && isnewfacets)
-        continue;
-      if (neighbor->visitid == visitid)
-	continue;
-      neighbor->visitid= visitid;
-      if (!neighbor->flipped) {  /* code duplicated above */
-	(*numpart)++;
-	qh_distplane (point, neighbor, dist);
-	if (*dist > bestdist) {
-	  if (!bestoutside && *dist >= qh MINoutside
-	  && (!neighbor->upperdelaunay || !noupper)) {
-	    bestfacet= neighbor;
-	    goto LABELreturn_best;
-	  }
-	  if (!neighbor->upperdelaunay) {
-	    bestfacet= neighbor;
-	    bestdist= *dist;
-	  }
-	  break; /* switch to neighor */
-	} /* end of *dist>bestdist */
-      } /* end of !flipped */
-    } /* end of FOREACHneighbor */
-    facet= neighbor;  /* non-NULL only if *dist>bestdist */
-  } /* end of while facet (directed search) */
-  if (isnewfacets) {
-    if (!bestfacet) {
-      bestdist= -REALmax/2;
-      bestfacet= qh_findbestnew (point, startfacet->next, &bestdist, bestoutside, isoutside, &numpartnew);
-      testhorizon= False; /* qh_findbestnew calls qh_findbesthorizon */
-    }else if (!qh findbest_notsharp && bestdist < - qh DISTround) {
-      if (qh_sharpnewfacets()) {
-	/* seldom used, qh_findbestnew will retest all facets */
-	zinc_(Zfindnewsharp);
-	bestfacet= qh_findbestnew (point, bestfacet, &bestdist, bestoutside, isoutside, &numpartnew);
-	testhorizon= False; /* qh_findbestnew calls qh_findbesthorizon */
-	qh findbestnew= True;
-      }else
-	qh findbest_notsharp= True;
-    }
-  }
-  if (!bestfacet) {
-    fprintf(qh ferr, "\n\
-qh_findbest: all neighbors of facet %d are flipped or upper Delaunay.\n\
-Please report this error to qhull_bug@geom.umn.edu with the input and all of the output.\n",
-       startfacet->id);
-    qh_errexit (qh_ERRqhull, startfacet, NULL);
-  }
-  if (testhorizon)
-    bestfacet= qh_findbesthorizon (!qh_IScheckmax, point, bestfacet, noupper, &bestdist, &numpartnew);
-  *dist= bestdist;
-  if (isoutside && bestdist < qh MINoutside)
-    *isoutside= False;
-LABELreturn_best:
-  zmax_(Zfindbestmax, *numpart);
-  (*numpart) += numpartnew;
-  qh IStracing= oldtrace;
-  return bestfacet;
-}  /* findbest */
-
-
-/*---------------------------------
-
-  qh_findbesthorizon( qh_IScheckmax, point, startfacet, qh_NOupper, &bestdist, &numpart )
-    search coplanar and better horizon facets from startfacet/bestdist
-    ischeckmax turns off statistics and minsearch update
-    all arguments must be initialized
-  returns (ischeckmax):
-    best facet
-  returns (!ischeckmax):
-    best facet that is not upperdelaunay
-    allows upperdelaunay that is clearly outside
-  returns:
-    bestdist is distance to bestfacet
-    numpart -- updates number of distance tests
-
-  notes:
-    no early out -- use qh_findbest() or qh_findbestnew()
-    Searches coplanar or better horizon facets
-
-  when called by qh_check_maxout() (qh_IScheckmax)
-    startfacet must be closest to the point
-      Otherwise, if point is beyond and below startfacet, startfacet may be a local minimum
-      even though other facets are below the point.
-    updates facet->maxoutside for good, visited facets
-    may return NULL
-
-    searchdist is qh.max_outside + 2 * DISTround
-      + max( MINvisible('Vn'), MAXcoplanar('Un'));
-    This setting is a guess.  It must be at least max_outside + 2*DISTround
-    because a facet may have a geometric neighbor across a vertex
-
-  design:
-    for each horizon facet of coplanar best facets
-      continue if clearly inside
-      unless upperdelaunay or clearly outside
-         update best facet
-*/
-facetT *qh_findbesthorizon (boolT ischeckmax, pointT* point, facetT *startfacet, boolT noupper, realT *bestdist, int *numpart) {
-  facetT *bestfacet= startfacet;
-  realT dist;
-  facetT *neighbor, **neighborp, *facet;
-  facetT *nextfacet= NULL; /* optimize last facet of coplanarset */
-  int numpartinit= *numpart, coplanarset_size;
-  unsigned int visitid= ++qh visit_id;
-  boolT newbest= False; /* for tracing */
-  realT minsearch, searchdist;  /* skip facets that are too far from point */
-
-  if (!ischeckmax) {
-    zinc_(Zfindhorizon);
-  }else {
-#if qh_MAXoutside
-    if ((!qh ONLYgood || startfacet->good) && *bestdist > startfacet->maxoutside)
-      startfacet->maxoutside= *bestdist;
-#endif
-  }
-  searchdist= qh_SEARCHdist; /* multiple of qh.max_outside and precision constants */
-  minsearch= *bestdist - searchdist;
-  if (ischeckmax) {
-    /* Always check coplanar facets.  Needed for RBOX 1000 s Z1 G1e-13 t996564279 | QHULL Tv */
-    minimize_(minsearch, -searchdist);
-  }
-  coplanarset_size= 0;
-  facet= startfacet;
-  while (True) {
-    trace4((qh ferr, "qh_findbesthorizon: neighbors of f%d bestdist %2.2g f%d ischeckmax? %d noupper? %d minsearch %2.2g searchdist %2.2g\n",
-		facet->id, *bestdist, getid_(bestfacet), ischeckmax, noupper,
-		minsearch, searchdist));
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid == visitid)
-	continue;
-      neighbor->visitid= visitid;
-      if (!neighbor->flipped) {
-	qh_distplane (point, neighbor, &dist);
-	(*numpart)++;
-	if (dist > *bestdist) {
-	  if (!neighbor->upperdelaunay || ischeckmax || (!noupper && dist >= qh MINoutside)) {
-	    bestfacet= neighbor;
-	    *bestdist= dist;
-	    newbest= True;
-	    if (!ischeckmax) {
-	      minsearch= dist - searchdist;
-	      if (dist > *bestdist + searchdist) {
-		zinc_(Zfindjump);  /* everything in qh.coplanarset at least searchdist below */
-		coplanarset_size= 0;
-	      }
-	    }
-	  }
-	}else if (dist < minsearch)
-	  continue;  /* if ischeckmax, dist can't be positive */
-#if qh_MAXoutside
-	if (ischeckmax && dist > neighbor->maxoutside)
-	  neighbor->maxoutside= dist;
-#endif
-      } /* end of !flipped */
-      if (nextfacet) {
-	if (!coplanarset_size++) {
-	  SETfirst_(qh coplanarset)= nextfacet;
-	  SETtruncate_(qh coplanarset, 1);
-	}else
-  	  qh_setappend (&qh coplanarset, nextfacet); /* Was needed for RBOX 1000 s W1e-13 P0 t996547055 | QHULL d Qbb Qc Tv
-						 and RBOX 1000 s Z1 G1e-13 t996564279 | qhull Tv  */
-      }
-      nextfacet= neighbor;
-    } /* end of EACHneighbor */
-    facet= nextfacet;
-    if (facet)
-      nextfacet= NULL;
-    else if (!coplanarset_size)
-      break;
-    else if (!--coplanarset_size) {
-      facet= SETfirst_(qh coplanarset);
-      SETtruncate_(qh coplanarset, 0);
-    }else
-      facet= (facetT*)qh_setdellast (qh coplanarset);
-  } /* while True, for each facet in qh.coplanarset */
-  if (!ischeckmax) {
-    zmax_(Zfindhorizonmax, *numpart - numpartinit);
-    if (newbest)
-      zinc_(Zparthorizon);
-  }
-  trace4((qh ferr, "qh_findbesthorizon: newbest? %d bestfacet f%d bestdist %2.2g\n", newbest, getid_(bestfacet), *bestdist));
-  return bestfacet;
-}  /* findbesthorizon */
-
-/*---------------------------------
-
-  qh_findbestnew( point, startfacet, dist, isoutside, numpart )
-    find best newfacet for point
-    searches all of qh.newfacet_list starting at startfacet
-    searches horizon facets of coplanar best newfacets
-    searches all facets if startfacet == qh.facet_list
-  returns:
-    best new or horizon facet that is not upperdelaunay
-    early out if isoutside and not 'Qf'
-    dist is distance to facet
-    isoutside is true if point is outside of facet
-    numpart is number of distance tests
-
-  notes:
-    Always used for merged new facets (see qh_USEfindbestnew)
-    Avoids upperdelaunay facet unless (isoutside and outside)
-
-    Uses qh.visit_id, qh.coplanarset.
-    If share visit_id with qh_findbest, coplanarset is incorrect.
-
-    If merging (testhorizon), searches horizon facets of coplanar best facets because
-    a point maybe coplanar to the bestfacet, below its horizon facet,
-    and above a horizon facet of a coplanar newfacet.  For example,
-      rbox 1000 s Z1 G1e-13 | qhull
-      rbox 1000 s W1e-13 P0 t992110337 | QHULL d Qbb Qc
-
-    qh_findbestnew() used if
-       qh_sharpnewfacets -- newfacets contains a sharp angle
-       if many merges, qh_premerge found a merge, or 'Qf' (qh.findbestnew)
-
-    qh_partitionall() and qh_findbest()
-
-  design:
-    for each new facet starting from startfacet
-      test distance from point to facet
-      return facet if clearly outside
-      unless upperdelaunay and a lowerdelaunay exists
-         update best facet
-    test horizon facets
-*/
-facetT *qh_findbestnew (pointT *point, facetT *startfacet,
-	   realT *dist, boolT bestoutside, boolT *isoutside, int *numpart) {
-  realT bestdist= -REALmax/2; /*, minsearch= -REALmax/2;*/
-  facetT *bestfacet= NULL, *facet;
-  int oldtrace= qh IStracing, i;
-  unsigned int visitid= ++qh visit_id;
-  realT distoutside= 0.0;
-  boolT isdistoutside; /* True if distoutside is defined */
-  boolT testhorizon = True; /* needed if precise, e.g., rbox c D6 | qhull Q0 Tv */
-
-  if (!startfacet) {
-    if (qh MERGING)
-      fprintf(qh ferr, "qhull precision error (qh_findbestnew): merging has formed and deleted a cone of new facets.  Can not continue.\n");
-    else
-      fprintf(qh ferr, "qhull internal error (qh_findbestnew): no new facets for point p%d\n",
-      	      qh furthest_id);
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }
-  zinc_(Zfindnew);
-  if (qh BESToutside || bestoutside)
-    isdistoutside= False;
-  else {
-    isdistoutside= True;
-    distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user.h */
-  }
-  if (isoutside)
-    *isoutside= True;
-  *numpart= 0;
-  if (qh IStracing >= 3 || (qh TRACElevel && qh TRACEpoint >= 0 && qh TRACEpoint == qh_pointid (point))) {
-    if (qh TRACElevel > qh IStracing)
-      qh IStracing= qh TRACElevel;
-    fprintf(qh ferr, "qh_findbestnew: point p%d facet f%d. Stop? %d if dist > %2.2g\n",
-	     qh_pointid(point), startfacet->id, isdistoutside, distoutside);
-    fprintf(qh ferr, "  Last point added p%d visitid %d.",  qh furthest_id, visitid);
-    fprintf(qh ferr, "  Last merge was #%d.\n", zzval_(Ztotmerge));
-  }
-  /* visit all new facets starting with startfacet, maybe qh facet_list */
-  for (i= 0, facet= startfacet; i < 2; i++, facet= qh newfacet_list) {
-    FORALLfacet_(facet) {
-      if (facet == startfacet && i)
-	break;
-      facet->visitid= visitid;
-      if (!facet->flipped) {
-	qh_distplane (point, facet, dist);
-	(*numpart)++;
-	if (*dist > bestdist) {
-	  if (!facet->upperdelaunay || *dist >= qh MINoutside) {
-	    bestfacet= facet;
-	    if (isdistoutside && *dist >= distoutside)
-	      goto LABELreturn_bestnew;
-	    bestdist= *dist;
-  	  }
-	}
-      } /* end of !flipped */
-    } /* FORALLfacet from startfacet or qh newfacet_list */
-  }
-  if (testhorizon || !bestfacet)
-    bestfacet= qh_findbesthorizon (!qh_IScheckmax, point, bestfacet ? bestfacet : startfacet,
-	                                !qh_NOupper, &bestdist, numpart);
-  *dist= bestdist;
-  if (isoutside && *dist < qh MINoutside)
-    *isoutside= False;
-LABELreturn_bestnew:
-  zmax_(Zfindnewmax, *numpart);
-  trace4((qh ferr, "qh_findbestnew: bestfacet f%d bestdist %2.2g\n", getid_(bestfacet), *dist));
-  qh IStracing= oldtrace;
-  return bestfacet;
-}  /* findbestnew */
-
-/* ============ hyperplane functions -- keep code together [?] ============ */
-
-/*---------------------------------
-
-  qh_backnormal( rows, numrow, numcol, sign, normal, nearzero )
-    given an upper-triangular rows array and a sign,
-    solve for normal equation x using back substitution over rows U
-
-  returns:
-     normal= x
-
-     if will not be able to divzero() when normalized (qh.MINdenom_2 and qh.MINdenom_1_2),
-       if fails on last row
-         this means that the hyperplane intersects [0,..,1]
-         sets last coordinate of normal to sign
-       otherwise
-         sets tail of normal to [...,sign,0,...], i.e., solves for b= [0...0]
-         sets nearzero
-
-  notes:
-     assumes numrow == numcol-1
-
-     see Golub & van Loan 4.4-9 for back substitution
-
-     solves Ux=b where Ax=b and PA=LU
-     b= [0,...,0,sign or 0]  (sign is either -1 or +1)
-     last row of A= [0,...,0,1]
-
-     1) Ly=Pb == y=b since P only permutes the 0's of   b
-
-  design:
-    for each row from end
-      perform back substitution
-      if near zero
-        use qh_divzero for division
-        if zero divide and not last row
-          set tail of normal to 0
-*/
-void qh_backnormal (realT **rows, int numrow, int numcol, boolT sign,
-  	coordT *normal, boolT *nearzero) {
-  int i, j;
-  coordT *normalp, *normal_tail, *ai, *ak;
-  realT diagonal;
-  boolT waszero;
-  int zerocol= -1;
-
-  normalp= normal + numcol - 1;
-  *normalp--= (sign ? -1.0 : 1.0);
-  for(i= numrow; i--; ) {
-    *normalp= 0.0;
-    ai= rows[i] + i + 1;
-    ak= normalp+1;
-    for(j= i+1; j < numcol; j++)
-      *normalp -= *ai++ * *ak++;
-    diagonal= (rows[i])[i];
-    if (fabs_(diagonal) > qh MINdenom_2)
-      *(normalp--) /= diagonal;
-    else {
-      waszero= False;
-      *normalp= qh_divzero (*normalp, diagonal, qh MINdenom_1_2, &waszero);
-      if (waszero) {
-        zerocol= i;
-	*(normalp--)= (sign ? -1.0 : 1.0);
-	for (normal_tail= normalp+2; normal_tail < normal + numcol; normal_tail++)
-	  *normal_tail= 0.0;
-      }else
-	normalp--;
-    }
-  }
-  if (zerocol != -1) {
-    zzinc_(Zback0);
-    *nearzero= True;
-    trace4((qh ferr, "qh_backnormal: zero diagonal at column %d.\n", i));
-    qh_precision ("zero diagonal on back substitution");
-  }
-} /* backnormal */
-
-/*---------------------------------
-
-  qh_gausselim( rows, numrow, numcol, sign )
-    Gaussian elimination with partial pivoting
-
-  returns:
-    rows is upper triangular (includes row exchanges)
-    flips sign for each row exchange
-    sets nearzero if pivot[k] < qh.NEARzero[k], else clears it
-
-  notes:
-    if nearzero, the determinant's sign may be incorrect.
-    assumes numrow <= numcol
-
-  design:
-    for each row
-      determine pivot and exchange rows if necessary
-      test for near zero
-      perform gaussian elimination step
-*/
-void qh_gausselim(realT **rows, int numrow, int numcol, boolT *sign, boolT *nearzero) {
-  realT *ai, *ak, *rowp, *pivotrow;
-  realT n, pivot, pivot_abs= 0.0, temp;
-  int i, j, k, pivoti, flip=0;
-
-  *nearzero= False;
-  for(k= 0; k < numrow; k++) {
-    pivot_abs= fabs_((rows[k])[k]);
-    pivoti= k;
-    for(i= k+1; i < numrow; i++) {
-      if ((temp= fabs_((rows[i])[k])) > pivot_abs) {
-	pivot_abs= temp;
-	pivoti= i;
-      }
-    }
-    if (pivoti != k) {
-      rowp= rows[pivoti];
-      rows[pivoti]= rows[k];
-      rows[k]= rowp;
-      *sign ^= 1;
-      flip ^= 1;
-    }
-    if (pivot_abs <= qh NEARzero[k]) {
-      *nearzero= True;
-      if (pivot_abs == 0.0) {   /* remainder of column == 0 */
-	if (qh IStracing >= 4) {
-	  fprintf (qh ferr, "qh_gausselim: 0 pivot at column %d. (%2.2g < %2.2g)\n", k, pivot_abs, qh DISTround);
-	  qh_printmatrix (qh ferr, "Matrix:", rows, numrow, numcol);
-	}
-	zzinc_(Zgauss0);
-        qh_precision ("zero pivot for Gaussian elimination");
-	goto LABELnextcol;
-      }
-    }
-    pivotrow= rows[k] + k;
-    pivot= *pivotrow++;  /* signed value of pivot, and remainder of row */
-    for(i= k+1; i < numrow; i++) {
-      ai= rows[i] + k;
-      ak= pivotrow;
-      n= (*ai++)/pivot;   /* divzero() not needed since |pivot| >= |*ai| */
-      for(j= numcol - (k+1); j--; )
-	*ai++ -= n * *ak++;
-    }
-  LABELnextcol:
-    ;
-  }
-  wmin_(Wmindenom, pivot_abs);  /* last pivot element */
-  if (qh IStracing >= 5)
-    qh_printmatrix (qh ferr, "qh_gausselem: result", rows, numrow, numcol);
-} /* gausselim */
-
-
-/*---------------------------------
-
-  qh_getangle( vect1, vect2 )
-    returns the dot product of two vectors
-    if qh.RANDOMdist, joggles result
-
-  notes:
-    the angle may be > 1.0 or < -1.0 because of roundoff errors
-
-*/
-realT qh_getangle(pointT *vect1, pointT *vect2) {
-  realT angle= 0, randr;
-  int k;
-
-  for(k= qh hull_dim; k--; )
-    angle += *vect1++ * *vect2++;
-  if (qh RANDOMdist) {
-    randr= qh_RANDOMint;
-    angle += (2.0 * randr / qh_RANDOMmax - 1.0) *
-      qh RANDOMfactor;
-  }
-  trace4((qh ferr, "qh_getangle: %2.2g\n", angle));
-  return(angle);
-} /* getangle */
-
-
-/*---------------------------------
-
-  qh_getcenter( vertices )
-    returns arithmetic center of a set of vertices as a new point
-
-  notes:
-    allocates point array for center
-*/
-pointT *qh_getcenter(setT *vertices) {
-  int k;
-  pointT *center, *coord;
-  vertexT *vertex, **vertexp;
-  int count= qh_setsize(vertices);
-
-  if (count < 2) {
-    fprintf (qh ferr, "qhull internal error (qh_getcenter): not defined for %d points\n", count);
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }
-  center= (pointT *)qh_memalloc(qh normal_size);
-  for (k=0; k < qh hull_dim; k++) {
-    coord= center+k;
-    *coord= 0.0;
-    FOREACHvertex_(vertices)
-      *coord += vertex->point[k];
-    *coord /= count;
-  }
-  return(center);
-} /* getcenter */
-
-
-/*---------------------------------
-
-  qh_getcentrum( facet )
-    returns the centrum for a facet as a new point
-
-  notes:
-    allocates the centrum
-*/
-pointT *qh_getcentrum(facetT *facet) {
-  realT dist;
-  pointT *centrum, *point;
-
-  point= qh_getcenter(facet->vertices);
-  zzinc_(Zcentrumtests);
-  qh_distplane (point, facet, &dist);
-  centrum= qh_projectpoint(point, facet, dist);
-  qh_memfree(point, qh normal_size);
-  trace4((qh ferr, "qh_getcentrum: for f%d, %d vertices dist= %2.2g\n",
-	  facet->id, qh_setsize(facet->vertices), dist));
-  return centrum;
-} /* getcentrum */
-
-
-/*---------------------------------
-
-  qh_getdistance( facet, neighbor, mindist, maxdist )
-    returns the maxdist and mindist distance of any vertex from neighbor
-
-  returns:
-    the max absolute value
-
-  design:
-    for each vertex of facet that is not in neighbor
-      test the distance from vertex to neighbor
-*/
-realT qh_getdistance(facetT *facet, facetT *neighbor, realT *mindist, realT *maxdist) {
-  vertexT *vertex, **vertexp;
-  realT dist, maxd, mind;
-
-  FOREACHvertex_(facet->vertices)
-    vertex->seen= False;
-  FOREACHvertex_(neighbor->vertices)
-    vertex->seen= True;
-  mind= 0.0;
-  maxd= 0.0;
-  FOREACHvertex_(facet->vertices) {
-    if (!vertex->seen) {
-      zzinc_(Zbestdist);
-      qh_distplane(vertex->point, neighbor, &dist);
-      if (dist < mind)
-	mind= dist;
-      else if (dist > maxd)
-	maxd= dist;
-    }
-  }
-  *mindist= mind;
-  *maxdist= maxd;
-  mind= -mind;
-  if (maxd > mind)
-    return maxd;
-  else
-    return mind;
-} /* getdistance */
-
-
-/*---------------------------------
-
-  qh_normalize( normal, dim, toporient )
-    normalize a vector and report if too small
-    does not use min norm
-
-  see:
-    qh_normalize2
-*/
-void qh_normalize (coordT *normal, int dim, boolT toporient) {
-  qh_normalize2( normal, dim, toporient, NULL, NULL);
-} /* normalize */
-
-/*---------------------------------
-
-  qh_normalize2( normal, dim, toporient, minnorm, ismin )
-    normalize a vector and report if too small
-    qh.MINdenom/MINdenom1 are the upper limits for divide overflow
-
-  returns:
-    normalized vector
-    flips sign if !toporient
-    if minnorm non-NULL,
-      sets ismin if normal < minnorm
-
-  notes:
-    if zero norm
-       sets all elements to sqrt(1.0/dim)
-    if divide by zero (divzero ())
-       sets largest element to   +/-1
-       bumps Znearlysingular
-
-  design:
-    computes norm
-    test for minnorm
-    if not near zero
-      normalizes normal
-    else if zero norm
-      sets normal to standard value
-    else
-      uses qh_divzero to normalize
-      if nearzero
-        sets norm to direction of maximum value
-*/
-void qh_normalize2 (coordT *normal, int dim, boolT toporient,
-            realT *minnorm, boolT *ismin) {
-  int k;
-  realT *colp, *maxp, norm= 0, temp, *norm1, *norm2, *norm3;
-  boolT zerodiv;
-
-  norm1= normal+1;
-  norm2= normal+2;
-  norm3= normal+3;
-  if (dim == 2)
-    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1));
-  else if (dim == 3)
-    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2));
-  else if (dim == 4) {
-    norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2)
-               + (*norm3)*(*norm3));
-  }else if (dim > 4) {
-    norm= (*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2)
-               + (*norm3)*(*norm3);
-    for (k= dim-4, colp= normal+4; k--; colp++)
-      norm += (*colp) * (*colp);
-    norm= sqrt(norm);
-  }
-  if (minnorm) {
-    if (norm < *minnorm)
-      *ismin= True;
-    else
-      *ismin= False;
-  }
-  wmin_(Wmindenom, norm);
-  if (norm > qh MINdenom) {
-    if (!toporient)
-      norm= -norm;
-    *normal /= norm;
-    *norm1 /= norm;
-    if (dim == 2)
-      ; /* all done */
-    else if (dim == 3)
-      *norm2 /= norm;
-    else if (dim == 4) {
-      *norm2 /= norm;
-      *norm3 /= norm;
-    }else if (dim >4) {
-      *norm2 /= norm;
-      *norm3 /= norm;
-      for (k= dim-4, colp= normal+4; k--; )
-        *colp++ /= norm;
-    }
-  }else if (norm == 0.0) {
-    temp= sqrt (1.0/dim);
-    for (k= dim, colp= normal; k--; )
-      *colp++ = temp;
-  }else {
-    if (!toporient)
-      norm= -norm;
-    for (k= dim, colp= normal; k--; colp++) { /* k used below */
-      temp= qh_divzero (*colp, norm, qh MINdenom_1, &zerodiv);
-      if (!zerodiv)
-	*colp= temp;
-      else {
-	maxp= qh_maxabsval(normal, dim);
-	temp= ((*maxp * norm >= 0.0) ? 1.0 : -1.0);
-	for (k= dim, colp= normal; k--; colp++)
-	  *colp= 0.0;
-	*maxp= temp;
-	zzinc_(Znearlysingular);
-	trace0((qh ferr, "qh_normalize: norm=%2.2g too small during p%d\n",
-	       norm, qh furthest_id));
-	return;
-      }
-    }
-  }
-} /* normalize */
-
-
-/*---------------------------------
-
-  qh_projectpoint( point, facet, dist )
-    project point onto a facet by dist
-
-  returns:
-    returns a new point
-
-  notes:
-    if dist= distplane(point,facet)
-      this projects point to hyperplane
-    assumes qh_memfree_() is valid for normal_size
-*/
-pointT *qh_projectpoint(pointT *point, facetT *facet, realT dist) {
-  pointT *newpoint, *np, *normal;
-  int normsize= qh normal_size,k;
-  void **freelistp; /* used !qh_NOmem */
-
-  qh_memalloc_(normsize, freelistp, newpoint, pointT);
-  np= newpoint;
-  normal= facet->normal;
-  for(k= qh hull_dim; k--; )
-    *(np++)= *point++ - dist * *normal++;
-  return(newpoint);
-} /* projectpoint */
-
-
-/*---------------------------------
-
-  qh_setfacetplane( facet )
-    sets the hyperplane for a facet
-    if qh.RANDOMdist, joggles hyperplane
-
-  notes:
-    uses global buffers qh.gm_matrix and qh.gm_row
-    overwrites facet->normal if already defined
-    sets facet->upperdelaunay if upper envelope of Delaunay triangulation
-
-  design:
-    copy vertex coordinates to qh.gm_matrix/gm_row
-    compute determinate
-    if nearzero
-      recompute determinate with gaussian elimination
-      if nearzero
-        force outside orientation by testing interior point
-*/
-void qh_setfacetplane(facetT *facet) {
-  pointT *point;
-  vertexT *vertex, **vertexp;
-  int k,i, normsize= qh normal_size, oldtrace= 0;
-  realT dist;
-  void **freelistp; /* used !qh_NOmem */
-  coordT *coord, *gmcoord;
-  pointT *point0= SETfirstt_(facet->vertices, vertexT)->point;
-  boolT nearzero= False;
-
-  zzinc_(Zsetplane);
-  if (!facet->normal)
-    qh_memalloc_(normsize, freelistp, facet->normal, coordT);
-  if (facet == qh tracefacet) {
-    oldtrace= qh IStracing;
-    qh IStracing= 5;
-    fprintf (qh ferr, "qh_setfacetplane: facet f%d created.\n", facet->id);
-    fprintf (qh ferr, "  Last point added to hull was p%d.", qh furthest_id);
-    if (zzval_(Ztotmerge))
-      fprintf(qh ferr, "  Last merge was #%d.", zzval_(Ztotmerge));
-    fprintf (qh ferr, "\n\nCurrent summary is:\n");
-      qh_printsummary (qh ferr);
-  }
-  if (qh hull_dim <= 4) {
-    i= 0;
-    if (qh RANDOMdist) {
-      gmcoord= qh gm_matrix;
-      FOREACHvertex_(facet->vertices) {
-        qh gm_row[i++]= gmcoord;
-	coord= vertex->point;
-	for (k= qh hull_dim; k--; )
-	  *(gmcoord++)= *coord++ * qh_randomfactor();
-      }
-    }else {
-      FOREACHvertex_(facet->vertices)
-       qh gm_row[i++]= vertex->point;
-    }
-    qh_sethyperplane_det(qh hull_dim, qh gm_row, point0, facet->toporient,
-                facet->normal, &facet->offset, &nearzero);
-  }
-  if (qh hull_dim > 4 || nearzero) {
-    i= 0;
-    gmcoord= qh gm_matrix;
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->point != point0) {
-	qh gm_row[i++]= gmcoord;
-	coord= vertex->point;
-	point= point0;
-	for(k= qh hull_dim; k--; )
-	  *(gmcoord++)= *coord++ - *point++;
-      }
-    }
-    qh gm_row[i]= gmcoord;  /* for areasimplex */
-    if (qh RANDOMdist) {
-      gmcoord= qh gm_matrix;
-      for (i= qh hull_dim-1; i--; ) {
-	for (k= qh hull_dim; k--; )
-	  *(gmcoord++) *= qh_randomfactor();
-      }
-    }
-    qh_sethyperplane_gauss(qh hull_dim, qh gm_row, point0, facet->toporient,
-           	facet->normal, &facet->offset, &nearzero);
-    if (nearzero) {
-      if (qh_orientoutside (facet)) {
-	trace0((qh ferr, "qh_setfacetplane: flipped orientation after testing interior_point during p%d\n", qh furthest_id));
-      /* this is part of using Gaussian Elimination.  For example in 5-d
-	   1 1 1 1 0
-	   1 1 1 1 1
-	   0 0 0 1 0
-	   0 1 0 0 0
-	   1 0 0 0 0
-	   norm= 0.38 0.38 -0.76 0.38 0
-	 has a determinate of 1, but g.e. after subtracting pt. 0 has
-	 0's in the diagonal, even with full pivoting.  It does work
-	 if you subtract pt. 4 instead. */
-      }
-    }
-  }
-  facet->upperdelaunay= False;
-  if (qh DELAUNAY) {
-    if (qh UPPERdelaunay) {     /* matches qh_triangulate_facet and qh.lower_threshold in qh_initbuild */
-      if (facet->normal[qh hull_dim -1] >= qh ANGLEround * qh_ZEROdelaunay)
-        facet->upperdelaunay= True;
-    }else {
-      if (facet->normal[qh hull_dim -1] > -qh ANGLEround * qh_ZEROdelaunay)
-        facet->upperdelaunay= True;
-    }
-  }
-  if (qh PRINTstatistics || qh IStracing || qh TRACElevel || qh JOGGLEmax < REALmax) {
-    qh old_randomdist= qh RANDOMdist;
-    qh RANDOMdist= False;
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->point != point0) {
-	boolT istrace= False;
-	zinc_(Zdiststat);
-        qh_distplane(vertex->point, facet, &dist);
-        dist= fabs_(dist);
-        zinc_(Znewvertex);
-        if (dist > wwval_(Wnewvertexmax)) {
-          wwval_(Wnewvertexmax)= dist;
-	  if (dist > qh max_outside) {
-	    qh max_outside= dist;  /* used by qh_maxouter() */
-	    if (dist > qh TRACEdist)
-	      istrace= True;
-	  }
-	}else if (-dist > qh TRACEdist)
-	  istrace= True;
-	if (istrace) {
-	  fprintf (qh ferr, "qh_setfacetplane: ====== vertex p%d (v%d) increases max_outside to %2.2g for new facet f%d last p%d\n",
-	        qh_pointid(vertex->point), vertex->id, dist, facet->id, qh furthest_id);
-	  qh_errprint ("DISTANT", facet, NULL, NULL, NULL);
-	}
-      }
-    }
-    qh RANDOMdist= qh old_randomdist;
-  }
-  if (qh IStracing >= 3) {
-    fprintf (qh ferr, "qh_setfacetplane: f%d offset %2.2g normal: ",
-	     facet->id, facet->offset);
-    for (k=0; k < qh hull_dim; k++)
-      fprintf (qh ferr, "%2.2g ", facet->normal[k]);
-    fprintf (qh ferr, "\n");
-  }
-  if (facet == qh tracefacet)
-    qh IStracing= oldtrace;
-} /* setfacetplane */
-
-
-/*---------------------------------
-
-  qh_sethyperplane_det( dim, rows, point0, toporient, normal, offset, nearzero )
-    given dim X dim array indexed by rows[], one row per point,
-        toporient (flips all signs),
-        and point0 (any row)
-    set normalized hyperplane equation from oriented simplex
-
-  returns:
-    normal (normalized)
-    offset (places point0 on the hyperplane)
-    sets nearzero if hyperplane not through points
-
-  notes:
-    only defined for dim == 2..4
-    rows[] is not modified
-    solves det(P-V_0, V_n-V_0, ..., V_1-V_0)=0, i.e. every point is on hyperplane
-    see Bower & Woodworth, A programmer's geometry, Butterworths 1983.
-
-  derivation of 3-d minnorm
-    Goal: all vertices V_i within qh.one_merge of hyperplane
-    Plan: exactly translate the facet so that V_0 is the origin
-          exactly rotate the facet so that V_1 is on the x-axis and y_2=0.
-          exactly rotate the effective perturbation to only effect n_0
-	     this introduces a factor of sqrt(3)
-    n_0 = ((y_2-y_0)*(z_1-z_0) - (z_2-z_0)*(y_1-y_0)) / norm
-    Let M_d be the max coordinate difference
-    Let M_a be the greater of M_d and the max abs. coordinate
-    Let u be machine roundoff and distround be max error for distance computation
-    The max error for n_0 is sqrt(3) u M_a M_d / norm.  n_1 is approx. 1 and n_2 is approx. 0
-    The max error for distance of V_1 is sqrt(3) u M_a M_d M_d / norm.  Offset=0 at origin
-    Then minnorm = 1.8 u M_a M_d M_d / qh.ONEmerge
-    Note that qh.one_merge is approx. 45.5 u M_a and norm is usually about M_d M_d
-
-  derivation of 4-d minnorm
-    same as above except rotate the facet so that V_1 on x-axis and w_2, y_3, w_3=0
-     [if two vertices fixed on x-axis, can rotate the other two in yzw.]
-    n_0 = det3_(...) = y_2 det2_(z_1, w_1, z_3, w_3) = - y_2 w_1 z_3
-     [all other terms contain at least two factors nearly zero.]
-    The max error for n_0 is sqrt(4) u M_a M_d M_d / norm
-    Then minnorm = 2 u M_a M_d M_d M_d / qh.ONEmerge
-    Note that qh.one_merge is approx. 82 u M_a and norm is usually about M_d M_d M_d
-*/
-void qh_sethyperplane_det (int dim, coordT **rows, coordT *point0,
-          boolT toporient, coordT *normal, realT *offset, boolT *nearzero) {
-  realT maxround, dist;
-  int i;
-  pointT *point;
-
-
-  if (dim == 2) {
-    normal[0]= dY(1,0);
-    normal[1]= dX(0,1);
-    qh_normalize2 (normal, dim, toporient, NULL, NULL);
-    *offset= -(point0[0]*normal[0]+point0[1]*normal[1]);
-    *nearzero= False;  /* since nearzero norm => incident points */
-  }else if (dim == 3) {
-    normal[0]= det2_(dY(2,0), dZ(2,0),
-		     dY(1,0), dZ(1,0));
-    normal[1]= det2_(dX(1,0), dZ(1,0),
-		     dX(2,0), dZ(2,0));
-    normal[2]= det2_(dX(2,0), dY(2,0),
-		     dX(1,0), dY(1,0));
-    qh_normalize2 (normal, dim, toporient, NULL, NULL);
-    *offset= -(point0[0]*normal[0] + point0[1]*normal[1]
-	       + point0[2]*normal[2]);
-    maxround= qh DISTround;
-    for (i=dim; i--; ) {
-      point= rows[i];
-      if (point != point0) {
-        dist= *offset + (point[0]*normal[0] + point[1]*normal[1]
-	       + point[2]*normal[2]);
-        if (dist > maxround || dist < -maxround) {
-  	  *nearzero= True;
-	  break;
-	}
-      }
-    }
-  }else if (dim == 4) {
-    normal[0]= - det3_(dY(2,0), dZ(2,0), dW(2,0),
-			dY(1,0), dZ(1,0), dW(1,0),
-			dY(3,0), dZ(3,0), dW(3,0));
-    normal[1]=   det3_(dX(2,0), dZ(2,0), dW(2,0),
-		        dX(1,0), dZ(1,0), dW(1,0),
-		        dX(3,0), dZ(3,0), dW(3,0));
-    normal[2]= - det3_(dX(2,0), dY(2,0), dW(2,0),
-			dX(1,0), dY(1,0), dW(1,0),
-			dX(3,0), dY(3,0), dW(3,0));
-    normal[3]=   det3_(dX(2,0), dY(2,0), dZ(2,0),
-		        dX(1,0), dY(1,0), dZ(1,0),
-		        dX(3,0), dY(3,0), dZ(3,0));
-    qh_normalize2 (normal, dim, toporient, NULL, NULL);
-    *offset= -(point0[0]*normal[0] + point0[1]*normal[1]
-	       + point0[2]*normal[2] + point0[3]*normal[3]);
-    maxround= qh DISTround;
-    for (i=dim; i--; ) {
-      point= rows[i];
-      if (point != point0) {
-        dist= *offset + (point[0]*normal[0] + point[1]*normal[1]
-	       + point[2]*normal[2] + point[3]*normal[3]);
-        if (dist > maxround || dist < -maxround) {
-  	  *nearzero= True;
-	  break;
-	}
-      }
-    }
-  }
-  if (*nearzero) {
-    zzinc_(Zminnorm);
-    trace0((qh ferr, "qh_sethyperplane_det: degenerate norm during p%d.\n", qh furthest_id));
-    zzinc_(Znearlysingular);
-  }
-} /* sethyperplane_det */
-
-
-/*---------------------------------
-
-  qh_sethyperplane_gauss( dim, rows, point0, toporient, normal, offset, nearzero )
-    given (dim-1) X dim array of rows[i]= V_{i+1} - V_0 (point0)
-    set normalized hyperplane equation from oriented simplex
-
-  returns:
-    normal (normalized)
-    offset (places point0 on the hyperplane)
-
-  notes:
-    if nearzero
-      orientation may be incorrect because of incorrect sign flips in gausselim
-    solves [V_n-V_0,...,V_1-V_0, 0 .. 0 1] * N == [0 .. 0 1]
-        or [V_n-V_0,...,V_1-V_0, 0 .. 0 1] * N == [0]
-    i.e., N is normal to the hyperplane, and the unnormalized
-        distance to [0 .. 1] is either 1 or   0
-
-  design:
-    perform gaussian elimination
-    flip sign for negative values
-    perform back substitution
-    normalize result
-    compute offset
-*/
-void qh_sethyperplane_gauss (int dim, coordT **rows, pointT *point0,
-		boolT toporient, coordT *normal, coordT *offset, boolT *nearzero) {
-  coordT *pointcoord, *normalcoef;
-  int k;
-  boolT sign= toporient, nearzero2= False;
-
-  qh_gausselim(rows, dim-1, dim, &sign, nearzero);
-  for(k= dim-1; k--; ) {
-    if ((rows[k])[k] < 0)
-      sign ^= 1;
-  }
-  if (*nearzero) {
-    zzinc_(Znearlysingular);
-    trace0((qh ferr, "qh_sethyperplane_gauss: nearly singular or axis parallel hyperplane during p%d.\n", qh furthest_id));
-    qh_backnormal(rows, dim-1, dim, sign, normal, &nearzero2);
-  }else {
-    qh_backnormal(rows, dim-1, dim, sign, normal, &nearzero2);
-    if (nearzero2) {
-      zzinc_(Znearlysingular);
-      trace0((qh ferr, "qh_sethyperplane_gauss: singular or axis parallel hyperplane at normalization during p%d.\n", qh furthest_id));
-    }
-  }
-  if (nearzero2)
-    *nearzero= True;
-  qh_normalize2(normal, dim, True, NULL, NULL);
-  pointcoord= point0;
-  normalcoef= normal;
-  *offset= -(*pointcoord++ * *normalcoef++);
-  for(k= dim-1; k--; )
-    *offset -= *pointcoord++ * *normalcoef++;
-} /* sethyperplane_gauss */
-
-
-
diff --git a/extern/qhull/src/geom.h b/extern/qhull/src/geom.h
deleted file mode 100644
index 32440cff56f..00000000000
--- a/extern/qhull/src/geom.h
+++ /dev/null
@@ -1,177 +0,0 @@
-/*  ---------------------------------
-
-  geom.h
-    header file for geometric routines
-
-   see qh-geom.htm and geom.c
-
-   copyright (c) 1993-2002 The Geometry Center
-*/
-
-#ifndef qhDEFgeom
-#define qhDEFgeom 1
-
-/* ============ -macros- ======================== */
-
-/*----------------------------------
-
-  fabs_(a)
-    returns the absolute value of a
-*/
-#define fabs_( a ) ((( a ) < 0 ) ? -( a ):( a ))
-
-/*----------------------------------
-
-  fmax_(a,b)
-    returns the maximum value of a and b
-*/
-#define fmax_( a,b )  ( ( a ) < ( b ) ? ( b ) : ( a ) )
-
-/*----------------------------------
-
-  fmin_(a,b)
-    returns the minimum value of a and b
-*/
-#define fmin_( a,b )  ( ( a ) > ( b ) ? ( b ) : ( a ) )
-
-/*----------------------------------
-
-  maximize_(maxval, val)
-    set maxval to val if val is greater than maxval
-*/
-#define maximize_( maxval, val ) {if (( maxval ) < ( val )) ( maxval )= ( val );}
-
-/*----------------------------------
-
-  minimize_(minval, val)
-    set minval to val if val is less than minval
-*/
-#define minimize_( minval, val ) {if (( minval ) > ( val )) ( minval )= ( val );}
-
-/*----------------------------------
-
-  det2_(a1, a2,
-        b1, b2)
-
-    compute a 2-d determinate
-*/
-#define det2_( a1,a2,b1,b2 ) (( a1 )*( b2 ) - ( a2 )*( b1 ))
-
-/*----------------------------------
-
-  det3_(a1, a2, a3,
-       b1, b2, b3,
-       c1, c2, c3)
-
-    compute a 3-d determinate
-*/
-#define det3_( a1,a2,a3,b1,b2,b3,c1,c2,c3 ) ( ( a1 )*det2_( b2,b3,c2,c3 ) \
-                - ( b1 )*det2_( a2,a3,c2,c3 ) + ( c1 )*det2_( a2,a3,b2,b3 ) )
-
-/*----------------------------------
-
-  dX( p1, p2 )
-  dY( p1, p2 )
-  dZ( p1, p2 )
-
-    given two indices into rows[],
-
-    compute the difference between X, Y, or Z coordinates
-*/
-#define dX( p1,p2 )  ( *( rows[p1] ) - *( rows[p2] ))
-#define dY( p1,p2 )  ( *( rows[p1]+1 ) - *( rows[p2]+1 ))
-#define dZ( p1,p2 )  ( *( rows[p1]+2 ) - *( rows[p2]+2 ))
-#define dW( p1,p2 )  ( *( rows[p1]+3 ) - *( rows[p2]+3 ))
-
-/*============= prototypes in alphabetical order, infrequent at end ======= */
-
-void    qh_backnormal (realT **rows, int numrow, int numcol, boolT sign, coordT *normal, boolT *nearzero);
-void	qh_distplane (pointT *point, facetT *facet, realT *dist);
-facetT *qh_findbest (pointT *point, facetT *startfacet,
-		     boolT bestoutside, boolT isnewfacets, boolT noupper,
-		     realT *dist, boolT *isoutside, int *numpart);
-facetT *qh_findbesthorizon (boolT ischeckmax, pointT *point,
-	             facetT *startfacet, boolT noupper, realT *bestdist, int *numpart);
-facetT *qh_findbestnew (pointT *point, facetT *startfacet, realT *dist,
-		     boolT bestoutside, boolT *isoutside, int *numpart);
-void 	qh_gausselim(realT **rows, int numrow, int numcol, boolT *sign, boolT *nearzero);
-realT   qh_getangle(pointT *vect1, pointT *vect2);
-pointT *qh_getcenter(setT *vertices);
-pointT *qh_getcentrum(facetT *facet);
-realT   qh_getdistance(facetT *facet, facetT *neighbor, realT *mindist, realT *maxdist);
-void    qh_normalize (coordT *normal, int dim, boolT toporient);
-void    qh_normalize2 (coordT *normal, int dim, boolT toporient,
-            realT *minnorm, boolT *ismin);
-pointT *qh_projectpoint(pointT *point, facetT *facet, realT dist);
-
-void    qh_setfacetplane(facetT *newfacets);
-void 	qh_sethyperplane_det (int dim, coordT **rows, coordT *point0,
-              boolT toporient, coordT *normal, realT *offset, boolT *nearzero);
-void 	qh_sethyperplane_gauss (int dim, coordT **rows, pointT *point0,
-	     boolT toporient, coordT *normal, coordT *offset, boolT *nearzero);
-boolT   qh_sharpnewfacets (void);
-
-/*========= infrequently used code in geom2.c =============*/
-
-
-coordT *qh_copypoints (coordT *points, int numpoints, int dimension);
-void    qh_crossproduct (int dim, realT vecA[3], realT vecB[3], realT vecC[3]);
-realT 	qh_determinant (realT **rows, int dim, boolT *nearzero);
-realT   qh_detjoggle (pointT *points, int numpoints, int dimension);
-void    qh_detroundoff (void);
-realT   qh_detsimplex(pointT *apex, setT *points, int dim, boolT *nearzero);
-realT   qh_distnorm (int dim, pointT *point, pointT *normal, realT *offsetp);
-realT   qh_distround (int dimension, realT maxabs, realT maxsumabs);
-realT   qh_divzero(realT numer, realT denom, realT mindenom1, boolT *zerodiv);
-realT   qh_facetarea (facetT *facet);
-realT   qh_facetarea_simplex (int dim, coordT *apex, setT *vertices,
-          vertexT *notvertex,  boolT toporient, coordT *normal, realT *offset);
-pointT *qh_facetcenter (setT *vertices);
-facetT *qh_findgooddist (pointT *point, facetT *facetA, realT *distp, facetT **facetlist);
-void    qh_getarea (facetT *facetlist);
-boolT   qh_gram_schmidt(int dim, realT **rows);
-boolT   qh_inthresholds (coordT *normal, realT *angle);
-void    qh_joggleinput (void);
-realT  *qh_maxabsval (realT *normal, int dim);
-setT   *qh_maxmin(pointT *points, int numpoints, int dimension);
-realT   qh_maxouter (void);
-void    qh_maxsimplex (int dim, setT *maxpoints, pointT *points, int numpoints, setT **simplex);
-realT   qh_minabsval (realT *normal, int dim);
-int     qh_mindiff (realT *vecA, realT *vecB, int dim);
-boolT   qh_orientoutside (facetT *facet);
-void    qh_outerinner (facetT *facet, realT *outerplane, realT *innerplane);
-coordT  qh_pointdist(pointT *point1, pointT *point2, int dim);
-void    qh_printmatrix (FILE *fp, char *string, realT **rows, int numrow, int numcol);
-void    qh_printpoints (FILE *fp, char *string, setT *points);
-void    qh_projectinput (void);
-void 	qh_projectpoints (signed char *project, int n, realT *points,
-             int numpoints, int dim, realT *newpoints, int newdim);
-int     qh_rand( void);
-void    qh_srand( int seed);
-realT   qh_randomfactor (void);
-void    qh_randommatrix (realT *buffer, int dim, realT **row);
-void    qh_rotateinput (realT **rows);
-void    qh_rotatepoints (realT *points, int numpoints, int dim, realT **rows);
-void    qh_scaleinput (void);
-void    qh_scalelast (coordT *points, int numpoints, int dim, coordT low,
-		   coordT high, coordT newhigh);
-void 	qh_scalepoints (pointT *points, int numpoints, int dim,
-  		realT *newlows, realT *newhighs);
-boolT   qh_sethalfspace (int dim, coordT *coords, coordT **nextp,
-              coordT *normal, coordT *offset, coordT *feasible);
-coordT *qh_sethalfspace_all (int dim, int count, coordT *halfspaces, pointT *feasible);
-pointT *qh_voronoi_center (int dim, setT *points);
-
-#endif /* qhDEFgeom */
-
-
-
diff --git a/extern/qhull/src/geom2.c b/extern/qhull/src/geom2.c
deleted file mode 100644
index bd58ce1282b..00000000000
--- a/extern/qhull/src/geom2.c
+++ /dev/null
@@ -1,2160 +0,0 @@
-/*  ---------------------------------
-
-
-   geom2.c
-   infrequently used geometric routines of qhull
-
-   see qh-geom.htm and geom.h
-
-   copyright (c) 1993-2002 The Geometry Center
-
-   frequently used code goes into geom.c
-*/
-
-#include "qhull_a.h"
-
-/*================== functions in alphabetic order ============*/
-
-/*---------------------------------
-
-  qh_copypoints( points, numpoints, dimension)
-    return malloc'd copy of points
-*/
-coordT *qh_copypoints (coordT *points, int numpoints, int dimension) {
-  int size;
-  coordT *newpoints;
-
-  size= numpoints * dimension * sizeof(coordT);
-  if (!(newpoints=(coordT*)malloc(size))) {
-    fprintf(qh ferr, "qhull error: insufficient memory to copy %d points\n",
-        numpoints);
-    qh_errexit(qh_ERRmem, NULL, NULL);
-  }
-  memcpy ((char *)newpoints, (char *)points, size);
-  return newpoints;
-} /* copypoints */
-
-/*---------------------------------
-
-  qh_crossproduct( dim, vecA, vecB, vecC )
-    crossproduct of 2 dim vectors
-    C= A x B
-
-  notes:
-    from Glasner, Graphics Gems I, p. 639
-    only defined for dim==3
-*/
-void qh_crossproduct (int dim, realT vecA[3], realT vecB[3], realT vecC[3]){
-
-  if (dim == 3) {
-    vecC[0]=   det2_(vecA[1], vecA[2],
-		     vecB[1], vecB[2]);
-    vecC[1]= - det2_(vecA[0], vecA[2],
-		     vecB[0], vecB[2]);
-    vecC[2]=   det2_(vecA[0], vecA[1],
-		     vecB[0], vecB[1]);
-  }
-} /* vcross */
-
-/*---------------------------------
-
-  qh_determinant( rows, dim, nearzero )
-    compute signed determinant of a square matrix
-    uses qh.NEARzero to test for degenerate matrices
-
-  returns:
-    determinant
-    overwrites rows and the matrix
-    if dim == 2 or 3
-      nearzero iff determinant < qh NEARzero[dim-1]
-      (not quite correct, not critical)
-    if dim >= 4
-      nearzero iff diagonal[k] < qh NEARzero[k]
-*/
-realT qh_determinant (realT **rows, int dim, boolT *nearzero) {
-  realT det=0;
-  int i;
-  boolT sign= False;
-
-  *nearzero= False;
-  if (dim < 2) {
-    fprintf (qh ferr, "qhull internal error (qh_determinate): only implemented for dimension >= 2\n");
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }else if (dim == 2) {
-    det= det2_(rows[0][0], rows[0][1],
-		 rows[1][0], rows[1][1]);
-    if (fabs_(det) < qh NEARzero[1])  /* not really correct, what should this be? */
-      *nearzero= True;
-  }else if (dim == 3) {
-    det= det3_(rows[0][0], rows[0][1], rows[0][2],
-		 rows[1][0], rows[1][1], rows[1][2],
-		 rows[2][0], rows[2][1], rows[2][2]);
-    if (fabs_(det) < qh NEARzero[2])  /* not really correct, what should this be? */
-      *nearzero= True;
-  }else {
-    qh_gausselim(rows, dim, dim, &sign, nearzero);  /* if nearzero, diagonal still ok*/
-    det= 1.0;
-    for (i= dim; i--; )
-      det *= (rows[i])[i];
-    if (sign)
-      det= -det;
-  }
-  return det;
-} /* determinant */
-
-/*---------------------------------
-
-  qh_detjoggle( points, numpoints, dimension )
-    determine default max joggle for point array
-      as qh_distround * qh_JOGGLEdefault
-
-  returns:
-    initial value for JOGGLEmax from points and REALepsilon
-
-  notes:
-    computes DISTround since qh_maxmin not called yet
-    if qh SCALElast, last dimension will be scaled later to MAXwidth
-
-    loop duplicated from qh_maxmin
-*/
-realT qh_detjoggle (pointT *points, int numpoints, int dimension) {
-  realT abscoord, distround, joggle, maxcoord, mincoord;
-  pointT *point, *pointtemp;
-  realT maxabs= -REALmax;
-  realT sumabs= 0;
-  realT maxwidth= 0;
-  int k;
-
-  for (k= 0; k < dimension; k++) {
-    if (qh SCALElast && k == dimension-1)
-      abscoord= maxwidth;
-    else if (qh DELAUNAY && k == dimension-1) /* will qh_setdelaunay() */
-      abscoord= 2 * maxabs * maxabs;  /* may be low by qh hull_dim/2 */
-    else {
-      maxcoord= -REALmax;
-      mincoord= REALmax;
-      FORALLpoint_(points, numpoints) {
-	maximize_(maxcoord, point[k]);
-        minimize_(mincoord, point[k]);
-      }
-      maximize_(maxwidth, maxcoord-mincoord);
-      abscoord= fmax_(maxcoord, -mincoord);
-    }
-    sumabs += abscoord;
-    maximize_(maxabs, abscoord);
-  } /* for k */
-  distround= qh_distround (qh hull_dim, maxabs, sumabs);
-  joggle= distround * qh_JOGGLEdefault;
-  maximize_(joggle, REALepsilon * qh_JOGGLEdefault);
-  trace2((qh ferr, "qh_detjoggle: joggle=%2.2g maxwidth=%2.2g\n", joggle, maxwidth));
-  return joggle;
-} /* detjoggle */
-
-/*---------------------------------
-
-  qh_detroundoff()
-    determine maximum roundoff errors from
-      REALepsilon, REALmax, REALmin, qh.hull_dim, qh.MAXabs_coord,
-      qh.MAXsumcoord, qh.MAXwidth, qh.MINdenom_1
-
-    accounts for qh.SETroundoff, qh.RANDOMdist, qh MERGEexact
-      qh.premerge_cos, qh.postmerge_cos, qh.premerge_centrum,
-      qh.postmerge_centrum, qh.MINoutside,
-      qh_RATIOnearinside, qh_COPLANARratio, qh_WIDEcoplanar
-
-  returns:
-    sets qh.DISTround, etc. (see below)
-    appends precision constants to qh.qhull_options
-
-  see:
-    qh_maxmin() for qh.NEARzero
-
-  design:
-    determine qh.DISTround for distance computations
-    determine minimum denominators for qh_divzero
-    determine qh.ANGLEround for angle computations
-    adjust qh.premerge_cos,... for roundoff error
-    determine qh.ONEmerge for maximum error due to a single merge
-    determine qh.NEARinside, qh.MAXcoplanar, qh.MINvisible,
-      qh.MINoutside, qh.WIDEfacet
-    initialize qh.max_vertex and qh.minvertex
-*/
-void qh_detroundoff (void) {
-
-  qh_option ("_max-width", NULL, &qh MAXwidth);
-  if (!qh SETroundoff) {
-    qh DISTround= qh_distround (qh hull_dim, qh MAXabs_coord, qh MAXsumcoord);
-    if (qh RANDOMdist)
-      qh DISTround += qh RANDOMfactor * qh MAXabs_coord;
-    qh_option ("Error-roundoff", NULL, &qh DISTround);
-  }
-  qh MINdenom= qh MINdenom_1 * qh MAXabs_coord;
-  qh MINdenom_1_2= sqrt (qh MINdenom_1 * qh hull_dim) ;  /* if will be normalized */
-  qh MINdenom_2= qh MINdenom_1_2 * qh MAXabs_coord;
-                                              /* for inner product */
-  qh ANGLEround= 1.01 * qh hull_dim * REALepsilon;
-  if (qh RANDOMdist)
-    qh ANGLEround += qh RANDOMfactor;
-  if (qh premerge_cos < REALmax/2) {
-    qh premerge_cos -= qh ANGLEround;
-    if (qh RANDOMdist)
-      qh_option ("Angle-premerge-with-random", NULL, &qh premerge_cos);
-  }
-  if (qh postmerge_cos < REALmax/2) {
-    qh postmerge_cos -= qh ANGLEround;
-    if (qh RANDOMdist)
-      qh_option ("Angle-postmerge-with-random", NULL, &qh postmerge_cos);
-  }
-  qh premerge_centrum += 2 * qh DISTround;    /*2 for centrum and distplane()*/
-  qh postmerge_centrum += 2 * qh DISTround;
-  if (qh RANDOMdist && (qh MERGEexact || qh PREmerge))
-    qh_option ("Centrum-premerge-with-random", NULL, &qh premerge_centrum);
-  if (qh RANDOMdist && qh POSTmerge)
-    qh_option ("Centrum-postmerge-with-random", NULL, &qh postmerge_centrum);
-  { /* compute ONEmerge, max vertex offset for merging simplicial facets */
-    realT maxangle= 1.0, maxrho;
-
-    minimize_(maxangle, qh premerge_cos);
-    minimize_(maxangle, qh postmerge_cos);
-    /* max diameter * sin theta + DISTround for vertex to its hyperplane */
-    qh ONEmerge= sqrt (qh hull_dim) * qh MAXwidth *
-      sqrt (1.0 - maxangle * maxangle) + qh DISTround;
-    maxrho= qh hull_dim * qh premerge_centrum + qh DISTround;
-    maximize_(qh ONEmerge, maxrho);
-    maxrho= qh hull_dim * qh postmerge_centrum + qh DISTround;
-    maximize_(qh ONEmerge, maxrho);
-    if (qh MERGING)
-      qh_option ("_one-merge", NULL, &qh ONEmerge);
-  }
-  qh NEARinside= qh ONEmerge * qh_RATIOnearinside; /* only used if qh KEEPnearinside */
-  if (qh JOGGLEmax < REALmax/2 && (qh KEEPcoplanar || qh KEEPinside)) {
-    realT maxdist;	       /* adjust qh.NEARinside for joggle */
-    qh KEEPnearinside= True;
-    maxdist= sqrt (qh hull_dim) * qh JOGGLEmax + qh DISTround;
-    maxdist= 2*maxdist;        /* vertex and coplanar point can joggle in opposite directions */
-    maximize_(qh NEARinside, maxdist);  /* must agree with qh_nearcoplanar() */
-  }
-  if (qh KEEPnearinside)
-    qh_option ("_near-inside", NULL, &qh NEARinside);
-  if (qh JOGGLEmax < qh DISTround) {
-    fprintf (qh ferr, "qhull error: the joggle for 'QJn', %.2g, is below roundoff for distance computations, %.2g\n",
-         qh JOGGLEmax, qh DISTround);
-    qh_errexit (qh_ERRinput, NULL, NULL);
-  }
-  if (qh MINvisible > REALmax/2) {
-    if (!qh MERGING)
-      qh MINvisible= qh DISTround;
-    else if (qh hull_dim <= 3)
-      qh MINvisible= qh premerge_centrum;
-    else
-      qh MINvisible= qh_COPLANARratio * qh premerge_centrum;
-    if (qh APPROXhull && qh MINvisible > qh MINoutside)
-      qh MINvisible= qh MINoutside;
-    qh_option ("Visible-distance", NULL, &qh MINvisible);
-  }
-  if (qh MAXcoplanar > REALmax/2) {
-    qh MAXcoplanar= qh MINvisible;
-    qh_option ("U-coplanar-distance", NULL, &qh MAXcoplanar);
-  }
-  if (!qh APPROXhull) {             /* user may specify qh MINoutside */
-    qh MINoutside= 2 * qh MINvisible;
-    if (qh premerge_cos < REALmax/2)
-      maximize_(qh MINoutside, (1- qh premerge_cos) * qh MAXabs_coord);
-    qh_option ("Width-outside", NULL, &qh MINoutside);
-  }
-  qh WIDEfacet= qh MINoutside;
-  maximize_(qh WIDEfacet, qh_WIDEcoplanar * qh MAXcoplanar);
-  maximize_(qh WIDEfacet, qh_WIDEcoplanar * qh MINvisible);
-  qh_option ("_wide-facet", NULL, &qh WIDEfacet);
-  if (qh MINvisible > qh MINoutside + 3 * REALepsilon
-  && !qh BESToutside && !qh FORCEoutput)
-    fprintf (qh ferr, "qhull input warning: minimum visibility V%.2g is greater than \nminimum outside W%.2g.  Flipped facets are likely.\n",
-	     qh MINvisible, qh MINoutside);
-  qh max_vertex= qh DISTround;
-  qh min_vertex= -qh DISTround;
-  /* numeric constants reported in printsummary */
-} /* detroundoff */
-
-/*---------------------------------
-
-  qh_detsimplex( apex, points, dim, nearzero )
-    compute determinant of a simplex with point apex and base points
-
-  returns:
-     signed determinant and nearzero from qh_determinant
-
-  notes:
-     uses qh.gm_matrix/qh.gm_row (assumes they're big enough)
-
-  design:
-    construct qm_matrix by subtracting apex from points
-    compute determinate
-*/
-realT qh_detsimplex(pointT *apex, setT *points, int dim, boolT *nearzero) {
-  pointT *coorda, *coordp, *gmcoord, *point, **pointp;
-  coordT **rows;
-  int k,  i=0;
-  realT det;
-
-  zinc_(Zdetsimplex);
-  gmcoord= qh gm_matrix;
-  rows= qh gm_row;
-  FOREACHpoint_(points) {
-    if (i == dim)
-      break;
-    rows[i++]= gmcoord;
-    coordp= point;
-    coorda= apex;
-    for (k= dim; k--; )
-      *(gmcoord++)= *coordp++ - *coorda++;
-  }
-  if (i < dim) {
-    fprintf (qh ferr, "qhull internal error (qh_detsimplex): #points %d < dimension %d\n",
-               i, dim);
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }
-  det= qh_determinant (rows, dim, nearzero);
-  trace2((qh ferr, "qh_detsimplex: det=%2.2g for point p%d, dim %d, nearzero? %d\n",
-	  det, qh_pointid(apex), dim, *nearzero));
-  return det;
-} /* detsimplex */
-
-/*---------------------------------
-
-  qh_distnorm( dim, point, normal, offset )
-    return distance from point to hyperplane at normal/offset
-
-  returns:
-    dist
-
-  notes:
-    dist > 0 if point is outside of hyperplane
-
-  see:
-    qh_distplane in geom.c
-*/
-realT qh_distnorm (int dim, pointT *point, pointT *normal, realT *offsetp) {
-  coordT *normalp= normal, *coordp= point;
-  realT dist;
-  int k;
-
-  dist= *offsetp;
-  for (k= dim; k--; )
-    dist += *(coordp++) * *(normalp++);
-  return dist;
-} /* distnorm */
-
-/*---------------------------------
-
-  qh_distround ( dimension, maxabs, maxsumabs )
-    compute maximum round-off error for a distance computation
-      to a normalized hyperplane
-    maxabs is the maximum absolute value of a coordinate
-    maxsumabs is the maximum possible sum of absolute coordinate values
-
-  returns:
-    max dist round for REALepsilon
-
-  notes:
-    calculate roundoff error according to
-    Lemma 3.2-1 of Golub and van Loan "Matrix Computation"
-    use sqrt(dim) since one vector is normalized
-      or use maxsumabs since one vector is < 1
-*/
-realT qh_distround (int dimension, realT maxabs, realT maxsumabs) {
-  realT maxdistsum, maxround;
-
-  maxdistsum= sqrt (dimension) * maxabs;
-  minimize_( maxdistsum, maxsumabs);
-  maxround= REALepsilon * (dimension * maxdistsum * 1.01 + maxabs);
-              /* adds maxabs for offset */
-  trace4((qh ferr, "qh_distround: %2.2g maxabs %2.2g maxsumabs %2.2g maxdistsum %2.2g\n",
-	         maxround, maxabs, maxsumabs, maxdistsum));
-  return maxround;
-} /* distround */
-
-/*---------------------------------
-
-  qh_divzero( numer, denom, mindenom1, zerodiv )
-    divide by a number that's nearly zero
-    mindenom1= minimum denominator for dividing into 1.0
-
-  returns:
-    quotient
-    sets zerodiv and returns 0.0 if it would overflow
-
-  design:
-    if numer is nearly zero and abs(numer) < abs(denom)
-      return numer/denom
-    else if numer is nearly zero
-      return 0 and zerodiv
-    else if denom/numer non-zero
-      return numer/denom
-    else
-      return 0 and zerodiv
-*/
-realT qh_divzero (realT numer, realT denom, realT mindenom1, boolT *zerodiv) {
-  realT temp, numerx, denomx;
-
-
-  if (numer < mindenom1 && numer > -mindenom1) {
-    numerx= fabs_(numer);
-    denomx= fabs_(denom);
-    if (numerx < denomx) {
-      *zerodiv= False;
-      return numer/denom;
-    }else {
-      *zerodiv= True;
-      return 0.0;
-    }
-  }
-  temp= denom/numer;
-  if (temp > mindenom1 || temp < -mindenom1) {
-    *zerodiv= False;
-    return numer/denom;
-  }else {
-    *zerodiv= True;
-    return 0.0;
-  }
-} /* divzero */
-
-
-/*---------------------------------
-
-  qh_facetarea( facet )
-    return area for a facet
-
-  notes:
-    if non-simplicial,
-      uses centrum to triangulate facet and sums the projected areas.
-    if (qh DELAUNAY),
-      computes projected area instead for last coordinate
-    assumes facet->normal exists
-    projecting tricoplanar facets to the hyperplane does not appear to make a difference
-
-  design:
-    if simplicial
-      compute area
-    else
-      for each ridge
-        compute area from centrum to ridge
-    negate area if upper Delaunay facet
-*/
-realT qh_facetarea (facetT *facet) {
-  vertexT *apex;
-  pointT *centrum;
-  realT area= 0.0;
-  ridgeT *ridge, **ridgep;
-
-  if (facet->simplicial) {
-    apex= SETfirstt_(facet->vertices, vertexT);
-    area= qh_facetarea_simplex (qh hull_dim, apex->point, facet->vertices,
-                    apex, facet->toporient, facet->normal, &facet->offset);
-  }else {
-    if (qh CENTERtype == qh_AScentrum)
-      centrum= facet->center;
-    else
-      centrum= qh_getcentrum (facet);
-    FOREACHridge_(facet->ridges)
-      area += qh_facetarea_simplex (qh hull_dim, centrum, ridge->vertices,
-                 NULL, (ridge->top == facet),  facet->normal, &facet->offset);
-    if (qh CENTERtype != qh_AScentrum)
-      qh_memfree (centrum, qh normal_size);
-  }
-  if (facet->upperdelaunay && qh DELAUNAY)
-    area= -area;  /* the normal should be [0,...,1] */
-  trace4((qh ferr, "qh_facetarea: f%d area %2.2g\n", facet->id, area));
-  return area;
-} /* facetarea */
-
-/*---------------------------------
-
-  qh_facetarea_simplex( dim, apex, vertices, notvertex, toporient, normal, offset )
-    return area for a simplex defined by
-      an apex, a base of vertices, an orientation, and a unit normal
-    if simplicial or tricoplanar facet,
-      notvertex is defined and it is skipped in vertices
-
-  returns:
-    computes area of simplex projected to plane [normal,offset]
-    returns 0 if vertex too far below plane (qh WIDEfacet)
-      vertex can't be apex of tricoplanar facet
-
-  notes:
-    if (qh DELAUNAY),
-      computes projected area instead for last coordinate
-    uses qh gm_matrix/gm_row and qh hull_dim
-    helper function for qh_facetarea
-
-  design:
-    if Notvertex
-      translate simplex to apex
-    else
-      project simplex to normal/offset
-      translate simplex to apex
-    if Delaunay
-      set last row/column to 0 with -1 on diagonal
-    else
-      set last row to Normal
-    compute determinate
-    scale and flip sign for area
-*/
-realT qh_facetarea_simplex (int dim, coordT *apex, setT *vertices,
-        vertexT *notvertex,  boolT toporient, coordT *normal, realT *offset) {
-  pointT *coorda, *coordp, *gmcoord;
-  coordT **rows, *normalp;
-  int k,  i=0;
-  realT area, dist;
-  vertexT *vertex, **vertexp;
-  boolT nearzero;
-
-  gmcoord= qh gm_matrix;
-  rows= qh gm_row;
-  FOREACHvertex_(vertices) {
-    if (vertex == notvertex)
-      continue;
-    rows[i++]= gmcoord;
-    coorda= apex;
-    coordp= vertex->point;
-    normalp= normal;
-    if (notvertex) {
-      for (k= dim; k--; )
-	*(gmcoord++)= *coordp++ - *coorda++;
-    }else {
-      dist= *offset;
-      for (k= dim; k--; )
-	dist += *coordp++ * *normalp++;
-      if (dist < -qh WIDEfacet) {
-	zinc_(Znoarea);
-	return 0.0;
-      }
-      coordp= vertex->point;
-      normalp= normal;
-      for (k= dim; k--; )
-	*(gmcoord++)= (*coordp++ - dist * *normalp++) - *coorda++;
-    }
-  }
-  if (i != dim-1) {
-    fprintf (qh ferr, "qhull internal error (qh_facetarea_simplex): #points %d != dim %d -1\n",
-               i, dim);
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }
-  rows[i]= gmcoord;
-  if (qh DELAUNAY) {
-    for (i= 0; i < dim-1; i++)
-      rows[i][dim-1]= 0.0;
-    for (k= dim; k--; )
-      *(gmcoord++)= 0.0;
-    rows[dim-1][dim-1]= -1.0;
-  }else {
-    normalp= normal;
-    for (k= dim; k--; )
-      *(gmcoord++)= *normalp++;
-  }
-  zinc_(Zdetsimplex);
-  area= qh_determinant (rows, dim, &nearzero);
-  if (toporient)
-    area= -area;
-  area *= qh AREAfactor;
-  trace4((qh ferr, "qh_facetarea_simplex: area=%2.2g for point p%d, toporient %d, nearzero? %d\n",
-	  area, qh_pointid(apex), toporient, nearzero));
-  return area;
-} /* facetarea_simplex */
-
-/*---------------------------------
-
-  qh_facetcenter( vertices )
-    return Voronoi center (Voronoi vertex) for a facet's vertices
-
-  returns:
-    return temporary point equal to the center
-
-  see:
-    qh_voronoi_center()
-*/
-pointT *qh_facetcenter (setT *vertices) {
-  setT *points= qh_settemp (qh_setsize (vertices));
-  vertexT *vertex, **vertexp;
-  pointT *center;
-
-  FOREACHvertex_(vertices)
-    qh_setappend (&points, vertex->point);
-  center= qh_voronoi_center (qh hull_dim-1, points);
-  qh_settempfree (&points);
-  return center;
-} /* facetcenter */
-
-/*---------------------------------
-
-  qh_findgooddist( point, facetA, dist, facetlist )
-    find best good facet visible for point from facetA
-    assumes facetA is visible from point
-
-  returns:
-    best facet, i.e., good facet that is furthest from point
-      distance to best facet
-      NULL if none
-
-    moves good, visible facets (and some other visible facets)
-      to end of qh facet_list
-
-  notes:
-    uses qh visit_id
-
-  design:
-    initialize bestfacet if facetA is good
-    move facetA to end of facetlist
-    for each facet on facetlist
-      for each unvisited neighbor of facet
-        move visible neighbors to end of facetlist
-        update best good neighbor
-        if no good neighbors, update best facet
-*/
-facetT *qh_findgooddist (pointT *point, facetT *facetA, realT *distp,
-               facetT **facetlist) {
-  realT bestdist= -REALmax, dist;
-  facetT *neighbor, **neighborp, *bestfacet=NULL, *facet;
-  boolT goodseen= False;
-
-  if (facetA->good) {
-    zinc_(Zcheckpart);  /* calls from check_bestdist occur after print stats */
-    qh_distplane (point, facetA, &bestdist);
-    bestfacet= facetA;
-    goodseen= True;
-  }
-  qh_removefacet (facetA);
-  qh_appendfacet (facetA);
-  *facetlist= facetA;
-  facetA->visitid= ++qh visit_id;
-  FORALLfacet_(*facetlist) {
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid == qh visit_id)
-        continue;
-      neighbor->visitid= qh visit_id;
-      if (goodseen && !neighbor->good)
-        continue;
-      zinc_(Zcheckpart);
-      qh_distplane (point, neighbor, &dist);
-      if (dist > 0) {
-        qh_removefacet (neighbor);
-        qh_appendfacet (neighbor);
-        if (neighbor->good) {
-          goodseen= True;
-          if (dist > bestdist) {
-            bestdist= dist;
-            bestfacet= neighbor;
-          }
-        }
-      }
-    }
-  }
-  if (bestfacet) {
-    *distp= bestdist;
-    trace2((qh ferr, "qh_findgooddist: p%d is %2.2g above good facet f%d\n",
-      qh_pointid(point), bestdist, bestfacet->id));
-    return bestfacet;
-  }
-  trace4((qh ferr, "qh_findgooddist: no good facet for p%d above f%d\n",
-      qh_pointid(point), facetA->id));
-  return NULL;
-}  /* findgooddist */
-
-/*---------------------------------
-
-  qh_getarea( facetlist )
-    set area of all facets in facetlist
-    collect statistics
-
-  returns:
-    sets qh totarea/totvol to total area and volume of convex hull
-    for Delaunay triangulation, computes projected area of the lower or upper hull
-      ignores upper hull if qh ATinfinity
-
-  notes:
-    could compute outer volume by expanding facet area by rays from interior
-    the following attempt at perpendicular projection underestimated badly:
-      qh.totoutvol += (-dist + facet->maxoutside + qh DISTround)
-                            * area/ qh hull_dim;
-  design:
-    for each facet on facetlist
-      compute facet->area
-      update qh.totarea and qh.totvol
-*/
-void qh_getarea (facetT *facetlist) {
-  realT area;
-  realT dist;
-  facetT *facet;
-
-  if (qh REPORTfreq)
-    fprintf (qh ferr, "computing area of each facet and volume of the convex hull\n");
-  else
-    trace1((qh ferr, "qh_getarea: computing volume and area for each facet\n"));
-  qh totarea= qh totvol= 0.0;
-  FORALLfacet_(facetlist) {
-    if (!facet->normal)
-      continue;
-    if (facet->upperdelaunay && qh ATinfinity)
-      continue;
-    facet->f.area= area= qh_facetarea (facet);
-    facet->isarea= True;
-    if (qh DELAUNAY) {
-      if (facet->upperdelaunay == qh UPPERdelaunay)
-	qh totarea += area;
-    }else {
-      qh totarea += area;
-      qh_distplane (qh interior_point, facet, &dist);
-      qh totvol += -dist * area/ qh hull_dim;
-    }
-    if (qh PRINTstatistics) {
-      wmax_(Wareamax, area);
-      wmin_(Wareamin, area);
-    }
-  }
-} /* getarea */
-
-/*---------------------------------
-
-  qh_gram_schmidt( dim, row )
-    implements Gram-Schmidt orthogonalization by rows
-
-  returns:
-    false if zero norm
-    overwrites rows[dim][dim]
-
-  notes:
-    see Golub & van Loan Algorithm 6.2-2
-    overflow due to small divisors not handled
-
-  design:
-    for each row
-      compute norm for row
-      if non-zero, normalize row
-      for each remaining rowA
-        compute inner product of row and rowA
-        reduce rowA by row * inner product
-*/
-boolT qh_gram_schmidt(int dim, realT **row) {
-  realT *rowi, *rowj, norm;
-  int i, j, k;
-
-  for(i=0; i < dim; i++) {
-    rowi= row[i];
-    for (norm= 0.0, k= dim; k--; rowi++)
-      norm += *rowi * *rowi;
-    norm= sqrt(norm);
-    wmin_(Wmindenom, norm);
-    if (norm == 0.0)  /* either 0 or overflow due to sqrt */
-      return False;
-    for(k= dim; k--; )
-      *(--rowi) /= norm;
-    for(j= i+1; j < dim; j++) {
-      rowj= row[j];
-      for(norm= 0.0, k=dim; k--; )
-	norm += *rowi++ * *rowj++;
-      for(k=dim; k--; )
-	*(--rowj) -= *(--rowi) * norm;
-    }
-  }
-  return True;
-} /* gram_schmidt */
-
-
-/*---------------------------------
-
-  qh_inthresholds( normal, angle )
-    return True if normal within qh.lower_/upper_threshold
-
-  returns:
-    estimate of angle by summing of threshold diffs
-      angle may be NULL
-      smaller "angle" is better
-
-  notes:
-    invalid if qh.SPLITthresholds
-
-  see:
-    qh.lower_threshold in qh_initbuild()
-    qh_initthresholds()
-
-  design:
-    for each dimension
-      test threshold
-*/
-boolT qh_inthresholds (coordT *normal, realT *angle) {
-  boolT within= True;
-  int k;
-  realT threshold;
-
-  if (angle)
-    *angle= 0.0;
-  for(k= 0; k < qh hull_dim; k++) {
-    threshold= qh lower_threshold[k];
-    if (threshold > -REALmax/2) {
-      if (normal[k] < threshold)
-        within= False;
-      if (angle) {
-	threshold -= normal[k];
-	*angle += fabs_(threshold);
-      }
-    }
-    if (qh upper_threshold[k] < REALmax/2) {
-      threshold= qh upper_threshold[k];
-      if (normal[k] > threshold)
-        within= False;
-      if (angle) {
-	threshold -= normal[k];
-	*angle += fabs_(threshold);
-      }
-    }
-  }
-  return within;
-} /* inthresholds */
-
-
-/*---------------------------------
-
-  qh_joggleinput()
-    randomly joggle input to Qhull by qh.JOGGLEmax
-    initial input is qh.first_point/qh.num_points of qh.hull_dim
-      repeated calls use qh.input_points/qh.num_points
-
-  returns:
-    joggles points at qh.first_point/qh.num_points
-    copies data to qh.input_points/qh.input_malloc if first time
-    determines qh.JOGGLEmax if it was zero
-    if qh.DELAUNAY
-      computes the Delaunay projection of the joggled points
-
-  notes:
-    if qh.DELAUNAY, unnecessarily joggles the last coordinate
-    the initial 'QJn' may be set larger than qh_JOGGLEmaxincrease
-
-  design:
-    if qh.DELAUNAY
-      set qh.SCALElast for reduced precision errors
-    if first call
-      initialize qh.input_points to the original input points
-      if qh.JOGGLEmax == 0
-        determine default qh.JOGGLEmax
-    else
-      increase qh.JOGGLEmax according to qh.build_cnt
-    joggle the input by adding a random number in [-qh.JOGGLEmax,qh.JOGGLEmax]
-    if qh.DELAUNAY
-      sets the Delaunay projection
-*/
-void qh_joggleinput (void) {
-  int size, i, seed;
-  coordT *coordp, *inputp;
-  realT randr, randa, randb;
-
-  if (!qh input_points) { /* first call */
-    qh input_points= qh first_point;
-    qh input_malloc= qh POINTSmalloc;
-    size= qh num_points * qh hull_dim * sizeof(coordT);
-    if (!(qh first_point=(coordT*)malloc(size))) {
-      fprintf(qh ferr, "qhull error: insufficient memory to joggle %d points\n",
-          qh num_points);
-      qh_errexit(qh_ERRmem, NULL, NULL);
-    }
-    qh POINTSmalloc= True;
-    if (qh JOGGLEmax == 0.0) {
-      qh JOGGLEmax= qh_detjoggle (qh input_points, qh num_points, qh hull_dim);
-      qh_option ("QJoggle", NULL, &qh JOGGLEmax);
-    }
-  }else {                 /* repeated call */
-    if (!qh RERUN && qh build_cnt > qh_JOGGLEretry) {
-      if (((qh build_cnt-qh_JOGGLEretry-1) % qh_JOGGLEagain) == 0) {
-	realT maxjoggle= qh MAXwidth * qh_JOGGLEmaxincrease;
-	if (qh JOGGLEmax < maxjoggle) {
-	  qh JOGGLEmax *= qh_JOGGLEincrease;
-	  minimize_(qh JOGGLEmax, maxjoggle);
-	}
-      }
-    }
-    qh_option ("QJoggle", NULL, &qh JOGGLEmax);
-  }
-  if (qh build_cnt > 1 && qh JOGGLEmax > fmax_(qh MAXwidth/4, 0.1)) {
-      fprintf (qh ferr, "qhull error: the current joggle for 'QJn', %.2g, is too large for the width\nof the input.  If possible, recompile Qhull with higher-precision reals.\n",
-	        qh JOGGLEmax);
-      qh_errexit (qh_ERRqhull, NULL, NULL);
-  }
-  /* for some reason, using qh ROTATErandom and qh_RANDOMseed does not repeat the run. Use 'TRn' instead */
-  seed= qh_RANDOMint;
-  qh_option ("_joggle-seed", &seed, NULL);
-  trace0((qh ferr, "qh_joggleinput: joggle input by %2.2g with seed %d\n",
-    qh JOGGLEmax, seed));
-  inputp= qh input_points;
-  coordp= qh first_point;
-  randa= 2.0 * qh JOGGLEmax/qh_RANDOMmax;
-  randb= -qh JOGGLEmax;
-  size= qh num_points * qh hull_dim;
-  for (i= size; i--; ) {
-    randr= qh_RANDOMint;
-    *(coordp++)= *(inputp++) + (randr * randa + randb);
-  }
-  if (qh DELAUNAY) {
-    qh last_low= qh last_high= qh last_newhigh= REALmax;
-    qh_setdelaunay (qh hull_dim, qh num_points, qh first_point);
-  }
-} /* joggleinput */
-
-/*---------------------------------
-
-  qh_maxabsval( normal, dim )
-    return pointer to maximum absolute value of a dim vector
-    returns NULL if dim=0
-*/
-realT *qh_maxabsval (realT *normal, int dim) {
-  realT maxval= -REALmax;
-  realT *maxp= NULL, *colp, absval;
-  int k;
-
-  for (k= dim, colp= normal; k--; colp++) {
-    absval= fabs_(*colp);
-    if (absval > maxval) {
-      maxval= absval;
-      maxp= colp;
-    }
-  }
-  return maxp;
-} /* maxabsval */
-
-
-/*---------------------------------
-
-  qh_maxmin( points, numpoints, dimension )
-    return max/min points for each dimension
-    determine max and min coordinates
-
-  returns:
-    returns a temporary set of max and min points
-      may include duplicate points. Does not include qh.GOODpoint
-    sets qh.NEARzero, qh.MAXabs_coord, qh.MAXsumcoord, qh.MAXwidth
-         qh.MAXlastcoord, qh.MINlastcoord
-    initializes qh.max_outside, qh.min_vertex, qh.WAScoplanar, qh.ZEROall_ok
-
-  notes:
-    loop duplicated in qh_detjoggle()
-
-  design:
-    initialize global precision variables
-    checks definition of REAL...
-    for each dimension
-      for each point
-        collect maximum and minimum point
-      collect maximum of maximums and minimum of minimums
-      determine qh.NEARzero for Gaussian Elimination
-*/
-setT *qh_maxmin(pointT *points, int numpoints, int dimension) {
-  int k;
-  realT maxcoord, temp;
-  pointT *minimum, *maximum, *point, *pointtemp;
-  setT *set;
-
-  qh max_outside= 0.0;
-  qh MAXabs_coord= 0.0;
-  qh MAXwidth= -REALmax;
-  qh MAXsumcoord= 0.0;
-  qh min_vertex= 0.0;
-  qh WAScoplanar= False;
-  if (qh ZEROcentrum)
-    qh ZEROall_ok= True;
-  if (REALmin < REALepsilon && REALmin < REALmax && REALmin > -REALmax
-  && REALmax > 0.0 && -REALmax < 0.0)
-    ; /* all ok */
-  else {
-    fprintf (qh ferr, "qhull error: floating point constants in user.h are wrong\n\
-REALepsilon %g REALmin %g REALmax %g -REALmax %g\n",
-	     REALepsilon, REALmin, REALmax, -REALmax);
-    qh_errexit (qh_ERRinput, NULL, NULL);
-  }
-  set= qh_settemp(2*dimension);
-  for(k= 0; k < dimension; k++) {
-    if (points == qh GOODpointp)
-      minimum= maximum= points + dimension;
-    else
-      minimum= maximum= points;
-    FORALLpoint_(points, numpoints) {
-      if (point == qh GOODpointp)
-	continue;
-      if (maximum[k] < point[k])
-	maximum= point;
-      else if (minimum[k] > point[k])
-	minimum= point;
-    }
-    if (k == dimension-1) {
-      qh MINlastcoord= minimum[k];
-      qh MAXlastcoord= maximum[k];
-    }
-    if (qh SCALElast && k == dimension-1)
-      maxcoord= qh MAXwidth;
-    else {
-      maxcoord= fmax_(maximum[k], -minimum[k]);
-      if (qh GOODpointp) {
-        temp= fmax_(qh GOODpointp[k], -qh GOODpointp[k]);
-        maximize_(maxcoord, temp);
-      }
-      temp= maximum[k] - minimum[k];
-      maximize_(qh MAXwidth, temp);
-    }
-    maximize_(qh MAXabs_coord, maxcoord);
-    qh MAXsumcoord += maxcoord;
-    qh_setappend (&set, maximum);
-    qh_setappend (&set, minimum);
-    /* calculation of qh NEARzero is based on error formula 4.4-13 of
-       Golub & van Loan, authors say n^3 can be ignored and 10 be used in
-       place of rho */
-    qh NEARzero[k]= 80 * qh MAXsumcoord * REALepsilon;
-  }
-  if (qh IStracing >=1)
-    qh_printpoints (qh ferr, "qh_maxmin: found the max and min points (by dim):", set);
-  return(set);
-} /* maxmin */
-
-/*---------------------------------
-
-  qh_maxouter()
-    return maximum distance from facet to outer plane
-    normally this is qh.max_outside+qh.DISTround
-    does not include qh.JOGGLEmax
-
-  see:
-    qh_outerinner()
-
-  notes:
-    need to add another qh.DISTround if testing actual point with computation
-
-  for joggle:
-    qh_setfacetplane() updated qh.max_outer for Wnewvertexmax (max distance to vertex)
-    need to use Wnewvertexmax since could have a coplanar point for a high
-      facet that is replaced by a low facet
-    need to add qh.JOGGLEmax if testing input points
-*/
-realT qh_maxouter (void) {
-  realT dist;
-
-  dist= fmax_(qh max_outside, qh DISTround);
-  dist += qh DISTround;
-  trace4((qh ferr, "qh_maxouter: max distance from facet to outer plane is %2.2g max_outside is %2.2g\n", dist, qh max_outside));
-  return dist;
-} /* maxouter */
-
-/*---------------------------------
-
-  qh_maxsimplex( dim, maxpoints, points, numpoints, simplex )
-    determines maximum simplex for a set of points
-    starts from points already in simplex
-    skips qh.GOODpointp (assumes that it isn't in maxpoints)
-
-  returns:
-    simplex with dim+1 points
-
-  notes:
-    assumes at least pointsneeded points in points
-    maximizes determinate for x,y,z,w, etc.
-    uses maxpoints as long as determinate is clearly non-zero
-
-  design:
-    initialize simplex with at least two points
-      (find points with max or min x coordinate)
-    for each remaining dimension
-      add point that maximizes the determinate
-        (use points from maxpoints first)
-*/
-void qh_maxsimplex (int dim, setT *maxpoints, pointT *points, int numpoints, setT **simplex) {
-  pointT *point, **pointp, *pointtemp, *maxpoint, *minx=NULL, *maxx=NULL;
-  boolT nearzero, maxnearzero= False;
-  int k, sizinit;
-  realT maxdet= -REALmax, det, mincoord= REALmax, maxcoord= -REALmax;
-
-  sizinit= qh_setsize (*simplex);
-  if (sizinit < 2) {
-    if (qh_setsize (maxpoints) >= 2) {
-      FOREACHpoint_(maxpoints) {
-        if (maxcoord < point[0]) {
-          maxcoord= point[0];
-          maxx= point;
-        }
-	if (mincoord > point[0]) {
-          mincoord= point[0];
-          minx= point;
-        }
-      }
-    }else {
-      FORALLpoint_(points, numpoints) {
-	if (point == qh GOODpointp)
-	  continue;
-        if (maxcoord < point[0]) {
-	  maxcoord= point[0];
-          maxx= point;
-        }
-	if (mincoord > point[0]) {
-          mincoord= point[0];
-          minx= point;
-	}
-      }
-    }
-    qh_setunique (simplex, minx);
-    if (qh_setsize (*simplex) < 2)
-      qh_setunique (simplex, maxx);
-    sizinit= qh_setsize (*simplex);
-    if (sizinit < 2) {
-      qh_precision ("input has same x coordinate");
-      if (zzval_(Zsetplane) > qh hull_dim+1) {
-	fprintf (qh ferr, "qhull precision error (qh_maxsimplex for voronoi_center):\n%d points with the same x coordinate.\n",
-		 qh_setsize(maxpoints)+numpoints);
-	qh_errexit (qh_ERRprec, NULL, NULL);
-      }else {
-	fprintf (qh ferr, "qhull input error: input is less than %d-dimensional since it has the same x coordinate\n", qh hull_dim);
-	qh_errexit (qh_ERRinput, NULL, NULL);
-      }
-    }
-  }
-  for(k= sizinit; k < dim+1; k++) {
-    maxpoint= NULL;
-    maxdet= -REALmax;
-    FOREACHpoint_(maxpoints) {
-      if (!qh_setin (*simplex, point)) {
-        det= qh_detsimplex(point, *simplex, k, &nearzero);
-        if ((det= fabs_(det)) > maxdet) {
-	  maxdet= det;
-          maxpoint= point;
-	  maxnearzero= nearzero;
-        }
-      }
-    }
-    if (!maxpoint || maxnearzero) {
-      zinc_(Zsearchpoints);
-      if (!maxpoint) {
-        trace0((qh ferr, "qh_maxsimplex: searching all points for %d-th initial vertex.\n", k+1));
-      }else {
-        trace0((qh ferr, "qh_maxsimplex: searching all points for %d-th initial vertex, better than p%d det %2.2g\n",
-		k+1, qh_pointid(maxpoint), maxdet));
-      }
-      FORALLpoint_(points, numpoints) {
-	if (point == qh GOODpointp)
-	  continue;
-        if (!qh_setin (*simplex, point)) {
-          det= qh_detsimplex(point, *simplex, k, &nearzero);
-          if ((det= fabs_(det)) > maxdet) {
-	    maxdet= det;
-            maxpoint= point;
-	    maxnearzero= nearzero;
-	  }
-        }
-      }
-    } /* !maxpoint */
-    if (!maxpoint) {
-      fprintf (qh ferr, "qhull internal error (qh_maxsimplex): not enough points available\n");
-      qh_errexit (qh_ERRqhull, NULL, NULL);
-    }
-    qh_setappend(simplex, maxpoint);
-    trace1((qh ferr, "qh_maxsimplex: selected point p%d for %d`th initial vertex, det=%2.2g\n",
-	    qh_pointid(maxpoint), k+1, maxdet));
-  } /* k */
-} /* maxsimplex */
-
-/*---------------------------------
-
-  qh_minabsval( normal, dim )
-    return minimum absolute value of a dim vector
-*/
-realT qh_minabsval (realT *normal, int dim) {
-  realT minval= 0;
-  realT maxval= 0;
-  realT *colp;
-  int k;
-
-  for (k= dim, colp= normal; k--; colp++) {
-    maximize_(maxval, *colp);
-    minimize_(minval, *colp);
-  }
-  return fmax_(maxval, -minval);
-} /* minabsval */
-
-
-/*---------------------------------
-
-  qh_mindif( vecA, vecB, dim )
-    return index of min abs. difference of two vectors
-*/
-int qh_mindiff (realT *vecA, realT *vecB, int dim) {
-  realT mindiff= REALmax, diff;
-  realT *vecAp= vecA, *vecBp= vecB;
-  int k, mink= 0;
-
-  for (k= 0; k < dim; k++) {
-    diff= *vecAp++ - *vecBp++;
-    diff= fabs_(diff);
-    if (diff < mindiff) {
-      mindiff= diff;
-      mink= k;
-    }
-  }
-  return mink;
-} /* mindiff */
-
-
-
-/*---------------------------------
-
-  qh_orientoutside( facet  )
-    make facet outside oriented via qh.interior_point
-
-  returns:
-    True if facet reversed orientation.
-*/
-boolT qh_orientoutside (facetT *facet) {
-  int k;
-  realT dist;
-
-  qh_distplane (qh interior_point, facet, &dist);
-  if (dist > 0) {
-    for (k= qh hull_dim; k--; )
-      facet->normal[k]= -facet->normal[k];
-    facet->offset= -facet->offset;
-    return True;
-  }
-  return False;
-} /* orientoutside */
-
-/*---------------------------------
-
-  qh_outerinner( facet, outerplane, innerplane  )
-    if facet and qh.maxoutdone (i.e., qh_check_maxout)
-      returns outer and inner plane for facet
-    else
-      returns maximum outer and inner plane
-    accounts for qh.JOGGLEmax
-
-  see:
-    qh_maxouter(), qh_check_bestdist(), qh_check_points()
-
-  notes:
-    outerplaner or innerplane may be NULL
-
-    includes qh.DISTround for actual points
-    adds another qh.DISTround if testing with floating point arithmetic
-*/
-void qh_outerinner (facetT *facet, realT *outerplane, realT *innerplane) {
-  realT dist, mindist;
-  vertexT *vertex, **vertexp;
-
-  if (outerplane) {
-    if (!qh_MAXoutside || !facet || !qh maxoutdone) {
-      *outerplane= qh_maxouter();       /* includes qh.DISTround */
-    }else { /* qh_MAXoutside ... */
-#if qh_MAXoutside
-      *outerplane= facet->maxoutside + qh DISTround;
-#endif
-
-    }
-    if (qh JOGGLEmax < REALmax/2)
-      *outerplane += qh JOGGLEmax * sqrt (qh hull_dim);
-  }
-  if (innerplane) {
-    if (facet) {
-      mindist= REALmax;
-      FOREACHvertex_(facet->vertices) {
-        zinc_(Zdistio);
-        qh_distplane (vertex->point, facet, &dist);
-        minimize_(mindist, dist);
-      }
-      *innerplane= mindist - qh DISTround;
-    }else
-      *innerplane= qh min_vertex - qh DISTround;
-    if (qh JOGGLEmax < REALmax/2)
-      *innerplane -= qh JOGGLEmax * sqrt (qh hull_dim);
-  }
-} /* outerinner */
-
-/*---------------------------------
-
-  qh_pointdist( point1, point2, dim )
-    return distance between two points
-
-  notes:
-    returns distance squared if 'dim' is negative
-*/
-coordT qh_pointdist(pointT *point1, pointT *point2, int dim) {
-  coordT dist, diff;
-  int k;
-
-  dist= 0.0;
-  for (k= (dim > 0 ? dim : -dim); k--; ) {
-    diff= *point1++ - *point2++;
-    dist += diff * diff;
-  }
-  if (dim > 0)
-    return(sqrt(dist));
-  return dist;
-} /* pointdist */
-
-
-/*---------------------------------
-
-  qh_printmatrix( fp, string, rows, numrow, numcol )
-    print matrix to fp given by row vectors
-
-  notes:
-    print a vector by qh_printmatrix(fp, "", &vect, 1, len)
-*/
-void qh_printmatrix (FILE *fp, char *string, realT **rows, int numrow, int numcol) {
-  realT *rowp;
-  realT r; /*bug fix*/
-  int i,k;
-
-  fprintf (fp, "%s\n", string);
-  for (i= 0; i < numrow; i++) {
-    rowp= rows[i];
-    for (k= 0; k < numcol; k++) {
-      r= *rowp++;
-      fprintf (fp, "%6.3g ", r);
-    }
-    fprintf (fp, "\n");
-  }
-} /* printmatrix */
-
-
-/*---------------------------------
-
-  qh_printpoints( fp, string, points )
-    print pointids to fp for a set of points
-    if string, prints string and 'p' point ids
-*/
-void qh_printpoints (FILE *fp, char *string, setT *points) {
-  pointT *point, **pointp;
-
-  if (string) {
-    fprintf (fp, "%s", string);
-    FOREACHpoint_(points)
-      fprintf (fp, " p%d", qh_pointid(point));
-    fprintf (fp, "\n");
-  }else {
-    FOREACHpoint_(points)
-      fprintf (fp, " %d", qh_pointid(point));
-    fprintf (fp, "\n");
-  }
-} /* printpoints */
-
-
-/*---------------------------------
-
-  qh_projectinput()
-    project input points using qh.lower_bound/upper_bound and qh DELAUNAY
-    if qh.lower_bound[k]=qh.upper_bound[k]= 0,
-      removes dimension k
-    if halfspace intersection
-      removes dimension k from qh.feasible_point
-    input points in qh first_point, num_points, input_dim
-
-  returns:
-    new point array in qh first_point of qh hull_dim coordinates
-    sets qh POINTSmalloc
-    if qh DELAUNAY
-      projects points to paraboloid
-      lowbound/highbound is also projected
-    if qh ATinfinity
-    if qh POINTSmalloc
-      frees old point array
-
-  notes:
-    checks that qh.hull_dim agrees with qh.input_dim, PROJECTinput, and DELAUNAY
-
-
-  design:
-    sets project[k] to -1 (delete), 0 (keep), 1 (add for Delaunay)
-    determines newdim and newnum for qh hull_dim and qh num_points
-    projects points to newpoints
-    projects qh.lower_bound to itself
-    projects qh.upper_bound to itself
-    if qh DELAUNAY
-      if qh ATINFINITY
-        projects points to paraboloid
-        computes "infinity" point as vertex average and 10% above all points
-      else
-        uses qh_setdelaunay to project points to paraboloid
-*/
-void qh_projectinput (void) {
-  int k,i;
-  int newdim= qh input_dim, newnum= qh num_points;
-  signed char *project;
-  int size= (qh input_dim+1)*sizeof(*project);
-  pointT *newpoints, *coord, *infinity;
-  realT paraboloid, maxboloid= 0;
-
-  project= (signed char*)qh_memalloc (size);
-  memset ((char*)project, 0, size);
-  for (k= 0; k < qh input_dim; k++) {   /* skip Delaunay bound */
-    if (qh lower_bound[k] == 0 && qh upper_bound[k] == 0) {
-      project[k]= -1;
-      newdim--;
-    }
-  }
-  if (qh DELAUNAY) {
-    project[k]= 1;
-    newdim++;
-    if (qh ATinfinity)
-      newnum++;
-  }
-  if (newdim != qh hull_dim) {
-    fprintf(qh ferr, "qhull internal error (qh_projectinput): dimension after projection %d != hull_dim %d\n", newdim, qh hull_dim);
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-  if (!(newpoints=(coordT*)malloc(newnum*newdim*sizeof(coordT)))){
-    fprintf(qh ferr, "qhull error: insufficient memory to project %d points\n",
-           qh num_points);
-    qh_errexit(qh_ERRmem, NULL, NULL);
-  }
-  qh_projectpoints (project, qh input_dim+1, qh first_point,
-                    qh num_points, qh input_dim, newpoints, newdim);
-  trace1((qh ferr, "qh_projectinput: updating lower and upper_bound\n"));
-  qh_projectpoints (project, qh input_dim+1, qh lower_bound,
-                    1, qh input_dim+1, qh lower_bound, newdim+1);
-  qh_projectpoints (project, qh input_dim+1, qh upper_bound,
-                    1, qh input_dim+1, qh upper_bound, newdim+1);
-  if (qh HALFspace) {
-    if (!qh feasible_point) {
-      fprintf(qh ferr, "qhull internal error (qh_projectinput): HALFspace defined without qh.feasible_point\n");
-      qh_errexit(qh_ERRqhull, NULL, NULL);
-    }
-    qh_projectpoints (project, qh input_dim, qh feasible_point,
-		      1, qh input_dim, qh feasible_point, newdim);
-  }
-  qh_memfree(project, ((qh input_dim+1)*sizeof(*project)));
-  if (qh POINTSmalloc)
-    free (qh first_point);
-  qh first_point= newpoints;
-  qh POINTSmalloc= True;
-  if (qh DELAUNAY && qh ATinfinity) {
-    coord= qh first_point;
-    infinity= qh first_point + qh hull_dim * qh num_points;
-    for (k=qh hull_dim-1; k--; )
-      infinity[k]= 0.0;
-    for (i=qh num_points; i--; ) {
-      paraboloid= 0.0;
-      for (k=qh hull_dim-1; k--; ) {
-        paraboloid += *coord * *coord;
-	infinity[k] += *coord;
-        coord++;
-      }
-      *(coord++)= paraboloid;
-      maximize_(maxboloid, paraboloid);
-    }
-    /* coord == infinity */
-    for (k=qh hull_dim-1; k--; )
-      *(coord++) /= qh num_points;
-    *(coord++)= maxboloid * 1.1;
-    qh num_points++;
-    trace0((qh ferr, "qh_projectinput: projected points to paraboloid for Delaunay\n"));
-  }else if (qh DELAUNAY)  /* !qh ATinfinity */
-    qh_setdelaunay( qh hull_dim, qh num_points, qh first_point);
-} /* projectinput */
-
-
-/*---------------------------------
-
-  qh_projectpoints( project, n, points, numpoints, dim, newpoints, newdim )
-    project points/numpoints/dim to newpoints/newdim
-    if project[k] == -1
-      delete dimension k
-    if project[k] == 1
-      add dimension k by duplicating previous column
-    n is size of project
-
-  notes:
-    newpoints may be points if only adding dimension at end
-
-  design:
-    check that 'project' and 'newdim' agree
-    for each dimension
-      if project == -1
-        skip dimension
-      else
-        determine start of column in newpoints
-        determine start of column in points
-          if project == +1, duplicate previous column
-        copy dimension (column) from points to newpoints
-*/
-void qh_projectpoints (signed char *project, int n, realT *points,
-        int numpoints, int dim, realT *newpoints, int newdim) {
-  int testdim= dim, oldk=0, newk=0, i,j=0,k;
-  realT *newp, *oldp;
-
-  for (k= 0; k < n; k++)
-    testdim += project[k];
-  if (testdim != newdim) {
-    fprintf (qh ferr, "qhull internal error (qh_projectpoints): newdim %d should be %d after projection\n",
-      newdim, testdim);
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }
-  for (j= 0; j= dim)
-	  continue;
-	oldp= points+oldk;
-      }else
-	oldp= points+oldk++;
-      for (i=numpoints; i--; ) {
-        *newp= *oldp;
-        newp += newdim;
-        oldp += dim;
-      }
-    }
-    if (oldk >= dim)
-      break;
-  }
-  trace1((qh ferr, "qh_projectpoints: projected %d points from dim %d to dim %d\n",
-    numpoints, dim, newdim));
-} /* projectpoints */
-
-
-/*---------------------------------
-
-  qh_rand()
-  qh_srand( seed )
-    generate pseudo-random number between 1 and 2^31 -2
-
-  notes:
-    from Park & Miller's minimimal standard random number generator
-       Communications of the ACM, 31:1192-1201, 1988.
-    does not use 0 or 2^31 -1
-       this is silently enforced by qh_srand()
-    can make 'Rn' much faster by moving qh_rand to qh_distplane
-*/
-int qh_rand_seed= 1;  /* define as global variable instead of using qh */
-
-int qh_rand( void) {
-#define qh_rand_a 16807
-#define qh_rand_m 2147483647
-#define qh_rand_q 127773  /* m div a */
-#define qh_rand_r 2836    /* m mod a */
-  int lo, hi, test;
-  int seed = qh_rand_seed;
-
-  hi = seed / qh_rand_q;  /* seed div q */
-  lo = seed % qh_rand_q;  /* seed mod q */
-  test = qh_rand_a * lo - qh_rand_r * hi;
-  if (test > 0)
-    seed= test;
-  else
-    seed= test + qh_rand_m;
-  qh_rand_seed= seed;
-  /* seed = seed < qh_RANDOMmax/2 ? 0 : qh_RANDOMmax;  for testing */
-  /* seed = qh_RANDOMmax;  for testing */
-  return seed;
-} /* rand */
-
-void qh_srand( int seed) {
-  if (seed < 1)
-    qh_rand_seed= 1;
-  else if (seed >= qh_rand_m)
-    qh_rand_seed= qh_rand_m - 1;
-  else
-    qh_rand_seed= seed;
-} /* qh_srand */
-
-/*---------------------------------
-
-  qh_randomfactor()
-    return a random factor within qh.RANDOMmax of 1.0
-
-  notes:
-    qh.RANDOMa/b are defined in global.c
-*/
-realT qh_randomfactor (void) {
-  realT randr;
-
-  randr= qh_RANDOMint;
-  return randr * qh RANDOMa + qh RANDOMb;
-} /* randomfactor */
-
-/*---------------------------------
-
-  qh_randommatrix( buffer, dim, rows )
-    generate a random dim X dim matrix in range [-1,1]
-    assumes buffer is [dim+1, dim]
-
-  returns:
-    sets buffer to random numbers
-    sets rows to rows of buffer
-      sets row[dim] as scratch row
-*/
-void qh_randommatrix (realT *buffer, int dim, realT **rows) {
-  int i, k;
-  realT **rowi, *coord, realr;
-
-  coord= buffer;
-  rowi= rows;
-  for (i=0; i < dim; i++) {
-    *(rowi++)= coord;
-    for (k=0; k < dim; k++) {
-      realr= qh_RANDOMint;
-      *(coord++)= 2.0 * realr/(qh_RANDOMmax+1) - 1.0;
-    }
-  }
-  *rowi= coord;
-} /* randommatrix */
-
-
-/*---------------------------------
-
-  qh_rotateinput( rows )
-    rotate input using row matrix
-    input points given by qh first_point, num_points, hull_dim
-    assumes rows[dim] is a scratch buffer
-    if qh POINTSmalloc, overwrites input points, else mallocs a new array
-
-  returns:
-    rotated input
-    sets qh POINTSmalloc
-
-  design:
-    see qh_rotatepoints
-*/
-void qh_rotateinput (realT **rows) {
-
-  if (!qh POINTSmalloc) {
-    qh first_point= qh_copypoints (qh first_point, qh num_points, qh hull_dim);
-    qh POINTSmalloc= True;
-  }
-  qh_rotatepoints (qh first_point, qh num_points, qh hull_dim, rows);
-}  /* rotateinput */
-
-/*---------------------------------
-
-  qh_rotatepoints( points, numpoints, dim, row )
-    rotate numpoints points by a d-dim row matrix
-    assumes rows[dim] is a scratch buffer
-
-  returns:
-    rotated points in place
-
-  design:
-    for each point
-      for each coordinate
-        use row[dim] to compute partial inner product
-      for each coordinate
-        rotate by partial inner product
-*/
-void qh_rotatepoints (realT *points, int numpoints, int dim, realT **row) {
-  realT *point, *rowi, *coord= NULL, sum, *newval;
-  int i,j,k;
-
-  if (qh IStracing >= 1)
-    qh_printmatrix (qh ferr, "qh_rotatepoints: rotate points by", row, dim, dim);
-  for (point= points, j= numpoints; j--; point += dim) {
-    newval= row[dim];
-    for (i= 0; i < dim; i++) {
-      rowi= row[i];
-      coord= point;
-      for (sum= 0.0, k= dim; k--; )
-        sum += *rowi++ * *coord++;
-      *(newval++)= sum;
-    }
-    for (k= dim; k--; )
-      *(--coord)= *(--newval);
-  }
-} /* rotatepoints */
-
-
-/*---------------------------------
-
-  qh_scaleinput()
-    scale input points using qh low_bound/high_bound
-    input points given by qh first_point, num_points, hull_dim
-    if qh POINTSmalloc, overwrites input points, else mallocs a new array
-
-  returns:
-    scales coordinates of points to low_bound[k], high_bound[k]
-    sets qh POINTSmalloc
-
-  design:
-    see qh_scalepoints
-*/
-void qh_scaleinput (void) {
-
-  if (!qh POINTSmalloc) {
-    qh first_point= qh_copypoints (qh first_point, qh num_points, qh hull_dim);
-    qh POINTSmalloc= True;
-  }
-  qh_scalepoints (qh first_point, qh num_points, qh hull_dim,
-       qh lower_bound, qh upper_bound);
-}  /* scaleinput */
-
-/*---------------------------------
-
-  qh_scalelast( points, numpoints, dim, low, high, newhigh )
-    scale last coordinate to [0,m] for Delaunay triangulations
-    input points given by points, numpoints, dim
-
-  returns:
-    changes scale of last coordinate from [low, high] to [0, newhigh]
-    overwrites last coordinate of each point
-    saves low/high/newhigh in qh.last_low, etc. for qh_setdelaunay()
-
-  notes:
-    when called by qh_setdelaunay, low/high may not match actual data
-
-  design:
-    compute scale and shift factors
-    apply to last coordinate of each point
-*/
-void qh_scalelast (coordT *points, int numpoints, int dim, coordT low,
-		   coordT high, coordT newhigh) {
-  realT scale, shift;
-  coordT *coord;
-  int i;
-  boolT nearzero= False;
-
-  trace4((qh ferr, "qh_scalelast: scale last coordinate from [%2.2g, %2.2g] to [0,%2.2g]\n",
-    low, high, newhigh));
-  qh last_low= low;
-  qh last_high= high;
-  qh last_newhigh= newhigh;
-  scale= qh_divzero (newhigh, high - low,
-                  qh MINdenom_1, &nearzero);
-  if (nearzero) {
-    if (qh DELAUNAY)
-      fprintf (qh ferr, "qhull input error: can not scale last coordinate.  Input is cocircular\n   or cospherical.   Use option 'Qz' to add a point at infinity.\n");
-    else
-      fprintf (qh ferr, "qhull input error: can not scale last coordinate.  New bounds [0, %2.2g] are too wide for\nexisting bounds [%2.2g, %2.2g] (width %2.2g)\n",
-		newhigh, low, high, high-low);
-    qh_errexit (qh_ERRinput, NULL, NULL);
-  }
-  shift= - low * newhigh / (high-low);
-  coord= points + dim - 1;
-  for (i= numpoints; i--; coord += dim)
-    *coord= *coord * scale + shift;
-} /* scalelast */
-
-/*---------------------------------
-
-  qh_scalepoints( points, numpoints, dim, newlows, newhighs )
-    scale points to new lowbound and highbound
-    retains old bound when newlow= -REALmax or newhigh= +REALmax
-
-  returns:
-    scaled points
-    overwrites old points
-
-  design:
-    for each coordinate
-      compute current low and high bound
-      compute scale and shift factors
-      scale all points
-      enforce new low and high bound for all points
-*/
-void qh_scalepoints (pointT *points, int numpoints, int dim,
-	realT *newlows, realT *newhighs) {
-  int i,k;
-  realT shift, scale, *coord, low, high, newlow, newhigh, mincoord, maxcoord;
-  boolT nearzero= False;
-
-  for (k= 0; k < dim; k++) {
-    newhigh= newhighs[k];
-    newlow= newlows[k];
-    if (newhigh > REALmax/2 && newlow < -REALmax/2)
-      continue;
-    low= REALmax;
-    high= -REALmax;
-    for (i= numpoints, coord= points+k; i--; coord += dim) {
-      minimize_(low, *coord);
-      maximize_(high, *coord);
-    }
-    if (newhigh > REALmax/2)
-      newhigh= high;
-    if (newlow < -REALmax/2)
-      newlow= low;
-    if (qh DELAUNAY && k == dim-1 && newhigh < newlow) {
-      fprintf (qh ferr, "qhull input error: 'Qb%d' or 'QB%d' inverts paraboloid since high bound %.2g < low bound %.2g\n",
-	       k, k, newhigh, newlow);
-      qh_errexit (qh_ERRinput, NULL, NULL);
-    }
-    scale= qh_divzero (newhigh - newlow, high - low,
-                  qh MINdenom_1, &nearzero);
-    if (nearzero) {
-      fprintf (qh ferr, "qhull input error: %d'th dimension's new bounds [%2.2g, %2.2g] too wide for\nexisting bounds [%2.2g, %2.2g]\n",
-              k, newlow, newhigh, low, high);
-      qh_errexit (qh_ERRinput, NULL, NULL);
-    }
-    shift= (newlow * high - low * newhigh)/(high-low);
-    coord= points+k;
-    for (i= numpoints; i--; coord += dim)
-      *coord= *coord * scale + shift;
-    coord= points+k;
-    if (newlow < newhigh) {
-      mincoord= newlow;
-      maxcoord= newhigh;
-    }else {
-      mincoord= newhigh;
-      maxcoord= newlow;
-    }
-    for (i= numpoints; i--; coord += dim) {
-      minimize_(*coord, maxcoord);  /* because of roundoff error */
-      maximize_(*coord, mincoord);
-    }
-    trace0((qh ferr, "qh_scalepoints: scaled %d'th coordinate [%2.2g, %2.2g] to [%.2g, %.2g] for %d points by %2.2g and shifted %2.2g\n",
-      k, low, high, newlow, newhigh, numpoints, scale, shift));
-  }
-} /* scalepoints */
-
-
-/*---------------------------------
-
-  qh_setdelaunay( dim, count, points )
-    project count points to dim-d paraboloid for Delaunay triangulation
-
-    dim is one more than the dimension of the input set
-    assumes dim is at least 3 (i.e., at least a 2-d Delaunay triangulation)
-
-    points is a dim*count realT array.  The first dim-1 coordinates
-    are the coordinates of the first input point.  array[dim] is
-    the first coordinate of the second input point.  array[2*dim] is
-    the first coordinate of the third input point.
-
-    if qh.last_low defined (i.e., 'Qbb' called qh_scalelast)
-      calls qh_scalelast to scale the last coordinate the same as the other points
-
-  returns:
-    for each point
-      sets point[dim-1] to sum of squares of coordinates
-    scale points to 'Qbb' if needed
-
-  notes:
-    to project one point, use
-      qh_setdelaunay (qh hull_dim, 1, point)
-
-    Do not use options 'Qbk', 'QBk', or 'QbB' since they scale
-    the coordinates after the original projection.
-
-*/
-void qh_setdelaunay (int dim, int count, pointT *points) {
-  int i, k;
-  coordT *coordp, coord;
-  realT paraboloid;
-
-  trace0((qh ferr, "qh_setdelaunay: project %d points to paraboloid for Delaunay triangulation\n", count));
-  coordp= points;
-  for (i= 0; i < count; i++) {
-    coord= *coordp++;
-    paraboloid= coord*coord;
-    for (k= dim-2; k--; ) {
-      coord= *coordp++;
-      paraboloid += coord*coord;
-    }
-    *coordp++ = paraboloid;
-  }
-  if (qh last_low < REALmax/2)
-    qh_scalelast (points, count, dim, qh last_low, qh last_high, qh last_newhigh);
-} /* setdelaunay */
-
-
-/*---------------------------------
-
-  qh_sethalfspace( dim, coords, nextp, normal, offset, feasible )
-    set point to dual of halfspace relative to feasible point
-    halfspace is normal coefficients and offset.
-
-  returns:
-    false if feasible point is outside of hull (error message already reported)
-    overwrites coordinates for point at dim coords
-    nextp= next point (coords)
-
-  design:
-    compute distance from feasible point to halfspace
-    divide each normal coefficient by -dist
-*/
-boolT qh_sethalfspace (int dim, coordT *coords, coordT **nextp,
-         coordT *normal, coordT *offset, coordT *feasible) {
-  coordT *normp= normal, *feasiblep= feasible, *coordp= coords;
-  realT dist;
-  realT r; /*bug fix*/
-  int k;
-  boolT zerodiv;
-
-  dist= *offset;
-  for (k= dim; k--; )
-    dist += *(normp++) * *(feasiblep++);
-  if (dist > 0)
-    goto LABELerroroutside;
-  normp= normal;
-  if (dist < -qh MINdenom) {
-    for (k= dim; k--; )
-      *(coordp++)= *(normp++) / -dist;
-  }else {
-    for (k= dim; k--; ) {
-      *(coordp++)= qh_divzero (*(normp++), -dist, qh MINdenom_1, &zerodiv);
-      if (zerodiv)
-        goto LABELerroroutside;
-    }
-  }
-  *nextp= coordp;
-  if (qh IStracing >= 4) {
-    fprintf (qh ferr, "qh_sethalfspace: halfspace at offset %6.2g to point: ", *offset);
-    for (k= dim, coordp= coords; k--; ) {
-      r= *coordp++;
-      fprintf (qh ferr, " %6.2g", r);
-    }
-    fprintf (qh ferr, "\n");
-  }
-  return True;
-LABELerroroutside:
-  feasiblep= feasible;
-  normp= normal;
-  fprintf(qh ferr, "qhull input error: feasible point is not clearly inside halfspace\nfeasible point: ");
-  for (k= dim; k--; )
-    fprintf (qh ferr, qh_REAL_1, r=*(feasiblep++));
-  fprintf (qh ferr, "\n     halfspace: ");
-  for (k= dim; k--; )
-    fprintf (qh ferr, qh_REAL_1, r=*(normp++));
-  fprintf (qh ferr, "\n     at offset: ");
-  fprintf (qh ferr, qh_REAL_1, *offset);
-  fprintf (qh ferr, " and distance: ");
-  fprintf (qh ferr, qh_REAL_1, dist);
-  fprintf (qh ferr, "\n");
-  return False;
-} /* sethalfspace */
-
-/*---------------------------------
-
-  qh_sethalfspace_all( dim, count, halfspaces, feasible )
-    generate dual for halfspace intersection with feasible point
-    array of count halfspaces
-      each halfspace is normal coefficients followed by offset
-      the origin is inside the halfspace if the offset is negative
-
-  returns:
-    malloc'd array of count X dim-1 points
-
-  notes:
-    call before qh_init_B or qh_initqhull_globals
-    unused/untested code: please email bradb@shore.net if this works ok for you
-    If using option 'Fp', also set qh feasible_point. It is a malloc'd array
-      that is freed by qh_freebuffers.
-
-  design:
-    see qh_sethalfspace
-*/
-coordT *qh_sethalfspace_all (int dim, int count, coordT *halfspaces, pointT *feasible) {
-  int i, newdim;
-  pointT *newpoints;
-  coordT *coordp, *normalp, *offsetp;
-
-  trace0((qh ferr, "qh_sethalfspace_all: compute dual for halfspace intersection\n"));
-  newdim= dim - 1;
-  if (!(newpoints=(coordT*)malloc(count*newdim*sizeof(coordT)))){
-    fprintf(qh ferr, "qhull error: insufficient memory to compute dual of %d halfspaces\n",
-          count);
-    qh_errexit(qh_ERRmem, NULL, NULL);
-  }
-  coordp= newpoints;
-  normalp= halfspaces;
-  for (i= 0; i < count; i++) {
-    offsetp= normalp + newdim;
-    if (!qh_sethalfspace (newdim, coordp, &coordp, normalp, offsetp, feasible)) {
-      fprintf (qh ferr, "The halfspace was at index %d\n", i);
-      qh_errexit (qh_ERRinput, NULL, NULL);
-    }
-    normalp= offsetp + 1;
-  }
-  return newpoints;
-} /* sethalfspace_all */
-
-
-/*---------------------------------
-
-  qh_sharpnewfacets()
-
-  returns:
-    true if could be an acute angle (facets in different quadrants)
-
-  notes:
-    for qh_findbest
-
-  design:
-    for all facets on qh.newfacet_list
-      if two facets are in different quadrants
-        set issharp
-*/
-boolT qh_sharpnewfacets () {
-  facetT *facet;
-  boolT issharp = False;
-
-  quadrant= (int*)qh_memalloc (qh hull_dim * sizeof(int));
-  FORALLfacet_(qh newfacet_list) {
-    if (facet == qh newfacet_list) {
-      for (k= qh hull_dim; k--; )
-      	quadrant[ k]= (facet->normal[ k] > 0);
-    }else {
-      for (k= qh hull_dim; k--; ) {
-        if (quadrant[ k] != (facet->normal[ k] > 0)) {
-          issharp= True;
-          break;
-        }
-      }
-    }
-    if (issharp)
-      break;
-  }
-  qh_memfree( quadrant, qh hull_dim * sizeof(int));
-  trace3((qh ferr, "qh_sharpnewfacets: %d\n", issharp));
-  return issharp;
-} /* sharpnewfacets */
-
-/*---------------------------------
-
-  qh_voronoi_center( dim, points )
-    return Voronoi center for a set of points
-    dim is the orginal dimension of the points
-    gh.gm_matrix/qh.gm_row are scratch buffers
-
-  returns:
-    center as a temporary point
-    if non-simplicial,
-      returns center for max simplex of points
-
-  notes:
-    from Bowyer & Woodwark, A Programmer's Geometry, 1983, p. 65
-
-  design:
-    if non-simplicial
-      determine max simplex for points
-    translate point0 of simplex to origin
-    compute sum of squares of diagonal
-    compute determinate
-    compute Voronoi center (see Bowyer & Woodwark)
-*/
-pointT *qh_voronoi_center (int dim, setT *points) {
-  pointT *point, **pointp, *point0;
-  pointT *center= (pointT*)qh_memalloc (qh center_size);
-  setT *simplex;
-  int i, j, k, size= qh_setsize(points);
-  coordT *gmcoord;
-  realT *diffp, sum2, *sum2row, *sum2p, det, factor;
-  boolT nearzero, infinite;
-
-  if (size == dim+1)
-    simplex= points;
-  else if (size < dim+1) {
-    fprintf (qh ferr, "qhull internal error (qh_voronoi_center):\n  need at least %d points to construct a Voronoi center\n",
-	     dim+1);
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }else {
-    simplex= qh_settemp (dim+1);
-    qh_maxsimplex (dim, points, NULL, 0, &simplex);
-  }
-  point0= SETfirstt_(simplex, pointT);
-  gmcoord= qh gm_matrix;
-  for (k=0; k < dim; k++) {
-    qh gm_row[k]= gmcoord;
-    FOREACHpoint_(simplex) {
-      if (point != point0)
-        *(gmcoord++)= point[k] - point0[k];
-    }
-  }
-  sum2row= gmcoord;
-  for (i=0; i < dim; i++) {
-    sum2= 0.0;
-    for (k= 0; k < dim; k++) {
-      diffp= qh gm_row[k] + i;
-      sum2 += *diffp * *diffp;
-    }
-    *(gmcoord++)= sum2;
-  }
-  det= qh_determinant (qh gm_row, dim, &nearzero);
-  factor= qh_divzero (0.5, det, qh MINdenom, &infinite);
-  if (infinite) {
-    for (k=dim; k--; )
-      center[k]= qh_INFINITE;
-    if (qh IStracing)
-      qh_printpoints (qh ferr, "qh_voronoi_center: at infinity for ", simplex);
-  }else {
-    for (i=0; i < dim; i++) {
-      gmcoord= qh gm_matrix;
-      sum2p= sum2row;
-      for (k=0; k < dim; k++) {
-	qh gm_row[k]= gmcoord;
-	if (k == i) {
-	  for (j= dim; j--; )
-	    *(gmcoord++)= *sum2p++;
-	}else {
-	  FOREACHpoint_(simplex) {
-	    if (point != point0)
-	      *(gmcoord++)= point[k] - point0[k];
-	  }
-	}
-      }
-      center[i]= qh_determinant (qh gm_row, dim, &nearzero)*factor + point0[i];
-    }
-#ifndef qh_NOtrace
-    if (qh IStracing >= 3) {
-      fprintf (qh ferr, "qh_voronoi_center: det %2.2g factor %2.2g ", det, factor);
-      qh_printmatrix (qh ferr, "center:", ¢er, 1, dim);
-      if (qh IStracing >= 5) {
-	qh_printpoints (qh ferr, "points", simplex);
-	FOREACHpoint_(simplex)
-	  fprintf (qh ferr, "p%d dist %.2g, ", qh_pointid (point),
-		   qh_pointdist (point, center, dim));
-	fprintf (qh ferr, "\n");
-      }
-    }
-#endif
-  }
-  if (simplex != points)
-    qh_settempfree (&simplex);
-  return center;
-} /* voronoi_center */
-
diff --git a/extern/qhull/src/global.c b/extern/qhull/src/global.c
deleted file mode 100644
index d3e141aa985..00000000000
--- a/extern/qhull/src/global.c
+++ /dev/null
@@ -1,2018 +0,0 @@
-/*  ---------------------------------
-
-   global.c
-   initializes all the globals of the qhull application
-
-
-   see qhull.h for qh.globals and function prototypes
-
-   see qhull_a.h for internal functions
-
-   copyright (c) 1993-2002, The Geometry Center
- */
-
-#include "qhull_a.h"
-
-/*========= qh definition =======================*/
-
-#if qh_QHpointer
-qhT *qh_qh= NULL;	/* pointer to all global variables */
-#else
-qhT qh_qh;     		/* all global variables.
-			   Add "= {0}" if this causes a compiler error.
-			   Also qh_qhstat in stat.c and qhmem in mem.c.  */
-#endif
-
-/*---------------------------------
-
-  qh_appendprint( printFormat )
-    append printFormat to qh.PRINTout unless already defined
-*/
-void qh_appendprint (qh_PRINT format) {
-  int i;
-
-  for (i=0; i < qh_PRINTEND; i++) {
-    if (qh PRINTout[i] == format && format != qh_PRINTqhull)
-      break;
-    if (!qh PRINTout[i]) {
-      qh PRINTout[i]= format;
-      break;
-    }
-  }
-} /* appendprint */
-
-/*---------------------------------
-
-  qh_checkflags( commandStr, hiddenFlags )
-    errors if commandStr contains hiddenFlags
-    hiddenFlags starts and ends with a space and is space deliminated (checked)
-
-  notes:
-    ignores first word (e.g., "qconvex i")
-    use qh_strtol/strtod since strtol/strtod may or may not skip trailing spaces
-
-  see:
-    qh_initflags() initializes Qhull according to commandStr
-*/
-void qh_checkflags(char *command, char *hiddenflags) {
-  char *s= command, *t, *chkerr, key, opt, prevopt;
-  char chkkey[]= "   ";
-  char chkopt[]=  "    ";
-  char chkopt2[]= "     ";
-
-  if (*hiddenflags != ' ' || hiddenflags[strlen(hiddenflags)-1] != ' ') {
-    fprintf(qh ferr, "qhull error (qh_checkflags): hiddenflags must start and end with a space: \"%s\"", hiddenflags);
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  if (strpbrk(hiddenflags, ",\n\r\t")) {
-    fprintf(qh ferr, "qhull error (qh_checkflags): hiddenflags contains commas, newlines, or tabs: \"%s\"", hiddenflags);
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  while (*s && !isspace(*s))  /* skip program name */
-    s++;
-  while (*s) {
-    while (*s && isspace(*s))
-      s++;
-    if (*s == '-')
-      s++;
-    if (!*s)
-      break;
-    key = *s++;
-    chkerr = NULL;
-    if (key == '\'') {         /* TO 'file name' */
-      t= strchr(s, '\'');
-      if (!t) {
-	fprintf(qh ferr, "qhull error (qh_checkflags): missing the 2nd single-quote for:\n%s\n", s-1);
-	qh_errexit(qh_ERRinput, NULL, NULL);
-      }
-      s= t+1;
-      continue;
-    }
-    chkkey[1]= key;
-    if (strstr(hiddenflags, chkkey)) {
-      chkerr= chkkey;
-    }else if (isupper(key)) {
-      opt= ' ';
-      prevopt= ' ';
-      chkopt[1]= key;
-      chkopt2[1]= key;
-      while (!chkerr && *s && !isspace(*s)) {
-	opt= *s++;
-	if (isalpha(opt)) {
-	  chkopt[2]= opt;
-	  if (strstr(hiddenflags, chkopt))
-	    chkerr= chkopt;
-	  if (prevopt != ' ') {
- 	    chkopt2[2]= prevopt;
- 	    chkopt2[3]= opt;
-	    if (strstr(hiddenflags, chkopt2))
-	      chkerr= chkopt2;
-	  }
-	}else if (key == 'Q' && isdigit(opt) && prevopt != 'b'
-	      && (prevopt == ' ' || islower(prevopt))) {
-  	    chkopt[2]= opt;
-	    if (strstr(hiddenflags, chkopt))
-	      chkerr= chkopt;
-	}else {
-	  qh_strtod (s-1, &t);
-	  if (s < t)
-	    s= t;
-	}
-        prevopt= opt;
-      }
-    }
-    if (chkerr) {
-      *chkerr= '\'';
-      chkerr[strlen(chkerr)-1]=  '\'';
-      fprintf(qh ferr, "qhull error: option %s is not used with this program.\n             It may be used with qhull.\n", chkerr);
-      qh_errexit(qh_ERRinput, NULL, NULL);
-    }
-  }
-} /* checkflags */
-
-/*---------------------------------
-
-  qh_clock()
-    return user CPU time in 100ths (qh_SECtick)
-    only defined for qh_CLOCKtype == 2
-
-  notes:
-    use first value to determine time 0
-    from Stevens '92 8.15
-*/
-unsigned long qh_clock (void) {
-
-#if (qh_CLOCKtype == 2)
-  struct tms time;
-  static long clktck;  /* initialized first call */
-  double ratio, cpu;
-  unsigned long ticks;
-
-  if (!clktck) {
-    if ((clktck= sysconf (_SC_CLK_TCK)) < 0) {
-      fprintf (qh ferr, "qhull internal error (qh_clock): sysconf() failed.  Use qh_CLOCKtype 1 in user.h\n");
-      qh_errexit (qh_ERRqhull, NULL, NULL);
-    }
-  }
-  if (times (&time) == -1) {
-    fprintf (qh ferr, "qhull internal error (qh_clock): times() failed.  Use qh_CLOCKtype 1 in user.h\n");
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }
-  ratio= qh_SECticks / (double)clktck;
-  ticks= time.tms_utime * ratio;
-  return ticks;
-#else
-  fprintf (qh ferr, "qhull internal error (qh_clock): use qh_CLOCKtype 2 in user.h\n");
-  qh_errexit (qh_ERRqhull, NULL, NULL); /* never returns */
-  return 0;
-#endif
-} /* clock */
-
-/*---------------------------------
-
-  qh_freebuffers()
-    free up global memory buffers
-
-  notes:
-    must match qh_initbuffers()
-*/
-void qh_freebuffers (void) {
-
-  trace5((qh ferr, "qh_freebuffers: freeing up global memory buffers\n"));
-  /* allocated by qh_initqhull_buffers */
-  qh_memfree (qh NEARzero, qh hull_dim * sizeof(realT));
-  qh_memfree (qh lower_threshold, (qh input_dim+1) * sizeof(realT));
-  qh_memfree (qh upper_threshold, (qh input_dim+1) * sizeof(realT));
-  qh_memfree (qh lower_bound, (qh input_dim+1) * sizeof(realT));
-  qh_memfree (qh upper_bound, (qh input_dim+1) * sizeof(realT));
-  qh_memfree (qh gm_matrix, (qh hull_dim+1) * qh hull_dim * sizeof(coordT));
-  qh_memfree (qh gm_row, (qh hull_dim+1) * sizeof(coordT *));
-  qh NEARzero= qh lower_threshold= qh upper_threshold= NULL;
-  qh lower_bound= qh upper_bound= NULL;
-  qh gm_matrix= NULL;
-  qh gm_row= NULL;
-  qh_setfree (&qh other_points);
-  qh_setfree (&qh del_vertices);
-  qh_setfree (&qh coplanarset);
-  if (qh line)                /* allocated by qh_readinput, freed if no error */
-    free (qh line);
-  if (qh half_space)
-    free (qh half_space);
-  if (qh temp_malloc)
-    free (qh temp_malloc);
-  if (qh feasible_point)      /* allocated by qh_readfeasible */
-    free (qh feasible_point);
-  if (qh feasible_string)     /* allocated by qh_initflags */
-    free (qh feasible_string);
-  qh line= qh feasible_string= NULL;
-  qh half_space= qh feasible_point= qh temp_malloc= NULL;
-  /* usually allocated by qh_readinput */
-  if (qh first_point && qh POINTSmalloc) {
-    free(qh first_point);
-    qh first_point= NULL;
-  }
-  if (qh input_points && qh input_malloc) { /* set by qh_joggleinput */
-    free (qh input_points);
-    qh input_points= NULL;
-  }
-  trace5((qh ferr, "qh_freebuffers: finished\n"));
-} /* freebuffers */
-
-
-/*---------------------------------
-
-  qh_freebuild( allmem )
-    free global memory used by qh_initbuild and qh_buildhull
-    if !allmem,
-      does not free short memory (freed by qh_memfreeshort)
-
-  design:
-    free centrums
-    free each vertex
-    mark unattached ridges
-    for each facet
-      free ridges
-      free outside set, coplanar set, neighbor set, ridge set, vertex set
-      free facet
-    free hash table
-    free interior point
-    free merge set
-    free temporary sets
-*/
-void qh_freebuild (boolT allmem) {
-  facetT *facet;
-  vertexT *vertex;
-  ridgeT *ridge, **ridgep;
-  mergeT *merge, **mergep;
-
-  trace1((qh ferr, "qh_freebuild: free memory from qh_inithull and qh_buildhull\n"));
-  if (qh del_vertices)
-    qh_settruncate (qh del_vertices, 0);
-  if (allmem) {
-    qh_clearcenters (qh_ASnone);
-    while ((vertex= qh vertex_list)) {
-      if (vertex->next)
-        qh_delvertex (vertex);
-      else {
-        qh_memfree (vertex, sizeof(vertexT));
-        qh newvertex_list= qh vertex_list= NULL;
-      }
-    }
-  }else if (qh VERTEXneighbors) {
-    FORALLvertices
-      qh_setfreelong (&(vertex->neighbors));
-  }
-  qh VERTEXneighbors= False;
-  qh GOODclosest= NULL;
-  if (allmem) {
-    FORALLfacets {
-      FOREACHridge_(facet->ridges)
-        ridge->seen= False;
-    }
-    FORALLfacets {
-      if (facet->visible) {
-	FOREACHridge_(facet->ridges) {
-	  if (!otherfacet_(ridge, facet)->visible)
-	    ridge->seen= True;  /* an unattached ridge */
-	}
-      }
-    }
-    while ((facet= qh facet_list)) {
-      FOREACHridge_(facet->ridges) {
-        if (ridge->seen) {
-          qh_setfree(&(ridge->vertices));
-          qh_memfree(ridge, sizeof(ridgeT));
-        }else
-          ridge->seen= True;
-      }
-      qh_setfree (&(facet->outsideset));
-      qh_setfree (&(facet->coplanarset));
-      qh_setfree (&(facet->neighbors));
-      qh_setfree (&(facet->ridges));
-      qh_setfree (&(facet->vertices));
-      if (facet->next)
-        qh_delfacet (facet);
-      else {
-        qh_memfree (facet, sizeof(facetT));
-        qh visible_list= qh newfacet_list= qh facet_list= NULL;
-      }
-    }
-  }else {
-    FORALLfacets {
-      qh_setfreelong (&(facet->outsideset));
-      qh_setfreelong (&(facet->coplanarset));
-      if (!facet->simplicial) {
-        qh_setfreelong (&(facet->neighbors));
-        qh_setfreelong (&(facet->ridges));
-        qh_setfreelong (&(facet->vertices));
-      }
-    }
-  }
-  qh_setfree (&(qh hash_table));
-  qh_memfree (qh interior_point, qh normal_size);
-  qh interior_point= NULL;
-  FOREACHmerge_(qh facet_mergeset)  /* usually empty */
-    qh_memfree (merge, sizeof(mergeT));
-  qh facet_mergeset= NULL;  /* temp set */
-  qh degen_mergeset= NULL;  /* temp set */
-  qh_settempfree_all();
-} /* freebuild */
-
-/*---------------------------------
-
-  qh_freeqhull( allmem )
-    free global memory
-    if !allmem,
-      does not free short memory (freed by qh_memfreeshort)
-
-  notes:
-    sets qh.NOerrexit in case caller forgets to
-
-  design:
-    free global and temporary memory from qh_initbuild and qh_buildhull
-    free buffers
-    free statistics
-*/
-void qh_freeqhull (boolT allmem) {
-
-  trace1((qh ferr, "qh_freeqhull: free global memory\n"));
-  qh NOerrexit= True;  /* no more setjmp since called at exit */
-  qh_freebuild (allmem);
-  qh_freebuffers();
-  qh_freestatistics();
-#if qh_QHpointer
-  free (qh_qh);
-  qh_qh= NULL;
-#else
-  memset((char *)&qh_qh, 0, sizeof(qhT));
-  qh NOerrexit= True;
-#endif
-} /* freeqhull */
-
-/*---------------------------------
-
-  qh_init_A( infile, outfile, errfile, argc, argv )
-    initialize memory and stdio files
-    convert input options to option string (qh.qhull_command)
-
-  notes:
-    infile may be NULL if qh_readpoints() is not called
-
-    errfile should always be defined.  It is used for reporting
-    errors.  outfile is used for output and format options.
-
-    argc/argv may be 0/NULL
-
-    called before error handling initialized
-    qh_errexit() may not be used
-*/
-void qh_init_A (FILE *infile, FILE *outfile, FILE *errfile, int argc, char *argv[]) {
-  qh_meminit (errfile);
-  qh_initqhull_start (infile, outfile, errfile);
-  qh_init_qhull_command (argc, argv);
-} /* init_A */
-
-/*---------------------------------
-
-  qh_init_B( points, numpoints, dim, ismalloc )
-    initialize globals for points array
-
-    points has numpoints dim-dimensional points
-      points[0] is the first coordinate of the first point
-      points[1] is the second coordinate of the first point
-      points[dim] is the first coordinate of the second point
-
-    ismalloc=True
-      Qhull will call free(points) on exit or input transformation
-    ismalloc=False
-      Qhull will allocate a new point array if needed for input transformation
-
-    qh.qhull_command
-      is the option string.
-      It is defined by qh_init_B(), qh_qhull_command(), or qh_initflags
-
-  returns:
-    if qh.PROJECTinput or (qh.DELAUNAY and qh.PROJECTdelaunay)
-      projects the input to a new point array
-
-        if qh.DELAUNAY,
-          qh.hull_dim is increased by one
-        if qh.ATinfinity,
-          qh_projectinput adds point-at-infinity for Delaunay tri.
-
-    if qh.SCALEinput
-      changes the upper and lower bounds of the input, see qh_scaleinput()
-
-    if qh.ROTATEinput
-      rotates the input by a random rotation, see qh_rotateinput()
-      if qh.DELAUNAY
-        rotates about the last coordinate
-
-  notes:
-    called after points are defined
-    qh_errexit() may be used
-*/
-void qh_init_B (coordT *points, int numpoints, int dim, boolT ismalloc) {
-  qh_initqhull_globals (points, numpoints, dim, ismalloc);
-  if (qhmem.LASTsize == 0)
-    qh_initqhull_mem();
-  /* mem.c and qset.c are initialized */
-  qh_initqhull_buffers();
-  qh_initthresholds (qh qhull_command);
-  if (qh PROJECTinput || (qh DELAUNAY && qh PROJECTdelaunay))
-    qh_projectinput();
-  if (qh SCALEinput)
-    qh_scaleinput();
-  if (qh ROTATErandom >= 0) {
-    qh_randommatrix (qh gm_matrix, qh hull_dim, qh gm_row);
-    if (qh DELAUNAY) {
-      int k, lastk= qh hull_dim-1;
-      for (k= 0; k < lastk; k++) {
-        qh gm_row[k][lastk]= 0.0;
-        qh gm_row[lastk][k]= 0.0;
-      }
-      qh gm_row[lastk][lastk]= 1.0;
-    }
-    qh_gram_schmidt (qh hull_dim, qh gm_row);
-    qh_rotateinput (qh gm_row);
-  }
-} /* init_B */
-
-/*---------------------------------
-
-  qh_init_qhull_command( argc, argv )
-    build qh.qhull_command from argc/argv
-
-  returns:
-    a space-deliminated string of options (just as typed)
-
-  notes:
-    makes option string easy to input and output
-
-    argc/argv may be 0/NULL
-*/
-void qh_init_qhull_command(int argc, char *argv[]) {
-  int i;
-  char *s;
-
-  if (argc) {
-    if ((s= strrchr( argv[0], '\\'))) /* Borland gives full path */
-      strcpy (qh qhull_command, s+1);
-    else
-      strcpy (qh qhull_command, argv[0]);
-    if ((s= strstr (qh qhull_command, ".EXE"))
-    ||  (s= strstr (qh qhull_command, ".exe")))
-      *s= '\0';
-  }
-  for (i=1; i < argc; i++) {
-    if (strlen (qh qhull_command) + strlen(argv[i]) + 1 < sizeof(qh qhull_command)) {
-      strcat (qh qhull_command, " ");
-      strcat (qh qhull_command, argv[i]);
-    }else {
-      fprintf (qh ferr, "qhull input error: more than %d characters in command line\n",
-        (int)sizeof(qh qhull_command));
-      exit (1);  /* can not use qh_errexit */
-    }
-  }
-} /* init_qhull_command */
-
-/*---------------------------------
-
-  qh_initflags( commandStr )
-    set flags and initialized constants from commandStr
-
-  returns:
-    sets qh.qhull_command to command if needed
-
-  notes:
-    ignores first word (e.g., "qhull d")
-    use qh_strtol/strtod since strtol/strtod may or may not skip trailing spaces
-
-  see:
-    qh_initthresholds() continues processing of 'Pdn' and 'PDn'
-    'prompt' in unix.c for documentation
-
-  design:
-    for each space-deliminated option group
-      if top-level option
-        check syntax
-        append approriate option to option string
-        set appropriate global variable or append printFormat to print options
-      else
-        for each sub-option
-          check syntax
-          append approriate option to option string
-          set appropriate global variable or append printFormat to print options
-
-
-*/
-void qh_initflags(char *command) {
-  int k, i, lastproject;
-  char *s= command, *t, *prev_s, *start, key;
-  boolT isgeom= False, wasproject;
-  realT r;
-
-  if (command != &qh qhull_command[0]) {
-    *qh qhull_command= '\0';
-    strncat( qh qhull_command, command, sizeof( qh qhull_command));
-  }
-  while (*s && !isspace(*s))  /* skip program name */
-    s++;
-  while (*s) {
-    while (*s && isspace(*s))
-      s++;
-    if (*s == '-')
-      s++;
-    if (!*s)
-      break;
-    prev_s= s;
-    switch (*s++) {
-    case 'd':
-      qh_option ("delaunay", NULL, NULL);
-      qh DELAUNAY= True;
-      break;
-    case 'f':
-      qh_option ("facets", NULL, NULL);
-      qh_appendprint (qh_PRINTfacets);
-      break;
-    case 'i':
-      qh_option ("incidence", NULL, NULL);
-      qh_appendprint (qh_PRINTincidences);
-      break;
-    case 'm':
-      qh_option ("mathematica", NULL, NULL);
-      qh_appendprint (qh_PRINTmathematica);
-      break;
-    case 'n':
-      qh_option ("normals", NULL, NULL);
-      qh_appendprint (qh_PRINTnormals);
-      break;
-    case 'o':
-      qh_option ("offFile", NULL, NULL);
-      qh_appendprint (qh_PRINToff);
-      break;
-    case 'p':
-      qh_option ("points", NULL, NULL);
-      qh_appendprint (qh_PRINTpoints);
-      break;
-    case 's':
-      qh_option ("summary", NULL, NULL);
-      qh PRINTsummary= True;
-      break;
-    case 'v':
-      qh_option ("voronoi", NULL, NULL);
-      qh VORONOI= True;
-      qh DELAUNAY= True;
-      break;
-    case 'A':
-      if (!isdigit(*s) && *s != '.' && *s != '-')
-	fprintf(qh ferr, "qhull warning: no maximum cosine angle given for option 'An'.  Ignored.\n");
-      else {
-	if (*s == '-') {
-	  qh premerge_cos= -qh_strtod (s, &s);
-          qh_option ("Angle-premerge-", NULL, &qh premerge_cos);
-	  qh PREmerge= True;
-	}else {
-	  qh postmerge_cos= qh_strtod (s, &s);
-          qh_option ("Angle-postmerge", NULL, &qh postmerge_cos);
-	  qh POSTmerge= True;
-	}
-	qh MERGING= True;
-      }
-      break;
-    case 'C':
-      if (!isdigit(*s) && *s != '.' && *s != '-')
-	fprintf(qh ferr, "qhull warning: no centrum radius given for option 'Cn'.  Ignored.\n");
-      else {
-	if (*s == '-') {
-	  qh premerge_centrum= -qh_strtod (s, &s);
-          qh_option ("Centrum-premerge-", NULL, &qh premerge_centrum);
-	  qh PREmerge= True;
-	}else {
-	  qh postmerge_centrum= qh_strtod (s, &s);
-          qh_option ("Centrum-postmerge", NULL, &qh postmerge_centrum);
-	  qh POSTmerge= True;
-	}
-	qh MERGING= True;
-      }
-      break;
-    case 'E':
-      if (*s == '-')
-	fprintf(qh ferr, "qhull warning: negative maximum roundoff given for option 'An'.  Ignored.\n");
-      else if (!isdigit(*s))
-	fprintf(qh ferr, "qhull warning: no maximum roundoff given for option 'En'.  Ignored.\n");
-      else {
-	qh DISTround= qh_strtod (s, &s);
-        qh_option ("Distance-roundoff", NULL, &qh DISTround);
-	qh SETroundoff= True;
-      }
-      break;
-    case 'H':
-      start= s;
-      qh HALFspace= True;
-      qh_strtod (s, &t);
-      while (t > s)  {
-        if (*t && !isspace (*t)) {
-	  if (*t == ',')
-	    t++;
-	  else
-	    fprintf (qh ferr, "qhull warning: origin for Halfspace intersection should be 'Hn,n,n,...'\n");
-	}
-        s= t;
-	qh_strtod (s, &t);
-      }
-      if (start < t) {
-        if (!(qh feasible_string= (char*)calloc (t-start+1, 1))) {
-          fprintf(qh ferr, "qhull error: insufficient memory for 'Hn,n,n'\n");
-          qh_errexit(qh_ERRmem, NULL, NULL);
-        }
-        strncpy (qh feasible_string, start, t-start);
-        qh_option (qh feasible_string, NULL, NULL);
-      }else
-        qh_option ("Halfspace", NULL, NULL);
-      break;
-    case 'R':
-      if (!isdigit(*s))
-	fprintf(qh ferr, "qhull warning: missing random perturbation for option 'Rn'.  Ignored\n");
-      else {
-	qh RANDOMfactor= qh_strtod (s, &s);
-        qh_option ("Random_perturb", NULL, &qh RANDOMfactor);
-        qh RANDOMdist= True;
-      }
-      break;
-    case 'V':
-      if (!isdigit(*s) && *s != '-')
-	fprintf(qh ferr, "qhull warning: missing visible distance for option 'Vn'.  Ignored\n");
-      else {
-	qh MINvisible= qh_strtod (s, &s);
-        qh_option ("Visible", NULL, &qh MINvisible);
-      }
-      break;
-    case 'U':
-      if (!isdigit(*s) && *s != '-')
-	fprintf(qh ferr, "qhull warning: missing coplanar distance for option 'Un'.  Ignored\n");
-      else {
-	qh MAXcoplanar= qh_strtod (s, &s);
-        qh_option ("U-coplanar", NULL, &qh MAXcoplanar);
-      }
-      break;
-    case 'W':
-      if (*s == '-')
-	fprintf(qh ferr, "qhull warning: negative outside width for option 'Wn'.  Ignored.\n");
-      else if (!isdigit(*s))
-	fprintf(qh ferr, "qhull warning: missing outside width for option 'Wn'.  Ignored\n");
-      else {
-	qh MINoutside= qh_strtod (s, &s);
-        qh_option ("W-outside", NULL, &qh MINoutside);
-        qh APPROXhull= True;
-      }
-      break;
-    case 'F':
-      while (*s && !isspace(*s)) {
-	switch(*s++) {
-	case 'a':
-	  qh_option ("Farea", NULL, NULL);
-	  qh_appendprint (qh_PRINTarea);
-	  qh GETarea= True;
-	  break;
-	case 'A':
-	  qh_option ("FArea-total", NULL, NULL);
-	  qh GETarea= True;
-	  break;
-        case 'c':
-          qh_option ("Fcoplanars", NULL, NULL);
-          qh_appendprint (qh_PRINTcoplanars);
-          break;
-        case 'C':
-          qh_option ("FCentrums", NULL, NULL);
-          qh_appendprint (qh_PRINTcentrums);
-          break;
-	case 'd':
-          qh_option ("Fd-cdd-in", NULL, NULL);
-	  qh CDDinput= True;
-	  break;
-	case 'D':
-          qh_option ("FD-cdd-out", NULL, NULL);
-	  qh CDDoutput= True;
-	  break;
-	case 'F':
-	  qh_option ("FFacets-xridge", NULL, NULL);
-          qh_appendprint (qh_PRINTfacets_xridge);
-	  break;
-        case 'i':
-          qh_option ("Finner", NULL, NULL);
-          qh_appendprint (qh_PRINTinner);
-          break;
-        case 'I':
-          qh_option ("FIDs", NULL, NULL);
-          qh_appendprint (qh_PRINTids);
-          break;
-        case 'm':
-          qh_option ("Fmerges", NULL, NULL);
-          qh_appendprint (qh_PRINTmerges);
-          break;
-        case 'n':
-          qh_option ("Fneighbors", NULL, NULL);
-          qh_appendprint (qh_PRINTneighbors);
-          break;
-        case 'N':
-          qh_option ("FNeighbors-vertex", NULL, NULL);
-          qh_appendprint (qh_PRINTvneighbors);
-          break;
-        case 'o':
-          qh_option ("Fouter", NULL, NULL);
-          qh_appendprint (qh_PRINTouter);
-          break;
-	case 'O':
-	  if (qh PRINToptions1st) {
-	    qh_option ("FOptions", NULL, NULL);
-	    qh_appendprint (qh_PRINToptions);
-	  }else
-	    qh PRINToptions1st= True;
-	  break;
-	case 'p':
-	  qh_option ("Fpoint-intersect", NULL, NULL);
-	  qh_appendprint (qh_PRINTpointintersect);
-	  break;
-	case 'P':
-	  qh_option ("FPoint-nearest", NULL, NULL);
-	  qh_appendprint (qh_PRINTpointnearest);
-	  break;
-	case 'Q':
-	  qh_option ("FQhull", NULL, NULL);
-	  qh_appendprint (qh_PRINTqhull);
-	  break;
-        case 's':
-          qh_option ("Fsummary", NULL, NULL);
-          qh_appendprint (qh_PRINTsummary);
-          break;
-        case 'S':
-          qh_option ("FSize", NULL, NULL);
-          qh_appendprint (qh_PRINTsize);
-          qh GETarea= True;
-          break;
-        case 't':
-          qh_option ("Ftriangles", NULL, NULL);
-          qh_appendprint (qh_PRINTtriangles);
-          break;
-        case 'v':
-          /* option set in qh_initqhull_globals */
-          qh_appendprint (qh_PRINTvertices);
-          break;
-        case 'V':
-          qh_option ("FVertex-average", NULL, NULL);
-          qh_appendprint (qh_PRINTaverage);
-          break;
-	case 'x':
-	  qh_option ("Fxtremes", NULL, NULL);
-	  qh_appendprint (qh_PRINTextremes);
-	  break;
-	default:
-	  s--;
-	  fprintf (qh ferr, "qhull warning: unknown 'F' output option %c, rest ignored\n", (int)s[0]);
-	  while (*++s && !isspace(*s));
-	  break;
-	}
-      }
-      break;
-    case 'G':
-      isgeom= True;
-      qh_appendprint (qh_PRINTgeom);
-      while (*s && !isspace(*s)) {
-	switch(*s++) {
-        case 'a':
-          qh_option ("Gall-points", NULL, NULL);
-          qh PRINTdots= True;
-          break;
-        case 'c':
-          qh_option ("Gcentrums", NULL, NULL);
-          qh PRINTcentrums= True;
-          break;
-	case 'h':
-          qh_option ("Gintersections", NULL, NULL);
-	  qh DOintersections= True;
-	  break;
-	case 'i':
-          qh_option ("Ginner", NULL, NULL);
-	  qh PRINTinner= True;
-	  break;
-	case 'n':
-          qh_option ("Gno-planes", NULL, NULL);
-	  qh PRINTnoplanes= True;
-	  break;
-	case 'o':
-          qh_option ("Gouter", NULL, NULL);
-	  qh PRINTouter= True;
-	  break;
-	case 'p':
-          qh_option ("Gpoints", NULL, NULL);
-	  qh PRINTcoplanar= True;
-	  break;
-	case 'r':
-          qh_option ("Gridges", NULL, NULL);
-	  qh PRINTridges= True;
-	  break;
-	case 't':
-          qh_option ("Gtransparent", NULL, NULL);
-	  qh PRINTtransparent= True;
-	  break;
-	case 'v':
-          qh_option ("Gvertices", NULL, NULL);
-	  qh PRINTspheres= True;
-	  break;
-	case 'D':
-	  if (!isdigit (*s))
-	    fprintf (qh ferr, "qhull input error: missing dimension for option 'GDn'\n");
-	  else {
-	    if (qh DROPdim >= 0)
-	      fprintf (qh ferr, "qhull warning: can only drop one dimension.  Previous 'GD%d' ignored\n",
-	           qh DROPdim);
-  	    qh DROPdim= qh_strtol (s, &s);
-            qh_option ("GDrop-dim", &qh DROPdim, NULL);
-          }
-	  break;
-	default:
-	  s--;
-	  fprintf (qh ferr, "qhull warning: unknown 'G' print option %c, rest ignored\n", (int)s[0]);
-	  while (*++s && !isspace(*s));
-	  break;
-	}
-      }
-      break;
-    case 'P':
-      while (*s && !isspace(*s)) {
-	switch(*s++) {
-	case 'd': case 'D':  /* see qh_initthresholds() */
-	  key= s[-1];
-	  i= qh_strtol (s, &s);
-	  r= 0;
-	  if (*s == ':') {
-	    s++;
-	    r= qh_strtod (s, &s);
-	  }
-	  if (key == 'd')
-  	    qh_option ("Pdrop-facets-dim-less", &i, &r);
-  	  else
-  	    qh_option ("PDrop-facets-dim-more", &i, &r);
-	  break;
-        case 'g':
-          qh_option ("Pgood-facets", NULL, NULL);
-          qh PRINTgood= True;
-          break;
-        case 'G':
-          qh_option ("PGood-facet-neighbors", NULL, NULL);
-          qh PRINTneighbors= True;
-          break;
-        case 'o':
-          qh_option ("Poutput-forced", NULL, NULL);
-          qh FORCEoutput= True;
-          break;
-        case 'p':
-          qh_option ("Pprecision-ignore", NULL, NULL);
-          qh PRINTprecision= False;
-          break;
-	case 'A':
-	  if (!isdigit (*s))
-	    fprintf (qh ferr, "qhull input error: missing facet count for keep area option 'PAn'\n");
-	  else {
-  	    qh KEEParea= qh_strtol (s, &s);
-            qh_option ("PArea-keep", &qh KEEParea, NULL);
-            qh GETarea= True;
-          }
-	  break;
-	case 'F':
-	  if (!isdigit (*s))
-	    fprintf (qh ferr, "qhull input error: missing facet area for option 'PFn'\n");
-	  else {
-  	    qh KEEPminArea= qh_strtod (s, &s);
-            qh_option ("PFacet-area-keep", NULL, &qh KEEPminArea);
-            qh GETarea= True;
-          }
-	  break;
-	case 'M':
-	  if (!isdigit (*s))
-	    fprintf (qh ferr, "qhull input error: missing merge count for option 'PMn'\n");
-	  else {
-  	    qh KEEPmerge= qh_strtol (s, &s);
-            qh_option ("PMerge-keep", &qh KEEPmerge, NULL);
-          }
-	  break;
-	default:
-	  s--;
-	  fprintf (qh ferr, "qhull warning: unknown 'P' print option %c, rest ignored\n", (int)s[0]);
-	  while (*++s && !isspace(*s));
-	  break;
-	}
-      }
-      break;
-    case 'Q':
-      lastproject= -1;
-      while (*s && !isspace(*s)) {
-	switch(*s++) {
-	case 'b': case 'B':  /* handled by qh_initthresholds */
-	  key= s[-1];
-	  if (key == 'b' && *s == 'B') {
-	    s++;
-	    r= qh_DEFAULTbox;
-	    qh SCALEinput= True;
-	    qh_option ("QbBound-unit-box", NULL, &r);
-	    break;
-	  }
-	  if (key == 'b' && *s == 'b') {
-	    s++;
-	    qh SCALElast= True;
-	    qh_option ("Qbbound-last", NULL, NULL);
-	    break;
-	  }
-	  k= qh_strtol (s, &s);
-	  r= 0.0;
-	  wasproject= False;
-	  if (*s == ':') {
-	    s++;
-	    if ((r= qh_strtod(s, &s)) == 0.0) {
- 	      t= s;            /* need true dimension for memory allocation */
-	      while (*t && !isspace(*t)) {
-	        if (toupper(*t++) == 'B'
-	         && k == qh_strtol (t, &t)
-	         && *t++ == ':'
-	         && qh_strtod(t, &t) == 0.0) {
-	          qh PROJECTinput++;
-	          trace2((qh ferr, "qh_initflags: project dimension %d\n", k));
-	          qh_option ("Qb-project-dim", &k, NULL);
-		  wasproject= True;
-	          lastproject= k;
-	          break;
-		}
-	      }
-	    }
-  	  }
-	  if (!wasproject) {
-	    if (lastproject == k && r == 0.0)
-	      lastproject= -1;  /* doesn't catch all possible sequences */
-	    else if (key == 'b') {
-	      qh SCALEinput= True;
-	      if (r == 0.0)
-		r= -qh_DEFAULTbox;
-	      qh_option ("Qbound-dim-low", &k, &r);
-	    }else {
-	      qh SCALEinput= True;
-	      if (r == 0.0)
-		r= qh_DEFAULTbox;
-	      qh_option ("QBound-dim-high", &k, &r);
-	    }
-	  }
-	  break;
-	case 'c':
-	  qh_option ("Qcoplanar-keep", NULL, NULL);
-	  qh KEEPcoplanar= True;
-	  break;
-	case 'f':
-	  qh_option ("Qfurthest-outside", NULL, NULL);
-	  qh BESToutside= True;
-	  break;
-	case 'g':
-	  qh_option ("Qgood-facets-only", NULL, NULL);
-	  qh ONLYgood= True;
-	  break;
-	case 'i':
-	  qh_option ("Qinterior-keep", NULL, NULL);
-	  qh KEEPinside= True;
-	  break;
-	case 'm':
-	  qh_option ("Qmax-outside-only", NULL, NULL);
-	  qh ONLYmax= True;
-	  break;
-	case 'r':
-	  qh_option ("Qrandom-outside", NULL, NULL);
-	  qh RANDOMoutside= True;
-	  break;
-	case 's':
-	  qh_option ("Qsearch-initial-simplex", NULL, NULL);
-	  qh ALLpoints= True;
-	  break;
-	case 't':
-	  qh_option ("Qtriangulate", NULL, NULL);
-	  qh TRIangulate= True;
-	  break;
-	case 'T':
-	  qh_option ("QTestPoints", NULL, NULL);
-	  if (!isdigit (*s))
-	    fprintf (qh ferr, "qhull input error: missing number of test points for option 'QTn'\n");
-	  else {
-  	    qh TESTpoints= qh_strtol (s, &s);
-            qh_option ("QTestPoints", &qh TESTpoints, NULL);
-          }
-	  break;
-	case 'u':
-	  qh_option ("QupperDelaunay", NULL, NULL);
-	  qh UPPERdelaunay= True;
-	  break;
-	case 'v':
-	  qh_option ("Qvertex-neighbors-convex", NULL, NULL);
-	  qh TESTvneighbors= True;
-	  break;
-	case 'x':
-	  qh_option ("Qxact-merge", NULL, NULL);
-	  qh MERGEexact= True;
-	  break;
-	case 'z':
-	  qh_option ("Qz-infinity-point", NULL, NULL);
-	  qh ATinfinity= True;
-	  break;
-	case '0':
-	  qh_option ("Q0-no-premerge", NULL, NULL);
-	  qh NOpremerge= True;
-	  break;
-	case '1':
-	  if (!isdigit(*s)) {
-	    qh_option ("Q1-no-angle-sort", NULL, NULL);
-	    qh ANGLEmerge= False;
-	    break;
-	  }
-	  switch(*s++) {
-  	  case '0':
-	    qh_option ("Q10-no-narrow", NULL, NULL);
-	    qh NOnarrow= True;
-	    break;
-  	  case '1':
-	    qh_option ("Q11-trinormals Qtriangulate", NULL, NULL);
-	    qh TRInormals= True;
-	    qh TRIangulate= True;
-	    break;
-	  default:
-	    s--;
-	    fprintf (qh ferr, "qhull warning: unknown 'Q' qhull option 1%c, rest ignored\n", (int)s[0]);
-	    while (*++s && !isspace(*s));
-	    break;
-	  }
-	  break;
-	case '2':
-	  qh_option ("Q2-no-merge-independent", NULL, NULL);
-	  qh MERGEindependent= False;
-	  goto LABELcheckdigit;
-	  break; /* no warnings */
-	case '3':
-	  qh_option ("Q3-no-merge-vertices", NULL, NULL);
-	  qh MERGEvertices= False;
-	LABELcheckdigit:
-	  if (isdigit(*s))
-	    fprintf (qh ferr, "qhull warning: can not follow '1', '2', or '3' with a digit.  '%c' skipped.\n",
-	             *s++);
-	  break;
-	case '4':
-	  qh_option ("Q4-avoid-old-into-new", NULL, NULL);
-	  qh AVOIDold= True;
-	  break;
-	case '5':
-	  qh_option ("Q5-no-check-outer", NULL, NULL);
-	  qh SKIPcheckmax= True;
-	  break;
-	case '6':
-	  qh_option ("Q6-no-concave-merge", NULL, NULL);
-	  qh SKIPconvex= True;
-	  break;
-	case '7':
-	  qh VIRTUALmemory= True;
-	  break;
-	case '8':
-	  qh_option ("Q8-no-near-inside", NULL, NULL);
-	  qh NOnearinside= True;
-	  break;
-	case '9':
-	  qh_option ("Q9-pick-furthest", NULL, NULL);
-	  qh PICKfurthest= True;
-	  break;
-	case 'G':
-	  i= qh_strtol (s, &t);
-	  if (qh GOODpoint)
-	    fprintf (qh ferr, "qhull warning: good point already defined for option 'QGn'.  Ignored\n");
-          else if (s == t)
-	    fprintf (qh ferr, "qhull warning: missing good point id for option 'QGn'.  Ignored\n");
-	  else if (i < 0 || *s == '-') {
- 	    qh GOODpoint= i-1;
-  	    qh_option ("QGood-if-dont-see-point", &i, NULL);
-	  }else {
- 	    qh GOODpoint= i+1;
-  	    qh_option ("QGood-if-see-point", &i, NULL);
-  	  }
- 	  s= t;
-	  break;
-	case 'J':
-          if (!isdigit(*s) && *s != '-')
-   	    qh JOGGLEmax= 0.0;
-	  else {
- 	    qh JOGGLEmax= (realT) qh_strtod (s, &s);
-            qh_option ("QJoggle", NULL, &qh JOGGLEmax);
-	  }
-	  break;
-	case 'R':
-          if (!isdigit(*s) && *s != '-')
-	    fprintf (qh ferr, "qhull warning: missing random seed for option 'QRn'.  Ignored\n");
-	  else {
- 	    qh ROTATErandom= i= qh_strtol(s, &s);
-   	    if (i > 0)
-   	      qh_option ("QRotate-id", &i, NULL );
-	    else if (i < -1)
-   	      qh_option ("QRandom-seed", &i, NULL );
-          }
-	  break;
-	case 'V':
-	  i= qh_strtol (s, &t);
-	  if (qh GOODvertex)
-	    fprintf (qh ferr, "qhull warning: good vertex already defined for option 'QVn'.  Ignored\n");
-          else if (s == t)
-	    fprintf (qh ferr, "qhull warning: no good point id given for option 'QVn'.  Ignored\n");
-	  else if (i < 0) {
- 	    qh GOODvertex= i - 1;
- 	    qh_option ("QV-good-facets-not-point", &i, NULL);
-	  }else {
-  	    qh_option ("QV-good-facets-point", &i, NULL);
-	    qh GOODvertex= i + 1;
-          }
- 	  s= t;
-	  break;
-	default:
-	  s--;
-	  fprintf (qh ferr, "qhull warning: unknown 'Q' qhull option %c, rest ignored\n", (int)s[0]);
-	  while (*++s && !isspace(*s));
-	  break;
-	}
-      }
-      break;
-    case 'T':
-      while (*s && !isspace(*s)) {
-	if (isdigit(*s) || *s == '-')
-	  qh IStracing= qh_strtol(s, &s);
-	else switch(*s++) {
-	case 'c':
-          qh_option ("Tcheck-frequently", NULL, NULL);
-	  qh CHECKfrequently= True;
-	  break;
-	case 's':
-          qh_option ("Tstatistics", NULL, NULL);
-	  qh PRINTstatistics= True;
-	  break;
-	case 'v':
-          qh_option ("Tverify", NULL, NULL);
-	  qh VERIFYoutput= True;
-	  break;
-	case 'z':
-	  if (!qh fout)
-	    fprintf (qh ferr, "qhull warning: output file undefined (stdout).  Option 'Tz' ignored.\n");
-	  else {
-	    qh_option ("Tz-stdout", NULL, NULL);
-  	    qh ferr= qh fout;
-  	    qhmem.ferr= qh fout;
-	  }
-	  break;
-	case 'C':
-	  if (!isdigit(*s))
-	    fprintf (qh ferr, "qhull warning: missing point id for cone for trace option 'TCn'.  Ignored\n");
-	  else {
-	    i= qh_strtol (s, &s);
-	    qh_option ("TCone-stop", &i, NULL);
-	    qh STOPcone= i + 1;
-          }
-	  break;
-	case 'F':
-	  if (!isdigit(*s))
-	    fprintf (qh ferr, "qhull warning: missing frequency count for trace option 'TFn'.  Ignored\n");
-	  else {
-	    qh REPORTfreq= qh_strtol (s, &s);
-            qh_option ("TFacet-log", &qh REPORTfreq, NULL);
-	    qh REPORTfreq2= qh REPORTfreq/2;  /* for tracemerging() */
-	  }
-	  break;
-	case 'I':
-	  if (s[0] != ' ' || s[1] == '\"' || s[1] == '\'' ||isspace (s[1])) {
-	    s++;
-	    fprintf (qh ferr, "qhull warning: option 'TI' mistyped.\nUse 'TI', one space, file name, and space or end-of-line.\nDo not use quotes.  Option 'FI' ignored.\n");
-	  }else {  /* not a procedure because of qh_option (filename, NULL, NULL); */
-	    char filename[500], *t= filename;
-
-	    s++;
-	    while (*s) {
-	      if (t - filename >= sizeof (filename)-2) {
-		fprintf (qh ferr, "qhull error: filename for 'TI' too long.\n");
-		qh_errexit (qh_ERRinput, NULL, NULL);
-	      }
-	      if (isspace (*s))
-		break;
-	      *(t++)= *s++;
-	    }
-	    *t= '\0';
-	    if (!freopen (filename, "r", stdin)) {
-	      fprintf (qh ferr, "qhull error: could not open file \"%s\".", filename);
-	      qh_errexit (qh_ERRinput, NULL, NULL);
-	    }else {
-	      qh_option ("TInput-file", NULL, NULL);
-	      qh_option (filename, NULL, NULL);
-	    }
-	  }
-	  break;
-	case 'O':
-	  if (s[0] != ' ' || s[1] == '\"' || isspace (s[1])) {
-	    s++;
-	    fprintf (qh ferr, "qhull warning: option 'TO' mistyped.\nUse 'TO', one space, file name, and space or end-of-line.\nThe file name may be enclosed in single quotes.\nDo not use double quotes.  Option 'FO' ignored.\n");
-	  }else {  /* not a procedure because of qh_option (filename, NULL, NULL); */
-	    char filename[500], *t= filename;
-	    boolT isquote= False;
-
-	    s++;
-	    if (*s == '\'') {
-	      isquote= True;
-	      s++;
-	    }
-	    while (*s) {
-	      if (t - filename >= sizeof (filename)-2) {
-		fprintf (qh ferr, "qhull error: filename for 'TO' too long.\n");
-		qh_errexit (qh_ERRinput, NULL, NULL);
-	      }
-	      if (isquote) {
-		if (*s == '\'') {
-		  s++;
-		  isquote= False;
-		  break;
-		}
-	      }else if (isspace (*s))
-		break;
-	      *(t++)= *s++;
-	    }
-	    *t= '\0';
-	    if (isquote)
-	      fprintf (qh ferr, "qhull error: missing end quote for option 'TO'.  Rest of line ignored.\n");
-	    else if (!freopen (filename, "w", stdout)) {
-	      fprintf (qh ferr, "qhull error: could not open file \"%s\".", filename);
-	      qh_errexit (qh_ERRinput, NULL, NULL);
-	    }else {
-	      qh_option ("TOutput-file", NULL, NULL);
-	      qh_option (filename, NULL, NULL);
-	    }
-	  }
-	  break;
-	case 'P':
-	  if (!isdigit(*s))
-	    fprintf (qh ferr, "qhull warning: missing point id for trace option 'TPn'.  Ignored\n");
-	  else {
-	    qh TRACEpoint= qh_strtol (s, &s);
-            qh_option ("Trace-point", &qh TRACEpoint, NULL);
-          }
-	  break;
-	case 'M':
-	  if (!isdigit(*s))
-	    fprintf (qh ferr, "qhull warning: missing merge id for trace option 'TMn'.  Ignored\n");
-	  else {
-	    qh TRACEmerge= qh_strtol (s, &s);
-            qh_option ("Trace-merge", &qh TRACEmerge, NULL);
-          }
-	  break;
-	case 'R':
-	  if (!isdigit(*s))
-	    fprintf (qh ferr, "qhull warning: missing rerun count for trace option 'TRn'.  Ignored\n");
-	  else {
-	    qh RERUN= qh_strtol (s, &s);
-            qh_option ("TRerun", &qh RERUN, NULL);
-          }
-	  break;
-	case 'V':
-	  i= qh_strtol (s, &t);
-	  if (s == t)
-	    fprintf (qh ferr, "qhull warning: missing furthest point id for trace option 'TVn'.  Ignored\n");
-	  else if (i < 0) {
-	    qh STOPpoint= i - 1;
-            qh_option ("TV-stop-before-point", &i, NULL);
-	  }else {
-	    qh STOPpoint= i + 1;
-            qh_option ("TV-stop-after-point", &i, NULL);
-          }
-          s= t;
-	  break;
-	case 'W':
-	  if (!isdigit(*s))
-	    fprintf (qh ferr, "qhull warning: missing max width for trace option 'TWn'.  Ignored\n");
-	  else {
- 	    qh TRACEdist= (realT) qh_strtod (s, &s);
-            qh_option ("TWide-trace", NULL, &qh TRACEdist);
-          }
-	  break;
-	default:
-	  s--;
-	  fprintf (qh ferr, "qhull warning: unknown 'T' trace option %c, rest ignored\n", (int)s[0]);
-	  while (*++s && !isspace(*s));
-	  break;
-	}
-      }
-      break;
-    default:
-      fprintf (qh ferr, "qhull warning: unknown flag %c (%x)\n", (int)s[-1],
-	       (int)s[-1]);
-      break;
-    }
-    if (s-1 == prev_s && *s && !isspace(*s)) {
-      fprintf (qh ferr, "qhull warning: missing space after flag %c (%x); reserved for menu. Skipped.\n",
-	       (int)*prev_s, (int)*prev_s);
-      while (*s && !isspace(*s))
-	s++;
-    }
-  }
-  if (isgeom && !qh FORCEoutput && qh PRINTout[1])
-    fprintf (qh ferr, "qhull warning: additional output formats are not compatible with Geomview\n");
-  /* set derived values in qh_initqhull_globals */
-} /* initflags */
-
-
-/*---------------------------------
-
-  qh_initqhull_buffers()
-    initialize global memory buffers
-
-  notes:
-    must match qh_freebuffers()
-*/
-void qh_initqhull_buffers (void) {
-  int k;
-
-  qh TEMPsize= (qhmem.LASTsize - sizeof (setT))/SETelemsize;
-  if (qh TEMPsize <= 0 || qh TEMPsize > qhmem.LASTsize)
-    qh TEMPsize= 8;  /* e.g., if qh_NOmem */
-  qh other_points= qh_setnew (qh TEMPsize);
-  qh del_vertices= qh_setnew (qh TEMPsize);
-  qh coplanarset= qh_setnew (qh TEMPsize);
-  qh NEARzero= (realT *)qh_memalloc(qh hull_dim * sizeof(realT));
-  qh lower_threshold= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
-  qh upper_threshold= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
-  qh lower_bound= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
-  qh upper_bound= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
-  for(k= qh input_dim+1; k--; ) {
-    qh lower_threshold[k]= -REALmax;
-    qh upper_threshold[k]= REALmax;
-    qh lower_bound[k]= -REALmax;
-    qh upper_bound[k]= REALmax;
-  }
-  qh gm_matrix= (coordT *)qh_memalloc((qh hull_dim+1) * qh hull_dim * sizeof(coordT));
-  qh gm_row= (coordT **)qh_memalloc((qh hull_dim+1) * sizeof(coordT *));
-} /* initqhull_buffers */
-
-/*---------------------------------
-
-  qh_initqhull_globals( points, numpoints, dim, ismalloc )
-    initialize globals
-    if ismalloc
-      points were malloc'd and qhull should free at end
-
-  returns:
-    sets qh.first_point, num_points, input_dim, hull_dim and others
-    seeds random number generator (seed=1 if tracing)
-    modifies qh.hull_dim if ((qh.DELAUNAY and qh.PROJECTdelaunay) or qh.PROJECTinput)
-    adjust user flags as needed
-    also checks DIM3 dependencies and constants
-
-  notes:
-    do not use qh_point() since an input transformation may move them elsewhere
-
-  see:
-    qh_initqhull_start() sets default values for non-zero globals
-
-  design:
-    initialize points array from input arguments
-    test for qh.ZEROcentrum
-      (i.e., use opposite vertex instead of cetrum for convexity testing)
-    test for qh.PRINTgood (i.e., only print 'good' facets)
-    initialize qh.CENTERtype, qh.normal_size,
-      qh.center_size, qh.TRACEpoint/level,
-    initialize and test random numbers
-    check for conflicting print output options
-*/
-void qh_initqhull_globals (coordT *points, int numpoints, int dim, boolT ismalloc) {
-  int seed, pointsneeded, extra= 0, i, randi, k;
-  boolT printgeom= False, printmath= False, printcoplanar= False;
-  realT randr;
-  realT factorial;
-
-  time_t timedata;
-
-  trace0((qh ferr, "qh_initqhull_globals: for %s | %s\n", qh rbox_command,
-      qh qhull_command));
-  qh POINTSmalloc= ismalloc;
-  qh first_point= points;
-  qh num_points= numpoints;
-  qh hull_dim= qh input_dim= dim;
-  if (!qh NOpremerge && !qh MERGEexact && !qh PREmerge && qh JOGGLEmax > REALmax/2) {
-    qh MERGING= True;
-    if (qh hull_dim <= 4) {
-      qh PREmerge= True;
-      qh_option ("_pre-merge", NULL, NULL);
-    }else {
-      qh MERGEexact= True;
-      qh_option ("Qxact_merge", NULL, NULL);
-    }
-  }else if (qh MERGEexact)
-    qh MERGING= True;
-  if (!qh NOpremerge && qh JOGGLEmax > REALmax/2) {
-#ifdef qh_NOmerge
-    qh JOGGLEmax= 0.0;
-#endif
-  }
-  if (qh TRIangulate && qh JOGGLEmax < REALmax/2 && qh PRINTprecision)
-    fprintf(qh ferr, "qhull warning: joggle ('QJ') always produces simplicial output.  Triangulated output ('Qt') does nothing.\n");
-  if (qh JOGGLEmax < REALmax/2 && qh DELAUNAY && !qh SCALEinput && !qh SCALElast) {
-    qh SCALElast= True;
-    qh_option ("Qbbound-last-qj", NULL, NULL);
-  }
-  if (qh MERGING && !qh POSTmerge && qh premerge_cos > REALmax/2
-  && qh premerge_centrum == 0) {
-    qh ZEROcentrum= True;
-    qh ZEROall_ok= True;
-    qh_option ("_zero-centrum", NULL, NULL);
-  }
-  if (qh JOGGLEmax < REALmax/2 && REALepsilon > 2e-8 && qh PRINTprecision)
-    fprintf(qh ferr, "qhull warning: real epsilon, %2.2g, is probably too large for joggle ('QJn')\nRecompile with double precision reals (see user.h).\n",
-          REALepsilon);
-#ifdef qh_NOmerge
-  if (qh MERGING) {
-    fprintf (qh ferr, "qhull input error: merging not installed (qh_NOmerge + 'Qx', 'Cn' or 'An')\n");
-    qh_errexit (qh_ERRinput, NULL, NULL);
-  }
-#endif
-  if (!(qh PRINTgood || qh PRINTneighbors)) {
-    if (qh KEEParea || qh KEEPminArea < REALmax/2 || qh KEEPmerge || qh DELAUNAY
-	|| (!qh ONLYgood && (qh GOODvertex || qh GOODpoint))) {
-      qh PRINTgood= True;
-      qh_option ("Pgood", NULL, NULL);
-    }
-  }
-  if (qh DELAUNAY && qh KEEPcoplanar && !qh KEEPinside) {
-    qh KEEPinside= True;
-    qh_option ("Qinterior-keep", NULL, NULL);
-  }
-  if (qh DELAUNAY && qh HALFspace) {
-    fprintf (qh ferr, "qhull input error: can not use Delaunay ('d') or Voronoi ('v') with halfspace intersection ('H')\n");
-    qh_errexit (qh_ERRinput, NULL, NULL);
-  }
-  if (!qh DELAUNAY && (qh UPPERdelaunay || qh ATinfinity)) {
-    fprintf (qh ferr, "qhull input error: use upper-Delaunay ('Qu') or infinity-point ('Qz') with Delaunay ('d') or Voronoi ('v')\n");
-    qh_errexit (qh_ERRinput, NULL, NULL);
-  }
-  if (qh UPPERdelaunay && qh ATinfinity) {
-    fprintf (qh ferr, "qhull input error: can not use infinity-point ('Qz') with upper-Delaunay ('Qu')\n");
-    qh_errexit (qh_ERRinput, NULL, NULL);
-  }
-  if (qh SCALElast && !qh DELAUNAY && qh PRINTprecision)
-    fprintf (qh ferr, "qhull input warning: option 'Qbb' (scale-last-coordinate) is normally used with 'd' or 'v'\n");
-  qh DOcheckmax= (!qh SKIPcheckmax && qh MERGING );
-  qh KEEPnearinside= (qh DOcheckmax && !(qh KEEPinside && qh KEEPcoplanar)
-                          && !qh NOnearinside);
-  if (qh MERGING)
-    qh CENTERtype= qh_AScentrum;
-  else if (qh VORONOI)
-    qh CENTERtype= qh_ASvoronoi;
-  if (qh TESTvneighbors && !qh MERGING) {
-    fprintf(qh ferr, "qhull input error: test vertex neighbors ('Qv') needs a merge option\n");
-    qh_errexit (qh_ERRinput, NULL ,NULL);
-  }
-  if (qh PROJECTinput || (qh DELAUNAY && qh PROJECTdelaunay)) {
-    qh hull_dim -= qh PROJECTinput;
-    if (qh DELAUNAY) {
-      qh hull_dim++;
-      extra= 1;
-    }
-  }
-  if (qh hull_dim <= 1) {
-    fprintf(qh ferr, "qhull error: dimension %d must be > 1\n", qh hull_dim);
-    qh_errexit (qh_ERRinput, NULL, NULL);
-  }
-  for (k= 2, factorial=1.0; k < qh hull_dim; k++)
-    factorial *= k;
-  qh AREAfactor= 1.0 / factorial;
-  trace2((qh ferr, "qh_initqhull_globals: initialize globals.  dim %d numpoints %d malloc? %d projected %d to hull_dim %d\n",
-	dim, numpoints, ismalloc, qh PROJECTinput, qh hull_dim));
-  qh normal_size= qh hull_dim * sizeof(coordT);
-  qh center_size= qh normal_size - sizeof(coordT);
-  pointsneeded= qh hull_dim+1;
-  if (qh hull_dim > qh_DIMmergeVertex) {
-    qh MERGEvertices= False;
-    qh_option ("Q3-no-merge-vertices-dim-high", NULL, NULL);
-  }
-  if (qh GOODpoint)
-    pointsneeded++;
-#ifdef qh_NOtrace
-  if (qh IStracing) {
-    fprintf (qh ferr, "qhull input error: tracing is not installed (qh_NOtrace in user.h)");
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }
-#endif
-  if (qh RERUN > 1) {
-    qh TRACElastrun= qh IStracing; /* qh_build_withrestart duplicates next conditional */
-    if (qh IStracing != -1)
-      qh IStracing= 0;
-  }else if (qh TRACEpoint != -1 || qh TRACEdist < REALmax/2 || qh TRACEmerge) {
-    qh TRACElevel= (qh IStracing? qh IStracing : 3);
-    qh IStracing= 0;
-  }
-  if (qh ROTATErandom == 0 || qh ROTATErandom == -1) {
-    seed= time (&timedata);
-    if (qh ROTATErandom  == -1) {
-      seed= -seed;
-      qh_option ("QRandom-seed", &seed, NULL );
-    }else
-      qh_option ("QRotate-random", &seed, NULL);
-    qh ROTATErandom= seed;
-  }
-  seed= qh ROTATErandom;
-  if (seed == INT_MIN)    /* default value */
-    seed= 1;
-  else if (seed < 0)
-    seed= -seed;
-  qh_RANDOMseed_(seed);
-  randr= 0.0;
-  for (i= 1000; i--; ) {
-    randi= qh_RANDOMint;
-    randr += randi;
-    if (randi > qh_RANDOMmax) {
-      fprintf (qh ferr, "\
-qhull configuration error (qh_RANDOMmax in user.h):\n\
-   random integer %d > qh_RANDOMmax (%.8g)\n",
-	       randi, qh_RANDOMmax);
-      qh_errexit (qh_ERRinput, NULL, NULL);
-    }
-  }
-  qh_RANDOMseed_(seed);
-  randr = randr/1000;
-  if (randr < qh_RANDOMmax/10
-  || randr > qh_RANDOMmax * 5)
-    fprintf (qh ferr, "\
-qhull configuration warning (qh_RANDOMmax in user.h):\n\
-   average of 1000 random integers (%.2g) is much different than expected (%.2g).\n\
-   Is qh_RANDOMmax (%.2g) wrong?\n",
-	     randr, qh_RANDOMmax/2.0, qh_RANDOMmax);
-  qh RANDOMa= 2.0 * qh RANDOMfactor/qh_RANDOMmax;
-  qh RANDOMb= 1.0 - qh RANDOMfactor;
-  if (qh_HASHfactor < 1.1) {
-    fprintf(qh ferr, "qhull internal error (qh_initqhull_globals): qh_HASHfactor %d must be at least 1.1.  Qhull uses linear hash probing\n",
-      qh_HASHfactor);
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }
-  if (numpoints+extra < pointsneeded) {
-    fprintf(qh ferr,"qhull input error: not enough points (%d) to construct initial simplex (need %d)\n",
-	    numpoints, pointsneeded);
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  if (qh PRINTtransparent) {
-    if (qh hull_dim != 4 || !qh DELAUNAY || qh VORONOI || qh DROPdim >= 0) {
-      fprintf(qh ferr,"qhull input error: transparent Delaunay ('Gt') needs 3-d Delaunay ('d') w/o 'GDn'\n");
-      qh_errexit(qh_ERRinput, NULL, NULL);
-    }
-    qh DROPdim = 3;
-    qh PRINTridges = True;
-  }
-  for (i= qh_PRINTEND; i--; ) {
-    if (qh PRINTout[i] == qh_PRINTgeom)
-      printgeom= True;
-    else if (qh PRINTout[i] == qh_PRINTmathematica)
-      printmath= True;
-    else if (qh PRINTout[i] == qh_PRINTcoplanars)
-      printcoplanar= True;
-    else if (qh PRINTout[i] == qh_PRINTpointnearest)
-      printcoplanar= True;
-    else if (qh PRINTout[i] == qh_PRINTpointintersect && !qh HALFspace) {
-      fprintf (qh ferr, "qhull input error: option 'Fp' is only used for \nhalfspace intersection ('Hn,n,n').\n");
-      qh_errexit (qh_ERRinput, NULL, NULL);
-    }else if (qh PRINTout[i] == qh_PRINTtriangles && (qh HALFspace || qh VORONOI)) {
-      fprintf (qh ferr, "qhull input error: option 'Ft' is not available for Voronoi vertices or halfspace intersection\n");
-      qh_errexit (qh_ERRinput, NULL, NULL);
-    }else if (qh PRINTout[i] == qh_PRINTcentrums && qh VORONOI) {
-      fprintf (qh ferr, "qhull input error: option 'FC' is not available for Voronoi vertices ('v')\n");
-      qh_errexit (qh_ERRinput, NULL, NULL);
-    }else if (qh PRINTout[i] == qh_PRINTvertices) {
-      if (qh VORONOI)
-        qh_option ("Fvoronoi", NULL, NULL);
-      else
-        qh_option ("Fvertices", NULL, NULL);
-    }
-  }
-  if (printcoplanar && qh DELAUNAY && qh JOGGLEmax < REALmax/2) {
-    if (qh PRINTprecision)
-      fprintf (qh ferr, "qhull input warning: 'QJ' (joggle) will usually prevent coincident input sites for options 'Fc' and 'FP'\n");
-  }
-  if (!qh KEEPcoplanar && !qh KEEPinside && !qh ONLYgood) {
-    if ((qh PRINTcoplanar && qh PRINTspheres) || printcoplanar) {
-      qh KEEPcoplanar = True;
-      qh_option ("Qcoplanar", NULL, NULL);
-    }
-  }
-  if (printmath && (qh hull_dim > 3 || qh VORONOI)) {
-    fprintf (qh ferr, "qhull input error: Mathematica output is only available for 2-d and 3-d convex hulls and 2-d Delaunay triangulations\n");
-    qh_errexit (qh_ERRinput, NULL, NULL);
-  }
-  if (printgeom) {
-    if (qh hull_dim > 4) {
-      fprintf (qh ferr, "qhull input error: Geomview output is only available for 2-d, 3-d and 4-d\n");
-      qh_errexit (qh_ERRinput, NULL, NULL);
-    }
-    if (qh PRINTnoplanes && !(qh PRINTcoplanar + qh PRINTcentrums
-     + qh PRINTdots + qh PRINTspheres + qh DOintersections + qh PRINTridges)) {
-      fprintf (qh ferr, "qhull input error: no output specified for Geomview\n");
-      qh_errexit (qh_ERRinput, NULL, NULL);
-    }
-    if (qh VORONOI && (qh hull_dim > 3 || qh DROPdim >= 0)) {
-      fprintf (qh ferr, "qhull input error: Geomview output for Voronoi diagrams only for 2-d\n");
-      qh_errexit (qh_ERRinput, NULL, NULL);
-    }
-    /* can not warn about furthest-site Geomview output: no lower_threshold */
-    if (qh hull_dim == 4 && qh DROPdim == -1 &&
-	(qh PRINTcoplanar || qh PRINTspheres || qh PRINTcentrums)) {
-      fprintf (qh ferr, "qhull input warning: coplanars, vertices, and centrums output not\n\
-available for 4-d output (ignored).  Could use 'GDn' instead.\n");
-      qh PRINTcoplanar= qh PRINTspheres= qh PRINTcentrums= False;
-    }
-  }
-  qh PRINTdim= qh hull_dim;
-  if (qh DROPdim >=0) {    /* after Geomview checks */
-    if (qh DROPdim < qh hull_dim) {
-      qh PRINTdim--;
-      if (!printgeom || qh hull_dim < 3)
-        fprintf (qh ferr, "qhull input warning: drop dimension 'GD%d' is only available for 3-d/4-d Geomview\n", qh DROPdim);
-    }else
-      qh DROPdim= -1;
-  }else if (qh VORONOI) {
-    qh DROPdim= qh hull_dim-1;
-    qh PRINTdim= qh hull_dim-1;
-  }
-} /* initqhull_globals */
-
-/*---------------------------------
-
-  qh_initqhull_mem(  )
-    initialize mem.c for qhull
-    qh.hull_dim and qh.normal_size determine some of the allocation sizes
-    if qh.MERGING,
-      includes ridgeT
-    calls qh_user_memsizes() to add up to 10 additional sizes for quick allocation
-      (see numsizes below)
-
-  returns:
-    mem.c already for qh_memalloc/qh_memfree (errors if called beforehand)
-
-  notes:
-    qh_produceoutput() prints memsizes
-
-*/
-void qh_initqhull_mem (void) {
-  int numsizes;
-  int i;
-
-  numsizes= 8+10;
-  qh_meminitbuffers (qh IStracing, qh_MEMalign, numsizes,
-                     qh_MEMbufsize,qh_MEMinitbuf);
-  qh_memsize(sizeof(vertexT));
-  if (qh MERGING) {
-    qh_memsize(sizeof(ridgeT));
-    qh_memsize(sizeof(mergeT));
-  }
-  qh_memsize(sizeof(facetT));
-  i= sizeof(setT) + (qh hull_dim - 1) * SETelemsize;  /* ridge.vertices */
-  qh_memsize(i);
-  qh_memsize(qh normal_size);        /* normal */
-  i += SETelemsize;                 /* facet.vertices, .ridges, .neighbors */
-  qh_memsize(i);
-  qh_user_memsizes();
-  qh_memsetup();
-} /* initqhull_mem */
-
-/*---------------------------------
-
-  qh_initqhull_start( infile, outfile, errfile )
-    start initialization of qhull
-    initialize statistics, stdio, default values for global variables
-
-  see:
-    qh_maxmin() determines the precision constants
-*/
-void qh_initqhull_start (FILE *infile, FILE *outfile, FILE *errfile) {
-
-  qh_CPUclock; /* start the clock */
-#if qh_QHpointer
-  if (!(qh_qh= (qhT *)malloc (sizeof(qhT)))) {
-    fprintf (errfile, "qhull error (qh_initqhull_globals): insufficient memory\n");
-    exit (qh_ERRmem);  /* no error handler */
-  }
-  memset((char *)qh_qh, 0, sizeof(qhT));   /* every field is 0, FALSE, NULL */
-#else
-  memset((char *)&qh_qh, 0, sizeof(qhT));
-#endif
-  strcat (qh qhull, "qhull");
-  qh_initstatistics();
-  qh ANGLEmerge= True;
-  qh DROPdim= -1;
-  qh ferr= errfile;
-  qh fin= infile;
-  qh fout= outfile;
-  qh furthest_id= -1;
-  qh JOGGLEmax= REALmax;
-  qh KEEPminArea = REALmax;
-  qh last_low= REALmax;
-  qh last_high= REALmax;
-  qh last_newhigh= REALmax;
-  qh max_outside= 0.0;
-  qh max_vertex= 0.0;
-  qh MAXabs_coord= 0.0;
-  qh MAXsumcoord= 0.0;
-  qh MAXwidth= -REALmax;
-  qh MERGEindependent= True;
-  qh MINdenom_1= fmax_(1.0/REALmax, REALmin); /* used by qh_scalepoints */
-  qh MINoutside= 0.0;
-  qh MINvisible= REALmax;
-  qh MAXcoplanar= REALmax;
-  qh outside_err= REALmax;
-  qh premerge_centrum= 0.0;
-  qh premerge_cos= REALmax;
-  qh PRINTprecision= True;
-  qh postmerge_cos= REALmax;
-  qh postmerge_centrum= 0.0;
-  qh ROTATErandom= INT_MIN;
-  qh MERGEvertices= True;
-  qh totarea= 0.0;
-  qh totvol= 0.0;
-  qh TRACEdist= REALmax;
-  qh TRACEpoint= -1; /* recompile or use 'TPn' */
-  qh tracefacet_id= UINT_MAX;  /* recompile to trace a facet */
-  qh tracevertex_id= UINT_MAX; /* recompile to trace a vertex */
-  qh_RANDOMseed_(1);
-} /* initqhull_start */
-
-/*---------------------------------
-
-  qh_initthresholds( commandString )
-    set thresholds for printing and scaling from commandString
-
-  returns:
-    sets qh.GOODthreshold or qh.SPLITthreshold if 'Pd0D1' used
-
-  see:
-    qh_initflags(), 'Qbk' 'QBk' 'Pdk' and 'PDk'
-    qh_inthresholds()
-
-  design:
-    for each 'Pdn' or 'PDn' option
-      check syntax
-      set qh.lower_threshold or qh.upper_threshold
-    set qh.GOODthreshold if an unbounded threshold is used
-    set qh.SPLITthreshold if a bounded threshold is used
-*/
-void qh_initthresholds(char *command) {
-  realT value;
-  int index, maxdim, k;
-  char *s= command;
-  char key;
-
-  maxdim= qh input_dim;
-  if (qh DELAUNAY && (qh PROJECTdelaunay || qh PROJECTinput))
-    maxdim++;
-  while (*s) {
-    if (*s == '-')
-      s++;
-    if (*s == 'P') {
-      s++;
-      while (*s && !isspace(key= *s++)) {
-	if (key == 'd' || key == 'D') {
-	  if (!isdigit(*s)) {
-	    fprintf(qh ferr, "qhull warning: no dimension given for Print option '%c' at: %s.  Ignored\n",
-		    key, s-1);
-	    continue;
-	  }
-	  index= qh_strtol (s, &s);
-	  if (index >= qh hull_dim) {
-	    fprintf(qh ferr, "qhull warning: dimension %d for Print option '%c' is >= %d.  Ignored\n",
-	        index, key, qh hull_dim);
-	    continue;
-	  }
-	  if (*s == ':') {
-	    s++;
-	    value= qh_strtod(s, &s);
-	    if (fabs((double)value) > 1.0) {
-	      fprintf(qh ferr, "qhull warning: value %2.4g for Print option %c is > +1 or < -1.  Ignored\n",
-	              value, key);
-	      continue;
-	    }
-	  }else
-	    value= 0.0;
-	  if (key == 'd')
-	    qh lower_threshold[index]= value;
-	  else
-	    qh upper_threshold[index]= value;
-	}
-      }
-    }else if (*s == 'Q') {
-      s++;
-      while (*s && !isspace(key= *s++)) {
-	if (key == 'b' && *s == 'B') {
-	  s++;
-	  for (k=maxdim; k--; ) {
-	    qh lower_bound[k]= -qh_DEFAULTbox;
-	    qh upper_bound[k]= qh_DEFAULTbox;
-	  }
-	}else if (key == 'b' && *s == 'b')
-	  s++;
-	else if (key == 'b' || key == 'B') {
-	  if (!isdigit(*s)) {
-	    fprintf(qh ferr, "qhull warning: no dimension given for Qhull option %c.  Ignored\n",
-		    key);
-	    continue;
-	  }
-	  index= qh_strtol (s, &s);
-	  if (index >= maxdim) {
-	    fprintf(qh ferr, "qhull warning: dimension %d for Qhull option %c is >= %d.  Ignored\n",
-	        index, key, maxdim);
-	    continue;
-	  }
-	  if (*s == ':') {
-	    s++;
-	    value= qh_strtod(s, &s);
-	  }else if (key == 'b')
-	    value= -qh_DEFAULTbox;
-	  else
-	    value= qh_DEFAULTbox;
-	  if (key == 'b')
-	    qh lower_bound[index]= value;
-	  else
-	    qh upper_bound[index]= value;
-	}
-      }
-    }else {
-      while (*s && !isspace (*s))
-        s++;
-    }
-    while (isspace (*s))
-      s++;
-  }
-  for (k= qh hull_dim; k--; ) {
-    if (qh lower_threshold[k] > -REALmax/2) {
-      qh GOODthreshold= True;
-      if (qh upper_threshold[k] < REALmax/2) {
-        qh SPLITthresholds= True;
-        qh GOODthreshold= False;
-        break;
-      }
-    }else if (qh upper_threshold[k] < REALmax/2)
-      qh GOODthreshold= True;
-  }
-} /* initthresholds */
-
-/*---------------------------------
-
-  qh_option( option, intVal, realVal )
-    add an option description to qh.qhull_options
-
-  notes:
-    will be printed with statistics ('Ts') and errors
-    strlen(option) < 40
-*/
-void qh_option (char *option, int *i, realT *r) {
-  char buf[200];
-  int len, maxlen;
-
-  sprintf (buf, "  %s", option);
-  if (i)
-    sprintf (buf+strlen(buf), " %d", *i);
-  if (r)
-    sprintf (buf+strlen(buf), " %2.2g", *r);
-  len= strlen(buf);
-  qh qhull_optionlen += len;
-  maxlen= sizeof (qh qhull_options) - len -1;
-  maximize_(maxlen, 0);
-  if (qh qhull_optionlen >= 80 && maxlen > 0) {
-    qh qhull_optionlen= len;
-    strncat (qh qhull_options, "\n", maxlen--);
-  }
-  strncat (qh qhull_options, buf, maxlen);
-} /* option */
-
-#if qh_QHpointer
-/*---------------------------------
-
-  qh_restore_qhull( oldqh )
-    restores a previously saved qhull
-    also restores qh_qhstat and qhmem.tempstack
-
-  notes:
-    errors if current qhull hasn't been saved or freed
-    uses qhmem for error reporting
-
-  NOTE 1998/5/11:
-    Freeing memory after qh_save_qhull and qh_restore_qhull
-    is complicated.  The procedures will be redesigned.
-
-  see:
-    qh_save_qhull()
-*/
-void qh_restore_qhull (qhT **oldqh) {
-
-  if (*oldqh && strcmp ((*oldqh)->qhull, "qhull")) {
-    fprintf (qhmem.ferr, "qhull internal error (qh_restore_qhull): %p is not a qhull data structure\n",
-                  *oldqh);
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }
-  if (qh_qh) {
-    fprintf (qhmem.ferr, "qhull internal error (qh_restore_qhull): did not save or free existing qhull\n");
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }
-  if (!*oldqh || !(*oldqh)->old_qhstat) {
-    fprintf (qhmem.ferr, "qhull internal error (qh_restore_qhull): did not previously save qhull %p\n",
-                  *oldqh);
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }
-  qh_qh= *oldqh;
-  *oldqh= NULL;
-  qh_qhstat= qh old_qhstat;
-  qhmem.tempstack= qh old_tempstack;
-  trace1((qh ferr, "qh_restore_qhull: restored qhull from %p\n", *oldqh));
-} /* restore_qhull */
-
-/*---------------------------------
-
-  qh_save_qhull(  )
-    saves qhull for a later qh_restore_qhull
-    also saves qh_qhstat and qhmem.tempstack
-
-  returns:
-    qh_qh=NULL
-
-  notes:
-    need to initialize qhull or call qh_restore_qhull before continuing
-
-  NOTE 1998/5/11:
-    Freeing memory after qh_save_qhull and qh_restore_qhull
-    is complicated.  The procedures will be redesigned.
-
-  see:
-    qh_restore_qhull()
-*/
-qhT *qh_save_qhull (void) {
-  qhT *oldqh;
-
-  trace1((qhmem.ferr, "qh_save_qhull: save qhull %p\n", qh_qh));
-  if (!qh_qh) {
-    fprintf (qhmem.ferr, "qhull internal error (qh_save_qhull): qhull not initialized\n");
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }
-  qh old_qhstat= qh_qhstat;
-  qh_qhstat= NULL;
-  qh old_tempstack= qhmem.tempstack;
-  qhmem.tempstack= NULL;
-  oldqh= qh_qh;
-  qh_qh= NULL;
-  return oldqh;
-} /* save_qhull */
-
-#endif
-
-/*---------------------------------
-
-  qh_strtol( s, endp) qh_strtod( s, endp)
-    internal versions of strtol() and strtod()
-    does not skip trailing spaces
-  notes:
-    some implementations of strtol()/strtod() skip trailing spaces
-*/
-double qh_strtod (const char *s, char **endp) {
-  double result;
-
-  result= strtod (s, endp);
-  if (s < (*endp) && (*endp)[-1] == ' ')
-    (*endp)--;
-  return result;
-} /* strtod */
-
-int qh_strtol (const char *s, char **endp) {
-  int result;
-
-  result= (int) strtol (s, endp, 10);
-  if (s< (*endp) && (*endp)[-1] == ' ')
-    (*endp)--;
-  return result;
-} /* strtol */
diff --git a/extern/qhull/src/io.c b/extern/qhull/src/io.c
deleted file mode 100644
index 9b0ccdd0b24..00000000000
--- a/extern/qhull/src/io.c
+++ /dev/null
@@ -1,4089 +0,0 @@
-/*  ---------------------------------
-
-   io.c
-   Input/Output routines of qhull application
-
-   see qh-io.htm and io.h
-
-   see user.c for qh_errprint and qh_printfacetlist
-
-   unix.c calls qh_readpoints and qh_produce_output
-
-   unix.c and user.c are the only callers of io.c functions
-
-   copyright (c) 1993-2002 The Geometry Center
-*/
-
-#include "qhull_a.h"
-
-/*========= -prototypes for internal functions ========= */
-
-static int qh_compare_facetarea(const void *p1, const void *p2);
-static int qh_compare_facetmerge(const void *p1, const void *p2);
-static int qh_compare_facetvisit(const void *p1, const void *p2);
-int qh_compare_vertexpoint(const void *p1, const void *p2); /* not used */
-
-/*========= -functions in alphabetical order after qh_produce_output()  =====*/
-
-/*---------------------------------
-
-  qh_produce_output()
-    prints out the result of qhull in desired format
-    if qh.GETarea
-      computes and prints area and volume
-    qh.PRINTout[] is an array of output formats
-
-  notes:
-    prints output in qh.PRINTout order
-*/
-void qh_produce_output(void) {
-  int i, tempsize= qh_setsize ((setT*)qhmem.tempstack), d_1;
-
-  if (qh VORONOI) {
-    qh_clearcenters (qh_ASvoronoi);
-    qh_vertexneighbors();
-  }
-  if (qh TRIangulate) {
-    qh_triangulate();
-    if (qh VERIFYoutput && !qh CHECKfrequently)
-      qh_checkpolygon (qh facet_list);
-  }
-  qh_findgood_all (qh facet_list);
-  if (qh GETarea)
-    qh_getarea(qh facet_list);
-  if (qh KEEParea || qh KEEPmerge || qh KEEPminArea < REALmax/2)
-    qh_markkeep (qh facet_list);
-  if (qh PRINTsummary)
-    qh_printsummary(qh ferr);
-  else if (qh PRINTout[0] == qh_PRINTnone)
-    qh_printsummary(qh fout);
-  for (i= 0; i < qh_PRINTEND; i++)
-    qh_printfacets (qh fout, qh PRINTout[i], qh facet_list, NULL, !qh_ALL);
-  qh_allstatistics();
-  if (qh PRINTprecision && !qh MERGING && (qh JOGGLEmax > REALmax/2 || qh RERUN))
-    qh_printstats (qh ferr, qhstat precision, NULL);
-  if (qh VERIFYoutput && (zzval_(Zridge) > 0 || zzval_(Zridgemid) > 0))
-    qh_printstats (qh ferr, qhstat vridges, NULL);
-  if (qh PRINTstatistics) {
-    qh_collectstatistics();
-    qh_printstatistics(qh ferr, "");
-    qh_memstatistics (qh ferr);
-    d_1= sizeof(setT) + (qh hull_dim - 1) * SETelemsize;
-    fprintf(qh ferr, "\
-    size in bytes: merge %ld ridge %ld vertex %ld facet %ld\n\
-         normal %d ridge vertices %d facet vertices or neighbors %ld\n",
-	    sizeof(mergeT), sizeof(ridgeT),
-	    sizeof(vertexT), sizeof(facetT),
-	    qh normal_size, d_1, d_1 + SETelemsize);
-  }
-  if (qh_setsize ((setT*)qhmem.tempstack) != tempsize) {
-    fprintf (qh ferr, "qhull internal error (qh_produce_output): temporary sets not empty (%d)\n",
-	     qh_setsize ((setT*)qhmem.tempstack));
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }
-} /* produce_output */
-
-
-/*---------------------------------
-
-  dfacet( id )
-    print facet by id, for debugging
-
-*/
-void dfacet (unsigned id) {
-  facetT *facet;
-
-  FORALLfacets {
-    if (facet->id == id) {
-      qh_printfacet (qh fout, facet);
-      break;
-    }
-  }
-} /* dfacet */
-
-
-/*---------------------------------
-
-  dvertex( id )
-    print vertex by id, for debugging
-*/
-void dvertex (unsigned id) {
-  vertexT *vertex;
-
-  FORALLvertices {
-    if (vertex->id == id) {
-      qh_printvertex (qh fout, vertex);
-      break;
-    }
-  }
-} /* dvertex */
-
-
-/*---------------------------------
-
-  qh_compare_vertexpoint( p1, p2 )
-    used by qsort() to order vertices by point id
-*/
-int qh_compare_vertexpoint(const void *p1, const void *p2) {
-  vertexT *a= *((vertexT **)p1), *b= *((vertexT **)p2);
-
-  return ((qh_pointid(a->point) > qh_pointid(b->point)?1:-1));
-} /* compare_vertexpoint */
-
-/*---------------------------------
-
-  qh_compare_facetarea( p1, p2 )
-    used by qsort() to order facets by area
-*/
-static int qh_compare_facetarea(const void *p1, const void *p2) {
-  facetT *a= *((facetT **)p1), *b= *((facetT **)p2);
-
-  if (!a->isarea)
-    return -1;
-  if (!b->isarea)
-    return 1;
-  if (a->f.area > b->f.area)
-    return 1;
-  else if (a->f.area == b->f.area)
-    return 0;
-  return -1;
-} /* compare_facetarea */
-
-/*---------------------------------
-
-  qh_compare_facetmerge( p1, p2 )
-    used by qsort() to order facets by number of merges
-*/
-static int qh_compare_facetmerge(const void *p1, const void *p2) {
-  facetT *a= *((facetT **)p1), *b= *((facetT **)p2);
-
-  return (a->nummerge - b->nummerge);
-} /* compare_facetvisit */
-
-/*---------------------------------
-
-  qh_compare_facetvisit( p1, p2 )
-    used by qsort() to order facets by visit id or id
-*/
-static int qh_compare_facetvisit(const void *p1, const void *p2) {
-  facetT *a= *((facetT **)p1), *b= *((facetT **)p2);
-  int i,j;
-
-  if (!(i= a->visitid))
-    i= - a->id; /* do not convert to int */
-  if (!(j= b->visitid))
-    j= - b->id;
-  return (i - j);
-} /* compare_facetvisit */
-
-/*---------------------------------
-
-  qh_countfacets( facetlist, facets, printall,
-          numfacets, numsimplicial, totneighbors, numridges, numcoplanar, numtricoplanars  )
-    count good facets for printing and set visitid
-    if allfacets, ignores qh_skipfacet()
-
-  notes:
-    qh_printsummary and qh_countfacets must match counts
-
-  returns:
-    numfacets, numsimplicial, total neighbors, numridges, coplanars
-    each facet with ->visitid indicating 1-relative position
-      ->visitid==0 indicates not good
-
-  notes
-    numfacets >= numsimplicial
-    if qh.NEWfacets,
-      does not count visible facets (matches qh_printafacet)
-
-  design:
-    for all facets on facetlist and in facets set
-      unless facet is skipped or visible (i.e., will be deleted)
-        mark facet->visitid
-        update counts
-*/
-void qh_countfacets (facetT *facetlist, setT *facets, boolT printall,
-    int *numfacetsp, int *numsimplicialp, int *totneighborsp, int *numridgesp, int *numcoplanarsp, int *numtricoplanarsp) {
-  facetT *facet, **facetp;
-  int numfacets= 0, numsimplicial= 0, numridges= 0, totneighbors= 0, numcoplanars= 0, numtricoplanars= 0;
-
-  FORALLfacet_(facetlist) {
-    if ((facet->visible && qh NEWfacets)
-    || (!printall && qh_skipfacet(facet)))
-      facet->visitid= 0;
-    else {
-      facet->visitid= ++numfacets;
-      totneighbors += qh_setsize (facet->neighbors);
-      if (facet->simplicial) {
-        numsimplicial++;
-	if (facet->keepcentrum && facet->tricoplanar)
-	  numtricoplanars++;
-      }else
-        numridges += qh_setsize (facet->ridges);
-      if (facet->coplanarset)
-        numcoplanars += qh_setsize (facet->coplanarset);
-    }
-  }
-  FOREACHfacet_(facets) {
-    if ((facet->visible && qh NEWfacets)
-    || (!printall && qh_skipfacet(facet)))
-      facet->visitid= 0;
-    else {
-      facet->visitid= ++numfacets;
-      totneighbors += qh_setsize (facet->neighbors);
-      if (facet->simplicial){
-        numsimplicial++;
-	if (facet->keepcentrum && facet->tricoplanar)
-	  numtricoplanars++;
-      }else
-        numridges += qh_setsize (facet->ridges);
-      if (facet->coplanarset)
-        numcoplanars += qh_setsize (facet->coplanarset);
-    }
-  }
-  qh visit_id += numfacets+1;
-  *numfacetsp= numfacets;
-  *numsimplicialp= numsimplicial;
-  *totneighborsp= totneighbors;
-  *numridgesp= numridges;
-  *numcoplanarsp= numcoplanars;
-  *numtricoplanarsp= numtricoplanars;
-} /* countfacets */
-
-/*---------------------------------
-
-  qh_detvnorm( vertex, vertexA, centers, offset )
-    compute separating plane of the Voronoi diagram for a pair of input sites
-    centers= set of facets (i.e., Voronoi vertices)
-      facet->visitid= 0 iff vertex-at-infinity (i.e., unbounded)
-
-  assumes:
-    qh_ASvoronoi and qh_vertexneighbors() already set
-
-  returns:
-    norm
-      a pointer into qh.gm_matrix to qh.hull_dim-1 reals
-      copy the data before reusing qh.gm_matrix
-    offset
-      if 'QVn'
-        sign adjusted so that qh.GOODvertexp is inside
-      else
-        sign adjusted so that vertex is inside
-
-    qh.gm_matrix= simplex of points from centers relative to first center
-
-  notes:
-    in io.c so that code for 'v Tv' can be removed by removing io.c
-    returns pointer into qh.gm_matrix to avoid tracking of temporary memory
-
-  design:
-    determine midpoint of input sites
-    build points as the set of Voronoi vertices
-    select a simplex from points (if necessary)
-      include midpoint if the Voronoi region is unbounded
-    relocate the first vertex of the simplex to the origin
-    compute the normalized hyperplane through the simplex
-    orient the hyperplane toward 'QVn' or 'vertex'
-    if 'Tv' or 'Ts'
-      if bounded
-        test that hyperplane is the perpendicular bisector of the input sites
-      test that Voronoi vertices not in the simplex are still on the hyperplane
-    free up temporary memory
-*/
-pointT *qh_detvnorm (vertexT *vertex, vertexT *vertexA, setT *centers, realT *offsetp) {
-  facetT *facet, **facetp;
-  int  i, k, pointid, pointidA, point_i, point_n;
-  setT *simplex= NULL;
-  pointT *point, **pointp, *point0, *midpoint, *normal, *inpoint;
-  coordT *coord, *gmcoord, *normalp;
-  setT *points= qh_settemp (qh TEMPsize);
-  boolT nearzero= False;
-  boolT unbounded= False;
-  int numcenters= 0;
-  int dim= qh hull_dim - 1;
-  realT dist, offset, angle, zero= 0.0;
-
-  midpoint= qh gm_matrix + qh hull_dim * qh hull_dim;  /* last row */
-  for (k= 0; k < dim; k++)
-    midpoint[k]= (vertex->point[k] + vertexA->point[k])/2;
-  FOREACHfacet_(centers) {
-    numcenters++;
-    if (!facet->visitid)
-      unbounded= True;
-    else {
-      if (!facet->center)
-        facet->center= qh_facetcenter (facet->vertices);
-      qh_setappend (&points, facet->center);
-    }
-  }
-  if (numcenters > dim) {
-    simplex= qh_settemp (qh TEMPsize);
-    qh_setappend (&simplex, vertex->point);
-    if (unbounded)
-      qh_setappend (&simplex, midpoint);
-    qh_maxsimplex (dim, points, NULL, 0, &simplex);
-    qh_setdelnth (simplex, 0);
-  }else if (numcenters == dim) {
-    if (unbounded)
-      qh_setappend (&points, midpoint);
-    simplex= points;
-  }else {
-    fprintf(qh ferr, "qh_detvnorm: too few points (%d) to compute separating plane\n", numcenters);
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }
-  i= 0;
-  gmcoord= qh gm_matrix;
-  point0= SETfirstt_(simplex, pointT);
-  FOREACHpoint_(simplex) {
-    if (qh IStracing >= 4)
-      qh_printmatrix(qh ferr, "qh_detvnorm: Voronoi vertex or midpoint",
-                              &point, 1, dim);
-    if (point != point0) {
-      qh gm_row[i++]= gmcoord;
-      coord= point0;
-      for (k= dim; k--; )
-        *(gmcoord++)= *point++ - *coord++;
-    }
-  }
-  qh gm_row[i]= gmcoord;  /* does not overlap midpoint, may be used later for qh_areasimplex */
-  normal= gmcoord;
-  qh_sethyperplane_gauss (dim, qh gm_row, point0, True,
-           	normal, &offset, &nearzero);
-  if (qh GOODvertexp == vertexA->point)
-    inpoint= vertexA->point;
-  else
-    inpoint= vertex->point;
-  zinc_(Zdistio);
-  dist= qh_distnorm (dim, inpoint, normal, &offset);
-  if (dist > 0) {
-    offset= -offset;
-    normalp= normal;
-    for (k= dim; k--; ) {
-      *normalp= -(*normalp);
-      normalp++;
-    }
-  }
-  if (qh VERIFYoutput || qh PRINTstatistics) {
-    pointid= qh_pointid (vertex->point);
-    pointidA= qh_pointid (vertexA->point);
-    if (!unbounded) {
-      zinc_(Zdiststat);
-      dist= qh_distnorm (dim, midpoint, normal, &offset);
-      if (dist < 0)
-        dist= -dist;
-      zzinc_(Zridgemid);
-      wwmax_(Wridgemidmax, dist);
-      trace4((qh ferr, "qh_detvnorm: points %d %d midpoint dist %2.2g\n",
-                 pointid, pointidA, dist));
-      for (k= 0; k < dim; k++)
-        midpoint[k]= vertexA->point[k] - vertex->point[k];  /* overwrites midpoint! */
-      qh_normalize (midpoint, dim, False);
-      angle= qh_distnorm (dim, midpoint, normal, &zero); /* qh_detangle uses dim+1 */
-      if (angle < 0.0)
-	angle= angle + 1.0;
-      else
-	angle= angle - 1.0;
-      if (angle < 0.0)
-	angle -= angle;
-      trace4((qh ferr, "qh_detvnorm: points %d %d angle %2.2g nearzero %d\n",
-                 pointid, pointidA, angle, nearzero));
-      if (nearzero) {
-        zzinc_(Zridge0);
-        wwmax_(Wridge0max, angle);
-      }else {
-        zzinc_(Zridgeok)
-        wwmax_(Wridgeokmax, angle);
-      }
-    }
-    if (simplex != points) {
-      FOREACHpoint_i_(points) {
-        if (!qh_setin (simplex, point)) {
-          facet= SETelemt_(centers, point_i, facetT);
-	  zinc_(Zdiststat);
-  	  dist= qh_distnorm (dim, point, normal, &offset);
-          if (dist < 0)
-            dist= -dist;
-	  zzinc_(Zridge);
-          wwmax_(Wridgemax, dist);
-          trace4((qh ferr, "qh_detvnorm: points %d %d Voronoi vertex %d dist %2.2g\n",
-                             pointid, pointidA, facet->visitid, dist));
-        }
-      }
-    }
-  }
-  *offsetp= offset;
-  if (simplex != points)
-    qh_settempfree (&simplex);
-  qh_settempfree (&points);
-  return normal;
-} /* detvnorm */
-
-/*---------------------------------
-
-  qh_detvridge( vertexA )
-    determine Voronoi ridge from 'seen' neighbors of vertexA
-    include one vertex-at-infinite if an !neighbor->visitid
-
-  returns:
-    temporary set of centers (facets, i.e., Voronoi vertices)
-    sorted by center id
-*/
-setT *qh_detvridge (vertexT *vertex) {
-  setT *centers= qh_settemp (qh TEMPsize);
-  setT *tricenters= qh_settemp (qh TEMPsize);
-  facetT *neighbor, **neighborp;
-  boolT firstinf= True;
-
-  FOREACHneighbor_(vertex) {
-    if (neighbor->seen) {
-      if (neighbor->visitid) {
-	if (!neighbor->tricoplanar || qh_setunique (&tricenters, neighbor->center))
-	  qh_setappend (¢ers, neighbor);
-      }else if (firstinf) {
-        firstinf= False;
-        qh_setappend (¢ers, neighbor);
-      }
-    }
-  }
-  qsort (SETaddr_(centers, facetT), qh_setsize (centers),
-             sizeof (facetT *), qh_compare_facetvisit);
-  qh_settempfree (&tricenters);
-  return centers;
-} /* detvridge */
-
-/*---------------------------------
-
-  qh_detvridge3( atvertex, vertex )
-    determine 3-d Voronoi ridge from 'seen' neighbors of atvertex and vertex
-    include one vertex-at-infinite for !neighbor->visitid
-    assumes all facet->seen2= True
-
-  returns:
-    temporary set of centers (facets, i.e., Voronoi vertices)
-    listed in adjacency order (not oriented)
-    all facet->seen2= True
-
-  design:
-    mark all neighbors of atvertex
-    for each adjacent neighbor of both atvertex and vertex
-      if neighbor selected
-        add neighbor to set of Voronoi vertices
-*/
-setT *qh_detvridge3 (vertexT *atvertex, vertexT *vertex) {
-  setT *centers= qh_settemp (qh TEMPsize);
-  setT *tricenters= qh_settemp (qh TEMPsize);
-  facetT *neighbor, **neighborp, *facet= NULL;
-  boolT firstinf= True;
-
-  FOREACHneighbor_(atvertex)
-    neighbor->seen2= False;
-  FOREACHneighbor_(vertex) {
-    if (!neighbor->seen2) {
-      facet= neighbor;
-      break;
-    }
-  }
-  while (facet) {
-    facet->seen2= True;
-    if (neighbor->seen) {
-      if (facet->visitid) {
-	if (!facet->tricoplanar || qh_setunique (&tricenters, facet->center))
-	  qh_setappend (¢ers, facet);
-      }else if (firstinf) {
-        firstinf= False;
-        qh_setappend (¢ers, facet);
-      }
-    }
-    FOREACHneighbor_(facet) {
-      if (!neighbor->seen2) {
-	if (qh_setin (vertex->neighbors, neighbor))
-          break;
-	else
-	  neighbor->seen2= True;
-      }
-    }
-    facet= neighbor;
-  }
-  if (qh CHECKfrequently) {
-    FOREACHneighbor_(vertex) {
-      if (!neighbor->seen2) {
-	fprintf (stderr, "qh_detvridge3: neigbors of vertex p%d are not connected at facet %d\n",
-	         qh_pointid (vertex->point), neighbor->id);
-	qh_errexit (qh_ERRqhull, neighbor, NULL);
-      }
-    }
-  }
-  FOREACHneighbor_(atvertex)
-    neighbor->seen2= True;
-  qh_settempfree (&tricenters);
-  return centers;
-} /* detvridge3 */
-
-/*---------------------------------
-
-  qh_eachvoronoi( fp, printvridge, vertex, visitall, innerouter, inorder )
-    if visitall,
-      visit all Voronoi ridges for vertex (i.e., an input site)
-    else
-      visit all unvisited Voronoi ridges for vertex
-      all vertex->seen= False if unvisited
-    assumes
-      all facet->seen= False
-      all facet->seen2= True (for qh_detvridge3)
-      all facet->visitid == 0 if vertex_at_infinity
-                         == index of Voronoi vertex
-                         >= qh.num_facets if ignored
-    innerouter:
-      qh_RIDGEall--  both inner (bounded) and outer (unbounded) ridges
-      qh_RIDGEinner- only inner
-      qh_RIDGEouter- only outer
-
-    if inorder
-      orders vertices for 3-d Voronoi diagrams
-
-  returns:
-    number of visited ridges (does not include previously visited ridges)
-
-    if printvridge,
-      calls printvridge( fp, vertex, vertexA, centers)
-        fp== any pointer (assumes FILE*)
-        vertex,vertexA= pair of input sites that define a Voronoi ridge
-        centers= set of facets (i.e., Voronoi vertices)
-                 ->visitid == index or 0 if vertex_at_infinity
-                 ordered for 3-d Voronoi diagram
-  notes:
-    uses qh.vertex_visit
-
-  see:
-    qh_eachvoronoi_all()
-
-  design:
-    mark selected neighbors of atvertex
-    for each selected neighbor (either Voronoi vertex or vertex-at-infinity)
-      for each unvisited vertex
-        if atvertex and vertex share more than d-1 neighbors
-          bump totalcount
-          if printvridge defined
-            build the set of shared neighbors (i.e., Voronoi vertices)
-            call printvridge
-*/
-int qh_eachvoronoi (FILE *fp, printvridgeT printvridge, vertexT *atvertex, boolT visitall, qh_RIDGE innerouter, boolT inorder) {
-  boolT unbounded;
-  int count;
-  facetT *neighbor, **neighborp, *neighborA, **neighborAp;
-  setT *centers;
-  setT *tricenters= qh_settemp (qh TEMPsize);
-
-  vertexT *vertex, **vertexp;
-  boolT firstinf;
-  unsigned int numfacets= (unsigned int)qh num_facets;
-  int totridges= 0;
-
-  qh vertex_visit++;
-  atvertex->seen= True;
-  if (visitall) {
-    FORALLvertices
-      vertex->seen= False;
-  }
-  FOREACHneighbor_(atvertex) {
-    if (neighbor->visitid < numfacets)
-      neighbor->seen= True;
-  }
-  FOREACHneighbor_(atvertex) {
-    if (neighbor->seen) {
-      FOREACHvertex_(neighbor->vertices) {
-        if (vertex->visitid != qh vertex_visit && !vertex->seen) {
-	  vertex->visitid= qh vertex_visit;
-          count= 0;
-          firstinf= True;
-	  qh_settruncate (tricenters, 0);
-          FOREACHneighborA_(vertex) {
-            if (neighborA->seen) {
-	      if (neighborA->visitid) {
-		if (!neighborA->tricoplanar || qh_setunique (&tricenters, neighborA->center))
-		  count++;
-              }else if (firstinf) {
-                count++;
-                firstinf= False;
-	      }
-	    }
-          }
-          if (count >= qh hull_dim - 1) {  /* e.g., 3 for 3-d Voronoi */
-            if (firstinf) {
-              if (innerouter == qh_RIDGEouter)
-                continue;
-              unbounded= False;
-            }else {
-              if (innerouter == qh_RIDGEinner)
-                continue;
-              unbounded= True;
-            }
-            totridges++;
-            trace4((qh ferr, "qh_eachvoronoi: Voronoi ridge of %d vertices between sites %d and %d\n",
-                  count, qh_pointid (atvertex->point), qh_pointid (vertex->point)));
-            if (printvridge) {
-	      if (inorder && qh hull_dim == 3+1) /* 3-d Voronoi diagram */
-                centers= qh_detvridge3 (atvertex, vertex);
-	      else
-                centers= qh_detvridge (vertex);
-              (*printvridge) (fp, atvertex, vertex, centers, unbounded);
-              qh_settempfree (¢ers);
-            }
-          }
-        }
-      }
-    }
-  }
-  FOREACHneighbor_(atvertex)
-    neighbor->seen= False;
-  qh_settempfree (&tricenters);
-} /* eachvoronoi */
-
-
-/*---------------------------------
-
-  qh_eachvoronoi_all( fp, printvridge, isupper, innerouter, inorder )
-    visit all Voronoi ridges
-
-    innerouter:
-      see qh_eachvoronoi()
-
-    if inorder
-      orders vertices for 3-d Voronoi diagrams
-
-  returns
-    total number of ridges
-
-    if isupper == facet->upperdelaunay  (i.e., a Vornoi vertex)
-      facet->visitid= Voronoi vertex index (same as 'o' format)
-    else
-      facet->visitid= 0
-
-    if printvridge,
-      calls printvridge( fp, vertex, vertexA, centers)
-      [see qh_eachvoronoi]
-
-  notes:
-    Not used for qhull.exe
-    same effect as qh_printvdiagram but ridges not sorted by point id
-*/
-int qh_eachvoronoi_all (FILE *fp, printvridgeT printvridge, boolT isupper, qh_RIDGE innerouter, boolT inorder) {
-  facetT *facet;
-  vertexT *vertex;
-  int numcenters= 1;  /* vertex 0 is vertex-at-infinity */
-  int totridges= 0;
-
-  qh_clearcenters (qh_ASvoronoi);
-  qh_vertexneighbors();
-  maximize_(qh visit_id, (unsigned) qh num_facets);
-  FORALLfacets {
-    facet->visitid= 0;
-    facet->seen= False;
-    facet->seen2= True;
-  }
-  FORALLfacets {
-    if (facet->upperdelaunay == isupper)
-      facet->visitid= numcenters++;
-  }
-  FORALLvertices
-    vertex->seen= False;
-  FORALLvertices {
-    if (qh GOODvertex > 0 && qh_pointid(vertex->point)+1 != qh GOODvertex)
-      continue;
-    totridges += qh_eachvoronoi (fp, printvridge, vertex,
-                   !qh_ALL, innerouter, inorder);
-  }
-} /* eachvoronoi_all */
-
-/*---------------------------------
-
-  qh_facet2point( facet, point0, point1, mindist )
-    return two projected temporary vertices for a 2-d facet
-    may be non-simplicial
-
-  returns:
-    point0 and point1 oriented and projected to the facet
-    returns mindist (maximum distance below plane)
-*/
-void qh_facet2point(facetT *facet, pointT **point0, pointT **point1, realT *mindist) {
-  vertexT *vertex0, *vertex1;
-  realT dist;
-
-  if (facet->toporient ^ qh_ORIENTclock) {
-    vertex0= SETfirstt_(facet->vertices, vertexT);
-    vertex1= SETsecondt_(facet->vertices, vertexT);
-  }else {
-    vertex1= SETfirstt_(facet->vertices, vertexT);
-    vertex0= SETsecondt_(facet->vertices, vertexT);
-  }
-  qh_distplane(vertex0->point, facet, &dist);
-  *mindist= dist;
-  *point0= qh_projectpoint(vertex0->point, facet, dist);
-  qh_distplane(vertex1->point, facet, &dist);
-  minimize_(*mindist, dist);
-  *point1= qh_projectpoint(vertex1->point, facet, dist);
-} /* facet2point */
-
-
-/*---------------------------------
-
-  qh_facetvertices( facetlist, facets, allfacets )
-    returns temporary set of vertices in a set and/or list of facets
-    if allfacets, ignores qh_skipfacet()
-
-  returns:
-    vertices with qh.vertex_visit
-
-  notes:
-    optimized for allfacets of facet_list
-
-  design:
-    if allfacets of facet_list
-      create vertex set from vertex_list
-    else
-      for each selected facet in facets or facetlist
-        append unvisited vertices to vertex set
-*/
-setT *qh_facetvertices (facetT *facetlist, setT *facets, boolT allfacets) {
-  setT *vertices;
-  facetT *facet, **facetp;
-  vertexT *vertex, **vertexp;
-
-  qh vertex_visit++;
-  if (facetlist == qh facet_list && allfacets && !facets) {
-    vertices= qh_settemp (qh num_vertices);
-    FORALLvertices {
-      vertex->visitid= qh vertex_visit;
-      qh_setappend (&vertices, vertex);
-    }
-  }else {
-    vertices= qh_settemp (qh TEMPsize);
-    FORALLfacet_(facetlist) {
-      if (!allfacets && qh_skipfacet (facet))
-        continue;
-      FOREACHvertex_(facet->vertices) {
-        if (vertex->visitid != qh vertex_visit) {
-          vertex->visitid= qh vertex_visit;
-          qh_setappend (&vertices, vertex);
-        }
-      }
-    }
-  }
-  FOREACHfacet_(facets) {
-    if (!allfacets && qh_skipfacet (facet))
-      continue;
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->visitid != qh vertex_visit) {
-        vertex->visitid= qh vertex_visit;
-        qh_setappend (&vertices, vertex);
-      }
-    }
-  }
-  return vertices;
-} /* facetvertices */
-
-/*---------------------------------
-
-  qh_geomplanes( facet, outerplane, innerplane )
-    return outer and inner planes for Geomview
-    qh.PRINTradius is size of vertices and points (includes qh.JOGGLEmax)
-
-  notes:
-    assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon
-*/
-void qh_geomplanes (facetT *facet, realT *outerplane, realT *innerplane) {
-
-  if (qh MERGING || qh JOGGLEmax < REALmax/2) {
-    qh_outerinner (facet, outerplane, innerplane);
-    if (qh JOGGLEmax < REALmax/2)
-      radius -= qh JOGGLEmax * sqrt (qh hull_dim);  /* already accounted for in qh_outerinner() */
-    if (qh PRINTcoplanar || qh PRINTspheres) {
-      *outerplane += qh MAXabs_coord * qh_GEOMepsilon;
-      *innerplane -= qh MAXabs_coord * qh_GEOMepsilon;
-    }
-  }else
-    *innerplane= *outerplane= 0;
-} /* geomplanes */
-
-
-/*---------------------------------
-
-  qh_markkeep( facetlist )
-    mark good facets that meet qh.KEEParea, qh.KEEPmerge, and qh.KEEPminArea
-    ignores visible facets (not part of convex hull)
-
-  returns:
-    may clear facet->good
-    recomputes qh.num_good
-
-  design:
-    get set of good facets
-    if qh.KEEParea
-      sort facets by area
-      clear facet->good for all but n largest facets
-    if qh.KEEPmerge
-      sort facets by merge count
-      clear facet->good for all but n most merged facets
-    if qh.KEEPminarea
-      clear facet->good if area too small
-    update qh.num_good
-*/
-void qh_markkeep (facetT *facetlist) {
-  facetT *facet, **facetp;
-  setT *facets= qh_settemp (qh num_facets);
-  int size, count;
-
-  trace2((qh ferr, "qh_markkeep: only keep %d largest and/or %d most merged facets and/or min area %.2g\n",
-          qh KEEParea, qh KEEPmerge, qh KEEPminArea));
-  FORALLfacet_(facetlist) {
-    if (!facet->visible && facet->good)
-      qh_setappend (&facets, facet);
-  }
-  size= qh_setsize (facets);
-  if (qh KEEParea) {
-             sizeof (facetT *), qh_compare_facetarea);
-    if ((count= size - qh KEEParea) > 0) {
-      FOREACHfacet_(facets) {
-        facet->good= False;
-        if (--count == 0)
-          break;
-      }
-    }
-  }
-  if (qh KEEPmerge) {
-             sizeof (facetT *), qh_compare_facetmerge);
-    if ((count= size - qh KEEPmerge) > 0) {
-      FOREACHfacet_(facets) {
-        facet->good= False;
-        if (--count == 0)
-          break;
-      }
-    }
-  }
-  if (qh KEEPminArea < REALmax/2) {
-    FOREACHfacet_(facets) {
-      if (!facet->isarea || facet->f.area < qh KEEPminArea)
-	facet->good= False;
-    }
-  }
-  qh_settempfree (&facets);
-  count= 0;
-  FORALLfacet_(facetlist) {
-    if (facet->good)
-      count++;
-  }
-  qh num_good= count;
-} /* markkeep */
-
-
-/*---------------------------------
-
-  qh_markvoronoi( facetlist, facets, printall, islower, numcenters )
-    mark voronoi vertices for printing by site pairs
-
-  returns:
-    temporary set of vertices indexed by pointid
-    islower set if printing lower hull (i.e., at least one facet is lower hull)
-    numcenters= total number of Voronoi vertices
-    bumps qh.printoutnum for vertex-at-infinity
-    clears all facet->seen and sets facet->seen2
-
-    if selected
-      facet->visitid= Voronoi vertex id
-    else if upper hull (or 'Qu' and lower hull)
-      facet->visitid= 0
-    else
-      facet->visitid >= qh num_facets
-
-  notes:
-    ignores qh.ATinfinity, if defined
-*/
-setT *qh_markvoronoi (facetT *facetlist, setT *facets, boolT printall, boolT *islowerp, int *numcentersp) {
-  int numcenters=0;
-  facetT *facet, **facetp;
-  setT *vertices;
-  boolT islower= False;
-
-  qh printoutnum++;
-  qh_clearcenters (qh_ASvoronoi);  /* in case, qh_printvdiagram2 called by user */
-  qh_vertexneighbors();
-  vertices= qh_pointvertex();
-  if (qh ATinfinity)
-    SETelem_(vertices, qh num_points-1)= NULL;
-  qh visit_id++;
-  maximize_(qh visit_id, (unsigned) qh num_facets);
-  FORALLfacet_(facetlist) {
-    if (printall || !qh_skipfacet (facet)) {
-      if (!facet->upperdelaunay) {
-        islower= True;
-	break;
-      }
-    }
-  }
-  FOREACHfacet_(facets) {
-    if (printall || !qh_skipfacet (facet)) {
-      if (!facet->upperdelaunay) {
-        islower= True;
-	break;
-      }
-    }
-  }
-  FORALLfacets {
-    if (facet->normal && (facet->upperdelaunay == islower))
-      facet->visitid= 0;  /* facetlist or facets may overwrite */
-    else
-      facet->visitid= qh visit_id;
-    facet->seen= False;
-    facet->seen2= True;
-  }
-  numcenters++;  /* qh_INFINITE */
-  FORALLfacet_(facetlist) {
-    if (printall || !qh_skipfacet (facet))
-      facet->visitid= numcenters++;
-  }
-  FOREACHfacet_(facets) {
-    if (printall || !qh_skipfacet (facet))
-      facet->visitid= numcenters++;
-  }
-  *islowerp= islower;
-  *numcentersp= numcenters;
-  trace2((qh ferr, "qh_markvoronoi: islower %d numcenters %d\n", islower, numcenters));
-  return vertices;
-} /* markvoronoi */
-
-/*---------------------------------
-
-  qh_order_vertexneighbors( vertex )
-    order facet neighbors of a 2-d or 3-d vertex by adjacency
-
-  notes:
-    does not orient the neighbors
-
-  design:
-    initialize a new neighbor set with the first facet in vertex->neighbors
-    while vertex->neighbors non-empty
-      select next neighbor in the previous facet's neighbor set
-    set vertex->neighbors to the new neighbor set
-*/
-void qh_order_vertexneighbors(vertexT *vertex) {
-  setT *newset;
-  facetT *facet, *neighbor, **neighborp;
-
-  trace4((qh ferr, "qh_order_vertexneighbors: order neighbors of v%d for 3-d\n", vertex->id));
-  newset= qh_settemp (qh_setsize (vertex->neighbors));
-  facet= (facetT*)qh_setdellast (vertex->neighbors);
-  qh_setappend (&newset, facet);
-  while (qh_setsize (vertex->neighbors)) {
-    FOREACHneighbor_(vertex) {
-      if (qh_setin (facet->neighbors, neighbor)) {
-        qh_setdel(vertex->neighbors, neighbor);
-        qh_setappend (&newset, neighbor);
-        facet= neighbor;
-        break;
-      }
-    }
-    if (!neighbor) {
-      fprintf (qh ferr, "qhull internal error (qh_order_vertexneighbors): no neighbor of v%d for f%d\n",
-        vertex->id, facet->id);
-      qh_errexit (qh_ERRqhull, facet, NULL);
-    }
-  }
-  qh_setfree (&vertex->neighbors);
-  qh_settemppop ();
-  vertex->neighbors= newset;
-} /* order_vertexneighbors */
-
-/*---------------------------------
-
-  qh_printafacet( fp, format, facet, printall )
-    print facet to fp in given output format (see qh.PRINTout)
-
-  returns:
-    nop if !printall and qh_skipfacet()
-    nop if visible facet and NEWfacets and format != PRINTfacets
-    must match qh_countfacets
-
-  notes
-    preserves qh.visit_id
-    facet->normal may be null if PREmerge/MERGEexact and STOPcone before merge
-
-  see
-    qh_printbegin() and qh_printend()
-
-  design:
-    test for printing facet
-    call appropriate routine for format
-    or output results directly
-*/
-void qh_printafacet(FILE *fp, int format, facetT *facet, boolT printall) {
-  realT color[4], offset, dist, outerplane, innerplane;
-  boolT zerodiv;
-  coordT *point, *normp, *coordp, **pointp, *feasiblep;
-  int k;
-  vertexT *vertex, **vertexp;
-  facetT *neighbor, **neighborp;
-
-  if (!printall && qh_skipfacet (facet))
-    return;
-  if (facet->visible && qh NEWfacets && format != qh_PRINTfacets)
-    return;
-  qh printoutnum++;
-  switch (format) {
-  case qh_PRINTarea:
-    if (facet->isarea) {
-      fprintf (fp, qh_REAL_1, facet->f.area);
-      fprintf (fp, "\n");
-    }else
-      fprintf (fp, "0\n");
-    break;
-  case qh_PRINTcoplanars:
-    fprintf (fp, "%d", qh_setsize (facet->coplanarset));
-    FOREACHpoint_(facet->coplanarset)
-      fprintf (fp, " %d", qh_pointid (point));
-    fprintf (fp, "\n");
-    break;
-  case qh_PRINTcentrums:
-    qh_printcenter (fp, format, NULL, facet);
-    break;
-  case qh_PRINTfacets:
-    qh_printfacet (fp, facet);
-    break;
-  case qh_PRINTfacets_xridge:
-    break;
-  case qh_PRINTgeom:  /* either 2 , 3, or 4-d by qh_printbegin */
-    if (!facet->normal)
-      break;
-    for (k= qh hull_dim; k--; ) {
-      color[k]= (facet->normal[k]+1.0)/2.0;
-      maximize_(color[k], -1.0);
-      minimize_(color[k], +1.0);
-    }
-    qh_projectdim3 (color, color);
-    if (qh PRINTdim != qh hull_dim)
-      qh_normalize2 (color, 3, True, NULL, NULL);
-    if (qh hull_dim <= 2)
-      qh_printfacet2geom (fp, facet, color);
-    else if (qh hull_dim == 3) {
-      if (facet->simplicial)
-        qh_printfacet3geom_simplicial (fp, facet, color);
-      else
-        qh_printfacet3geom_nonsimplicial (fp, facet, color);
-    }else {
-      if (facet->simplicial)
-        qh_printfacet4geom_simplicial (fp, facet, color);
-      else
-        qh_printfacet4geom_nonsimplicial (fp, facet, color);
-    }
-    break;
-  case qh_PRINTids:
-    fprintf (fp, "%d\n", facet->id);
-    break;
-  case qh_PRINTincidences:
-  case qh_PRINToff:
-  case qh_PRINTtriangles:
-    if (qh hull_dim == 3 && format != qh_PRINTtriangles)
-      qh_printfacet3vertex (fp, facet, format);
-    else if (facet->simplicial || qh hull_dim == 2 || format == qh_PRINToff)
-      qh_printfacetNvertex_simplicial (fp, facet, format);
-    else
-      qh_printfacetNvertex_nonsimplicial (fp, facet, qh printoutvar++, format);
-    break;
-  case qh_PRINTinner:
-    qh_outerinner (facet, NULL, &innerplane);
-    offset= facet->offset - innerplane;
-    goto LABELprintnorm;
-    break; /* prevent warning */
-  case qh_PRINTmerges:
-    fprintf (fp, "%d\n", facet->nummerge);
-    break;
-  case qh_PRINTnormals:
-    offset= facet->offset;
-    goto LABELprintnorm;
-    break; /* prevent warning */
-  case qh_PRINTouter:
-    qh_outerinner (facet, &outerplane, NULL);
-    offset= facet->offset - outerplane;
-  LABELprintnorm:
-    if (!facet->normal) {
-      fprintf (fp, "no normal for facet f%d\n", facet->id);
-      break;
-    }
-    if (qh CDDoutput) {
-      fprintf (fp, qh_REAL_1, -offset);
-      for (k=0; k < qh hull_dim; k++)
-	fprintf (fp, qh_REAL_1, -facet->normal[k]);
-    }else {
-      for (k=0; k < qh hull_dim; k++)
-	fprintf (fp, qh_REAL_1, facet->normal[k]);
-      fprintf (fp, qh_REAL_1, offset);
-    }
-    fprintf (fp, "\n");
-    break;
-  case qh_PRINTmathematica:  /* either 2 or 3-d by qh_printbegin */
-    if (qh hull_dim == 2)
-      qh_printfacet2math (fp, facet, qh printoutvar++);
-    else
-      qh_printfacet3math (fp, facet, qh printoutvar++);
-    break;
-  case qh_PRINTneighbors:
-    fprintf (fp, "%d", qh_setsize (facet->neighbors));
-    FOREACHneighbor_(facet)
-      fprintf (fp, " %d",
-	       neighbor->visitid ? neighbor->visitid - 1: - neighbor->id);
-    fprintf (fp, "\n");
-    break;
-  case qh_PRINTpointintersect:
-    if (!qh feasible_point) {
-      fprintf (fp, "qhull input error (qh_printafacet): option 'Fp' needs qh feasible_point\n");
-      qh_errexit( qh_ERRinput, NULL, NULL);
-    }
-    if (facet->offset > 0)
-      goto LABELprintinfinite;
-    point= coordp= (coordT*)qh_memalloc (qh normal_size);
-    normp= facet->normal;
-    feasiblep= qh feasible_point;
-    if (facet->offset < -qh MINdenom) {
-      for (k= qh hull_dim; k--; )
-        *(coordp++)= (*(normp++) / - facet->offset) + *(feasiblep++);
-    }else {
-      for (k= qh hull_dim; k--; ) {
-        *(coordp++)= qh_divzero (*(normp++), facet->offset, qh MINdenom_1,
-				 &zerodiv) + *(feasiblep++);
-        if (zerodiv) {
-          qh_memfree (point, qh normal_size);
-          goto LABELprintinfinite;
-        }
-      }
-    }
-    qh_printpoint (fp, NULL, point);
-    qh_memfree (point, qh normal_size);
-    break;
-  LABELprintinfinite:
-    for (k= qh hull_dim; k--; )
-      fprintf (fp, qh_REAL_1, qh_INFINITE);
-    fprintf (fp, "\n");
-    break;
-  case qh_PRINTpointnearest:
-    FOREACHpoint_(facet->coplanarset) {
-      int id, id2;
-      vertex= qh_nearvertex (facet, point, &dist);
-      id= qh_pointid (vertex->point);
-      id2= qh_pointid (point);
-      fprintf (fp, "%d %d %d " qh_REAL_1 "\n", id, id2, facet->id, dist);
-    }
-    break;
-  case qh_PRINTpoints:  /* VORONOI only by qh_printbegin */
-    if (qh CDDoutput)
-      fprintf (fp, "1 ");
-    qh_printcenter (fp, format, NULL, facet);
-    break;
-  case qh_PRINTvertices:
-    fprintf (fp, "%d", qh_setsize (facet->vertices));
-    FOREACHvertex_(facet->vertices)
-      fprintf (fp, " %d", qh_pointid (vertex->point));
-    fprintf (fp, "\n");
-    break;
-  }
-} /* printafacet */
-
-/*---------------------------------
-
-  qh_printbegin(  )
-    prints header for all output formats
-
-  returns:
-    checks for valid format
-
-  notes:
-    uses qh.visit_id for 3/4off
-    changes qh.interior_point if printing centrums
-    qh_countfacets clears facet->visitid for non-good facets
-
-  see
-    qh_printend() and qh_printafacet()
-
-  design:
-    count facets and related statistics
-*/
-void qh_printbegin (FILE *fp, int format, facetT *facetlist, setT *facets, boolT printall) {
-  int numfacets, numsimplicial, numridges, totneighbors, numcoplanars, numtricoplanars;
-  int i, num;
-  facetT *facet, **facetp;
-  vertexT *vertex, **vertexp;
-  setT *vertices;
-  pointT *point, **pointp, *pointtemp;
-
-  qh printoutnum= 0;
-  qh_countfacets (facetlist, facets, printall, &numfacets, &numsimplicial,
-      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);
-  switch (format) {
-  case qh_PRINTnone:
-    break;
-  case qh_PRINTarea:
-    fprintf (fp, "%d\n", numfacets);
-    break;
-  case qh_PRINTcoplanars:
-    fprintf (fp, "%d\n", numfacets);
-    break;
-  case qh_PRINTcentrums:
-    if (qh CENTERtype == qh_ASnone)
-      qh_clearcenters (qh_AScentrum);
-    fprintf (fp, "%d\n%d\n", qh hull_dim, numfacets);
-    break;
-  case qh_PRINTfacets:
-  case qh_PRINTfacets_xridge:
-    if (facetlist)
-      qh_printvertexlist (fp, "Vertices and facets:\n", facetlist, facets, printall);
-    break;
-  case qh_PRINTgeom:
-    if (qh hull_dim > 4)  /* qh_initqhull_globals also checks */
-      goto LABELnoformat;
-    if (qh VORONOI && qh hull_dim > 3)  /* PRINTdim == DROPdim == hull_dim-1 */
-      goto LABELnoformat;
-    if (qh hull_dim == 2 && (qh PRINTridges || qh DOintersections))
-      fprintf (qh ferr, "qhull warning: output for ridges and intersections not implemented in 2-d\n");
-    if (qh hull_dim == 4 && (qh PRINTinner || qh PRINTouter ||
-			     (qh PRINTdim == 4 && qh PRINTcentrums)))
-      fprintf (qh ferr, "qhull warning: output for outer/inner planes and centrums not implemented in 4-d\n");
-    if (qh PRINTdim == 4 && (qh PRINTspheres))
-      fprintf (qh ferr, "qhull warning: output for vertices not implemented in 4-d\n");
-    if (qh PRINTdim == 4 && qh DOintersections && qh PRINTnoplanes)
-      fprintf (qh ferr, "qhull warning: 'Gnh' generates no output in 4-d\n");
-    if (qh PRINTdim == 2) {
-      fprintf(fp, "{appearance {linewidth 3} LIST # %s | %s\n",
-	      qh rbox_command, qh qhull_command);
-    }else if (qh PRINTdim == 3) {
-      fprintf(fp, "{appearance {+edge -evert linewidth 2} LIST # %s | %s\n",
-	      qh rbox_command, qh qhull_command);
-    }else if (qh PRINTdim == 4) {
-      qh visit_id++;
-      num= 0;
-      FORALLfacet_(facetlist)    /* get number of ridges to be printed */
-        qh_printend4geom (NULL, facet, &num, printall);
-      FOREACHfacet_(facets)
-        qh_printend4geom (NULL, facet, &num, printall);
-      qh ridgeoutnum= num;
-      qh printoutvar= 0;  /* counts number of ridges in output */
-      fprintf (fp, "LIST # %s | %s\n", qh rbox_command, qh qhull_command);
-    }
-    if (qh PRINTdots) {
-      qh printoutnum++;
-      num= qh num_points + qh_setsize (qh other_points);
-      if (qh DELAUNAY && qh ATinfinity)
-	num--;
-      if (qh PRINTdim == 4)
-        fprintf (fp, "4VECT %d %d 1\n", num, num);
-      else
-	fprintf (fp, "VECT %d %d 1\n", num, num);
-      for (i= num; i--; ) {
-        if (i % 20 == 0)
-          fprintf (fp, "\n");
-	fprintf (fp, "1 ");
-      }
-      fprintf (fp, "# 1 point per line\n1 ");
-      for (i= num-1; i--; ) {
-        if (i % 20 == 0)
-          fprintf (fp, "\n");
-	fprintf (fp, "0 ");
-      }
-      fprintf (fp, "# 1 color for all\n");
-      FORALLpoints {
-        if (!qh DELAUNAY || !qh ATinfinity || qh_pointid(point) != qh num_points-1) {
-	  if (qh PRINTdim == 4)
-	    qh_printpoint (fp, NULL, point);
-	  else
-	    qh_printpoint3 (fp, point);
-	}
-      }
-      FOREACHpoint_(qh other_points) {
-	if (qh PRINTdim == 4)
-	  qh_printpoint (fp, NULL, point);
-	else
-	  qh_printpoint3 (fp, point);
-      }
-      fprintf (fp, "0 1 1 1  # color of points\n");
-    }
-    if (qh PRINTdim == 4  && !qh PRINTnoplanes)
-      /* 4dview loads up multiple 4OFF objects slowly */
-      fprintf(fp, "4OFF %d %d 1\n", 3*qh ridgeoutnum, qh ridgeoutnum);
-    qh PRINTcradius= 2 * qh DISTround;  /* include test DISTround */
-    if (qh PREmerge) {
-      maximize_(qh PRINTcradius, qh premerge_centrum + qh DISTround);
-    }else if (qh POSTmerge)
-      maximize_(qh PRINTcradius, qh postmerge_centrum + qh DISTround);
-    if (qh PRINTspheres + qh PRINTcoplanar)
-    if (qh premerge_cos < REALmax/2) {
-      maximize_(qh PRINTradius, (1- qh premerge_cos) * qh MAXabs_coord);
-    }else if (!qh PREmerge && qh POSTmerge && qh postmerge_cos < REALmax/2) {
-      maximize_(qh PRINTradius, (1- qh postmerge_cos) * qh MAXabs_coord);
-    }
-    if (qh JOGGLEmax < REALmax/2)
-      qh PRINTradius += qh JOGGLEmax * sqrt (qh hull_dim);
-    if (qh PRINTdim != 4 &&
-	(qh PRINTcoplanar || qh PRINTspheres || qh PRINTcentrums)) {
-      vertices= qh_facetvertices (facetlist, facets, printall);
-      if (qh PRINTspheres && qh PRINTdim <= 3)
-         qh_printspheres (fp, vertices, qh PRINTradius);
-      if (qh PRINTcoplanar || qh PRINTcentrums) {
-        qh firstcentrum= True;
-        if (qh PRINTcoplanar&& !qh PRINTspheres) {
-          FOREACHvertex_(vertices)
-            qh_printpointvect2 (fp, vertex->point, NULL,
-	}
-        FORALLfacet_(facetlist) {
-	  if (!printall && qh_skipfacet(facet))
-	    continue;
-	  if (!facet->normal)
-	    continue;
-          if (qh PRINTcentrums && qh PRINTdim <= 3)
-            qh_printcentrum (fp, facet, qh PRINTcradius);
-	  if (!qh PRINTcoplanar)
-	    continue;
-          FOREACHpoint_(facet->coplanarset)
-            qh_printpointvect2 (fp, point, facet->normal, NULL, qh PRINTradius);
-          FOREACHpoint_(facet->outsideset)
-            qh_printpointvect2 (fp, point, facet->normal, NULL, qh PRINTradius);
-        }
-        FOREACHfacet_(facets) {
-	  if (!printall && qh_skipfacet(facet))
-	    continue;
-	  if (!facet->normal)
-	    continue;
-          if (qh PRINTcentrums && qh PRINTdim <= 3)
-            qh_printcentrum (fp, facet, qh PRINTcradius);
-	  if (!qh PRINTcoplanar)
-	    continue;
-          FOREACHpoint_(facet->coplanarset)
-            qh_printpointvect2 (fp, point, facet->normal, NULL, qh PRINTradius);
-          FOREACHpoint_(facet->outsideset)
-            qh_printpointvect2 (fp, point, facet->normal, NULL, qh PRINTradius);
-        }
-      }
-      qh_settempfree (&vertices);
-    }
-    qh visit_id++; /* for printing hyperplane intersections */
-    break;
-  case qh_PRINTids:
-    fprintf (fp, "%d\n", numfacets);
-    break;
-  case qh_PRINTincidences:
-    if (qh VORONOI && qh PRINTprecision)
-      fprintf (qh ferr, "qhull warning: writing Delaunay.  Use 'p' or 'o' for Voronoi centers\n");
-    qh printoutvar= qh vertex_id;  /* centrum id for non-simplicial facets */
-    if (qh hull_dim <= 3)
-      fprintf(fp, "%d\n", numfacets);
-    else
-      fprintf(fp, "%d\n", numsimplicial+numridges);
-    break;
-  case qh_PRINTinner:
-  case qh_PRINTnormals:
-  case qh_PRINTouter:
-    if (qh CDDoutput)
-      fprintf (fp, "%s | %s\nbegin\n    %d %d real\n", qh rbox_command,
-              qh qhull_command, numfacets, qh hull_dim+1);
-    else
-      fprintf (fp, "%d\n%d\n", qh hull_dim+1, numfacets);
-    break;
-  case qh_PRINTmathematica:
-    if (qh hull_dim > 3)  /* qh_initbuffers also checks */
-      goto LABELnoformat;
-    if (qh VORONOI)
-      fprintf (qh ferr, "qhull warning: output is the Delaunay triangulation\n");
-    fprintf(fp, "{\n");
-    qh printoutvar= 0;   /* counts number of facets for notfirst */
-    break;
-  case qh_PRINTmerges:
-    fprintf (fp, "%d\n", numfacets);
-    break;
-  case qh_PRINTpointintersect:
-    fprintf (fp, "%d\n%d\n", qh hull_dim, numfacets);
-    break;
-  case qh_PRINTneighbors:
-    fprintf (fp, "%d\n", numfacets);
-    break;
-  case qh_PRINToff:
-  case qh_PRINTtriangles:
-    if (qh VORONOI)
-      goto LABELnoformat;
-    num = qh hull_dim;
-    if (format == qh_PRINToff || qh hull_dim == 2)
-      fprintf (fp, "%d\n%d %d %d\n", num,
-        qh num_points+qh_setsize (qh other_points), numfacets, totneighbors/2);
-    else { /* qh_PRINTtriangles */
-      qh printoutvar= qh num_points+qh_setsize (qh other_points); /* first centrum */
-      if (qh DELAUNAY)
-        num--;  /* drop last dimension */
-      fprintf (fp, "%d\n%d %d %d\n", num, qh printoutvar
-	+ numfacets - numsimplicial, numsimplicial + numridges, totneighbors/2);
-    }
-    FORALLpoints
-      qh_printpointid (qh fout, NULL, num, point, -1);
-    FOREACHpoint_(qh other_points)
-      qh_printpointid (qh fout, NULL, num, point, -1);
-    if (format == qh_PRINTtriangles && qh hull_dim > 2) {
-      FORALLfacets {
-	if (!facet->simplicial && facet->visitid)
-          qh_printcenter (qh fout, format, NULL, facet);
-      }
-    }
-    break;
-  case qh_PRINTpointnearest:
-    fprintf (fp, "%d\n", numcoplanars);
-    break;
-  case qh_PRINTpoints:
-    if (!qh VORONOI)
-      goto LABELnoformat;
-    if (qh CDDoutput)
-      fprintf (fp, "%s | %s\nbegin\n%d %d real\n", qh rbox_command,
-             qh qhull_command, numfacets, qh hull_dim);
-    else
-      fprintf (fp, "%d\n%d\n", qh hull_dim-1, numfacets);
-    break;
-  case qh_PRINTvertices:
-    fprintf (fp, "%d\n", numfacets);
-    break;
-  case qh_PRINTsummary:
-  default:
-  LABELnoformat:
-    fprintf (qh ferr, "qhull internal error (qh_printbegin): can not use this format for dimension %d\n",
-         qh hull_dim);
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }
-} /* printbegin */
-
-/*---------------------------------
-
-  qh_printcenter( fp, string, facet )
-    print facet->center as centrum or Voronoi center
-    string may be NULL.  Don't include '%' codes.
-    nop if qh CENTERtype neither CENTERvoronoi nor CENTERcentrum
-    if upper envelope of Delaunay triangulation and point at-infinity
-
-  notes:
-    defines facet->center if needed
-    if format=PRINTgeom, adds a 0 if would otherwise be 2-d
-*/
-void qh_printcenter (FILE *fp, int format, char *string, facetT *facet) {
-  int k, num;
-
-  if (qh CENTERtype != qh_ASvoronoi && qh CENTERtype != qh_AScentrum)
-    return;
-  if (string)
-    fprintf (fp, string, facet->id);
-  if (qh CENTERtype == qh_ASvoronoi) {
-    num= qh hull_dim-1;
-    if (!facet->normal || !facet->upperdelaunay || !qh ATinfinity) {
-      if (!facet->center)
-        facet->center= qh_facetcenter (facet->vertices);
-      for (k=0; k < num; k++)
-        fprintf (fp, qh_REAL_1, facet->center[k]);
-    }else {
-      for (k=0; k < num; k++)
-        fprintf (fp, qh_REAL_1, qh_INFINITE);
-    }
-  }else /* qh CENTERtype == qh_AScentrum */ {
-    num= qh hull_dim;
-    if (format == qh_PRINTtriangles && qh DELAUNAY)
-      num--;
-    if (!facet->center)
-      facet->center= qh_getcentrum (facet);
-    for (k=0; k < num; k++)
-      fprintf (fp, qh_REAL_1, facet->center[k]);
-  }
-  if (format == qh_PRINTgeom && num == 2)
-    fprintf (fp, " 0\n");
-  else
-    fprintf (fp, "\n");
-} /* printcenter */
-
-/*---------------------------------
-
-  qh_printcentrum( fp, facet, radius )
-    print centrum for a facet in OOGL format
-    radius defines size of centrum
-    2-d or 3-d only
-
-  returns:
-    defines facet->center if needed
-*/
-void qh_printcentrum (FILE *fp, facetT *facet, realT radius) {
-  pointT *centrum, *projpt;
-  boolT tempcentrum= False;
-  realT xaxis[4], yaxis[4], normal[4], dist;
-  realT green[3]={0, 1, 0};
-  vertexT *apex;
-  int k;
-
-  if (qh CENTERtype == qh_AScentrum) {
-    if (!facet->center)
-      facet->center= qh_getcentrum (facet);
-    centrum= facet->center;
-  }else {
-    centrum= qh_getcentrum (facet);
-    tempcentrum= True;
-  }
-  fprintf (fp, "{appearance {-normal -edge normscale 0} ");
-  if (qh firstcentrum) {
-    qh firstcentrum= False;
-    fprintf (fp, "{INST geom { define centrum CQUAD  # f%d\n\
--0.3 -0.3 0.0001     0 0 1 1\n\
- 0.3 -0.3 0.0001     0 0 1 1\n\
- 0.3  0.3 0.0001     0 0 1 1\n\
--0.3  0.3 0.0001     0 0 1 1 } transform { \n", facet->id);
-  }else
-    fprintf (fp, "{INST geom { : centrum } transform { # f%d\n", facet->id);
-  apex= SETfirstt_(facet->vertices, vertexT);
-  qh_distplane(apex->point, facet, &dist);
-  projpt= qh_projectpoint(apex->point, facet, dist);
-  for (k= qh hull_dim; k--; ) {
-    xaxis[k]= projpt[k] - centrum[k];
-    normal[k]= facet->normal[k];
-  }
-  if (qh hull_dim == 2) {
-    xaxis[2]= 0;
-    normal[2]= 0;
-  }else if (qh hull_dim == 4) {
-    qh_projectdim3 (xaxis, xaxis);
-    qh_projectdim3 (normal, normal);
-    qh_normalize2 (normal, qh PRINTdim, True, NULL, NULL);
-  }
-  qh_crossproduct (3, xaxis, normal, yaxis);
-  fprintf (fp, "%8.4g %8.4g %8.4g 0\n", xaxis[0], xaxis[1], xaxis[2]);
-  fprintf (fp, "%8.4g %8.4g %8.4g 0\n", yaxis[0], yaxis[1], yaxis[2]);
-  fprintf (fp, "%8.4g %8.4g %8.4g 0\n", normal[0], normal[1], normal[2]);
-  qh_printpoint3 (fp, centrum);
-  fprintf (fp, "1 }}}\n");
-  qh_memfree (projpt, qh normal_size);
-  qh_printpointvect (fp, centrum, facet->normal, NULL, radius, green);
-  if (tempcentrum)
-    qh_memfree (centrum, qh normal_size);
-} /* printcentrum */
-
-/*---------------------------------
-
-  qh_printend( fp, format )
-    prints trailer for all output formats
-
-  see:
-    qh_printbegin() and qh_printafacet()
-
-*/
-void qh_printend (FILE *fp, int format, facetT *facetlist, setT *facets, boolT printall) {
-  int num;
-  facetT *facet, **facetp;
-
-  if (!qh printoutnum)
-    fprintf (qh ferr, "qhull warning: no facets printed\n");
-  switch (format) {
-  case qh_PRINTgeom:
-    if (qh hull_dim == 4 && qh DROPdim < 0  && !qh PRINTnoplanes) {
-      qh visit_id++;
-      num= 0;
-      FORALLfacet_(facetlist)
-        qh_printend4geom (fp, facet,&num, printall);
-      FOREACHfacet_(facets)
-        qh_printend4geom (fp, facet, &num, printall);
-      if (num != qh ridgeoutnum || qh printoutvar != qh ridgeoutnum) {
-	fprintf (qh ferr, "qhull internal error (qh_printend): number of ridges %d != number printed %d and at end %d\n", qh ridgeoutnum, qh printoutvar, num);
-	qh_errexit (qh_ERRqhull, NULL, NULL);
-      }
-    }else
-      fprintf(fp, "}\n");
-    break;
-  case qh_PRINTinner:
-  case qh_PRINTnormals:
-  case qh_PRINTouter:
-    if (qh CDDoutput)
-      fprintf (fp, "end\n");
-    break;
-  case qh_PRINTmathematica:
-    fprintf(fp, "}\n");
-    break;
-  case qh_PRINTpoints:
-    if (qh CDDoutput)
-      fprintf (fp, "end\n");
-    break;
-  }
-} /* printend */
-
-/*---------------------------------
-
-  qh_printend4geom( fp, facet, numridges, printall )
-    helper function for qh_printbegin/printend
-
-  returns:
-    number of printed ridges
-
-  notes:
-    just counts printed ridges if fp=NULL
-    uses facet->visitid
-    must agree with qh_printfacet4geom...
-
-  design:
-    computes color for facet from its normal
-    prints each ridge of facet
-*/
-void qh_printend4geom (FILE *fp, facetT *facet, int *nump, boolT printall) {
-  realT color[3];
-  int i, num= *nump;
-  facetT *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-
-  if (!printall && qh_skipfacet(facet))
-    return;
-  if (qh PRINTnoplanes || (facet->visible && qh NEWfacets))
-    return;
-  if (!facet->normal)
-    return;
-  if (fp) {
-    for (i=0; i < 3; i++) {
-      color[i]= (facet->normal[i]+1.0)/2.0;
-      maximize_(color[i], -1.0);
-      minimize_(color[i], +1.0);
-    }
-  }
-  facet->visitid= qh visit_id;
-  if (facet->simplicial) {
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid != qh visit_id) {
-	if (fp)
-          fprintf (fp, "3 %d %d %d %8.4g %8.4g %8.4g 1 # f%d f%d\n",
-		 3*num, 3*num+1, 3*num+2, color[0], color[1], color[2],
-		 facet->id, neighbor->id);
-	num++;
-      }
-    }
-  }else {
-    FOREACHridge_(facet->ridges) {
-      neighbor= otherfacet_(ridge, facet);
-      if (neighbor->visitid != qh visit_id) {
-	if (fp)
-          fprintf (fp, "3 %d %d %d %8.4g %8.4g %8.4g 1 #r%d f%d f%d\n",
-		 3*num, 3*num+1, 3*num+2, color[0], color[1], color[2],
-		 ridge->id, facet->id, neighbor->id);
-	num++;
-      }
-    }
-  }
-  *nump= num;
-} /* printend4geom */
-
-/*---------------------------------
-
-  qh_printextremes( fp, facetlist, facets, printall )
-    print extreme points for convex hulls or halfspace intersections
-
-  notes:
-    #points, followed by ids, one per line
-
-    sorted by id
-    same order as qh_printpoints_out if no coplanar/interior points
-*/
-void qh_printextremes (FILE *fp, facetT *facetlist, setT *facets, int printall) {
-  setT *vertices, *points;
-  pointT *point;
-  vertexT *vertex, **vertexp;
-  int id;
-  int numpoints=0, point_i, point_n;
-  int allpoints= qh num_points + qh_setsize (qh other_points);
-
-  points= qh_settemp (allpoints);
-  qh_setzero (points, 0, allpoints);
-  vertices= qh_facetvertices (facetlist, facets, printall);
-  FOREACHvertex_(vertices) {
-    id= qh_pointid (vertex->point);
-    if (id >= 0) {
-      SETelem_(points, id)= vertex->point;
-      numpoints++;
-    }
-  }
-  qh_settempfree (&vertices);
-  fprintf (fp, "%d\n", numpoints);
-  FOREACHpoint_i_(points) {
-    if (point)
-      fprintf (fp, "%d\n", point_i);
-  }
-  qh_settempfree (&points);
-} /* printextremes */
-
-/*---------------------------------
-
-  qh_printextremes_2d( fp, facetlist, facets, printall )
-    prints point ids for facets in qh_ORIENTclock order
-
-  notes:
-    #points, followed by ids, one per line
-    if facetlist/facets are disjoint than the output includes skips
-    errors if facets form a loop
-    does not print coplanar points
-*/
-void qh_printextremes_2d (FILE *fp, facetT *facetlist, setT *facets, int printall) {
-  int numfacets, numridges, totneighbors, numcoplanars, numsimplicial, numtricoplanars;
-  setT *vertices;
-  facetT *facet, *startfacet, *nextfacet;
-  vertexT *vertexA, *vertexB;
-
-  qh_countfacets (facetlist, facets, printall, &numfacets, &numsimplicial,
-      &totneighbors, &numridges, &numcoplanars, &numtricoplanars); /* marks qh visit_id */
-  vertices= qh_facetvertices (facetlist, facets, printall);
-  fprintf(fp, "%d\n", qh_setsize (vertices));
-  qh_settempfree (&vertices);
-  if (!numfacets)
-    return;
-  facet= startfacet= facetlist ? facetlist : SETfirstt_(facets, facetT);
-  qh vertex_visit++;
-  qh visit_id++;
-  do {
-    if (facet->toporient ^ qh_ORIENTclock) {
-      vertexA= SETfirstt_(facet->vertices, vertexT);
-      vertexB= SETsecondt_(facet->vertices, vertexT);
-      nextfacet= SETfirstt_(facet->neighbors, facetT);
-    }else {
-      vertexA= SETsecondt_(facet->vertices, vertexT);
-      vertexB= SETfirstt_(facet->vertices, vertexT);
-      nextfacet= SETsecondt_(facet->neighbors, facetT);
-    }
-    if (facet->visitid == qh visit_id) {
-      fprintf(qh ferr, "qh_printextremes_2d: loop in facet list.  facet %d nextfacet %d\n",
-                 facet->id, nextfacet->id);
-      qh_errexit2 (qh_ERRqhull, facet, nextfacet);
-    }
-    if (facet->visitid) {
-      if (vertexA->visitid != qh vertex_visit) {
-	vertexA->visitid= qh vertex_visit;
-	fprintf(fp, "%d\n", qh_pointid (vertexA->point));
-      }
-      if (vertexB->visitid != qh vertex_visit) {
-	vertexB->visitid= qh vertex_visit;
-	fprintf(fp, "%d\n", qh_pointid (vertexB->point));
-      }
-    }
-    facet->visitid= qh visit_id;
-    facet= nextfacet;
-  }while (facet && facet != startfacet);
-} /* printextremes_2d */
-
-/*---------------------------------
-
-  qh_printextremes_d( fp, facetlist, facets, printall )
-    print extreme points of input sites for Delaunay triangulations
-
-  notes:
-    #points, followed by ids, one per line
-
-    unordered
-*/
-void qh_printextremes_d (FILE *fp, facetT *facetlist, setT *facets, int printall) {
-  setT *vertices;
-  vertexT *vertex, **vertexp;
-  boolT upperseen, lowerseen;
-  facetT *neighbor, **neighborp;
-  int numpoints=0;
-
-  vertices= qh_facetvertices (facetlist, facets, printall);
-  qh_vertexneighbors();
-  FOREACHvertex_(vertices) {
-    upperseen= lowerseen= False;
-    FOREACHneighbor_(vertex) {
-      if (neighbor->upperdelaunay)
-        upperseen= True;
-      else
-        lowerseen= True;
-    }
-    if (upperseen && lowerseen) {
-      vertex->seen= True;
-      numpoints++;
-    }else
-      vertex->seen= False;
-  }
-  fprintf (fp, "%d\n", numpoints);
-  FOREACHvertex_(vertices) {
-    if (vertex->seen)
-      fprintf (fp, "%d\n", qh_pointid (vertex->point));
-  }
-  qh_settempfree (&vertices);
-} /* printextremes_d */
-
-/*---------------------------------
-
-  qh_printfacet( fp, facet )
-    prints all fields of a facet to fp
-
-  notes:
-    ridges printed in neighbor order
-*/
-void qh_printfacet(FILE *fp, facetT *facet) {
-
-  if (facet->ridges)
-    qh_printfacetridges (fp, facet);
-} /* printfacet */
-
-
-/*---------------------------------
-
-  qh_printfacet2geom( fp, facet, color )
-    print facet as part of a 2-d VECT for Geomview
-
-    notes:
-      assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon
-      mindist is calculated within io.c.  maxoutside is calculated elsewhere
-      so a DISTround error may have occured.
-*/
-void qh_printfacet2geom(FILE *fp, facetT *facet, realT color[3]) {
-  pointT *point0, *point1;
-  realT mindist, innerplane, outerplane;
-  int k;
-
-  qh_facet2point (facet, &point0, &point1, &mindist);
-  qh_geomplanes (facet, &outerplane, &innerplane);
-  if (qh PRINTouter || (!qh PRINTnoplanes && !qh PRINTinner))
-    qh_printfacet2geom_points(fp, point0, point1, facet, outerplane, color);
-  if (qh PRINTinner || (!qh PRINTnoplanes && !qh PRINTouter &&
-                outerplane - innerplane > 2 * qh MAXabs_coord * qh_GEOMepsilon)) {
-    for(k= 3; k--; )
-      color[k]= 1.0 - color[k];
-    qh_printfacet2geom_points(fp, point0, point1, facet, innerplane, color);
-  }
-  qh_memfree (point1, qh normal_size);
-  qh_memfree (point0, qh normal_size);
-} /* printfacet2geom */
-
-/*---------------------------------
-
-  qh_printfacet2geom_points( fp, point1, point2, facet, offset, color )
-    prints a 2-d facet as a VECT with 2 points at some offset.
-    The points are on the facet's plane.
-*/
-void qh_printfacet2geom_points(FILE *fp, pointT *point1, pointT *point2,
-			       facetT *facet, realT offset, realT color[3]) {
-  pointT *p1= point1, *p2= point2;
-
-  fprintf(fp, "VECT 1 2 1 2 1 # f%d\n", facet->id);
-  if (offset != 0.0) {
-    p1= qh_projectpoint (p1, facet, -offset);
-    p2= qh_projectpoint (p2, facet, -offset);
-  }
-  fprintf(fp, "%8.4g %8.4g %8.4g\n%8.4g %8.4g %8.4g\n",
-           p1[0], p1[1], 0.0, p2[0], p2[1], 0.0);
-  if (offset != 0.0) {
-    qh_memfree (p1, qh normal_size);
-    qh_memfree (p2, qh normal_size);
-  }
-  fprintf(fp, "%8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
-} /* printfacet2geom_points */
-
-
-/*---------------------------------
-
-  qh_printfacet2math( fp, facet, notfirst )
-    print 2-d Mathematica output for a facet
-    may be non-simplicial
-
-  notes:
-    use %16.8f since Mathematica 2.2 does not handle exponential format
-*/
-void qh_printfacet2math(FILE *fp, facetT *facet, int notfirst) {
-  pointT *point0, *point1;
-  realT mindist;
-
-  qh_facet2point (facet, &point0, &point1, &mindist);
-  if (notfirst)
-    fprintf(fp, ",");
-  fprintf(fp, "Line[{{%16.8f, %16.8f}, {%16.8f, %16.8f}}]\n",
-	  point0[0], point0[1], point1[0], point1[1]);
-  qh_memfree (point1, qh normal_size);
-  qh_memfree (point0, qh normal_size);
-} /* printfacet2math */
-
-
-/*---------------------------------
-
-  qh_printfacet3geom_nonsimplicial( fp, facet, color )
-    print Geomview OFF for a 3-d nonsimplicial facet.
-    if DOintersections, prints ridges to unvisited neighbors (qh visit_id)
-
-  notes
-    uses facet->visitid for intersections and ridges
-*/
-void qh_printfacet3geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]) {
-  ridgeT *ridge, **ridgep;
-  setT *projectedpoints, *vertices;
-  vertexT *vertex, **vertexp, *vertexA, *vertexB;
-  pointT *projpt, *point, **pointp;
-  facetT *neighbor;
-  realT dist, outerplane, innerplane;
-  int cntvertices, k;
-  realT black[3]={0, 0, 0}, green[3]={0, 1, 0};
-
-  qh_geomplanes (facet, &outerplane, &innerplane);
-  vertices= qh_facet3vertex (facet); /* oriented */
-  cntvertices= qh_setsize(vertices);
-  projectedpoints= qh_settemp(cntvertices);
-  FOREACHvertex_(vertices) {
-    zinc_(Zdistio);
-    qh_distplane(vertex->point, facet, &dist);
-    projpt= qh_projectpoint(vertex->point, facet, dist);
-    qh_setappend (&projectedpoints, projpt);
-  }
-  if (qh PRINTouter || (!qh PRINTnoplanes && !qh PRINTinner))
-    qh_printfacet3geom_points(fp, projectedpoints, facet, outerplane, color);
-  if (qh PRINTinner || (!qh PRINTnoplanes && !qh PRINTouter &&
-                outerplane - innerplane > 2 * qh MAXabs_coord * qh_GEOMepsilon)) {
-    for (k=3; k--; )
-      color[k]= 1.0 - color[k];
-    qh_printfacet3geom_points(fp, projectedpoints, facet, innerplane, color);
-  }
-  FOREACHpoint_(projectedpoints)
-    qh_memfree (point, qh normal_size);
-  qh_settempfree(&projectedpoints);
-  qh_settempfree(&vertices);
-  if ((qh DOintersections || qh PRINTridges)
-  && (!facet->visible || !qh NEWfacets)) {
-    facet->visitid= qh visit_id;
-    FOREACHridge_(facet->ridges) {
-      neighbor= otherfacet_(ridge, facet);
-      if (neighbor->visitid != qh visit_id) {
-        if (qh DOintersections)
-          qh_printhyperplaneintersection(fp, facet, neighbor, ridge->vertices, black);
-        if (qh PRINTridges) {
-          vertexA= SETfirstt_(ridge->vertices, vertexT);
-          vertexB= SETsecondt_(ridge->vertices, vertexT);
-          qh_printline3geom (fp, vertexA->point, vertexB->point, green);
-        }
-      }
-    }
-  }
-} /* printfacet3geom_nonsimplicial */
-
-/*---------------------------------
-
-  qh_printfacet3geom_points( fp, points, facet, offset )
-    prints a 3-d facet as OFF Geomview object.
-    offset is relative to the facet's hyperplane
-    Facet is determined as a list of points
-*/
-void qh_printfacet3geom_points(FILE *fp, setT *points, facetT *facet, realT offset, realT color[3]) {
-  int k, n= qh_setsize(points), i;
-  pointT *point, **pointp;
-  setT *printpoints;
-
-  fprintf(fp, "{ OFF %d 1 1 # f%d\n", n, facet->id);
-  if (offset != 0.0) {
-    printpoints= qh_settemp (n);
-    FOREACHpoint_(points)
-      qh_setappend (&printpoints, qh_projectpoint(point, facet, -offset));
-  }else
-    printpoints= points;
-  FOREACHpoint_(printpoints) {
-    for (k=0; k < qh hull_dim; k++) {
-      if (k == qh DROPdim)
-        fprintf(fp, "0 ");
-      else
-        fprintf(fp, "%8.4g ", point[k]);
-    }
-    if (printpoints != points)
-      qh_memfree (point, qh normal_size);
-    fprintf (fp, "\n");
-  }
-  if (printpoints != points)
-    qh_settempfree (&printpoints);
-  fprintf(fp, "%d ", n);
-  for(i= 0; i < n; i++)
-    fprintf(fp, "%d ", i);
-  fprintf(fp, "%8.4g %8.4g %8.4g 1.0 }\n", color[0], color[1], color[2]);
-} /* printfacet3geom_points */
-
-
-/*---------------------------------
-
-  qh_printfacet3geom_simplicial(  )
-    print Geomview OFF for a 3-d simplicial facet.
-
-  notes:
-    may flip color
-    uses facet->visitid for intersections and ridges
-
-    assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon
-    innerplane may be off by qh DISTround.  Maxoutside is calculated elsewhere
-    so a DISTround error may have occured.
-*/
-void qh_printfacet3geom_simplicial(FILE *fp, facetT *facet, realT color[3]) {
-  setT *points, *vertices;
-  vertexT *vertex, **vertexp, *vertexA, *vertexB;
-  facetT *neighbor, **neighborp;
-  realT outerplane, innerplane;
-  realT black[3]={0, 0, 0}, green[3]={0, 1, 0};
-  int k;
-
-  qh_geomplanes (facet, &outerplane, &innerplane);
-  vertices= qh_facet3vertex (facet);
-  points= qh_settemp (qh TEMPsize);
-  FOREACHvertex_(vertices)
-    qh_setappend(&points, vertex->point);
-  if (qh PRINTouter || (!qh PRINTnoplanes && !qh PRINTinner))
-    qh_printfacet3geom_points(fp, points, facet, outerplane, color);
-  if (qh PRINTinner || (!qh PRINTnoplanes && !qh PRINTouter &&
-              outerplane - innerplane > 2 * qh MAXabs_coord * qh_GEOMepsilon)) {
-    for (k= 3; k--; )
-      color[k]= 1.0 - color[k];
-    qh_printfacet3geom_points(fp, points, facet, innerplane, color);
-  }
-  qh_settempfree(&points);
-  qh_settempfree(&vertices);
-  if ((qh DOintersections || qh PRINTridges)
-  && (!facet->visible || !qh NEWfacets)) {
-    facet->visitid= qh visit_id;
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid != qh visit_id) {
-	vertices= qh_setnew_delnthsorted (facet->vertices, qh hull_dim,
-	                  SETindex_(facet->neighbors, neighbor), 0);
-        if (qh DOintersections)
-	   qh_printhyperplaneintersection(fp, facet, neighbor, vertices, black);
-        if (qh PRINTridges) {
-          vertexA= SETfirstt_(vertices, vertexT);
-          vertexB= SETsecondt_(vertices, vertexT);
-          qh_printline3geom (fp, vertexA->point, vertexB->point, green);
-        }
-	qh_setfree(&vertices);
-      }
-    }
-  }
-} /* printfacet3geom_simplicial */
-
-/*---------------------------------
-
-  qh_printfacet3math( fp, facet, notfirst )
-    print 3-d Mathematica output for a facet
-
-  notes:
-    may be non-simplicial
-    use %16.8f since Mathematica 2.2 does not handle exponential format
-*/
-void qh_printfacet3math (FILE *fp, facetT *facet, int notfirst) {
-  vertexT *vertex, **vertexp;
-  setT *points, *vertices;
-  pointT *point, **pointp;
-  boolT firstpoint= True;
-  realT dist;
-
-  if (notfirst)
-    fprintf(fp, ",\n");
-  vertices= qh_facet3vertex (facet);
-  points= qh_settemp (qh_setsize (vertices));
-  FOREACHvertex_(vertices) {
-    zinc_(Zdistio);
-    qh_distplane(vertex->point, facet, &dist);
-    point= qh_projectpoint(vertex->point, facet, dist);
-    qh_setappend (&points, point);
-  }
-  fprintf(fp, "Polygon[{");
-  FOREACHpoint_(points) {
-    if (firstpoint)
-      firstpoint= False;
-    else
-      fprintf(fp, ",\n");
-    fprintf(fp, "{%16.8f, %16.8f, %16.8f}", point[0], point[1], point[2]);
-  }
-  FOREACHpoint_(points)
-    qh_memfree (point, qh normal_size);
-  qh_settempfree(&points);
-  qh_settempfree(&vertices);
-  fprintf(fp, "}]");
-} /* printfacet3math */
-
-
-/*---------------------------------
-
-  qh_printfacet3vertex( fp, facet, format )
-    print vertices in a 3-d facet as point ids
-
-  notes:
-    prints number of vertices first if format == qh_PRINToff
-    the facet may be non-simplicial
-*/
-void qh_printfacet3vertex(FILE *fp, facetT *facet, int format) {
-  vertexT *vertex, **vertexp;
-  setT *vertices;
-
-  vertices= qh_facet3vertex (facet);
-  if (format == qh_PRINToff)
-    fprintf (fp, "%d ", qh_setsize (vertices));
-  FOREACHvertex_(vertices)
-    fprintf (fp, "%d ", qh_pointid(vertex->point));
-  fprintf (fp, "\n");
-  qh_settempfree(&vertices);
-} /* printfacet3vertex */
-
-
-/*---------------------------------
-
-  qh_printfacet4geom_nonsimplicial(  )
-    print Geomview 4OFF file for a 4d nonsimplicial facet
-    prints all ridges to unvisited neighbors (qh.visit_id)
-    if qh.DROPdim
-      prints in OFF format
-
-  notes:
-    must agree with printend4geom()
-*/
-void qh_printfacet4geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]) {
-  facetT *neighbor;
-  ridgeT *ridge, **ridgep;
-  vertexT *vertex, **vertexp;
-  pointT *point;
-  int k;
-  realT dist;
-
-  facet->visitid= qh visit_id;
-  if (qh PRINTnoplanes || (facet->visible && qh NEWfacets))
-    return;
-  FOREACHridge_(facet->ridges) {
-    neighbor= otherfacet_(ridge, facet);
-    if (neighbor->visitid == qh visit_id)
-      continue;
-    if (qh PRINTtransparent && !neighbor->good)
-      continue;
-    if (qh DOintersections)
-      qh_printhyperplaneintersection(fp, facet, neighbor, ridge->vertices, color);
-    else {
-      if (qh DROPdim >= 0)
-	fprintf(fp, "OFF 3 1 1 # f%d\n", facet->id);
-      else {
-	qh printoutvar++;
-	fprintf (fp, "# r%d between f%d f%d\n", ridge->id, facet->id, neighbor->id);
-      }
-      FOREACHvertex_(ridge->vertices) {
-	zinc_(Zdistio);
-	qh_distplane(vertex->point,facet, &dist);
-	point=qh_projectpoint(vertex->point,facet, dist);
-	for(k= 0; k < qh hull_dim; k++) {
-	  if (k != qh DROPdim)
-  	    fprintf(fp, "%8.4g ", point[k]);
-  	}
-	fprintf (fp, "\n");
-	qh_memfree (point, qh normal_size);
-      }
-      if (qh DROPdim >= 0)
-        fprintf(fp, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);
-    }
-  }
-} /* printfacet4geom_nonsimplicial */
-
-
-/*---------------------------------
-
-  qh_printfacet4geom_simplicial( fp, facet, color )
-    print Geomview 4OFF file for a 4d simplicial facet
-    prints triangles for unvisited neighbors (qh.visit_id)
-
-  notes:
-    must agree with printend4geom()
-*/
-void qh_printfacet4geom_simplicial(FILE *fp, facetT *facet, realT color[3]) {
-  setT *vertices;
-  facetT *neighbor, **neighborp;
-  vertexT *vertex, **vertexp;
-  int k;
-
-  facet->visitid= qh visit_id;
-  if (qh PRINTnoplanes || (facet->visible && qh NEWfacets))
-    return;
-  FOREACHneighbor_(facet) {
-    if (neighbor->visitid == qh visit_id)
-      continue;
-    if (qh PRINTtransparent && !neighbor->good)
-      continue;
-    vertices= qh_setnew_delnthsorted (facet->vertices, qh hull_dim,
-	                  SETindex_(facet->neighbors, neighbor), 0);
-    if (qh DOintersections)
-      qh_printhyperplaneintersection(fp, facet, neighbor, vertices, color);
-    else {
-      if (qh DROPdim >= 0)
-	fprintf(fp, "OFF 3 1 1 # ridge between f%d f%d\n",
-		facet->id, neighbor->id);
-      else {
-	qh printoutvar++;
-	fprintf (fp, "# ridge between f%d f%d\n", facet->id, neighbor->id);
-      }
-      FOREACHvertex_(vertices) {
-	for(k= 0; k < qh hull_dim; k++) {
-	  if (k != qh DROPdim)
-  	    fprintf(fp, "%8.4g ", vertex->point[k]);
-  	}
-	fprintf (fp, "\n");
-      }
-      if (qh DROPdim >= 0)
-        fprintf(fp, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);
-    }
-    qh_setfree(&vertices);
-  }
-} /* printfacet4geom_simplicial */
-
-
-/*---------------------------------
-
-  qh_printfacetNvertex_nonsimplicial( fp, facet, id, format )
-    print vertices for an N-d non-simplicial facet
-    triangulates each ridge to the id
-*/
-void qh_printfacetNvertex_nonsimplicial(FILE *fp, facetT *facet, int id, int format) {
-  vertexT *vertex, **vertexp;
-  ridgeT *ridge, **ridgep;
-
-  if (facet->visible && qh NEWfacets)
-    return;
-  FOREACHridge_(facet->ridges) {
-    if (format == qh_PRINTtriangles)
-      fprintf(fp, "%d ", qh hull_dim);
-    fprintf(fp, "%d ", id);
-    if ((ridge->top == facet) ^ qh_ORIENTclock) {
-      FOREACHvertex_(ridge->vertices)
-        fprintf(fp, "%d ", qh_pointid(vertex->point));
-    }else {
-      FOREACHvertexreverse12_(ridge->vertices)
-        fprintf(fp, "%d ", qh_pointid(vertex->point));
-    }
-    fprintf(fp, "\n");
-  }
-} /* printfacetNvertex_nonsimplicial */
-
-
-/*---------------------------------
-
-  qh_printfacetNvertex_simplicial( fp, facet, format )
-    print vertices for an N-d simplicial facet
-    prints vertices for non-simplicial facets
-      2-d facets (orientation preserved by qh_mergefacet2d)
-      PRINToff ('o') for 4-d and higher
-*/
-void qh_printfacetNvertex_simplicial(FILE *fp, facetT *facet, int format) {
-  vertexT *vertex, **vertexp;
-
-  if (format == qh_PRINToff || format == qh_PRINTtriangles)
-    fprintf (fp, "%d ", qh_setsize (facet->vertices));
-  if ((facet->toporient ^ qh_ORIENTclock)
-  || (qh hull_dim > 2 && !facet->simplicial)) {
-    FOREACHvertex_(facet->vertices)
-      fprintf(fp, "%d ", qh_pointid(vertex->point));
-  }else {
-    FOREACHvertexreverse12_(facet->vertices)
-      fprintf(fp, "%d ", qh_pointid(vertex->point));
-  }
-  fprintf(fp, "\n");
-} /* printfacetNvertex_simplicial */
-
-
-/*---------------------------------
-
-    prints header fields of a facet to fp
-
-  notes:
-    for 'f' output and debugging
-*/
-void qh_printfacetheader(FILE *fp, facetT *facet) {
-  pointT *point, **pointp, *furthest;
-  facetT *neighbor, **neighborp;
-  realT dist;
-
-  if (facet == qh_MERGEridge) {
-    fprintf (fp, " MERGEridge\n");
-    return;
-  }else if (facet == qh_DUPLICATEridge) {
-    fprintf (fp, " DUPLICATEridge\n");
-    return;
-  }else if (!facet) {
-    fprintf (fp, " NULLfacet\n");
-    return;
-  }
-  qh old_randomdist= qh RANDOMdist;
-  qh RANDOMdist= False;
-  fprintf(fp, "- f%d\n", facet->id);
-  fprintf(fp, "    - flags:");
-  if (facet->toporient)
-    fprintf(fp, " top");
-  else
-    fprintf(fp, " bottom");
-  if (facet->simplicial)
-    fprintf(fp, " simplicial");
-  if (facet->tricoplanar)
-    fprintf(fp, " tricoplanar");
-  if (facet->upperdelaunay)
-    fprintf(fp, " upperDelaunay");
-  if (facet->visible)
-    fprintf(fp, " visible");
-  if (facet->newfacet)
-    fprintf(fp, " new");
-  if (facet->tested)
-    fprintf(fp, " tested");
-  if (!facet->good)
-    fprintf(fp, " notG");
-  if (facet->seen)
-    fprintf(fp, " seen");
-  if (facet->coplanar)
-    fprintf(fp, " coplanar");
-  if (facet->mergehorizon)
-    fprintf(fp, " mergehorizon");
-  if (facet->keepcentrum)
-    fprintf(fp, " keepcentrum");
-  if (facet->dupridge)
-    fprintf(fp, " dupridge");
-  if (facet->mergeridge && !facet->mergeridge2)
-    fprintf(fp, " mergeridge1");
-  if (facet->mergeridge2)
-    fprintf(fp, " mergeridge2");
-  if (facet->newmerge)
-    fprintf(fp, " newmerge");
-  if (facet->flipped)
-    fprintf(fp, " flipped");
-  if (facet->notfurthest)
-    fprintf(fp, " notfurthest");
-  if (facet->degenerate)
-    fprintf(fp, " degenerate");
-  if (facet->redundant)
-    fprintf(fp, " redundant");
-  fprintf(fp, "\n");
-  if (facet->isarea)
-    fprintf(fp, "    - area: %2.2g\n", facet->f.area);
-  else if (qh NEWfacets && facet->visible && facet->f.replace)
-    fprintf(fp, "    - replacement: f%d\n", facet->f.replace->id);
-  else if (facet->newfacet) {
-    if (facet->f.samecycle && facet->f.samecycle != facet)
-      fprintf(fp, "    - shares same visible/horizon as f%d\n", facet->f.samecycle->id);
-  }else if (facet->tricoplanar /* !isarea */) {
-    if (facet->f.triowner)
-      fprintf(fp, "    - owner of normal & centrum is facet f%d\n", facet->f.triowner->id);
-  }else if (facet->f.newcycle)
-    fprintf(fp, "    - was horizon to f%d\n", facet->f.newcycle->id);
-  if (facet->nummerge)
-    fprintf(fp, "    - merges: %d\n", facet->nummerge);
-  qh_printpointid(fp, "    - normal: ", qh hull_dim, facet->normal, -1);
-  fprintf(fp, "    - offset: %10.7g\n", facet->offset);
-  if (qh CENTERtype == qh_ASvoronoi || facet->center)
-    qh_printcenter (fp, qh_PRINTfacets, "    - center: ", facet);
-#if qh_MAXoutside
-  if (facet->maxoutside > qh DISTround)
-    fprintf(fp, "    - maxoutside: %10.7g\n", facet->maxoutside);
-#endif
-  if (!SETempty_(facet->outsideset)) {
-    furthest= (pointT*)qh_setlast(facet->outsideset);
-    if (qh_setsize (facet->outsideset) < 6) {
-      fprintf(fp, "    - outside set (furthest p%d):\n", qh_pointid(furthest));
-      FOREACHpoint_(facet->outsideset)
-	qh_printpoint(fp, "     ", point);
-    }else if (qh_setsize (facet->outsideset) < 21) {
-      qh_printpoints(fp, "    - outside set:", facet->outsideset);
-    }else {
-      fprintf(fp, "    - outside set:  %d points.", qh_setsize(facet->outsideset));
-      qh_printpoint(fp, "  Furthest", furthest);
-    }
-#if !qh_COMPUTEfurthest
-    fprintf(fp, "    - furthest distance= %2.2g\n", facet->furthestdist);
-#endif
-  }
-  if (!SETempty_(facet->coplanarset)) {
-    furthest= (pointT*)qh_setlast(facet->coplanarset);
-    if (qh_setsize (facet->coplanarset) < 6) {
-      fprintf(fp, "    - coplanar set (furthest p%d):\n", qh_pointid(furthest));
-      FOREACHpoint_(facet->coplanarset)
-	qh_printpoint(fp, "     ", point);
-    }else if (qh_setsize (facet->coplanarset) < 21) {
-      qh_printpoints(fp, "    - coplanar set:", facet->coplanarset);
-    }else {
-      fprintf(fp, "    - coplanar set:  %d points.", qh_setsize(facet->coplanarset));
-      qh_printpoint(fp, "  Furthest", furthest);
-    }
-    zinc_(Zdistio);
-    qh_distplane (furthest, facet, &dist);
-    fprintf(fp, "      furthest distance= %2.2g\n", dist);
-  }
-  qh_printvertices (fp, "    - vertices:", facet->vertices);
-  fprintf(fp, "    - neighboring facets: ");
-  FOREACHneighbor_(facet) {
-    if (neighbor == qh_MERGEridge)
-      fprintf(fp, " MERGE");
-    else if (neighbor == qh_DUPLICATEridge)
-      fprintf(fp, " DUP");
-    else
-      fprintf(fp, " f%d", neighbor->id);
-  }
-  fprintf(fp, "\n");
-  qh RANDOMdist= qh old_randomdist;
-
-
-/*---------------------------------
-
-  qh_printfacetridges( fp, facet )
-    prints ridges of a facet to fp
-
-  notes:
-    ridges printed in neighbor order
-    assumes the ridges exist
-    for 'f' output
-*/
-void qh_printfacetridges(FILE *fp, facetT *facet) {
-  facetT *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-  int numridges= 0;
-
-
-  if (facet->visible && qh NEWfacets) {
-    fprintf(fp, "    - ridges (ids may be garbage):");
-    FOREACHridge_(facet->ridges)
-      fprintf(fp, " r%d", ridge->id);
-    fprintf(fp, "\n");
-  }else {
-    fprintf(fp, "    - ridges:\n");
-    FOREACHridge_(facet->ridges)
-      ridge->seen= False;
-    if (qh hull_dim == 3) {
-      ridge= SETfirstt_(facet->ridges, ridgeT);
-      while (ridge && !ridge->seen) {
-	ridge->seen= True;
-	qh_printridge(fp, ridge);
-	numridges++;
-	ridge= qh_nextridge3d (ridge, facet, NULL);
-	}
-    }else {
-      FOREACHneighbor_(facet) {
-	FOREACHridge_(facet->ridges) {
-	  if (otherfacet_(ridge,facet) == neighbor) {
-	    ridge->seen= True;
-	    qh_printridge(fp, ridge);
-	    numridges++;
-	  }
-	}
-      }
-    }
-    if (numridges != qh_setsize (facet->ridges)) {
-      fprintf (fp, "     - all ridges:");
-      FOREACHridge_(facet->ridges)
-	fprintf (fp, " r%d", ridge->id);
-        fprintf (fp, "\n");
-    }
-    FOREACHridge_(facet->ridges) {
-      if (!ridge->seen)
-	qh_printridge(fp, ridge);
-    }
-  }
-} /* printfacetridges */
-
-/*---------------------------------
-
-  qh_printfacets( fp, format, facetlist, facets, printall )
-    prints facetlist and/or facet set in output format
-
-  notes:
-    also used for specialized formats ('FO' and summary)
-    turns off 'Rn' option since want actual numbers
-*/
-void qh_printfacets(FILE *fp, int format, facetT *facetlist, setT *facets, boolT printall) {
-  int numfacets, numsimplicial, numridges, totneighbors, numcoplanars, numtricoplanars;
-  facetT *facet, **facetp;
-  setT *vertices;
-  coordT *center;
-  realT outerplane, innerplane;
-
-  qh old_randomdist= qh RANDOMdist;
-  qh RANDOMdist= False;
-  if (qh CDDoutput && (format == qh_PRINTcentrums || format == qh_PRINTpointintersect || format == qh_PRINToff))
-    fprintf (qh ferr, "qhull warning: CDD format is not available for centrums, halfspace\nintersections, and OFF file format.\n");
-  if (format == qh_PRINTnone)
-    ; /* print nothing */
-  else if (format == qh_PRINTaverage) {
-    vertices= qh_facetvertices (facetlist, facets, printall);
-    center= qh_getcenter (vertices);
-    fprintf (fp, "%d 1\n", qh hull_dim);
-    qh_printpointid (fp, NULL, qh hull_dim, center, -1);
-    qh_memfree (center, qh normal_size);
-    qh_settempfree (&vertices);
-  }else if (format == qh_PRINTextremes) {
-    if (qh DELAUNAY)
-      qh_printextremes_d (fp, facetlist, facets, printall);
-    else if (qh hull_dim == 2)
-      qh_printextremes_2d (fp, facetlist, facets, printall);
-    else
-      qh_printextremes (fp, facetlist, facets, printall);
-  }else if (format == qh_PRINToptions)
-    fprintf(fp, "Options selected for Qhull %s:\n%s\n", qh_VERSION, qh qhull_options);
-  else if (format == qh_PRINTpoints && !qh VORONOI)
-    qh_printpoints_out (fp, facetlist, facets, printall);
-  else if (format == qh_PRINTqhull)
-    fprintf (fp, "%s | %s\n", qh rbox_command, qh qhull_command);
-  else if (format == qh_PRINTsize) {
-    fprintf (fp, "0\n2 ");
-    fprintf (fp, qh_REAL_1, qh totarea);
-    fprintf (fp, qh_REAL_1, qh totvol);
-    fprintf (fp, "\n");
-  }else if (format == qh_PRINTsummary) {
-    qh_countfacets (facetlist, facets, printall, &numfacets, &numsimplicial,
-      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);
-    vertices= qh_facetvertices (facetlist, facets, printall);
-    fprintf (fp, "10 %d %d %d %d %d %d %d %d %d %d\n2 ", qh hull_dim,
-                qh num_points + qh_setsize (qh other_points),
-                qh num_vertices, qh num_facets - qh num_visible,
-                qh_setsize (vertices), numfacets, numcoplanars,
-		numfacets - numsimplicial, zzval_(Zdelvertextot),
-		numtricoplanars);
-    qh_settempfree (&vertices);
-    qh_outerinner (NULL, &outerplane, &innerplane);
-    fprintf (fp, qh_REAL_2n, outerplane, innerplane);
-  }else if (format == qh_PRINTvneighbors)
-    qh_printvneighbors (fp, facetlist, facets, printall);
-  else if (qh VORONOI && format == qh_PRINToff)
-    qh_printvoronoi (fp, format, facetlist, facets, printall);
-  else if (qh VORONOI && format == qh_PRINTgeom) {
-    qh_printbegin (fp, format, facetlist, facets, printall);
-    qh_printvoronoi (fp, format, facetlist, facets, printall);
-    qh_printend (fp, format, facetlist, facets, printall);
-  }else if (qh VORONOI
-  && (format == qh_PRINTvertices || format == qh_PRINTinner || format == qh_PRINTouter))
-    qh_printvdiagram (fp, format, facetlist, facets, printall);
-  else {
-    qh_printbegin (fp, format, facetlist, facets, printall);
-    FORALLfacet_(facetlist)
-      qh_printafacet (fp, format, facet, printall);
-    FOREACHfacet_(facets)
-      qh_printafacet (fp, format, facet, printall);
-    qh_printend (fp, format, facetlist, facets, printall);
-  }
-  qh RANDOMdist= qh old_randomdist;
-} /* printfacets */
-
-
-/*---------------------------------
-
-  qh_printhelp_degenerate( fp )
-    prints descriptive message for precision error
-
-  notes:
-    no message if qh_QUICKhelp
-*/
-void qh_printhelp_degenerate(FILE *fp) {
-
-  if (qh MERGEexact || qh PREmerge || qh JOGGLEmax < REALmax/2)
-    fprintf(fp, "\n\
-A Qhull error has occurred.  Qhull should have corrected the above\n\
-precision error.  Please send the input and all of the output to\n\
-qhull_bug@geom.umn.edu\n");
-  else if (!qh_QUICKhelp) {
-    fprintf(fp, "\n\
-Precision problems were detected during construction of the convex hull.\n\
-This occurs because convex hull algorithms assume that calculations are\n\
-exact, but floating-point arithmetic has roundoff errors.\n\
-\n\
-To correct for precision problems, do not use 'Q0'.  By default, Qhull\n\
-selects 'C-0' or 'Qx' and merges non-convex facets.  With option 'QJ',\n\
-Qhull joggles the input to prevent precision problems.  See \"Imprecision\n\
-in Qhull\" (qh-impre.htm).\n\
-\n\
-If you use 'Q0', the output may include\n\
-coplanar ridges, concave ridges, and flipped facets.  In 4-d and higher,\n\
-Qhull may produce a ridge with four neighbors or two facets with the same \n\
-vertices.  Qhull reports these events when they occur.  It stops when a\n\
-concave ridge, flipped facet, or duplicate facet occurs.\n");
-#if REALfloat
-    fprintf (fp, "\
-\n\
-Qhull is currently using single precision arithmetic.  The following\n\
-will probably remove the precision problems:\n\
-  - recompile qhull for double precision (#define REALfloat 0 in user.h).\n");
-#endif
-    if (qh DELAUNAY && !qh SCALElast && qh MAXabs_coord > 1e4)
-      fprintf( fp, "\
-\n\
-When computing the Delaunay triangulation of coordinates > 1.0,\n\
-  - use 'Qbb' to scale the last coordinate to [0,m] (max previous coordinate)\n");
-    if (qh DELAUNAY && !qh ATinfinity)
-      fprintf( fp, "\
-When computing the Delaunay triangulation:\n\
-  - use 'Qz' to add a point at-infinity.  This reduces precision problems.\n");
-
-    fprintf(fp, "\
-\n\
-If you need triangular output:\n\
-  - use option 'Qt' to triangulate the output\n\
-  - use option 'QJ' to joggle the input points and remove precision errors\n\
-  - use option 'Ft'.  It triangulates non-simplicial facets with added points.\n\
-\n\
-If you must use 'Q0',\n\
-try one or more of the following options.  They can not guarantee an output.\n\
-  - use 'QbB' to scale the input to a cube.\n\
-  - use 'Po' to produce output and prevent partitioning for flipped facets\n\
-  - use 'V0' to set min. distance to visible facet as 0 instead of roundoff\n\
-  - use 'En' to specify a maximum roundoff error less than %2.2g.\n\
-  - options 'Qf', 'Qbb', and 'QR0' may also help\n",
-               qh DISTround);
-    fprintf(fp, "\
-\n\
-To guarantee simplicial output:\n\
-  - use option 'Qt' to triangulate the output\n\
-  - use option 'QJ' to joggle the input points and remove precision errors\n\
-  - use option 'Ft' to triangulate the output by adding points\n\
-  - use exact arithmetic (see \"Imprecision in Qhull\", qh-impre.htm)\n\
-");
-  }
-} /* printhelp_degenerate */
-
-
-/*---------------------------------
-
-  qh_printhelp_singular( fp )
-    prints descriptive message for singular input
-*/
-void qh_printhelp_singular(FILE *fp) {
-  facetT *facet;
-  vertexT *vertex, **vertexp;
-  realT min, max, *coord, dist;
-  int i,k;
-
-  fprintf(fp, "\n\
-The input to qhull appears to be less than %d dimensional, or a\n\
-computation has overflowed.\n\n\
-Qhull could not construct a clearly convex simplex from points:\n",
-           qh hull_dim);
-  qh_printvertexlist (fp, "", qh facet_list, NULL, qh_ALL);
-  if (!qh_QUICKhelp)
-    fprintf(fp, "\n\
-The center point is coplanar with a facet, or a vertex is coplanar\n\
-with a neighboring facet.  The maximum round off error for\n\
-computing distances is %2.2g.  The center point, facets and distances\n\
-to the center point are as follows:\n\n", qh DISTround);
-  qh_printpointid (fp, "center point", qh hull_dim, qh interior_point, -1);
-  fprintf (fp, "\n");
-  FORALLfacets {
-    fprintf (fp, "facet");
-    FOREACHvertex_(facet->vertices)
-      fprintf (fp, " p%d", qh_pointid(vertex->point));
-    zinc_(Zdistio);
-    qh_distplane(qh interior_point, facet, &dist);
-    fprintf (fp, " distance= %4.2g\n", dist);
-  }
-  if (!qh_QUICKhelp) {
-    if (qh HALFspace)
-      fprintf (fp, "\n\
-These points are the dual of the given halfspaces.  They indicate that\n\
-the intersection is degenerate.\n");
-    fprintf (fp,"\n\
-These points either have a maximum or minimum x-coordinate, or\n\
-they maximize the determinant for k coordinates.  Trial points\n\
-are first selected from points that maximize a coordinate.\n");
-    if (qh hull_dim >= qh_INITIALmax)
-      fprintf (fp, "\n\
-Because of the high dimension, the min x-coordinate and max-coordinate\n\
-points are used if the determinant is non-zero.  Option 'Qs' will\n\
-do a better, though much slower, job.  Instead of 'Qs', you can change\n\
-the points by randomly rotating the input with 'QR0'.\n");
-  }
-  fprintf (fp, "\nThe min and max coordinates for each dimension are:\n");
-  for (k=0; k < qh hull_dim; k++) {
-    min= REALmax;
-    max= -REALmin;
-    for (i=qh num_points, coord= qh first_point+k; i--; coord += qh hull_dim) {
-      maximize_(max, *coord);
-      minimize_(min, *coord);
-    }
-    fprintf (fp, "  %d:  %8.4g  %8.4g  difference= %4.4g\n", k, min, max, max-min);
-  }
-  if (!qh_QUICKhelp) {
-    fprintf (fp, "\n\
-If the input should be full dimensional, you have several options that\n\
-may determine an initial simplex:\n\
-  - use 'QJ'  to joggle the input and make it full dimensional\n\
-  - use 'QbB' to scale the points to the unit cube\n\
-  - use 'QR0' to randomly rotate the input for different maximum points\n\
-  - use 'Qs'  to search all points for the initial simplex\n\
-  - use 'En'  to specify a maximum roundoff error less than %2.2g.\n\
-  - trace execution with 'T3' to see the determinant for each point.\n",
-                     qh DISTround);
-#if REALfloat
-    fprintf (fp, "\
-  - recompile qhull for double precision (#define REALfloat 0 in qhull.h).\n");
-#endif
-    fprintf (fp, "\n\
-If the input is lower dimensional:\n\
-  - use 'QJ' to joggle the input and make it full dimensional\n\
-  - use 'Qbk:0Bk:0' to delete coordinate k from the input.  You should\n\
-    pick the coordinate with the least range.  The hull will have the\n\
-    correct topology.\n\
-  - determine the flat containing the points, rotate the points\n\
-    into a coordinate plane, and delete the other coordinates.\n\
-  - add one or more points to make the input full dimensional.\n\
-");
-    if (qh DELAUNAY && !qh ATinfinity)
-      fprintf (fp, "\n\n\
-This is a Delaunay triangulation and the input is co-circular or co-spherical:\n\
-  - use 'Qz' to add a point \"at infinity\" (i.e., above the paraboloid)\n\
-  - or use 'QJ' to joggle the input and avoid co-circular data\n");
-  }
-} /* printhelp_singular */
-
-/*---------------------------------
-
-  qh_printhyperplaneintersection( fp, facet1, facet2, vertices, color )
-    print Geomview OFF or 4OFF for the intersection of two hyperplanes in 3-d or 4-d
-*/
-void qh_printhyperplaneintersection(FILE *fp, facetT *facet1, facetT *facet2,
-		   setT *vertices, realT color[3]) {
-  realT costheta, denominator, dist1, dist2, s, t, mindenom, p[4];
-  vertexT *vertex, **vertexp;
-  int i, k;
-  boolT nearzero1, nearzero2;
-
-  costheta= qh_getangle(facet1->normal, facet2->normal);
-  denominator= 1 - costheta * costheta;
-  i= qh_setsize(vertices);
-  if (qh hull_dim == 3)
-    fprintf(fp, "VECT 1 %d 1 %d 1 ", i, i);
-  else if (qh hull_dim == 4 && qh DROPdim >= 0)
-    fprintf(fp, "OFF 3 1 1 ");
-  else
-    qh printoutvar++;
-  fprintf (fp, "# intersect f%d f%d\n", facet1->id, facet2->id);
-  mindenom= 1 / (10.0 * qh MAXabs_coord);
-  FOREACHvertex_(vertices) {
-    qh_distplane(vertex->point, facet1, &dist1);
-    qh_distplane(vertex->point, facet2, &dist2);
-    s= qh_divzero (-dist1 + costheta * dist2, denominator,mindenom,&nearzero1);
-    t= qh_divzero (-dist2 + costheta * dist1, denominator,mindenom,&nearzero2);
-    if (nearzero1 || nearzero2)
-      s= t= 0.0;
-    for(k= qh hull_dim; k--; )
-      p[k]= vertex->point[k] + facet1->normal[k] * s + facet2->normal[k] * t;
-    if (qh PRINTdim <= 3) {
-      qh_projectdim3 (p, p);
-      fprintf(fp, "%8.4g %8.4g %8.4g # ", p[0], p[1], p[2]);
-    }else
-      fprintf(fp, "%8.4g %8.4g %8.4g %8.4g # ", p[0], p[1], p[2], p[3]);
-    if (nearzero1+nearzero2)
-      fprintf (fp, "p%d (coplanar facets)\n", qh_pointid (vertex->point));
-    else
-      fprintf (fp, "projected p%d\n", qh_pointid (vertex->point));
-  }
-  if (qh hull_dim == 3)
-    fprintf(fp, "%8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
-  else if (qh hull_dim == 4 && qh DROPdim >= 0)
-    fprintf(fp, "3 0 1 2 %8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
-} /* printhyperplaneintersection */
-
-/*---------------------------------
-
-  qh_printline3geom( fp, pointA, pointB, color )
-    prints a line as a VECT
-    prints 0's for qh.DROPdim
-
-  notes:
-    if pointA == pointB,
-      it's a 1 point VECT
-*/
-void qh_printline3geom (FILE *fp, pointT *pointA, pointT *pointB, realT color[3]) {
-  int k;
-  realT pA[4], pB[4];
-
-  qh_projectdim3(pointA, pA);
-  qh_projectdim3(pointB, pB);
-  if ((fabs(pA[0] - pB[0]) > 1e-3) ||
-      (fabs(pA[1] - pB[1]) > 1e-3) ||
-      (fabs(pA[2] - pB[2]) > 1e-3)) {
-    fprintf (fp, "VECT 1 2 1 2 1\n");
-    for (k= 0; k < 3; k++)
-       fprintf (fp, "%8.4g ", pB[k]);
-    fprintf (fp, " # p%d\n", qh_pointid (pointB));
-  }else
-    fprintf (fp, "VECT 1 1 1 1 1\n");
-  for (k=0; k < 3; k++)
-    fprintf (fp, "%8.4g ", pA[k]);
-  fprintf (fp, " # p%d\n", qh_pointid (pointA));
-  fprintf (fp, "%8.4g %8.4g %8.4g 1\n", color[0], color[1], color[2]);
-}
-
-/*---------------------------------
-
-  qh_printneighborhood( fp, format, facetA, facetB, printall )
-    print neighborhood of one or two facets
-
-  notes:
-    calls qh_findgood_all()
-    bumps qh.visit_id
-*/
-void qh_printneighborhood (FILE *fp, int format, facetT *facetA, facetT *facetB, boolT printall) {
-  facetT *neighbor, **neighborp, *facet;
-  setT *facets;
-
-  if (format == qh_PRINTnone)
-    return;
-  qh_findgood_all (qh facet_list);
-  if (facetA == facetB)
-    facetB= NULL;
-  facets= qh_settemp (2*(qh_setsize (facetA->neighbors)+1));
-  qh visit_id++;
-  for (facet= facetA; facet; facet= ((facet == facetA) ? facetB : NULL)) {
-    if (facet->visitid != qh visit_id) {
-      facet->visitid= qh visit_id;
-      qh_setappend (&facets, facet);
-    }
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid == qh visit_id)
-        continue;
-      neighbor->visitid= qh visit_id;
-      if (printall || !qh_skipfacet (neighbor))
-        qh_setappend (&facets, neighbor);
-    }
-  }
-  qh_printfacets (fp, format, NULL, facets, printall);
-  qh_settempfree (&facets);
-} /* printneighborhood */
-
-/*---------------------------------
-
-  qh_printpoint( fp, string, point )
-  qh_printpointid( fp, string, dim, point, id )
-    prints the coordinates of a point
-
-  returns:
-    if string is defined
-      prints 'string p%d' (skips p%d if id=-1)
-
-  notes:
-    nop if point is NULL
-    prints id unless it is undefined (-1)
-*/
-void qh_printpoint(FILE *fp, char *string, pointT *point) {
-  int id= qh_pointid( point);
-
-  qh_printpointid( fp, string, qh hull_dim, point, id);
-} /* printpoint */
-
-void qh_printpointid(FILE *fp, char *string, int dim, pointT *point, int id) {
-  int k;
-  realT r; /*bug fix*/
-
-  if (!point)
-    return;
-  if (string) {
-    fputs (string, fp);
-   if (id != -1)
-      fprintf(fp, " p%d: ", id);
-  }
-  for(k= dim; k--; ) {
-    r= *point++;
-    if (string)
-      fprintf(fp, " %8.4g", r);
-    else
-      fprintf(fp, qh_REAL_1, r);
-  }
-  fprintf(fp, "\n");
-} /* printpointid */
-
-/*---------------------------------
-
-  qh_printpoint3( fp, point )
-    prints 2-d, 3-d, or 4-d point as Geomview 3-d coordinates
-*/
-void qh_printpoint3 (FILE *fp, pointT *point) {
-  int k;
-  realT p[4];
-
-  qh_projectdim3 (point, p);
-  for (k=0; k < 3; k++)
-    fprintf (fp, "%8.4g ", p[k]);
-  fprintf (fp, " # p%d\n", qh_pointid (point));
-} /* printpoint3 */
-
-/*----------------------------------------
--printpoints- print pointids for a set of points starting at index
-   see geom.c
-*/
-
-/*---------------------------------
-
-  qh_printpoints_out( fp, facetlist, facets, printall )
-    prints vertices, coplanar/inside points, for facets by their point coordinates
-    allows qh.CDDoutput
-
-  notes:
-    same format as qhull input
-    if no coplanar/interior points,
-      same order as qh_printextremes
-*/
-void qh_printpoints_out (FILE *fp, facetT *facetlist, setT *facets, int printall) {
-  int allpoints= qh num_points + qh_setsize (qh other_points);
-  int numpoints=0, point_i, point_n;
-  setT *vertices, *points;
-  facetT *facet, **facetp;
-  pointT *point, **pointp;
-  vertexT *vertex, **vertexp;
-  int id;
-
-  points= qh_settemp (allpoints);
-  qh_setzero (points, 0, allpoints);
-  vertices= qh_facetvertices (facetlist, facets, printall);
-  FOREACHvertex_(vertices) {
-    id= qh_pointid (vertex->point);
-    if (id >= 0)
-      SETelem_(points, id)= vertex->point;
-  }
-  if (qh KEEPinside || qh KEEPcoplanar || qh KEEPnearinside) {
-    FORALLfacet_(facetlist) {
-      if (!printall && qh_skipfacet(facet))
-        continue;
-      FOREACHpoint_(facet->coplanarset) {
-        id= qh_pointid (point);
-        if (id >= 0)
-          SETelem_(points, id)= point;
-      }
-    }
-    FOREACHfacet_(facets) {
-      if (!printall && qh_skipfacet(facet))
-        continue;
-      FOREACHpoint_(facet->coplanarset) {
-        id= qh_pointid (point);
-        if (id >= 0)
-          SETelem_(points, id)= point;
-      }
-    }
-  }
-  qh_settempfree (&vertices);
-  FOREACHpoint_i_(points) {
-    if (point)
-      numpoints++;
-  }
-  if (qh CDDoutput)
-    fprintf (fp, "%s | %s\nbegin\n%d %d real\n", qh rbox_command,
-             qh qhull_command, numpoints, qh hull_dim + 1);
-  else
-    fprintf (fp, "%d\n%d\n", qh hull_dim, numpoints);
-  FOREACHpoint_i_(points) {
-    if (point) {
-      if (qh CDDoutput)
-	fprintf (fp, "1 ");
-      qh_printpoint (fp, NULL, point);
-    }
-  }
-  if (qh CDDoutput)
-    fprintf (fp, "end\n");
-  qh_settempfree (&points);
-} /* printpoints_out */
-
-
-/*---------------------------------
-
-  qh_printpointvect( fp, point, normal, center, radius, color )
-    prints a 2-d, 3-d, or 4-d point as 3-d VECT's relative to normal or to center point
-*/
-void qh_printpointvect (FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius, realT color[3]) {
-  realT diff[4], pointA[4];
-  int k;
-
-  for (k= qh hull_dim; k--; ) {
-    if (center)
-      diff[k]= point[k]-center[k];
-    else if (normal)
-      diff[k]= normal[k];
-    else
-      diff[k]= 0;
-  }
-  if (center)
-    qh_normalize2 (diff, qh hull_dim, True, NULL, NULL);
-  for (k= qh hull_dim; k--; )
-  qh_printline3geom (fp, point, pointA, color);
-} /* printpointvect */
-
-/*---------------------------------
-
-  qh_printpointvect2( fp, point, normal, center, radius )
-    prints a 2-d, 3-d, or 4-d point as 2 3-d VECT's for an imprecise point
-*/
-void qh_printpointvect2 (FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius) {
-  realT red[3]={1, 0, 0}, yellow[3]={1, 1, 0};
-
-  qh_printpointvect (fp, point, normal, center, radius, red);
-  qh_printpointvect (fp, point, normal, center, -radius, yellow);
-} /* printpointvect2 */
-
-/*---------------------------------
-
-  qh_printridge( fp, ridge )
-    prints the information in a ridge
-
-  notes:
-    for qh_printfacetridges()
-*/
-void qh_printridge(FILE *fp, ridgeT *ridge) {
-
-  fprintf(fp, "     - r%d", ridge->id);
-  if (ridge->tested)
-    fprintf (fp, " tested");
-  if (ridge->nonconvex)
-    fprintf (fp, " nonconvex");
-  fprintf (fp, "\n");
-  qh_printvertices (fp, "           vertices:", ridge->vertices);
-  if (ridge->top && ridge->bottom)
-    fprintf(fp, "           between f%d and f%d\n",
-	    ridge->top->id, ridge->bottom->id);
-} /* printridge */
-
-/*---------------------------------
-
-  qh_printspheres( fp, vertices, radius )
-    prints 3-d vertices as OFF spheres
-
-  notes:
-    inflated octahedron from Stuart Levy earth/mksphere2
-*/
-void qh_printspheres(FILE *fp, setT *vertices, realT radius) {
-  vertexT *vertex, **vertexp;
-
-  qh printoutnum++;
-  fprintf (fp, "{appearance {-edge -normal normscale 0} {\n\
-INST geom {define vsphere OFF\n\
-18 32 48\n\
-\n\
-0 0 1\n\
-1 0 0\n\
-0 1 0\n\
--1 0 0\n\
-0 -1 0\n\
-0 0 -1\n\
-0.707107 0 0.707107\n\
-0 -0.707107 0.707107\n\
-0.707107 -0.707107 0\n\
--0.707107 0 0.707107\n\
--0.707107 -0.707107 0\n\
-0 0.707107 0.707107\n\
--0.707107 0.707107 0\n\
-0.707107 0.707107 0\n\
-0.707107 0 -0.707107\n\
-0 0.707107 -0.707107\n\
--0.707107 0 -0.707107\n\
-0 -0.707107 -0.707107\n\
-\n\
-3 0 6 11\n\
-3 0 7 6	\n\
-3 0 9 7	\n\
-3 0 11 9\n\
-3 1 6 8	\n\
-3 1 8 14\n\
-3 1 13 6\n\
-3 1 14 13\n\
-3 2 11 13\n\
-3 2 12 11\n\
-3 2 13 15\n\
-3 2 15 12\n\
-3 3 9 12\n\
-3 3 10 9\n\
-3 3 12 16\n\
-3 3 16 10\n\
-3 4 7 10\n\
-3 4 8 7\n\
-3 4 10 17\n\
-3 4 17 8\n\
-3 5 14 17\n\
-3 5 15 14\n\
-3 5 16 15\n\
-3 5 17 16\n\
-3 6 13 11\n\
-3 7 8 6\n\
-3 9 10 7\n\
-3 11 12 9\n\
-3 14 8 17\n\
-3 15 13 14\n\
-3 16 12 15\n\
-3 17 10 16\n} transforms { TLIST\n");
-  FOREACHvertex_(vertices) {
-    fprintf(fp, "%8.4g 0 0 0 # v%d\n 0 %8.4g 0 0\n0 0 %8.4g 0\n",
-    qh_printpoint3 (fp, vertex->point);
-    fprintf (fp, "1\n");
-  }
-  fprintf (fp, "}}}\n");
-} /* printspheres */
-
-
-/*----------------------------------------------
--printsummary-
-                see qhull.c
-*/
-
-/*---------------------------------
-
-  qh_printvdiagram( fp, format, facetlist, facets, printall )
-    print voronoi diagram
-      # of pairs of input sites
-      #indices site1 site2 vertex1 ...
-
-    sites indexed by input point id
-      point 0 is the first input point
-    vertices indexed by 'o' and 'p' order
-      vertex 0 is the 'vertex-at-infinity'
-      vertex 1 is the first Voronoi vertex
-
-  see:
-    qh_printvoronoi()
-    qh_eachvoronoi_all()
-
-  notes:
-    if all facets are upperdelaunay,
-      prints upper hull (furthest-site Voronoi diagram)
-*/
-void qh_printvdiagram (FILE *fp, int format, facetT *facetlist, setT *facets, boolT printall) {
-  setT *vertices;
-  int totcount, numcenters;
-  boolT islower;
-  qh_RIDGE innerouter= qh_RIDGEall;
-  printvridgeT printvridge= NULL;
-
-  if (format == qh_PRINTvertices) {
-    innerouter= qh_RIDGEall;
-    printvridge= qh_printvridge;
-  }else if (format == qh_PRINTinner) {
-    innerouter= qh_RIDGEinner;
-    printvridge= qh_printvnorm;
-  }else if (format == qh_PRINTouter) {
-    innerouter= qh_RIDGEouter;
-    printvridge= qh_printvnorm;
-  }else {
-    fprintf(qh ferr, "qh_printvdiagram: unknown print format %d.\n", format);
-    qh_errexit (qh_ERRinput, NULL, NULL);
-  }
-  vertices= qh_markvoronoi (facetlist, facets, printall, &islower, &numcenters);
-  totcount= qh_printvdiagram2 (NULL, NULL, vertices, innerouter, False);
-  fprintf (fp, "%d\n", totcount);
-  totcount= qh_printvdiagram2 (fp, printvridge, vertices, innerouter, True /* inorder*/);
-  qh_settempfree (&vertices);
-#if 0  /* for testing qh_eachvoronoi_all */
-  fprintf (fp, "\n");
-  totcount= qh_eachvoronoi_all(fp, printvridge, qh UPPERdelaunay, innerouter, True /* inorder*/);
-  fprintf (fp, "%d\n", totcount);
-#endif
-} /* printvdiagram */
-
-/*---------------------------------
-
-  qh_printvdiagram2( fp, printvridge, vertices, innerouter, inorder )
-    visit all pairs of input sites (vertices) for selected Voronoi vertices
-    vertices may include NULLs
-
-  innerouter:
-    qh_RIDGEall   print inner ridges (bounded) and outer ridges (unbounded)
-    qh_RIDGEinner print only inner ridges
-    qh_RIDGEouter print only outer ridges
-
-  inorder:
-    print 3-d Voronoi vertices in order
-
-  assumes:
-    qh_markvoronoi marked facet->visitid for Voronoi vertices
-    all facet->seen= False
-    all facet->seen2= True
-
-  returns:
-    total number of Voronoi ridges
-    if printvridge,
-      calls printvridge( fp, vertex, vertexA, centers) for each ridge
-      [see qh_eachvoronoi()]
-
-  see:
-    qh_eachvoronoi_all()
-*/
-int qh_printvdiagram2 (FILE *fp, printvridgeT printvridge, setT *vertices, qh_RIDGE innerouter, boolT inorder) {
-  int totcount= 0;
-  int vertex_i, vertex_n;
-  vertexT *vertex;
-
-  FORALLvertices
-    vertex->seen= False;
-  FOREACHvertex_i_(vertices) {
-    if (vertex) {
-      if (qh GOODvertex > 0 && qh_pointid(vertex->point)+1 != qh GOODvertex)
-	continue;
-      totcount += qh_eachvoronoi (fp, printvridge, vertex, !qh_ALL, innerouter, inorder);
-    }
-  }
-} /* printvdiagram2 */
-
-/*---------------------------------
-
-  qh_printvertex( fp, vertex )
-    prints the information in a vertex
-*/
-void qh_printvertex(FILE *fp, vertexT *vertex) {
-  pointT *point;
-  int k, count= 0;
-  facetT *neighbor, **neighborp;
-  realT r; /*bug fix*/
-
-  if (!vertex) {
-    fprintf (fp, "  NULLvertex\n");
-    return;
-  }
-  fprintf(fp, "- p%d (v%d):", qh_pointid(vertex->point), vertex->id);
-  point= vertex->point;
-  if (point) {
-    for(k= qh hull_dim; k--; ) {
-      r= *point++;
-      fprintf(fp, " %5.2g", r);
-    }
-  }
-  if (vertex->deleted)
-    fprintf(fp, " deleted");
-  if (vertex->delridge)
-    fprintf (fp, " ridgedeleted");
-  fprintf(fp, "\n");
-  if (vertex->neighbors) {
-    fprintf(fp, "  neighbors:");
-    FOREACHneighbor_(vertex) {
-      if (++count % 100 == 0)
-	fprintf (fp, "\n     ");
-      fprintf(fp, " f%d", neighbor->id);
-    }
-    fprintf(fp, "\n");
-  }
-} /* printvertex */
-
-
-/*---------------------------------
-
-  qh_printvertexlist( fp, string, facetlist, facets, printall )
-    prints vertices used by a facetlist or facet set
-    tests qh_skipfacet() if !printall
-*/
-void qh_printvertexlist (FILE *fp, char* string, facetT *facetlist,
-                         setT *facets, boolT printall) {
-  vertexT *vertex, **vertexp;
-  setT *vertices;
-
-  vertices= qh_facetvertices (facetlist, facets, printall);
-  fputs (string, fp);
-  FOREACHvertex_(vertices)
-    qh_printvertex(fp, vertex);
-  qh_settempfree (&vertices);
-} /* printvertexlist */
-
-
-/*---------------------------------
-
-  qh_printvertices( fp, string, vertices )
-    prints vertices in a set
-*/
-void qh_printvertices(FILE *fp, char* string, setT *vertices) {
-  vertexT *vertex, **vertexp;
-
-  fputs (string, fp);
-  FOREACHvertex_(vertices)
-    fprintf (fp, " p%d (v%d)", qh_pointid(vertex->point), vertex->id);
-  fprintf(fp, "\n");
-} /* printvertices */
-
-/*---------------------------------
-
-  qh_printvneighbors( fp, facetlist, facets, printall )
-    print vertex neighbors of vertices in facetlist and facets ('FN')
-
-  notes:
-    qh_countfacets clears facet->visitid for non-printed facets
-
-  design:
-    collect facet count and related statistics
-    if necessary, build neighbor sets for each vertex
-    collect vertices in facetlist and facets
-    build a point array for point->vertex and point->coplanar facet
-    for each point
-      list vertex neighbors or coplanar facet
-*/
-void qh_printvneighbors (FILE *fp, facetT* facetlist, setT *facets, boolT printall) {
-  int numfacets, numsimplicial, numridges, totneighbors, numneighbors, numcoplanars, numtricoplanars;
-  setT *vertices, *vertex_points, *coplanar_points;
-  int numpoints= qh num_points + qh_setsize (qh other_points);
-  vertexT *vertex, **vertexp;
-  int vertex_i, vertex_n;
-  facetT *facet, **facetp, *neighbor, **neighborp;
-  pointT *point, **pointp;
-
-  qh_countfacets (facetlist, facets, printall, &numfacets, &numsimplicial,
-      &totneighbors, &numridges, &numcoplanars, &numtricoplanars);  /* sets facet->visitid */
-  fprintf (fp, "%d\n", numpoints);
-  qh_vertexneighbors();
-  vertices= qh_facetvertices (facetlist, facets, printall);
-  vertex_points= qh_settemp (numpoints);
-  coplanar_points= qh_settemp (numpoints);
-  qh_setzero (vertex_points, 0, numpoints);
-  qh_setzero (coplanar_points, 0, numpoints);
-  FOREACHvertex_(vertices)
-  FORALLfacet_(facetlist) {
-    FOREACHpoint_(facet->coplanarset)
-  }
-  FOREACHfacet_(facets) {
-    FOREACHpoint_(facet->coplanarset)
-  }
-  FOREACHvertex_i_(vertex_points) {
-    if (vertex) {
-      numneighbors= qh_setsize (vertex->neighbors);
-      fprintf (fp, "%d", numneighbors);
-      if (qh hull_dim == 3)
-        qh_order_vertexneighbors (vertex);
-      else if (qh hull_dim >= 4)
-             sizeof (facetT *), qh_compare_facetvisit);
-      FOREACHneighbor_(vertex)
-        fprintf (fp, " %d",
-		 neighbor->visitid ? neighbor->visitid - 1 : - neighbor->id);
-      fprintf (fp, "\n");
-    }else if ((facet= SETelemt_(coplanar_points, vertex_i, facetT)))
-      fprintf (fp, "1 %d\n",
-                  facet->visitid ? facet->visitid - 1 : - facet->id);
-    else
-      fprintf (fp, "0\n");
-  }
-  qh_settempfree (&coplanar_points);
-  qh_settempfree (&vertex_points);
-  qh_settempfree (&vertices);
-} /* printvneighbors */
-
-/*---------------------------------
-
-  qh_printvoronoi( fp, format, facetlist, facets, printall )
-    print voronoi diagram in 'o' or 'G' format
-    for 'o' format
-      prints voronoi centers for each facet and for infinity
-      for each vertex, lists ids of printed facets or infinity
-      assumes facetlist and facets are disjoint
-    for 'G' format
-      prints an OFF object
-      adds a 0 coordinate to center
-      prints infinity but does not list in vertices
-
-  see:
-    qh_printvdiagram()
-
-  notes:
-    if 'o',
-      prints a line for each point except "at-infinity"
-    if all facets are upperdelaunay,
-      reverses lower and upper hull
-*/
-void qh_printvoronoi (FILE *fp, int format, facetT *facetlist, setT *facets, boolT printall) {
-  int k, numcenters, numvertices= 0, numneighbors, numinf, vid=1, vertex_i, vertex_n;
-  facetT *facet, **facetp, *neighbor, **neighborp;
-  setT *vertices;
-  vertexT *vertex;
-  boolT islower;
-  unsigned int numfacets= (unsigned int) qh num_facets;
-
-  vertices= qh_markvoronoi (facetlist, facets, printall, &islower, &numcenters);
-  FOREACHvertex_i_(vertices) {
-    if (vertex) {
-      numvertices++;
-      numneighbors = numinf = 0;
-      FOREACHneighbor_(vertex) {
-        if (neighbor->visitid == 0)
-	  numinf= 1;
-        else if (neighbor->visitid < numfacets)
-          numneighbors++;
-      }
-      if (numinf && !numneighbors) {
-	SETelem_(vertices, vertex_i)= NULL;
-	numvertices--;
-      }
-    }
-  }
-  if (format == qh_PRINTgeom)
-    fprintf (fp, "{appearance {+edge -face} OFF %d %d 1 # Voronoi centers and cells\n",
-                numcenters, numvertices);
-  else
-    fprintf (fp, "%d\n%d %d 1\n", qh hull_dim-1, numcenters, qh_setsize(vertices));
-  if (format == qh_PRINTgeom) {
-    for (k= qh hull_dim-1; k--; )
-      fprintf (fp, qh_REAL_1, 0.0);
-    fprintf (fp, " 0 # infinity not used\n");
-  }else {
-    for (k= qh hull_dim-1; k--; )
-      fprintf (fp, qh_REAL_1, qh_INFINITE);
-    fprintf (fp, "\n");
-  }
-  FORALLfacet_(facetlist) {
-    if (facet->visitid && facet->visitid < numfacets) {
-      if (format == qh_PRINTgeom)
-        fprintf (fp, "# %d f%d\n", vid++, facet->id);
-      qh_printcenter (fp, format, NULL, facet);
-    }
-  }
-  FOREACHfacet_(facets) {
-    if (facet->visitid && facet->visitid < numfacets) {
-      if (format == qh_PRINTgeom)
-        fprintf (fp, "# %d f%d\n", vid++, facet->id);
-      qh_printcenter (fp, format, NULL, facet);
-    }
-  }
-  FOREACHvertex_i_(vertices) {
-    numneighbors= 0;
-    numinf=0;
-    if (vertex) {
-      if (qh hull_dim == 3)
-        qh_order_vertexneighbors(vertex);
-      else if (qh hull_dim >= 4)
-	     qh_setsize (vertex->neighbors),
-	     sizeof (facetT *), qh_compare_facetvisit);
-      FOREACHneighbor_(vertex) {
-        if (neighbor->visitid == 0)
-	  numinf= 1;
-	else if (neighbor->visitid < numfacets)
-          numneighbors++;
-      }
-    }
-    if (format == qh_PRINTgeom) {
-      if (vertex) {
-	fprintf (fp, "%d", numneighbors);
-	if (vertex) {
-	  FOREACHneighbor_(vertex) {
-	    if (neighbor->visitid && neighbor->visitid < numfacets)
-	      fprintf (fp, " %d", neighbor->visitid);
-	  }
-	}
-	fprintf (fp, " # p%d (v%d)\n", vertex_i, vertex->id);
-      }else
-	fprintf (fp, " # p%d is coplanar or isolated\n", vertex_i);
-    }else {
-      if (numinf)
-	numneighbors++;
-      fprintf (fp, "%d", numneighbors);
-      if (vertex) {
-        FOREACHneighbor_(vertex) {
-  	  if (neighbor->visitid == 0) {
-  	    if (numinf) {
-  	      numinf= 0;
-	      fprintf (fp, " %d", neighbor->visitid);
-	    }
-	  }else if (neighbor->visitid < numfacets)
-	    fprintf (fp, " %d", neighbor->visitid);
-	}
-      }
-      fprintf (fp, "\n");
-    }
-  }
-  if (format == qh_PRINTgeom)
-    fprintf (fp, "}\n");
-  qh_settempfree (&vertices);
-} /* printvoronoi */
-
-/*---------------------------------
-
-  qh_printvnorm( fp, vertex, vertexA, centers, unbounded )
-    print one separating plane of the Voronoi diagram for a pair of input sites
-    unbounded==True if centers includes vertex-at-infinity
-
-  assumes:
-    qh_ASvoronoi and qh_vertexneighbors() already set
-
-  see:
-    qh_printvdiagram()
-    qh_eachvoronoi()
-*/
-void qh_printvnorm (FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded) {
-  pointT *normal;
-  realT offset;
-  int k;
-
-  normal= qh_detvnorm (vertex, vertexA, centers, &offset);
-  fprintf (fp, "%d %d %d ",
-      2+qh hull_dim, qh_pointid (vertex->point), qh_pointid (vertexA->point));
-  for (k= 0; k< qh hull_dim-1; k++)
-    fprintf (fp, qh_REAL_1, normal[k]);
-  fprintf (fp, qh_REAL_1, offset);
-  fprintf (fp, "\n");
-} /* printvnorm */
-
-/*---------------------------------
-
-  qh_printvridge( fp, vertex, vertexA, centers, unbounded )
-    print one ridge of the Voronoi diagram for a pair of input sites
-    unbounded==True if centers includes vertex-at-infinity
-
-  see:
-    qh_printvdiagram()
-
-  notes:
-    the user may use a different function
-*/
-void qh_printvridge (FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded) {
-  facetT *facet, **facetp;
-
-  fprintf (fp, "%d %d %d", qh_setsize (centers)+2,
-       qh_pointid (vertex->point), qh_pointid (vertexA->point));
-  FOREACHfacet_(centers)
-    fprintf (fp, " %d", facet->visitid);
-  fprintf (fp, "\n");
-} /* printvridge */
-
-/*---------------------------------
-
-  qh_projectdim3( source, destination )
-    project 2-d 3-d or 4-d point to a 3-d point
-    uses qh.DROPdim and qh.hull_dim
-    source and destination may be the same
-
-  notes:
-    allocate 4 elements to destination just in case
-*/
-void qh_projectdim3 (pointT *source, pointT *destination) {
-  int i,k;
-
-  for (k= 0, i=0; k < qh hull_dim; k++) {
-    if (qh hull_dim == 4) {
-      if (k != qh DROPdim)
-        destination[i++]= source[k];
-    }else if (k == qh DROPdim)
-      destination[i++]= 0;
-    else
-      destination[i++]= source[k];
-  }
-  while (i < 3)
-    destination[i++]= 0.0;
-} /* projectdim3 */
-
-/*---------------------------------
-
-    read feasible point from remainder string and qh.fin
-
-  returns:
-    number of lines read from qh.fin
-    sets qh.FEASIBLEpoint with malloc'd coordinates
-
-  notes:
-    checks for qh.HALFspace
-    assumes dim > 1
-
-  see:
-    qh_setfeasible
-*/
-int qh_readfeasible (int dim, char *remainder) {
-  boolT isfirst= True;
-  int linecount= 0, tokcount= 0;
-  char *s, *t, firstline[qh_MAXfirst+1];
-  coordT *coords, value;
-
-  if (!qh HALFspace) {
-    fprintf  (qh ferr, "qhull input error: feasible point (dim 1 coords) is only valid for halfspace intersection\n");
-    qh_errexit (qh_ERRinput, NULL, NULL);
-  }
-  if (qh feasible_string)
-    fprintf  (qh ferr, "qhull input warning: feasible point (dim 1 coords) overrides 'Hn,n,n' feasible point for halfspace intersection\n");
-  if (!(qh feasible_point= (coordT*)malloc (dim* sizeof(coordT)))) {
-    fprintf(qh ferr, "qhull error: insufficient memory for feasible point\n");
-    qh_errexit(qh_ERRmem, NULL, NULL);
-  }
-  coords= qh feasible_point;
-  while ((s= (isfirst ?  remainder : fgets(firstline, qh_MAXfirst, qh fin)))) {
-    if (isfirst)
-      isfirst= False;
-    else
-      linecount++;
-    while (*s) {
-      while (isspace(*s))
-        s++;
-      value= qh_strtod (s, &t);
-      if (s == t)
-        break;
-      s= t;
-      *(coords++)= value;
-      if (++tokcount == dim) {
-        while (isspace (*s))
-          s++;
-        qh_strtod (s, &t);
-        if (s != t) {
-          fprintf (qh ferr, "qhull input error: coordinates for feasible point do not finish out the line: %s\n",
-               s);
-          qh_errexit (qh_ERRinput, NULL, NULL);
-        }
-        return linecount;
-      }
-    }
-  }
-  fprintf (qh ferr, "qhull input error: only %d coordinates.  Could not read %d-d feasible point.\n",
-           tokcount, dim);
-  qh_errexit (qh_ERRinput, NULL, NULL);
-  return 0;
-
-/*---------------------------------
-
-  qh_readpoints( numpoints, dimension, ismalloc )
-    read points from qh.fin into qh.first_point, qh.num_points
-    qh.fin is lines of coordinates, one per vertex, first line number of points
-    if 'rbox D4',
-      gives message
-    if qh.ATinfinity,
-      adds point-at-infinity for Delaunay triangulations
-
-  returns:
-    number of points, array of point coordinates, dimension, ismalloc True
-    if qh.DELAUNAY & !qh.PROJECTinput, projects points to paraboloid
-        and clears qh.PROJECTdelaunay
-        converts to dual.
-
-  for feasible point in "cdd format" in 3-d:
-    3 1
-    coordinates
-    begin
-    n 4 real/integer
-    ...
-    end
-
-  notes:
-    dimension will change in qh_initqhull_globals if qh.PROJECTinput
-    uses malloc() since qh_mem not initialized
-    FIXUP: this routine needs rewriting
-*/
-coordT *qh_readpoints(int *numpoints, int *dimension, boolT *ismalloc) {
-  coordT *points, *coords, *infinity= NULL;
-  realT paraboloid, maxboloid= -REALmax, value;
-  realT *coordp= NULL, *offsetp= NULL, *normalp= NULL;
-  char *s, *t, firstline[qh_MAXfirst+1];
-  int diminput=0, numinput=0, dimfeasible= 0, newnum, k, tempi;
-  int firsttext=0, firstshort=0, firstlong=0, firstpoint=0;
-  int tokcount= 0, linecount=0, maxcount, coordcount=0;
-  boolT islong, isfirst= True, wasbegin= False;
-  boolT isdelaunay= qh DELAUNAY && !qh PROJECTinput;
-
-  if (qh CDDinput) {
-    while ((s= fgets(firstline, qh_MAXfirst, qh fin))) {
-      linecount++;
-      if (qh HALFspace && linecount == 1 && isdigit(*s)) {
-	dimfeasible= qh_strtol (s, &s);
-	while (isspace(*s))
-          s++;
-        if (qh_strtol (s, &s) == 1)
-          linecount += qh_readfeasible (dimfeasible, s);
-        else
-          dimfeasible= 0;
-      }else if (!memcmp (firstline, "begin", 5) || !memcmp (firstline, "BEGIN", 5))
-        break;
-      else if (!*qh rbox_command)
-	strncat(qh rbox_command, s, sizeof (qh rbox_command)-1);
-    }
-    if (!s) {
-      fprintf (qh ferr, "qhull input error: missing \"begin\" for cdd-formated input\n");
-      qh_errexit (qh_ERRinput, NULL, NULL);
-    }
-  }
-  while(!numinput && (s= fgets(firstline, qh_MAXfirst, qh fin))) {
-    linecount++;
-    if (!memcmp (s, "begin", 5) || !memcmp (s, "BEGIN", 5))
-      wasbegin= True;
-    while (*s) {
-      while (isspace(*s))
-        s++;
-      if (!*s)
-        break;
-      if (!isdigit(*s)) {
-        if (!*qh rbox_command) {
-          strncat(qh rbox_command, s, sizeof (qh rbox_command)-1);
-	  firsttext= linecount;
-        }
-        break;
-      }
-      if (!diminput)
-        diminput= qh_strtol (s, &s);
-      else {
-        numinput= qh_strtol (s, &s);
-        if (numinput == 1 && diminput >= 2 && qh HALFspace && !qh CDDinput) {
-          linecount += qh_readfeasible (diminput, s); /* checks if ok */
-          dimfeasible= diminput;
-          diminput= numinput= 0;
-        }else
-          break;
-      }
-    }
-  }
-  if (!s) {
-    fprintf(qh ferr, "qhull input error: short input file.  Did not find dimension and number of points\n");
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  if (diminput > numinput) {
-    tempi= diminput;	/* exchange dim and n, e.g., for cdd input format */
-    diminput= numinput;
-    numinput= tempi;
-  }
-  if (diminput < 2) {
-    fprintf(qh ferr,"qhull input error: dimension %d (first number) should be at least 2\n",
-	    diminput);
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  if (isdelaunay) {
-    qh PROJECTdelaunay= False;
-    if (qh CDDinput)
-      *dimension= diminput;
-    else
-      *dimension= diminput+1;
-    *numpoints= numinput;
-    if (qh ATinfinity)
-      (*numpoints)++;
-  }else if (qh HALFspace) {
-    *dimension= diminput - 1;
-    *numpoints= numinput;
-    if (diminput < 3) {
-      fprintf(qh ferr,"qhull input error: dimension %d (first number, includes offset) should be at least 3 for halfspaces\n",
-  	    diminput);
-      qh_errexit(qh_ERRinput, NULL, NULL);
-    }
-    if (dimfeasible) {
-      if (dimfeasible != *dimension) {
-        fprintf(qh ferr,"qhull input error: dimension %d of feasible point is not one less than dimension %d for halfspaces\n",
-          dimfeasible, diminput);
-        qh_errexit(qh_ERRinput, NULL, NULL);
-      }
-    }else
-      qh_setfeasible (*dimension);
-  }else {
-    if (qh CDDinput)
-      *dimension= diminput-1;
-    else
-      *dimension= diminput;
-    *numpoints= numinput;
-  }
-  qh normal_size= *dimension * sizeof(coordT); /* for tracing with qh_printpoint */
-  if (qh HALFspace) {
-    qh half_space= coordp= (coordT*) malloc (qh normal_size + sizeof(coordT));
-    if (qh CDDinput) {
-      offsetp= qh half_space;
-      normalp= offsetp + 1;
-    }else {
-      normalp= qh half_space;
-      offsetp= normalp + *dimension;
-    }
-  }
-  qh maxline= diminput * (qh_REALdigits + 5);
-  maximize_(qh maxline, 500);
-  qh line= (char*)malloc ((qh maxline+1) * sizeof (char));
-  *ismalloc= True;  /* use malloc since memory not setup */
-  coords= points= qh temp_malloc=
-        (coordT*)malloc((*numpoints)*(*dimension)*sizeof(coordT));
-  if (!coords || !qh line || (qh HALFspace && !qh half_space)) {
-    fprintf(qh ferr, "qhull error: insufficient memory to read %d points\n",
-	    numinput);
-    qh_errexit(qh_ERRmem, NULL, NULL);
-  }
-  if (isdelaunay && qh ATinfinity) {
-    infinity= points + numinput * (*dimension);
-    for (k= (*dimension) - 1; k--; )
-      infinity[k]= 0.0;
-  }
-  maxcount= numinput * diminput;
-  paraboloid= 0.0;
-  while ((s= (isfirst ?  s : fgets(qh line, qh maxline, qh fin)))) {
-    if (!isfirst) {
-      linecount++;
-      if (*s == 'e' || *s == 'E') {
-	if (!memcmp (s, "end", 3) || !memcmp (s, "END", 3)) {
-	  if (qh CDDinput )
-	    break;
-	  else if (wasbegin)
-	    fprintf (qh ferr, "qhull input warning: the input appears to be in cdd format.  If so, use 'Fd'\n");
-	}
-      }
-    }
-    islong= False;
-    while (*s) {
-      while (isspace(*s))
-        s++;
-      value= qh_strtod (s, &t);
-      if (s == t) {
-        if (!*qh rbox_command)
- 	 strncat(qh rbox_command, s, sizeof (qh rbox_command)-1);
-        if (*s && !firsttext)
-          firsttext= linecount;
-        if (!islong && !firstshort && coordcount)
-          firstshort= linecount;
-        break;
-      }
-      if (!firstpoint)
-	firstpoint= linecount;
-      s= t;
-      if (++tokcount > maxcount)
-        continue;
-      if (qh HALFspace) {
-	if (qh CDDinput)
-	  *(coordp++)= -value; /* both coefficients and offset */
-	else
-	  *(coordp++)= value;
-      }else {
-        *(coords++)= value;
-        if (qh CDDinput && !coordcount) {
-          if (value != 1.0) {
-            fprintf (qh ferr, "qhull input error: for cdd format, point at line %d does not start with '1'\n",
-                   linecount);
-            qh_errexit (qh_ERRinput, NULL, NULL);
-          }
-          coords--;
-        }else if (isdelaunay) {
-	  paraboloid += value * value;
-	  if (qh ATinfinity) {
-	    if (qh CDDinput)
-	      infinity[coordcount-1] += value;
-	    else
-	      infinity[coordcount] += value;
-	  }
-	}
-      }
-      if (++coordcount == diminput) {
-        coordcount= 0;
-        if (isdelaunay) {
-          *(coords++)= paraboloid;
-          maximize_(maxboloid, paraboloid);
-          paraboloid= 0.0;
-        }else if (qh HALFspace) {
-          if (!qh_sethalfspace (*dimension, coords, &coords, normalp, offsetp, qh feasible_point)) {
-	    fprintf (qh ferr, "The halfspace was on line %d\n", linecount);
-	    if (wasbegin)
-	      fprintf (qh ferr, "The input appears to be in cdd format.  If so, you should use option 'Fd'\n");
-	    qh_errexit (qh_ERRinput, NULL, NULL);
-	  }
-          coordp= qh half_space;
-        }
-        while (isspace(*s))
-          s++;
-        if (*s) {
-          islong= True;
-          if (!firstlong)
-            firstlong= linecount;
-	}
-      }
-    }
-    if (!islong && !firstshort && coordcount)
-      firstshort= linecount;
-    if (!isfirst && s - qh line >= qh maxline) {
-      fprintf(qh ferr, "qhull input error: line %d contained more than %d characters\n",
-	      linecount, (int) (s - qh line));
-      qh_errexit(qh_ERRinput, NULL, NULL);
-    }
-    isfirst= False;
-  }
-  if (tokcount != maxcount) {
-    newnum= fmin_(numinput, tokcount/diminput);
-    fprintf(qh ferr,"\
-qhull warning: instead of %d %d-dimensional points, input contains\n\
-%d points and %d extra coordinates.  Line %d is the first\npoint",
-       numinput, diminput, tokcount/diminput, tokcount % diminput, firstpoint);
-    if (firsttext)
-      fprintf(qh ferr, ", line %d is the first comment", firsttext);
-    if (firstshort)
-      fprintf(qh ferr, ", line %d is the first short\nline", firstshort);
-    if (firstlong)
-      fprintf(qh ferr, ", line %d is the first long line", firstlong);
-    fprintf(qh ferr, ".  Continue with %d points.\n", newnum);
-    numinput= newnum;
-    if (isdelaunay && qh ATinfinity) {
-      for (k= tokcount % diminput; k--; )
-	infinity[k] -= *(--coords);
-      *numpoints= newnum+1;
-    }else {
-      coords -= tokcount % diminput;
-      *numpoints= newnum;
-    }
-  }
-  if (isdelaunay && qh ATinfinity) {
-    for (k= (*dimension) -1; k--; )
-      infinity[k] /= numinput;
-    if (coords == infinity)
-      coords += (*dimension) -1;
-    else {
-      for (k= 0; k < (*dimension) -1; k++)
-	*(coords++)= infinity[k];
-    }
-    *(coords++)= maxboloid * 1.1;
-  }
-  if (qh rbox_command[0]) {
-    qh rbox_command[strlen(qh rbox_command)-1]= '\0';
-    if (!strcmp (qh rbox_command, "./rbox D4"))
-      fprintf (qh ferr, "\n\
-This is the qhull test case.  If any errors or core dumps occur,\n\
-recompile qhull with 'make new'.  If errors still occur, there is\n\
-an incompatibility.  You should try a different compiler.  You can also\n\
-change the choices in user.h.  If you discover the source of the problem,\n\
-\n\
-Type 'qhull' for a short list of options.\n");
-  }
-  free (qh line);
-  qh line= NULL;
-  if (qh half_space) {
-    free (qh half_space);
-    qh half_space= NULL;
-  }
-  qh temp_malloc= NULL;
-	  numinput, diminput));
-  return(points);
-
-
-/*---------------------------------
-
-  qh_setfeasible( dim )
-    set qh.FEASIBLEpoint from qh.feasible_string in "n,n,n" or "n n n" format
-
-  notes:
-    "n,n,n" already checked by qh_initflags()
-*/
-void qh_setfeasible (int dim) {
-  int tokcount= 0;
-  char *s;
-  coordT *coords, value;
-
-  if (!(s= qh feasible_string)) {
-    fprintf(qh ferr, "\
-qhull input error: halfspace intersection needs a feasible point.\n\
-Either prepend the input with 1 point or use 'Hn,n,n'.  See manual.\n");
-    qh_errexit (qh_ERRinput, NULL, NULL);
-  }
-  if (!(qh feasible_point= (pointT*)malloc (dim* sizeof(coordT)))) {
-    fprintf(qh ferr, "qhull error: insufficient memory for 'Hn,n,n'\n");
-    qh_errexit(qh_ERRmem, NULL, NULL);
-  }
-  coords= qh feasible_point;
-  while (*s) {
-    value= qh_strtod (s, &s);
-    if (++tokcount > dim) {
-      fprintf (qh ferr, "qhull input warning: more coordinates for 'H%s' than dimension %d\n",
-          qh feasible_string, dim);
-      break;
-    }
-    *(coords++)= value;
-    if (*s)
-      s++;
-  }
-  while (++tokcount <= dim)
-    *(coords++)= 0.0;
-} /* setfeasible */
-
-/*---------------------------------
-
-  qh_skipfacet( facet )
-    returns 'True' if this facet is not to be printed
-
-  notes:
-    based on the user provided slice thresholds and 'good' specifications
-*/
-boolT qh_skipfacet(facetT *facet) {
-  facetT *neighbor, **neighborp;
-
-  if (qh PRINTneighbors) {
-    if (facet->good)
-      return !qh PRINTgood;
-    FOREACHneighbor_(facet) {
-      if (neighbor->good)
-	return False;
-    }
-    return True;
-  }else if (qh PRINTgood)
-    return !facet->good;
-  else if (!facet->normal)
-    return True;
-  return (!qh_inthresholds (facet->normal, NULL));
-} /* skipfacet */
-
diff --git a/extern/qhull/src/io.h b/extern/qhull/src/io.h
deleted file mode 100644
index 351d56b3708..00000000000
--- a/extern/qhull/src/io.h
+++ /dev/null
@@ -1,149 +0,0 @@
-/*  ---------------------------------
-
-   io.h
-   declarations of Input/Output functions
-
-   see README, qhull.h and io.c
-
-   copyright (c) 1993-2002, The Geometry Center
-*/
-
-#ifndef qhDEFio
-#define qhDEFio 1
-
-/*============ constants and flags ==================*/
-
-/*----------------------------------
-
-  qh_MAXfirst
-    maximum length of first two lines of stdin
-*/
-#define qh_MAXfirst  200
-
-/*----------------------------------
-
-    min radius for Gp and Gv, fraction of maxcoord
-*/
-
-/*----------------------------------
-
-  qh_GEOMepsilon
-    adjust outer planes for 'lines closer' and geomview roundoff.
-    This prevents bleed through.
-*/
-#define qh_GEOMepsilon 2e-3
-
-/*----------------------------------
-
-  qh_WHITESPACE
-    possible values of white space
-*/
-#define qh_WHITESPACE " \n\t\v\r\f"
-
-
-/*----------------------------------
-
-  qh_RIDGE
-    to select which ridges to print in qh_eachvoronoi
-*/
-typedef enum
-{
-    qh_RIDGEall = 0, qh_RIDGEinner, qh_RIDGEouter
-}
-qh_RIDGE;
-
-/*----------------------------------
-
-  printvridgeT
-    prints results of qh_printvdiagram
-
-  see:
-    qh_printvridge for an example
-*/
-typedef void (*printvridgeT)(FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
-
-/*============== -prototypes in alphabetical order =========*/
-
-void    dfacet( unsigned id);
-void    dvertex( unsigned id);
-void    qh_countfacets (facetT *facetlist, setT *facets, boolT printall,
-              int *numfacetsp, int *numsimplicialp, int *totneighborsp,
-              int *numridgesp, int *numcoplanarsp, int *numnumtricoplanarsp);
-pointT *qh_detvnorm (vertexT *vertex, vertexT *vertexA, setT *centers, realT *offsetp);
-setT   *qh_detvridge (vertexT *vertex);
-setT   *qh_detvridge3 (vertexT *atvertex, vertexT *vertex);
-int     qh_eachvoronoi (FILE *fp, printvridgeT printvridge, vertexT *atvertex, boolT visitall, qh_RIDGE innerouter, boolT inorder);
-int     qh_eachvoronoi_all (FILE *fp, printvridgeT printvridge, boolT isupper, qh_RIDGE innerouter, boolT inorder);
-void	qh_facet2point(facetT *facet, pointT **point0, pointT **point1, realT *mindist);
-setT   *qh_facetvertices (facetT *facetlist, setT *facets, boolT allfacets);
-void    qh_geomplanes (facetT *facet, realT *outerplane, realT *innerplane);
-void    qh_markkeep (facetT *facetlist);
-setT   *qh_markvoronoi (facetT *facetlist, setT *facets, boolT printall, boolT *islowerp, int *numcentersp);
-void    qh_order_vertexneighbors(vertexT *vertex);
-void	qh_printafacet(FILE *fp, int format, facetT *facet, boolT printall);
-void    qh_printbegin (FILE *fp, int format, facetT *facetlist, setT *facets, boolT printall);
-void 	qh_printcenter (FILE *fp, int format, char *string, facetT *facet);
-void    qh_printcentrum (FILE *fp, facetT *facet, realT radius);
-void    qh_printend (FILE *fp, int format, facetT *facetlist, setT *facets, boolT printall);
-void    qh_printend4geom (FILE *fp, facetT *facet, int *num, boolT printall);
-void    qh_printextremes (FILE *fp, facetT *facetlist, setT *facets, int printall);
-void    qh_printextremes_2d (FILE *fp, facetT *facetlist, setT *facets, int printall);
-void    qh_printextremes_d (FILE *fp, facetT *facetlist, setT *facets, int printall);
-void	qh_printfacet(FILE *fp, facetT *facet);
-void	qh_printfacet2math(FILE *fp, facetT *facet, int notfirst);
-void	qh_printfacet2geom(FILE *fp, facetT *facet, realT color[3]);
-void    qh_printfacet2geom_points(FILE *fp, pointT *point1, pointT *point2,
-			       facetT *facet, realT offset, realT color[3]);
-void	qh_printfacet3math (FILE *fp, facetT *facet, int notfirst);
-void	qh_printfacet3geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]);
-void	qh_printfacet3geom_points(FILE *fp, setT *points, facetT *facet, realT offset, realT color[3]);
-void	qh_printfacet3geom_simplicial(FILE *fp, facetT *facet, realT color[3]);
-void	qh_printfacet3vertex(FILE *fp, facetT *facet, int format);
-void	qh_printfacet4geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]);
-void	qh_printfacet4geom_simplicial(FILE *fp, facetT *facet, realT color[3]);
-void	qh_printfacetNvertex_nonsimplicial(FILE *fp, facetT *facet, int id, int format);
-void	qh_printfacetNvertex_simplicial(FILE *fp, facetT *facet, int format);
-void    qh_printfacetridges(FILE *fp, facetT *facet);
-void	qh_printfacets(FILE *fp, int format, facetT *facetlist, setT *facets, boolT printall);
-void	qh_printhelp_degenerate(FILE *fp);
-void	qh_printhelp_singular(FILE *fp);
-void	qh_printhyperplaneintersection(FILE *fp, facetT *facet1, facetT *facet2,
-  		   setT *vertices, realT color[3]);
-void	qh_printneighborhood (FILE *fp, int format, facetT *facetA, facetT *facetB, boolT printall);
-void    qh_printline3geom (FILE *fp, pointT *pointA, pointT *pointB, realT color[3]);
-void	qh_printpoint(FILE *fp, char *string, pointT *point);
-void	qh_printpointid(FILE *fp, char *string, int dim, pointT *point, int id);
-void    qh_printpoint3 (FILE *fp, pointT *point);
-void    qh_printpoints_out (FILE *fp, facetT *facetlist, setT *facets, int printall);
-void    qh_printpointvect (FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius, realT color[3]);
-void    qh_printpointvect2 (FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius);
-void	qh_printridge(FILE *fp, ridgeT *ridge);
-void    qh_printspheres(FILE *fp, setT *vertices, realT radius);
-void    qh_printvdiagram (FILE *fp, int format, facetT *facetlist, setT *facets, boolT printall);
-int     qh_printvdiagram2 (FILE *fp, printvridgeT printvridge, setT *vertices, qh_RIDGE innerouter, boolT inorder);
-void	qh_printvertex(FILE *fp, vertexT *vertex);
-void	qh_printvertexlist (FILE *fp, char* string, facetT *facetlist,
-                         setT *facets, boolT printall);
-void	qh_printvertices (FILE *fp, char* string, setT *vertices);
-void    qh_printvneighbors (FILE *fp, facetT* facetlist, setT *facets, boolT printall);
-void    qh_printvoronoi (FILE *fp, int format, facetT *facetlist, setT *facets, boolT printall);
-void    qh_printvnorm (FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
-void    qh_printvridge (FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded);
-void	qh_produce_output(void);
-void    qh_projectdim3 (pointT *source, pointT *destination);
-int     qh_readfeasible (int dim, char *remainder);
-coordT *qh_readpoints(int *numpoints, int *dimension, boolT *ismalloc);
-void    qh_setfeasible (int dim);
-boolT	qh_skipfacet(facetT *facet);
-
-#endif /* qhDEFio */
diff --git a/extern/qhull/src/mem.c b/extern/qhull/src/mem.c
deleted file mode 100644
index 72934626684..00000000000
--- a/extern/qhull/src/mem.c
+++ /dev/null
@@ -1,447 +0,0 @@
-/*  ---------------------------------
-
-  mem.c
-    memory management routines for qhull
-
-  This is a standalone program.
-
-  To initialize memory:
-
-    qh_meminit (stderr);
-    qh_meminitbuffers (qh IStracing, qh_MEMalign, 7, qh_MEMbufsize,qh_MEMinitbuf);
-    qh_memsize(sizeof(facetT));
-    qh_memsize(sizeof(facetT));
-    ...
-    qh_memsetup();
-
-  To free up all memory buffers:
-    qh_memfreeshort (&curlong, &totlong);
-
-  if qh_NOmem,
-    malloc/free is used instead of mem.c
-
-  notes:
-    uses Quickfit algorithm (freelists for commonly allocated sizes)
-
-  see:
-    qh-mem.htm and mem.h
-    global.c (qh_initbuffers) for an example of using mem.c
-
-  copyright (c) 1993-2002 The Geometry Center
-*/
-
-#include
-#include
-#include
-#include "mem.h"
-
-#ifndef qhDEFqhull
-typedef struct ridgeT ridgeT;
-typedef struct facetT facetT;
-void    qh_errexit(int exitcode, facetT *, ridgeT *);
-#endif
-
-/*============ -global data structure ==============
-    see mem.h for definition
-*/
-
-qhmemT qhmem= {0};     /* remove "= {0}" if this causes a compiler error */
-
-#ifndef qh_NOmem
-
-/*============= internal functions ==============*/
-
-static int qh_intcompare(const void *i, const void *j);
-
-/*========== functions in alphabetical order ======== */
-
-/*---------------------------------
-
-  qh_intcompare( i, j )
-    used by qsort and bsearch to compare two integers
-*/
-static int qh_intcompare(const void *i, const void *j) {
-  return(*((int *)i) - *((int *)j));
-} /* intcompare */
-
-
-/*----------------------------------
-
-  qh_memalloc( insize )
-    returns object of insize bytes
-    qhmem is the global memory structure
-
-  returns:
-    pointer to allocated memory
-    errors if insufficient memory
-
-  notes:
-    use explicit type conversion to avoid type warnings on some compilers
-    actual object may be larger than insize
-    use qh_memalloc_() for inline code for quick allocations
-    logs allocations if 'T5'
-
-  design:
-    if size < qhmem.LASTsize
-      if qhmem.freelists[size] non-empty
-        return first object on freelist
-      else
-        round up request to size of qhmem.freelists[size]
-        allocate new allocation buffer if necessary
-        allocate object from allocation buffer
-    else
-      allocate object with malloc()
-*/
-void *qh_memalloc(int insize) {
-  void **freelistp, *newbuffer;
-  int index, size;
-  int outsize, bufsize;
-  void *object;
-
-  if ((unsigned) insize <= (unsigned) qhmem.LASTsize) {
-    index= qhmem.indextable[insize];
-    freelistp= qhmem.freelists+index;
-    if ((object= *freelistp)) {
-      qhmem.cntquick++;
-      *freelistp= *((void **)*freelistp);  /* replace freelist with next object */
-      return (object);
-    }else {
-      outsize= qhmem.sizetable[index];
-      qhmem.cntshort++;
-      if (outsize > qhmem .freesize) {
-	if (!qhmem.curbuffer)
-	  bufsize= qhmem.BUFinit;
-        else
-	  bufsize= qhmem.BUFsize;
-        qhmem.totshort += bufsize;
-	if (!(newbuffer= malloc(bufsize))) {
-	  fprintf(qhmem.ferr, "qhull error (qh_memalloc): insufficient memory\n");
-	  qh_errexit(qhmem_ERRmem, NULL, NULL);
-	}
-	*((void **)newbuffer)= qhmem.curbuffer;  /* prepend newbuffer to curbuffer
-						    list */
-	qhmem.curbuffer= newbuffer;
-	qhmem.freemem= (void *)((char *)newbuffer+size);
-	qhmem.freesize= bufsize - size;
-      }
-      object= qhmem.freemem;
-      qhmem.freemem= (void *)((char *)qhmem.freemem + outsize);
-      qhmem.freesize -= outsize;
-      return object;
-    }
-  }else {                     /* long allocation */
-    if (!qhmem.indextable) {
-      fprintf (qhmem.ferr, "qhull internal error (qh_memalloc): qhmem has not been initialized.\n");
-      qh_errexit(qhmem_ERRqhull, NULL, NULL);
-    }
-    outsize= insize;
-    qhmem .cntlong++;
-    qhmem .curlong++;
-    qhmem .totlong += outsize;
-    if (qhmem.maxlong < qhmem.totlong)
-      qhmem.maxlong= qhmem.totlong;
-    if (!(object= malloc(outsize))) {
-      fprintf(qhmem.ferr, "qhull error (qh_memalloc): insufficient memory\n");
-      qh_errexit(qhmem_ERRmem, NULL, NULL);
-    }
-    if (qhmem.IStracing >= 5)
-      fprintf (qhmem.ferr, "qh_memalloc long: %d bytes at %p\n", outsize, object);
-  }
-  return (object);
-} /* memalloc */
-
-
-/*----------------------------------
-
-  qh_memfree( object, size )
-    free up an object of size bytes
-    size is insize from qh_memalloc
-
-  notes:
-    object may be NULL
-    type checking warns if using (void **)object
-    use qh_memfree_() for quick free's of small objects
-
-  design:
-    if size <= qhmem.LASTsize
-      append object to corresponding freelist
-    else
-      call free(object)
-*/
-void qh_memfree(void *object, int size) {
-  void **freelistp;
-
-  if (!object)
-    return;
-  if (size <= qhmem.LASTsize) {
-    qhmem .freeshort++;
-    freelistp= qhmem.freelists + qhmem.indextable[size];
-    *((void **)object)= *freelistp;
-    *freelistp= object;
-  }else {
-    qhmem .freelong++;
-    qhmem .totlong -= size;
-    free (object);
-    if (qhmem.IStracing >= 5)
-      fprintf (qhmem.ferr, "qh_memfree long: %d bytes at %p\n", size, object);
-  }
-} /* memfree */
-
-
-/*---------------------------------
-
-  qh_memfreeshort( curlong, totlong )
-    frees up all short and qhmem memory allocations
-
-  returns:
-    number and size of current long allocations
-*/
-void qh_memfreeshort (int *curlong, int *totlong) {
-  void *buffer, *nextbuffer;
-
-  *curlong= qhmem .cntlong - qhmem .freelong;
-  *totlong= qhmem .totlong;
-  for(buffer= qhmem.curbuffer; buffer; buffer= nextbuffer) {
-    nextbuffer= *((void **) buffer);
-    free(buffer);
-  }
-  qhmem.curbuffer= NULL;
-  if (qhmem .LASTsize) {
-    free (qhmem .indextable);
-    free (qhmem .freelists);
-    free (qhmem .sizetable);
-  }
-  memset((char *)&qhmem, 0, sizeof qhmem);  /* every field is 0, FALSE, NULL */
-} /* memfreeshort */
-
-
-/*----------------------------------
-
-  qh_meminit( ferr )
-    initialize qhmem and test sizeof( void*)
-*/
-void qh_meminit (FILE *ferr) {
-
-  memset((char *)&qhmem, 0, sizeof qhmem);  /* every field is 0, FALSE, NULL */
-  qhmem.ferr= ferr;
-  if (sizeof(void*) < sizeof(int)) {
-    fprintf (ferr, "qhull internal error (qh_meminit): sizeof(void*) < sizeof(int).  qset.c will not work\n");
-    exit (1);  /* can not use qh_errexit() */
-  }
-} /* meminit */
-
-/*---------------------------------
-
-  qh_meminitbuffers( tracelevel, alignment, numsizes, bufsize, bufinit )
-    initialize qhmem
-    if tracelevel >= 5, trace memory allocations
-    alignment= desired address alignment for memory allocations
-    numsizes= number of freelists
-    bufsize=  size of additional memory buffers for short allocations
-    bufinit=  size of initial memory buffer for short allocations
-*/
-void qh_meminitbuffers (int tracelevel, int alignment, int numsizes, int bufsize, int bufinit) {
-
-  qhmem.IStracing= tracelevel;
-  qhmem.NUMsizes= numsizes;
-  qhmem.BUFsize= bufsize;
-  qhmem.BUFinit= bufinit;
-    fprintf (qhmem.ferr, "qhull internal error (qh_meminit): memory alignment %d is not a power of 2\n", alignment);
-    qh_errexit (qhmem_ERRqhull, NULL, NULL);
-  }
-  qhmem.sizetable= (int *) calloc (numsizes, sizeof(int));
-  qhmem.freelists= (void **) calloc (numsizes, sizeof(void *));
-  if (!qhmem.sizetable || !qhmem.freelists) {
-    fprintf(qhmem.ferr, "qhull error (qh_meminit): insufficient memory\n");
-    qh_errexit (qhmem_ERRmem, NULL, NULL);
-  }
-  if (qhmem.IStracing >= 1)
-    fprintf (qhmem.ferr, "qh_meminitbuffers: memory initialized with alignment %d\n", alignment);
-} /* meminitbuffers */
-
-/*---------------------------------
-
-  qh_memsetup()
-    set up memory after running memsize()
-*/
-void qh_memsetup (void) {
-  int k,i;
-
-  qsort(qhmem.sizetable, qhmem.TABLEsize, sizeof(int), qh_intcompare);
-  qhmem.LASTsize= qhmem.sizetable[qhmem.TABLEsize-1];
-  if (qhmem .LASTsize >= qhmem .BUFsize || qhmem.LASTsize >= qhmem .BUFinit) {
-    fprintf (qhmem.ferr, "qhull error (qh_memsetup): largest mem size %d is >= buffer size %d or initial buffer size %d\n",
-            qhmem .LASTsize, qhmem .BUFsize, qhmem .BUFinit);
-    qh_errexit(qhmem_ERRmem, NULL, NULL);
-  }
-  if (!(qhmem.indextable= (int *)malloc((qhmem.LASTsize+1) * sizeof(int)))) {
-    fprintf(qhmem.ferr, "qhull error (qh_memsetup): insufficient memory\n");
-    qh_errexit(qhmem_ERRmem, NULL, NULL);
-  }
-  for(k=qhmem.LASTsize+1; k--; )
-    qhmem.indextable[k]= k;
-  i= 0;
-  for(k= 0; k <= qhmem.LASTsize; k++) {
-    if (qhmem.indextable[k] <= qhmem.sizetable[i])
-      qhmem.indextable[k]= i;
-    else
-      qhmem.indextable[k]= ++i;
-  }
-} /* memsetup */
-
-/*---------------------------------
-
-  qh_memsize( size )
-    define a free list for this size
-*/
-void qh_memsize(int size) {
-  int k;
-
-  if (qhmem .LASTsize) {
-    fprintf (qhmem .ferr, "qhull error (qh_memsize): called after qhmem_setup\n");
-    qh_errexit (qhmem_ERRqhull, NULL, NULL);
-  }
-  for(k= qhmem.TABLEsize; k--; ) {
-    if (qhmem.sizetable[k] == size)
-      return;
-  }
-  if (qhmem.TABLEsize < qhmem.NUMsizes)
-    qhmem.sizetable[qhmem.TABLEsize++]= size;
-  else
-    fprintf(qhmem.ferr, "qhull warning (memsize): free list table has room for only %d sizes\n", qhmem.NUMsizes);
-} /* memsize */
-
-
-/*---------------------------------
-
-  qh_memstatistics( fp )
-    print out memory statistics
-
-  notes:
-    does not account for wasted memory at the end of each block
-*/
-void qh_memstatistics (FILE *fp) {
-  int i, count, totfree= 0;
-  void *object;
-
-  for (i=0; i < qhmem.TABLEsize; i++) {
-    count=0;
-    for (object= qhmem .freelists[i]; object; object= *((void **)object))
-      count++;
-    totfree += qhmem.sizetable[i] * count;
-  }
-  fprintf (fp, "\nmemory statistics:\n\
-%7d quick allocations\n\
-%7d short allocations\n\
-%7d long allocations\n\
-%7d short frees\n\
-%7d long frees\n\
-%7d bytes of short memory in use\n\
-%7d bytes of short memory in freelists\n\
-%7d bytes of long memory allocated (except for input)\n\
-%7d bytes of long memory in use (in %d pieces)\n\
-%7d bytes per memory buffer (initially %d bytes)\n",
-	   qhmem .cntquick, qhmem.cntshort, qhmem.cntlong,
-	   qhmem .freeshort, qhmem.freelong,
-	   qhmem .totshort - qhmem .freesize - totfree,
-	   totfree,
-	   qhmem .maxlong, qhmem .totlong, qhmem .cntlong - qhmem .freelong,
-	   qhmem .BUFsize, qhmem .BUFinit);
-  if (qhmem.cntlarger) {
-    fprintf (fp, "%7d calls to qh_setlarger\n%7.2g     average copy size\n",
-	   qhmem.cntlarger, ((float) qhmem.totlarger)/ qhmem.cntlarger);
-    fprintf (fp, "  freelists (bytes->count):");
-  }
-  for (i=0; i < qhmem.TABLEsize; i++) {
-    count=0;
-    for (object= qhmem .freelists[i]; object; object= *((void **)object))
-      count++;
-    fprintf (fp, " %d->%d", qhmem.sizetable[i], count);
-  }
-  fprintf (fp, "\n\n");
-} /* memstatistics */
-
-
-/*---------------------------------
-
-  qh_NOmem
-    turn off quick-fit memory allocation
-
-  notes:
-    uses malloc() and free() instead
-*/
-#else /* qh_NOmem */
-
-void *qh_memalloc(int insize) {
-  void *object;
-
-  if (!(object= malloc(insize))) {
-    fprintf(qhmem.ferr, "qhull error (qh_memalloc): insufficient memory\n");
-    qh_errexit(qhmem_ERRmem, NULL, NULL);
-  }
-  if (qhmem.IStracing >= 5)
-    fprintf (qhmem.ferr, "qh_memalloc long: %d bytes at %p\n", insize, object);
-  return object;
-}
-
-void qh_memfree(void *object, int size) {
-
-  if (!object)
-    return;
-  free (object);
-  if (qhmem.IStracing >= 5)
-    fprintf (qhmem.ferr, "qh_memfree long: %d bytes at %p\n", size, object);
-}
-
-void qh_memfreeshort (int *curlong, int *totlong) {
-
-  memset((char *)&qhmem, 0, sizeof qhmem);  /* every field is 0, FALSE, NULL */
-  *curlong= 0;
-  *totlong= 0;
-}
-
-void qh_meminit (FILE *ferr) {
-
-  memset((char *)&qhmem, 0, sizeof qhmem);  /* every field is 0, FALSE, NULL */
-  qhmem.ferr= ferr;
-  if (sizeof(void*) < sizeof(int)) {
-    fprintf (ferr, "qhull internal error (qh_meminit): sizeof(void*) < sizeof(int).  qset.c will not work\n");
-    qh_errexit (qhmem_ERRqhull, NULL, NULL);
-  }
-}
-
-void qh_meminitbuffers (int tracelevel, int alignment, int numsizes, int bufsize, int bufinit) {
-
-  qhmem.IStracing= tracelevel;
-
-}
-
-void qh_memsetup (void) {
-
-}
-
-void qh_memsize(int size) {
-
-}
-
-void qh_memstatistics (FILE *fp) {
-
-}
-
-#endif /* qh_NOmem */
diff --git a/extern/qhull/src/mem.h b/extern/qhull/src/mem.h
deleted file mode 100644
index e9ebd1bb9bc..00000000000
--- a/extern/qhull/src/mem.h
+++ /dev/null
@@ -1,174 +0,0 @@
-/*  ---------------------------------
-
-   mem.h
-     prototypes for memory management functions
-
-   see qh-mem.htm, mem.c and qset.h
-
-   for error handling, writes message and calls
-     qh_errexit (qhmem_ERRmem, NULL, NULL) if insufficient memory
-       and
-     qh_errexit (qhmem_ERRqhull, NULL, NULL) otherwise
-
-   copyright (c) 1993-2002, The Geometry Center
-*/
-
-#ifndef qhDEFmem
-#define qhDEFmem
-
-/*---------------------------------
-
-  qh_NOmem
-    turn off quick-fit memory allocation
-
-  notes:
-    mem.c implements Quickfit memory allocation for about 20% time
-    savings.  If it fails on your machine, try to locate the
-    problem, and send the answer to qhull@geom.umn.edu.  If this can
-    not be done, define qh_NOmem to use malloc/free instead.
-
-   #define qh_NOmem
-*/
-
-/*-------------------------------------------
-    to avoid bus errors, memory allocation must consider alignment requirements.
-    malloc() automatically takes care of alignment.   Since mem.c manages
-    its own memory, we need to explicitly specify alignment in
-    qh_meminitbuffers().
-
-    A safe choice is sizeof(double).  sizeof(float) may be used if doubles
-    do not occur in data structures and pointers are the same size.  Be careful
-    of machines (e.g., DEC Alpha) with large pointers.  If gcc is available,
-    use __alignof__(double) or fmax_(__alignof__(float), __alignof__(void *)).
-
-   see qh_MEMalign in user.h for qhull's alignment
-*/
-
-#define qhmem_ERRmem 4    /* matches qh_ERRmem in qhull.h */
-#define qhmem_ERRqhull 5  /* matches qh_ERRqhull in qhull.h */
-
-/*----------------------------------
-
-  ptr_intT
-    for casting a void* to an integer-type
-
-  notes:
-    On 64-bit machines, a pointer may be larger than an 'int'.
-    qh_meminit() checks that 'long' holds a 'void*'
-*/
-typedef unsigned long ptr_intT;
-
-/*----------------------------------
-
-  qhmemT
-    global memory structure for mem.c
-
- notes:
-   users should ignore qhmem except for writing extensions
-   qhmem is allocated in mem.c
-
-   qhmem could be swapable like qh and qhstat, but then
-   multiple qh's and qhmem's would need to keep in synch.
-   A swapable qhmem would also waste memory buffers.  As long
-   as memory operations are atomic, there is no problem with
-   multiple qh structures being active at the same time.
-   If you need separate address spaces, you can swap the
-   contents of qhmem.
-*/
-typedef struct qhmemT qhmemT;
-extern qhmemT qhmem;
-
-struct qhmemT {               /* global memory management variables */
-  int      BUFsize;	      /* size of memory allocation buffer */
-  int      BUFinit;	      /* initial size of memory allocation buffer */
-  int      TABLEsize;         /* actual number of sizes in free list table */
-  int      NUMsizes;          /* maximum number of sizes in free list table */
-  int      LASTsize;          /* last size in free list table */
-  int      ALIGNmask;         /* worst-case alignment, must be 2^n-1 */
-  void	 **freelists;          /* free list table, linked by offset 0 */
-  int     *sizetable;         /* size of each freelist */
-  int     *indextable;        /* size->index table */
-  void    *curbuffer;         /* current buffer, linked by offset 0 */
-  void    *freemem;           /*   free memory in curbuffer */
-  int 	   freesize;          /*   size of free memory in bytes */
-  void 	  *tempstack;         /* stack of temporary memory, managed by users */
-  FILE    *ferr;              /* file for reporting errors */
-  int      IStracing;         /* =5 if tracing memory allocations */
-  int      cntquick;          /* count of quick allocations */
-                              /* remove statistics doesn't effect speed */
-  int      cntshort;          /* count of short allocations */
-  int      cntlong;           /* count of long allocations */
-  int      curlong;           /* current count of inuse, long allocations */
-  int      freeshort;	      /* count of short memfrees */
-  int      freelong;	      /* count of long memfrees */
-  int      totshort;          /* total size of short allocations */
-  int      totlong;           /* total size of long allocations */
-  int      maxlong;           /* maximum totlong */
-  int      cntlarger;         /* count of setlarger's */
-  int      totlarger;         /* total copied by setlarger */
-};
-
-
-/*==================== -macros ====================*/
-
-/*----------------------------------
-
-  qh_memalloc_(size, object, type)
-    returns object of size bytes
-	assumes size<=qhmem.LASTsize and void **freelistp is a temp
-*/
-
-#ifdef qh_NOmem
-#define qh_memalloc_(size, freelistp, object, type) {\
-  object= (type*)qh_memalloc (size); }
-#else /* !qh_NOmem */
-
-#define qh_memalloc_(size, freelistp, object, type) {\
-  freelistp= qhmem.freelists + qhmem.indextable[size];\
-  if ((object= (type*)*freelistp)) {\
-    qhmem.cntquick++;  \
-    *freelistp= *((void **)*freelistp);\
-  }else object= (type*)qh_memalloc (size);}
-#endif
-
-/*----------------------------------
-
-  qh_memfree_(object, size)
-    free up an object
-
-  notes:
-    object may be NULL
-    assumes size<=qhmem.LASTsize and void **freelistp is a temp
-*/
-#ifdef qh_NOmem
-#define qh_memfree_(object, size, freelistp) {\
-  qh_memfree (object, size); }
-#else /* !qh_NOmem */
-
-#define qh_memfree_(object, size, freelistp) {\
-  if (object) { \
-    qhmem .freeshort++;\
-    freelistp= qhmem.freelists + qhmem.indextable[size];\
-    *((void **)object)= *freelistp;\
-    *freelistp= object;}}
-#endif
-
-/*=============== prototypes in alphabetical order ============*/
-
-void *qh_memalloc(int insize);
-void qh_memfree (void *object, int size);
-void qh_memfreeshort (int *curlong, int *totlong);
-void qh_meminit (FILE *ferr);
-void qh_meminitbuffers (int tracelevel, int alignment, int numsizes,
-			int bufsize, int bufinit);
-void qh_memsetup (void);
-void qh_memsize(int size);
-void qh_memstatistics (FILE *fp);
-
-#endif /* qhDEFmem */
diff --git a/extern/qhull/src/merge.c b/extern/qhull/src/merge.c
deleted file mode 100644
index 34ecda1865f..00000000000
--- a/extern/qhull/src/merge.c
+++ /dev/null
@@ -1,3626 +0,0 @@
-/*  ---------------------------------
-
-   merge.c
-   merges non-convex facets
-
-   see qh-merge.htm and merge.h
-
-   other modules call qh_premerge() and qh_postmerge()
-
-   the user may call qh_postmerge() to perform additional merges.
-
-   To remove deleted facets and vertices (qhull() in qhull.c):
-     qh_partitionvisible (!qh_ALL, &numoutside);  // visible_list, newfacet_list
-     qh_deletevisible ();         // qh.visible_list
-     qh_resetlists (False, qh_RESETvisible);       // qh.visible_list newvertex_list newfacet_list
-
-   assumes qh.CENTERtype= centrum
-
-   merges occur in qh_mergefacet and in qh_mergecycle
-   vertex->neighbors not set until the first merge occurs
-
-   copyright (c) 1993-2002 The Geometry Center
-*/
-
-#include "qhull_a.h"
-
-#ifndef qh_NOmerge
-
-/*=========== internal prototypes =========*/
-
-static int qh_compareangle(const void *p1, const void *p2);
-static int qh_comparemerge(const void *p1, const void *p2);
-static int qh_comparevisit (const void *p1, const void *p2);
-
-
-/*===== functions (alphabetical after premerge and postmerge) ======*/
-
-/*---------------------------------
-
-  qh_premerge( apex, maxcentrum )
-    pre-merge nonconvex facets in qh.newfacet_list for apex
-    maxcentrum defines coplanar and concave (qh_test_appendmerge)
-
-  returns:
-    deleted facets added to qh.visible_list with facet->visible set
-
-  notes:
-    uses globals, qh.MERGEexact, qh.PREmerge
-
-  design:
-    mark duplicate ridges in qh.newfacet_list
-    merge facet cycles in qh.newfacet_list
-    merge duplicate ridges and concave facets in qh.newfacet_list
-    check merged facet cycles for degenerate and redundant facets
-    merge degenerate and redundant facets
-    collect coplanar and concave facets
-    merge concave, coplanar, degenerate, and redundant facets
-*/
-void qh_premerge (vertexT *apex, realT maxcentrum, realT maxangle) {
-  boolT othermerge= False;
-  facetT *newfacet;
-
-  if (qh ZEROcentrum && qh_checkzero(!qh_ALL))
-    return;
-  trace2((qh ferr, "qh_premerge: premerge centrum %2.2g angle %2.2g for apex v%d facetlist f%d\n",
-	    maxcentrum, maxangle, apex->id, getid_(qh newfacet_list)));
-  if (qh IStracing >= 4 && qh num_facets < 50)
-    qh_printlists();
-  qh cos_max= maxangle;
-  qh degen_mergeset= qh_settemp (qh TEMPsize);
-  qh facet_mergeset= qh_settemp (qh TEMPsize);
-  if (qh hull_dim >=3) {
-    qh_mark_dupridges (qh newfacet_list); /* facet_mergeset */
-    qh_mergecycle_all (qh newfacet_list, &othermerge);
-    qh_forcedmerges (&othermerge /* qh facet_mergeset */);
-    FORALLnew_facets {  /* test samecycle merges */
-      if (!newfacet->simplicial && !newfacet->mergeridge)
-	qh_degen_redundant_neighbors (newfacet, NULL);
-    }
-    if (qh_merge_degenredundant())
-      othermerge= True;
-  }else /* qh hull_dim == 2 */
-    qh_mergecycle_all (qh newfacet_list, &othermerge);
-  qh_flippedmerges (qh newfacet_list, &othermerge);
-  if (!qh MERGEexact || zzval_(Ztotmerge)) {
-    zinc_(Zpremergetot);
-    qh POSTmerging= False;
-    qh_getmergeset_initial (qh newfacet_list);
-    qh_all_merges (othermerge, False);
-  }
-  qh_settempfree(&qh facet_mergeset);
-  qh_settempfree(&qh degen_mergeset);
-} /* premerge */
-
-/*---------------------------------
-
-  qh_postmerge( reason, maxcentrum, maxangle, vneighbors )
-    post-merge nonconvex facets as defined by maxcentrum and maxangle
-    'reason' is for reporting progress
-    if vneighbors,
-      calls qh_test_vneighbors at end of qh_all_merge
-    if firstmerge,
-      calls qh_reducevertices before qh_getmergeset
-
-  returns:
-    if first call (qh.visible_list != qh.facet_list),
-      builds qh.facet_newlist, qh.newvertex_list
-    deleted facets added to qh.visible_list with facet->visible
-    qh.visible_list == qh.facet_list
-
-  notes:
-
-
-  design:
-    if first call
-      set qh.visible_list and qh.newfacet_list to qh.facet_list
-      add all facets to qh.newfacet_list
-      mark non-simplicial facets, facet->newmerge
-      set qh.newvertext_list to qh.vertex_list
-      add all vertices to qh.newvertex_list
-      if a pre-merge occured
-        set vertex->delridge {will retest the ridge}
-        if qh.MERGEexact
-          call qh_reducevertices()
-      if no pre-merging
-        merge flipped facets
-    determine non-convex facets
-    merge all non-convex facets
-*/
-void qh_postmerge (char *reason, realT maxcentrum, realT maxangle,
-                      boolT vneighbors) {
-  facetT *newfacet;
-  boolT othermerges= False;
-  vertexT *vertex;
-
-  if (qh REPORTfreq || qh IStracing) {
-    qh_buildtracing (NULL, NULL);
-    qh_printsummary (qh ferr);
-    if (qh PRINTstatistics)
-      qh_printallstatistics (qh ferr, "reason");
-    fprintf (qh ferr, "\n%s with 'C%.2g' and 'A%.2g'\n",
-        reason, maxcentrum, maxangle);
-  }
-  trace2((qh ferr, "qh_postmerge: postmerge.  test vneighbors? %d\n",
-	    vneighbors));
-  qh cos_max= maxangle;
-  qh POSTmerging= True;
-  qh degen_mergeset= qh_settemp (qh TEMPsize);
-  qh facet_mergeset= qh_settemp (qh TEMPsize);
-  if (qh visible_list != qh facet_list) {  /* first call */
-    qh NEWfacets= True;
-    qh visible_list= qh newfacet_list= qh facet_list;
-    FORALLnew_facets {
-      newfacet->newfacet= True;
-       if (!newfacet->simplicial)
-        newfacet->newmerge= True;
-     zinc_(Zpostfacets);
-    }
-    qh newvertex_list= qh vertex_list;
-    FORALLvertices
-      vertex->newlist= True;
-    if (qh VERTEXneighbors) { /* a merge has occurred */
-      FORALLvertices
-	vertex->delridge= True; /* test for redundant, needed? */
-      if (qh MERGEexact) {
-	if (qh hull_dim <= qh_DIMreduceBuild)
-	  qh_reducevertices(); /* was skipped during pre-merging */
-      }
-    }
-    if (!qh PREmerge && !qh MERGEexact)
-      qh_flippedmerges (qh newfacet_list, &othermerges);
-  }
-  qh_getmergeset_initial (qh newfacet_list);
-  qh_all_merges (False, vneighbors);
-  qh_settempfree(&qh facet_mergeset);
-  qh_settempfree(&qh degen_mergeset);
-} /* post_merge */
-
-/*---------------------------------
-
-  qh_all_merges( othermerge, vneighbors )
-    merge all non-convex facets
-
-    set othermerge if already merged facets (for qh_reducevertices)
-    if vneighbors
-      tests vertex neighbors for convexity at end
-    qh.facet_mergeset lists the non-convex ridges in qh_newfacet_list
-    qh.degen_mergeset is defined
-    if qh.MERGEexact && !qh.POSTmerging,
-      does not merge coplanar facets
-
-  returns:
-    deleted facets added to qh.visible_list with facet->visible
-    deleted vertices added qh.delvertex_list with vertex->delvertex
-
-  notes:
-    unless !qh.MERGEindependent,
-      merges facets in independent sets
-    uses qh.newfacet_list as argument since merges call qh_removefacet()
-
-  design:
-    while merges occur
-      for each merge in qh.facet_mergeset
-        unless one of the facets was already merged in this pass
-          merge the facets
-        test merged facets for additional merges
-      if vertices record neighboring facets
-        rename redundant vertices
-          update qh.facet_mergeset
-    if vneighbors ??
-      tests vertex neighbors for convexity at end
-*/
-void qh_all_merges (boolT othermerge, boolT vneighbors) {
-  facetT *facet1, *facet2;
-  mergeT *merge;
-  boolT wasmerge= True, isreduce;
-  void **freelistp;  /* used !qh_NOmem */
-  vertexT *vertex;
-  mergeType mergetype;
-  int numcoplanar=0, numconcave=0, numdegenredun= 0, numnewmerges= 0;
-
-  trace2((qh ferr, "qh_all_merges: starting to merge facets beginning from f%d\n",
-	    getid_(qh newfacet_list)));
-  while (True) {
-    wasmerge= False;
-    while (qh_setsize (qh facet_mergeset)) {
-      while ((merge= (mergeT*)qh_setdellast(qh facet_mergeset))) {
-	facet1= merge->facet1;
-	facet2= merge->facet2;
-	mergetype= merge->type;
-	qh_memfree_(merge, sizeof(mergeT), freelistp);
-	if (facet1->visible || facet2->visible) /*deleted facet*/
-	  continue;
-	if ((facet1->newfacet && !facet1->tested)
-	        || (facet2->newfacet && !facet2->tested)) {
-	  if (qh MERGEindependent && mergetype <= MRGanglecoplanar)
-	    continue;      /* perform independent sets of merges */
-	}
-	qh_merge_nonconvex (facet1, facet2, mergetype);
-        numdegenredun += qh_merge_degenredundant();
-        numnewmerges++;
-        wasmerge= True;
-	if (mergetype == MRGconcave)
-	  numconcave++;
-	else /* MRGcoplanar or MRGanglecoplanar */
-	  numcoplanar++;
-      } /* while setdellast */
-      if (qh POSTmerging && qh hull_dim <= qh_DIMreduceBuild
-      && numnewmerges > qh_MAXnewmerges) {
-	numnewmerges= 0;
-	qh_reducevertices();  /* otherwise large post merges too slow */
-      }
-      qh_getmergeset (qh newfacet_list); /* facet_mergeset */
-    } /* while mergeset */
-    if (qh VERTEXneighbors) {
-      isreduce= False;
-      if (qh hull_dim >=4 && qh POSTmerging) {
-	FORALLvertices
-	  vertex->delridge= True;
-	isreduce= True;
-      }
-      if ((wasmerge || othermerge) && (!qh MERGEexact || qh POSTmerging)
-	  && qh hull_dim <= qh_DIMreduceBuild) {
-	othermerge= False;
-	isreduce= True;
-      }
-      if (isreduce) {
-	if (qh_reducevertices()) {
-	  qh_getmergeset (qh newfacet_list); /* facet_mergeset */
-	  continue;
-	}
-      }
-    }
-    if (vneighbors && qh_test_vneighbors(/* qh newfacet_list */))
-      continue;
-    break;
-  } /* while (True) */
-  if (qh CHECKfrequently && !qh MERGEexact) {
-    qh old_randomdist= qh RANDOMdist;
-    qh RANDOMdist= False;
-    qh_checkconvex (qh newfacet_list, qh_ALGORITHMfault);
-    /* qh_checkconnect (); [this is slow and it changes the facet order] */
-    qh RANDOMdist= qh old_randomdist;
-  }
-  trace1((qh ferr, "qh_all_merges: merged %d coplanar facets %d concave facets and %d degen or redundant facets.\n",
-    numcoplanar, numconcave, numdegenredun));
-  if (qh IStracing >= 4 && qh num_facets < 50)
-    qh_printlists ();
-} /* all_merges */
-
-
-/*---------------------------------
-
-  qh_appendmergeset( facet, neighbor, mergetype, angle )
-    appends an entry to qh.facet_mergeset or qh.degen_mergeset
-
-    angle ignored if NULL or !qh.ANGLEmerge
-
-  returns:
-    merge appended to facet_mergeset or degen_mergeset
-      sets ->degenerate or ->redundant if degen_mergeset
-
-  see:
-    qh_test_appendmerge()
-
-  design:
-    allocate merge entry
-    if regular merge
-      append to qh.facet_mergeset
-    else if degenerate merge and qh.facet_mergeset is all degenerate
-      append to qh.degen_mergeset
-    else if degenerate merge
-      prepend to qh.degen_mergeset
-    else if redundant merge
-      append to qh.degen_mergeset
-*/
-void qh_appendmergeset(facetT *facet, facetT *neighbor, mergeType mergetype, realT *angle) {
-  mergeT *merge, *lastmerge;
-  void **freelistp; /* used !qh_NOmem */
-
-  if (facet->redundant)
-    return;
-  if (facet->degenerate && mergetype == MRGdegen)
-    return;
-  qh_memalloc_(sizeof(mergeT), freelistp, merge, mergeT);
-  merge->facet1= facet;
-  merge->facet2= neighbor;
-  merge->type= mergetype;
-  if (angle && qh ANGLEmerge)
-    merge->angle= *angle;
-  if (mergetype < MRGdegen)
-    qh_setappend (&(qh facet_mergeset), merge);
-  else if (mergetype == MRGdegen) {
-    facet->degenerate= True;
-    if (!(lastmerge= (mergeT*)qh_setlast (qh degen_mergeset))
-    || lastmerge->type == MRGdegen)
-      qh_setappend (&(qh degen_mergeset), merge);
-    else
-      qh_setaddnth (&(qh degen_mergeset), 0, merge);
-  }else if (mergetype == MRGredundant) {
-    facet->redundant= True;
-    qh_setappend (&(qh degen_mergeset), merge);
-  }else /* mergetype == MRGmirror */ {
-    if (facet->redundant || neighbor->redundant) {
-      fprintf(qh ferr, "qhull error (qh_appendmergeset): facet f%d or f%d is already a mirrored facet\n",
-	   facet->id, neighbor->id);
-      qh_errexit2 (qh_ERRqhull, facet, neighbor);
-    }
-    if (!qh_setequal (facet->vertices, neighbor->vertices)) {
-      fprintf(qh ferr, "qhull error (qh_appendmergeset): mirrored facets f%d and f%d do not have the same vertices\n",
-	   facet->id, neighbor->id);
-      qh_errexit2 (qh_ERRqhull, facet, neighbor);
-    }
-    facet->redundant= True;
-    neighbor->redundant= True;
-    qh_setappend (&(qh degen_mergeset), merge);
-  }
-} /* appendmergeset */
-
-
-/*---------------------------------
-
-  qh_basevertices( samecycle )
-    return temporary set of base vertices for samecycle
-    samecycle is first facet in the cycle
-    assumes apex is SETfirst_( samecycle->vertices )
-
-  returns:
-    vertices (settemp)
-    all ->seen are cleared
-
-  notes:
-    uses qh_vertex_visit;
-
-  design:
-    for each facet in samecycle
-      for each unseen vertex in facet->vertices
-        append to result
-*/
-setT *qh_basevertices (facetT *samecycle) {
-  facetT *same;
-  vertexT *apex, *vertex, **vertexp;
-  setT *vertices= qh_settemp (qh TEMPsize);
-
-  apex= SETfirstt_(samecycle->vertices, vertexT);
-  apex->visitid= ++qh vertex_visit;
-  FORALLsame_cycle_(samecycle) {
-    if (same->mergeridge)
-      continue;
-    FOREACHvertex_(same->vertices) {
-      if (vertex->visitid != qh vertex_visit) {
-        qh_setappend (&vertices, vertex);
-        vertex->visitid= qh vertex_visit;
-        vertex->seen= False;
-      }
-    }
-  }
-  trace4((qh ferr, "qh_basevertices: found %d vertices\n",
-         qh_setsize (vertices)));
-  return vertices;
-} /* basevertices */
-
-/*---------------------------------
-
-  qh_checkconnect()
-    check that new facets are connected
-    new facets are on qh.newfacet_list
-
-  notes:
-    this is slow and it changes the order of the facets
-    uses qh.visit_id
-
-  design:
-    move first new facet to end of qh.facet_list
-    for all newly appended facets
-      append unvisited neighbors to end of qh.facet_list
-    for all new facets
-*/
-void qh_checkconnect (void /* qh newfacet_list */) {
-  facetT *facet, *newfacet, *errfacet= NULL, *neighbor, **neighborp;
-
-  facet= qh newfacet_list;
-  qh_removefacet (facet);
-  qh_appendfacet (facet);
-  facet->visitid= ++qh visit_id;
-  FORALLfacet_(facet) {
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid != qh visit_id) {
-        qh_removefacet (neighbor);
-        qh_appendfacet (neighbor);
-        neighbor->visitid= qh visit_id;
-      }
-    }
-  }
-  FORALLnew_facets {
-    if (newfacet->visitid == qh visit_id)
-      break;
-    fprintf(qh ferr, "qhull error: f%d is not attached to the new facets\n",
-         newfacet->id);
-    errfacet= newfacet;
-  }
-  if (errfacet)
-    qh_errexit (qh_ERRqhull, errfacet, NULL);
-} /* checkconnect */
-
-/*---------------------------------
-
-  qh_checkzero( testall )
-    check that facets are clearly convex for qh.DISTround with qh.MERGEexact
-
-    if testall,
-      test all facets for qh.MERGEexact post-merging
-    else
-      test qh.newfacet_list
-
-    if qh.MERGEexact,
-      allows coplanar ridges
-      skips convexity test while qh.ZEROall_ok
-
-  returns:
-    True if all facets !flipped, !dupridge, normal
-         if all horizon facets are simplicial
-         if all vertices are clearly below neighbor
-         if all opposite vertices of horizon are below
-    clears qh.ZEROall_ok if any problems or coplanar facets
-
-  notes:
-    uses qh.vertex_visit
-    horizon facets may define multiple new facets
-
-  design:
-    for all facets in qh.newfacet_list or qh.facet_list
-      check for flagged faults (flipped, etc.)
-    for all facets in qh.newfacet_list or qh.facet_list
-      for each neighbor of facet
-        skip horizon facets for qh.newfacet_list
-        test the opposite vertex
-      if qh.newfacet_list
-        test the other vertices in the facet's horizon facet
-*/
-boolT qh_checkzero (boolT testall) {
-  facetT *facet, *neighbor, **neighborp;
-  facetT *horizon, *facetlist;
-  int neighbor_i;
-  vertexT *vertex, **vertexp;
-  realT dist;
-
-  if (testall)
-    facetlist= qh facet_list;
-  else {
-    facetlist= qh newfacet_list;
-    FORALLfacet_(facetlist) {
-      horizon= SETfirstt_(facet->neighbors, facetT);
-      if (!horizon->simplicial)
-        goto LABELproblem;
-      if (facet->flipped || facet->dupridge || !facet->normal)
-        goto LABELproblem;
-    }
-    if (qh MERGEexact && qh ZEROall_ok) {
-      trace2((qh ferr, "qh_checkzero: skip convexity check until first pre-merge\n"));
-      return True;
-    }
-  }
-  FORALLfacet_(facetlist) {
-    qh vertex_visit++;
-    neighbor_i= 0;
-    horizon= NULL;
-    FOREACHneighbor_(facet) {
-      if (!neighbor_i && !testall) {
-        horizon= neighbor;
-	neighbor_i++;
-        continue; /* horizon facet tested in qh_findhorizon */
-      }
-      vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
-      vertex->visitid= qh vertex_visit;
-      zzinc_(Zdistzero);
-      qh_distplane (vertex->point, neighbor, &dist);
-      if (dist >= -qh DISTround) {
-        qh ZEROall_ok= False;
-        if (!qh MERGEexact || testall || dist > qh DISTround)
-          goto LABELnonconvex;
-      }
-    }
-    if (!testall) {
-      FOREACHvertex_(horizon->vertices) {
-	if (vertex->visitid != qh vertex_visit) {
-	  zzinc_(Zdistzero);
-	  qh_distplane (vertex->point, facet, &dist);
-	  if (dist >= -qh DISTround) {
-	    qh ZEROall_ok= False;
-	    if (!qh MERGEexact || dist > qh DISTround)
-	      goto LABELnonconvex;
-	  }
-	  break;
-	}
-      }
-    }
-  }
-  trace2((qh ferr, "qh_checkzero: testall %d, facets are %s\n", testall,
-        (qh MERGEexact && !testall) ?
-           "not concave, flipped, or duplicate ridged" : "clearly convex"));
-  return True;
-
- LABELproblem:
-  qh ZEROall_ok= False;
-  trace2((qh ferr, "qh_checkzero: facet f%d needs pre-merging\n",
-       facet->id));
-  return False;
-
- LABELnonconvex:
-  trace2((qh ferr, "qh_checkzero: facet f%d and f%d are not clearly convex.  v%d dist %.2g\n",
-         facet->id, neighbor->id, vertex->id, dist));
-  return False;
-} /* checkzero */
-
-/*---------------------------------
-
-  qh_compareangle( angle1, angle2 )
-    used by qsort() to order merges by angle
-*/
-static int qh_compareangle(const void *p1, const void *p2) {
-  mergeT *a= *((mergeT **)p1), *b= *((mergeT **)p2);
-
-  return ((a->angle > b->angle) ? 1 : -1);
-} /* compareangle */
-
-/*---------------------------------
-
-  qh_comparemerge( merge1, merge2 )
-    used by qsort() to order merges
-*/
-static int qh_comparemerge(const void *p1, const void *p2) {
-  mergeT *a= *((mergeT **)p1), *b= *((mergeT **)p2);
-
-  return (a->type - b->type);
-} /* comparemerge */
-
-/*---------------------------------
-
-  qh_comparevisit( vertex1, vertex2 )
-    used by qsort() to order vertices by their visitid
-*/
-static int qh_comparevisit (const void *p1, const void *p2) {
-  vertexT *a= *((vertexT **)p1), *b= *((vertexT **)p2);
-
-  return (a->visitid - b->visitid);
-} /* comparevisit */
-
-/*---------------------------------
-
-  qh_copynonconvex( atridge )
-    set non-convex flag on other ridges (if any) between same neighbors
-
-  notes:
-    may be faster if use smaller ridge set
-
-  design:
-    for each ridge of atridge's top facet
-      if ridge shares the same neighbor
-        set nonconvex flag
-*/
-void qh_copynonconvex (ridgeT *atridge) {
-  facetT *facet, *otherfacet;
-  ridgeT *ridge, **ridgep;
-
-  facet= atridge->top;
-  otherfacet= atridge->bottom;
-  FOREACHridge_(facet->ridges) {
-    if (otherfacet == otherfacet_(ridge, facet) && ridge != atridge) {
-      ridge->nonconvex= True;
-      trace4((qh ferr, "qh_copynonconvex: moved nonconvex flag from r%d to r%d\n",
-	      atridge->id, ridge->id));
-      break;
-    }
-  }
-} /* copynonconvex */
-
-/*---------------------------------
-
-  qh_degen_redundant_facet( facet )
-    check facet for degen. or redundancy
-
-  notes:
-    bumps vertex_visit
-    called if a facet was redundant but no longer is (qh_merge_degenredundant)
-    qh_appendmergeset() only appends first reference to facet (i.e., redundant)
-
-  see:
-    qh_degen_redundant_neighbors()
-
-  design:
-    test for redundant neighbor
-    test for degenerate facet
-*/
-void qh_degen_redundant_facet (facetT *facet) {
-  vertexT *vertex, **vertexp;
-  facetT *neighbor, **neighborp;
-
-  trace4((qh ferr, "qh_degen_redundant_facet: test facet f%d for degen/redundant\n",
-	  facet->id));
-  FOREACHneighbor_(facet) {
-    qh vertex_visit++;
-    FOREACHvertex_(neighbor->vertices)
-      vertex->visitid= qh vertex_visit;
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->visitid != qh vertex_visit)
-	break;
-    }
-    if (!vertex) {
-      qh_appendmergeset (facet, neighbor, MRGredundant, NULL);
-      trace2((qh ferr, "qh_degen_redundant_facet: f%d is contained in f%d.  merge\n", facet->id, neighbor->id));
-      return;
-    }
-  }
-  if (qh_setsize (facet->neighbors) < qh hull_dim) {
-    qh_appendmergeset (facet, facet, MRGdegen, NULL);
-    trace2((qh ferr, "qh_degen_redundant_neighbors: f%d is degenerate.\n", facet->id));
-  }
-} /* degen_redundant_facet */
-
-
-/*---------------------------------
-
-  qh_degen_redundant_neighbors( facet, delfacet,  )
-    append degenerate and redundant neighbors to facet_mergeset
-    if delfacet,
-      only checks neighbors of both delfacet and facet
-    also checks current facet for degeneracy
-
-  notes:
-    bumps vertex_visit
-    called for each qh_mergefacet() and qh_mergecycle()
-    merge and statistics occur in merge_nonconvex
-    qh_appendmergeset() only appends first reference to facet (i.e., redundant)
-      it appends redundant facets after degenerate ones
-
-    a degenerate facet has fewer than hull_dim neighbors
-    a redundant facet's vertices is a subset of its neighbor's vertices
-    tests for redundant merges first (appendmergeset is nop for others)
-    in a merge, only needs to test neighbors of merged facet
-
-  see:
-    qh_merge_degenredundant() and qh_degen_redundant_facet()
-
-  design:
-    test for degenerate facet
-    test for redundant neighbor
-    test for degenerate neighbor
-*/
-void qh_degen_redundant_neighbors (facetT *facet, facetT *delfacet) {
-  vertexT *vertex, **vertexp;
-  facetT *neighbor, **neighborp;
-  int size;
-
-  trace4((qh ferr, "qh_degen_redundant_neighbors: test neighbors of f%d with delfacet f%d\n",
-	  facet->id, getid_(delfacet)));
-  if ((size= qh_setsize (facet->neighbors)) < qh hull_dim) {
-    qh_appendmergeset (facet, facet, MRGdegen, NULL);
-    trace2((qh ferr, "qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors.\n", facet->id, size));
-  }
-  if (!delfacet)
-    delfacet= facet;
-  qh vertex_visit++;
-  FOREACHvertex_(facet->vertices)
-    vertex->visitid= qh vertex_visit;
-  FOREACHneighbor_(delfacet) {
-    /* uses early out instead of checking vertex count */
-    if (neighbor == facet)
-      continue;
-    FOREACHvertex_(neighbor->vertices) {
-      if (vertex->visitid != qh vertex_visit)
-        break;
-    }
-    if (!vertex) {
-      qh_appendmergeset (neighbor, facet, MRGredundant, NULL);
-      trace2((qh ferr, "qh_degen_redundant_neighbors: f%d is contained in f%d.  merge\n", neighbor->id, facet->id));
-    }
-  }
-  FOREACHneighbor_(delfacet) {   /* redundant merges occur first */
-    if (neighbor == facet)
-      continue;
-    if ((size= qh_setsize (neighbor->neighbors)) < qh hull_dim) {
-      qh_appendmergeset (neighbor, neighbor, MRGdegen, NULL);
-      trace2((qh ferr, "qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors.  Neighbor of f%d.\n", neighbor->id, size, facet->id));
-    }
-  }
-} /* degen_redundant_neighbors */
-
-
-/*---------------------------------
-
-  qh_find_newvertex( oldvertex, vertices, ridges )
-    locate new vertex for renaming old vertex
-    vertices is a set of possible new vertices
-      vertices sorted by number of deleted ridges
-
-  returns:
-    newvertex or NULL
-      each ridge includes both vertex and oldvertex
-    vertices sorted by number of deleted ridges
-
-  notes:
-    modifies vertex->visitid
-    new vertex is in one of the ridges
-    renaming will not cause a duplicate ridge
-    renaming will minimize the number of deleted ridges
-    newvertex may not be adjacent in the dual (though unlikely)
-
-  design:
-    for each vertex in vertices
-      set vertex->visitid to number of references in ridges
-    remove unvisited vertices
-    set qh.vertex_visit above all possible values
-    sort vertices by number of references in ridges
-    add each ridge to qh.hash_table
-    for each vertex in vertices
-      look for a vertex that would not cause a duplicate ridge after a rename
-*/
-vertexT *qh_find_newvertex (vertexT *oldvertex, setT *vertices, setT *ridges) {
-  vertexT *vertex, **vertexp;
-  setT *newridges;
-  ridgeT *ridge, **ridgep;
-  int size, hashsize;
-  int hash;
-
-#ifndef qh_NOtrace
-  if (qh IStracing >= 4) {
-    fprintf (qh ferr, "qh_find_newvertex: find new vertex for v%d from ",
-	     oldvertex->id);
-    FOREACHvertex_(vertices)
-      fprintf (qh ferr, "v%d ", vertex->id);
-    FOREACHridge_(ridges)
-      fprintf (qh ferr, "r%d ", ridge->id);
-    fprintf (qh ferr, "\n");
-  }
-#endif
-  FOREACHvertex_(vertices)
-    vertex->visitid= 0;
-  FOREACHridge_(ridges) {
-    FOREACHvertex_(ridge->vertices)
-      vertex->visitid++;
-  }
-  FOREACHvertex_(vertices) {
-    if (!vertex->visitid) {
-      qh_setdelnth (vertices, SETindex_(vertices,vertex));
-      vertexp--; /* repeat since deleted this vertex */
-    }
-  }
-  qh vertex_visit += qh_setsize (ridges);
-  if (!qh_setsize (vertices)) {
-    trace4((qh ferr, "qh_find_newvertex: vertices not in ridges for v%d\n",
-	    oldvertex->id));
-    return NULL;
-  }
-  qsort (SETaddr_(vertices, vertexT), qh_setsize (vertices),
-	        sizeof (vertexT *), qh_comparevisit);
-  /* can now use qh vertex_visit */
-  if (qh PRINTstatistics) {
-    size= qh_setsize (vertices);
-    zinc_(Zintersect);
-    zmax_(Zintersectmax, size);
-  }
-  hashsize= qh_newhashtable (qh_setsize (ridges));
-  FOREACHridge_(ridges)
-    qh_hashridge (qh hash_table, hashsize, ridge, oldvertex);
-  FOREACHvertex_(vertices) {
-    newridges= qh_vertexridges (vertex);
-    FOREACHridge_(newridges) {
-      if (qh_hashridge_find (qh hash_table, hashsize, ridge, vertex, oldvertex, &hash)) {
-	zinc_(Zdupridge);
-	break;
-      }
-    }
-    qh_settempfree (&newridges);
-    if (!ridge)
-      break;  /* found a rename */
-  }
-  if (vertex) {
-    /* counted in qh_renamevertex */
-    trace2((qh ferr, "qh_find_newvertex: found v%d for old v%d from %d vertices and %d ridges.\n",
-      vertex->id, oldvertex->id, qh_setsize (vertices), qh_setsize (ridges)));
-  }else {
-    zinc_(Zfindfail);
-    trace0((qh ferr, "qh_find_newvertex: no vertex for renaming v%d (all duplicated ridges) during p%d\n",
-      oldvertex->id, qh furthest_id));
-  }
-  qh_setfree (&qh hash_table);
-  return vertex;
-} /* find_newvertex */
-
-/*---------------------------------
-
-  qh_findbest_test( testcentrum, facet, neighbor, bestfacet, dist, mindist, maxdist )
-    test neighbor of facet for qh_findbestneighbor()
-    if testcentrum,
-      tests centrum (assumes it is defined)
-    else
-      tests vertices
-
-  returns:
-    if a better facet (i.e., vertices/centrum of facet closer to neighbor)
-      updates bestfacet, dist, mindist, and maxdist
-*/
-void qh_findbest_test (boolT testcentrum, facetT *facet, facetT *neighbor,
-      facetT **bestfacet, realT *distp, realT *mindistp, realT *maxdistp) {
-  realT dist, mindist, maxdist;
-
-  if (testcentrum) {
-    zzinc_(Zbestdist);
-    qh_distplane(facet->center, neighbor, &dist);
-    dist *= qh hull_dim; /* estimate furthest vertex */
-    if (dist < 0) {
-      maxdist= 0;
-      mindist= dist;
-      dist= -dist;
-    }else
-      maxdist= dist;
-  }else
-    dist= qh_getdistance (facet, neighbor, &mindist, &maxdist);
-  if (dist < *distp) {
-    *bestfacet= neighbor;
-    *mindistp= mindist;
-    *maxdistp= maxdist;
-    *distp= dist;
-  }
-} /* findbest_test */
-
-/*---------------------------------
-
-  qh_findbestneighbor( facet, dist, mindist, maxdist )
-    finds best neighbor (least dist) of a facet for merging
-
-  returns:
-    returns min and max distances and their max absolute value
-
-  notes:
-    avoids merging old into new
-    assumes ridge->nonconvex only set on one ridge between a pair of facets
-    could use an early out predicate but not worth it
-
-  design:
-    if a large facet
-      will test centrum
-    else
-      will test vertices
-    if a large facet
-      test nonconvex neighbors for best merge
-    else
-      test all neighbors for the best merge
-    if testing centrum
-      get distance information
-*/
-facetT *qh_findbestneighbor(facetT *facet, realT *distp, realT *mindistp, realT *maxdistp) {
-  facetT *neighbor, **neighborp, *bestfacet= NULL;
-  ridgeT *ridge, **ridgep;
-  boolT nonconvex= True, testcentrum= False;
-  int size= qh_setsize (facet->vertices);
-
-  *distp= REALmax;
-  if (size > qh_BESTcentrum2 * qh hull_dim + qh_BESTcentrum) {
-    testcentrum= True;
-    zinc_(Zbestcentrum);
-    if (!facet->center)
-       facet->center= qh_getcentrum (facet);
-  }
-  if (size > qh hull_dim + qh_BESTnonconvex) {
-    FOREACHridge_(facet->ridges) {
-      if (ridge->nonconvex) {
-        neighbor= otherfacet_(ridge, facet);
-	qh_findbest_test (testcentrum, facet, neighbor,
-			  &bestfacet, distp, mindistp, maxdistp);
-      }
-    }
-  }
-  if (!bestfacet) {
-    nonconvex= False;
-    FOREACHneighbor_(facet)
-      qh_findbest_test (testcentrum, facet, neighbor,
-			&bestfacet, distp, mindistp, maxdistp);
-  }
-  if (!bestfacet) {
-    fprintf (qh ferr, "qhull internal error (qh_findbestneighbor): no neighbors for f%d\n", facet->id);
-
-    qh_errexit (qh_ERRqhull, facet, NULL);
-  }
-  if (testcentrum)
-    qh_getdistance (facet, bestfacet, mindistp, maxdistp);
-  trace3((qh ferr, "qh_findbestneighbor: f%d is best neighbor for f%d testcentrum? %d nonconvex? %d dist %2.2g min %2.2g max %2.2g\n",
-     bestfacet->id, facet->id, testcentrum, nonconvex, *distp, *mindistp, *maxdistp));
-  return(bestfacet);
-} /* findbestneighbor */
-
-
-/*---------------------------------
-
-  qh_flippedmerges( facetlist, wasmerge )
-    merge flipped facets into best neighbor
-    assumes qh.facet_mergeset at top of temporary stack
-
-  returns:
-    no flipped facets on facetlist
-    sets wasmerge if merge occurred
-    degen/redundant merges passed through
-
-  notes:
-    othermerges not needed since qh.facet_mergeset is empty before & after
-      keep it in case of change
-
-  design:
-    append flipped facets to qh.facetmergeset
-    for each flipped merge
-      find best neighbor
-      merge facet into neighbor
-      merge degenerate and redundant facets
-    remove flipped merges from qh.facet_mergeset
-*/
-void qh_flippedmerges(facetT *facetlist, boolT *wasmerge) {
-  facetT *facet, *neighbor, *facet1;
-  realT dist, mindist, maxdist;
-  mergeT *merge, **mergep;
-  setT *othermerges;
-  int nummerge=0;
-
-  trace4((qh ferr, "qh_flippedmerges: begin\n"));
-  FORALLfacet_(facetlist) {
-    if (facet->flipped && !facet->visible)
-      qh_appendmergeset (facet, facet, MRGflip, NULL);
-  }
-  othermerges= qh_settemppop(); /* was facet_mergeset */
-  qh facet_mergeset= qh_settemp (qh TEMPsize);
-  qh_settemppush (othermerges);
-  FOREACHmerge_(othermerges) {
-    facet1= merge->facet1;
-    if (merge->type != MRGflip || facet1->visible)
-      continue;
-    if (qh TRACEmerge-1 == zzval_(Ztotmerge))
-      qhmem.IStracing= qh IStracing= qh TRACElevel;
-    neighbor= qh_findbestneighbor (facet1, &dist, &mindist, &maxdist);
-    trace0((qh ferr, "qh_flippedmerges: merge flipped f%d into f%d dist %2.2g during p%d\n",
-      facet1->id, neighbor->id, dist, qh furthest_id));
-    qh_mergefacet (facet1, neighbor, &mindist, &maxdist, !qh_MERGEapex);
-    nummerge++;
-    if (qh PRINTstatistics) {
-      zinc_(Zflipped);
-      wmax_(Wflippedmax, dist);
-    }
-    qh_merge_degenredundant();
-  }
-  FOREACHmerge_(othermerges) {
-    if (merge->facet1->visible || merge->facet2->visible)
-      qh_memfree (merge, sizeof(mergeT));
-    else
-      qh_setappend (&qh facet_mergeset, merge);
-  }
-  qh_settempfree (&othermerges);
-  if (nummerge)
-    *wasmerge= True;
-  trace1((qh ferr, "qh_flippedmerges: merged %d flipped facets into a good neighbor\n", nummerge));
-} /* flippedmerges */
-
-
-/*---------------------------------
-
-  qh_forcedmerges( wasmerge )
-    merge duplicated ridges
-
-  returns:
-    removes all duplicate ridges on facet_mergeset
-    wasmerge set if merge
-    qh.facet_mergeset may include non-forced merges (none for now)
-    qh.degen_mergeset includes degen/redun merges
-
-  notes:
-    duplicate ridges occur when the horizon is pinched,
-        i.e. a subridge occurs in more than two horizon ridges.
-     could rename vertices that pinch the horizon
-    assumes qh_merge_degenredundant() has not be called
-    othermerges isn't needed since facet_mergeset is empty afterwards
-      keep it in case of change
-
-  design:
-    for each duplicate ridge
-      find current facets by chasing f.replace links
-      determine best direction for facet
-      merge one facet into the other
-      remove duplicate ridges from qh.facet_mergeset
-*/
-void qh_forcedmerges(boolT *wasmerge) {
-  facetT *facet1, *facet2;
-  mergeT *merge, **mergep;
-  realT dist1, dist2, mindist1, mindist2, maxdist1, maxdist2;
-  setT *othermerges;
-  int nummerge=0, numflip=0;
-
-  if (qh TRACEmerge-1 == zzval_(Ztotmerge))
-    qhmem.IStracing= qh IStracing= qh TRACElevel;
-  trace4((qh ferr, "qh_forcedmerges: begin\n"));
-  othermerges= qh_settemppop(); /* was facet_mergeset */
-  qh facet_mergeset= qh_settemp (qh TEMPsize);
-  qh_settemppush (othermerges);
-  FOREACHmerge_(othermerges) {
-    if (merge->type != MRGridge)
-    	continue;
-    facet1= merge->facet1;
-    facet2= merge->facet2;
-    while (facet1->visible)    	 /* must exist, no qh_merge_degenredunant */
-      facet1= facet1->f.replace; /* previously merged facet */
-    while (facet2->visible)
-      facet2= facet2->f.replace; /* previously merged facet */
-    if (facet1 == facet2)
-      continue;
-    if (!qh_setin (facet2->neighbors, facet1)) {
-      fprintf (qh ferr, "qhull internal error (qh_forcedmerges): f%d and f%d had a duplicate ridge but as f%d and f%d they are no longer neighbors\n",
-	       merge->facet1->id, merge->facet2->id, facet1->id, facet2->id);
-      qh_errexit2 (qh_ERRqhull, facet1, facet2);
-    }
-    if (qh TRACEmerge-1 == zzval_(Ztotmerge))
-      qhmem.IStracing= qh IStracing= qh TRACElevel;
-    dist1= qh_getdistance (facet1, facet2, &mindist1, &maxdist1);
-    dist2= qh_getdistance (facet2, facet1, &mindist2, &maxdist2);
-    trace0((qh ferr, "qh_forcedmerges: duplicate ridge between f%d and f%d, dist %2.2g and reverse dist %2.2g during p%d\n",
-	    facet1->id, facet2->id, dist1, dist2, qh furthest_id));
-    if (dist1 < dist2)
-      qh_mergefacet (facet1, facet2, &mindist1, &maxdist1, !qh_MERGEapex);
-    else {
-      qh_mergefacet (facet2, facet1, &mindist2, &maxdist2, !qh_MERGEapex);
-      dist1= dist2;
-      facet1= facet2;
-    }
-    if (facet1->flipped) {
-      zinc_(Zmergeflipdup);
-      numflip++;
-    }else
-      nummerge++;
-    if (qh PRINTstatistics) {
-      zinc_(Zduplicate);
-      wmax_(Wduplicatemax, dist1);
-    }
-  }
-  FOREACHmerge_(othermerges) {
-    if (merge->type == MRGridge)
-      qh_memfree (merge, sizeof(mergeT));
-    else
-      qh_setappend (&qh facet_mergeset, merge);
-  }
-  qh_settempfree (&othermerges);
-  if (nummerge)
-    *wasmerge= True;
-  trace1((qh ferr, "qh_forcedmerges: merged %d facets and %d flipped facets across duplicated ridges\n",
-                nummerge, numflip));
-} /* forcedmerges */
-
-
-/*---------------------------------
-
-  qh_getmergeset( facetlist )
-    determines nonconvex facets on facetlist
-    tests !tested ridges and nonconvex ridges of !tested facets
-
-  returns:
-    returns sorted qh.facet_mergeset of facet-neighbor pairs to be merged
-    all ridges tested
-
-  notes:
-    assumes no nonconvex ridges with both facets tested
-    uses facet->tested/ridge->tested to prevent duplicate tests
-    can not limit tests to modified ridges since the centrum changed
-    uses qh.visit_id
-
-  see:
-    qh_getmergeset_initial()
-
-  design:
-    for each facet on facetlist
-      for each ridge of facet
-        if untested ridge
-          test ridge for convexity
-          if non-convex
-            append ridge to qh.facet_mergeset
-    sort qh.facet_mergeset by angle
-*/
-void qh_getmergeset(facetT *facetlist) {
-  facetT *facet, *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-  int nummerges;
-
-  nummerges= qh_setsize (qh facet_mergeset);
-  trace4((qh ferr, "qh_getmergeset: started.\n"));
-  qh visit_id++;
-  FORALLfacet_(facetlist) {
-    if (facet->tested)
-      continue;
-    facet->visitid= qh visit_id;
-    facet->tested= True;  /* must be non-simplicial due to merge */
-    FOREACHneighbor_(facet)
-      neighbor->seen= False;
-    FOREACHridge_(facet->ridges) {
-      if (ridge->tested && !ridge->nonconvex)
-	continue;
-      /* if tested & nonconvex, need to append merge */
-      neighbor= otherfacet_(ridge, facet);
-      if (neighbor->seen) {
-	ridge->tested= True;
-	ridge->nonconvex= False;
-      }else if (neighbor->visitid != qh visit_id) {
-        ridge->tested= True;
-        ridge->nonconvex= False;
-	neighbor->seen= True;      /* only one ridge is marked nonconvex */
-	if (qh_test_appendmerge (facet, neighbor))
-	  ridge->nonconvex= True;
-      }
-    }
-  }
-  nummerges= qh_setsize (qh facet_mergeset);
-  if (qh ANGLEmerge)
-    qsort(SETaddr_(qh facet_mergeset, mergeT), nummerges,sizeof(mergeT *),qh_compareangle);
-  else
-    qsort(SETaddr_(qh facet_mergeset, mergeT), nummerges,sizeof(mergeT *),qh_comparemerge);
-  if (qh POSTmerging) {
-  }else {
-    zmax_(Zmergesetmax, nummerges);
-  }
-  trace2((qh ferr, "qh_getmergeset: %d merges found\n", nummerges));
-} /* getmergeset */
-
-
-/*---------------------------------
-
-  qh_getmergeset_initial( facetlist )
-    determine initial qh.facet_mergeset for facets
-    tests all facet/neighbor pairs on facetlist
-
-  returns:
-    sorted qh.facet_mergeset with nonconvex ridges
-    sets facet->tested, ridge->tested, and ridge->nonconvex
-
-  notes:
-    uses visit_id, assumes ridge->nonconvex is False
-
-  see:
-    qh_getmergeset()
-
-  design:
-    for each facet on facetlist
-      for each untested neighbor of facet
-        test facet and neighbor for convexity
-        if non-convex
-          append merge to qh.facet_mergeset
-          mark one of the ridges as nonconvex
-    sort qh.facet_mergeset by angle
-*/
-void qh_getmergeset_initial (facetT *facetlist) {
-  facetT *facet, *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-  int nummerges;
-
-  qh visit_id++;
-  FORALLfacet_(facetlist) {
-    facet->visitid= qh visit_id;
-    facet->tested= True;
-    FOREACHneighbor_(facet) {
-      if (neighbor->visitid != qh visit_id) {
-        if (qh_test_appendmerge (facet, neighbor)) {
-          FOREACHridge_(neighbor->ridges) {
-            if (facet == otherfacet_(ridge, neighbor)) {
-              ridge->nonconvex= True;
-              break;	/* only one ridge is marked nonconvex */
-            }
-          }
-        }
-      }
-    }
-    FOREACHridge_(facet->ridges)
-      ridge->tested= True;
-  }
-  nummerges= qh_setsize (qh facet_mergeset);
-  if (qh ANGLEmerge)
-    qsort(SETaddr_(qh facet_mergeset, mergeT), nummerges,sizeof(mergeT *),qh_compareangle);
-  else
-    qsort(SETaddr_(qh facet_mergeset, mergeT), nummerges,sizeof(mergeT *),qh_comparemerge);
-  if (qh POSTmerging) {
-  }else {
-    zmax_(Zmergeinitmax, nummerges);
-  }
-  trace2((qh ferr, "qh_getmergeset_initial: %d merges found\n", nummerges));
-} /* getmergeset_initial */
-
-
-/*---------------------------------
-
-  qh_hashridge( hashtable, hashsize, ridge, oldvertex )
-    add ridge to hashtable without oldvertex
-
-  notes:
-    assumes hashtable is large enough
-
-  design:
-    determine hash value for ridge without oldvertex
-    find next empty slot for ridge
-*/
-void qh_hashridge (setT *hashtable, int hashsize, ridgeT *ridge, vertexT *oldvertex) {
-  int hash;
-  ridgeT *ridgeA;
-
-  hash= (int)qh_gethash (hashsize, ridge->vertices, qh hull_dim-1, 0, oldvertex);
-  while (True) {
-    if (!(ridgeA= SETelemt_(hashtable, hash, ridgeT))) {
-      SETelem_(hashtable, hash)= ridge;
-      break;
-    }else if (ridgeA == ridge)
-      break;
-    if (++hash == hashsize)
-      hash= 0;
-  }
-} /* hashridge */
-
-
-/*---------------------------------
-
-  qh_hashridge_find( hashtable, hashsize, ridge, vertex, oldvertex, hashslot )
-    returns matching ridge without oldvertex in hashtable
-      for ridge without vertex
-    if oldvertex is NULL
-      matches with any one skip
-
-  returns:
-    matching ridge or NULL
-    if no match,
-      if ridge already in   table
-        hashslot= -1
-      else
-        hashslot= next NULL index
-
-  notes:
-    assumes hashtable is large enough
-    can't match ridge to itself
-
-  design:
-    get hash value for ridge without vertex
-    for each hashslot
-      return match if ridge matches ridgeA without oldvertex
-*/
-ridgeT *qh_hashridge_find (setT *hashtable, int hashsize, ridgeT *ridge,
-              vertexT *vertex, vertexT *oldvertex, int *hashslot) {
-  int hash;
-  ridgeT *ridgeA;
-
-  *hashslot= 0;
-  zinc_(Zhashridge);
-  hash= (int)qh_gethash (hashsize, ridge->vertices, qh hull_dim-1, 0, vertex);
-  while ((ridgeA= SETelemt_(hashtable, hash, ridgeT))) {
-    if (ridgeA == ridge)
-      *hashslot= -1;
-    else {
-      zinc_(Zhashridgetest);
-      if (qh_setequal_except (ridge->vertices, vertex, ridgeA->vertices, oldvertex))
-        return ridgeA;
-    }
-    if (++hash == hashsize)
-      hash= 0;
-  }
-  if (!*hashslot)
-    *hashslot= hash;
-  return NULL;
-} /* hashridge_find */
-
-
-/*---------------------------------
-
-  qh_makeridges( facet )
-    creates explicit ridges between simplicial facets
-
-  returns:
-    facet with ridges and without qh_MERGEridge
-    ->simplicial is False
-
-  notes:
-    allows qh_MERGEridge flag
-    uses existing ridges
-    duplicate neighbors ok if ridges already exist (qh_mergecycle_ridges)
-
-  see:
-    qh_mergecycle_ridges()
-
-  design:
-    look for qh_MERGEridge neighbors
-    mark neighbors that already have ridges
-    for each unprocessed neighbor of facet
-      create a ridge for neighbor and facet
-    if any qh_MERGEridge neighbors
-      delete qh_MERGEridge flags (already handled by qh_mark_dupridges)
-*/
-void qh_makeridges(facetT *facet) {
-  facetT *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-  int neighbor_i, neighbor_n;
-  boolT toporient, mergeridge= False;
-
-  if (!facet->simplicial)
-    return;
-  trace4((qh ferr, "qh_makeridges: make ridges for f%d\n", facet->id));
-  facet->simplicial= False;
-  FOREACHneighbor_(facet) {
-    if (neighbor == qh_MERGEridge)
-      mergeridge= True;
-    else
-      neighbor->seen= False;
-  }
-  FOREACHridge_(facet->ridges)
-    otherfacet_(ridge, facet)->seen= True;
-  FOREACHneighbor_i_(facet) {
-    if (neighbor == qh_MERGEridge)
-      continue;  /* fixed by qh_mark_dupridges */
-    else if (!neighbor->seen) {  /* no current ridges */
-      ridge= qh_newridge();
-      ridge->vertices= qh_setnew_delnthsorted (facet->vertices, qh hull_dim,
-					                  neighbor_i, 0);
-      toporient= facet->toporient ^ (neighbor_i & 0x1);
-      if (toporient) {
-        ridge->top= facet;
-        ridge->bottom= neighbor;
-      }else {
-        ridge->top= neighbor;
-        ridge->bottom= facet;
-      }
-#if 0 /* this also works */
-      flip= (facet->toporient ^ neighbor->toporient)^(skip1 & 0x1) ^ (skip2 & 0x1);
-      if (facet->toporient ^ (skip1 & 0x1) ^ flip) {
-        ridge->top= neighbor;
-        ridge->bottom= facet;
-      }else {
-        ridge->top= facet;
-        ridge->bottom= neighbor;
-      }
-#endif
-      qh_setappend(&(facet->ridges), ridge);
-      qh_setappend(&(neighbor->ridges), ridge);
-    }
-  }
-  if (mergeridge) {
-    while (qh_setdel (facet->neighbors, qh_MERGEridge))
-      ; /* delete each one */
-  }
-} /* makeridges */
-
-
-/*---------------------------------
-
-  qh_mark_dupridges( facetlist )
-    add duplicated ridges to qh.facet_mergeset
-    facet->dupridge is true
-
-  returns:
-    duplicate ridges on qh.facet_mergeset
-    ->mergeridge/->mergeridge2 set
-    duplicate ridges marked by qh_MERGEridge and both sides facet->dupridge
-    no MERGEridges in neighbor sets
-
-  notes:
-    duplicate ridges occur when the horizon is pinched,
-        i.e. a subridge occurs in more than two horizon ridges.
-    could rename vertices that pinch the horizon
-    uses qh.visit_id
-
-  design:
-    for all facets on facetlist
-      if facet contains a duplicate ridge
-        for each neighbor of facet
-          if neighbor marked qh_MERGEridge (one side of the merge)
-            set facet->mergeridge
-          else
-            if neighbor contains a duplicate ridge
-            and the back link is qh_MERGEridge
-              append duplicate ridge to qh.facet_mergeset
-   for each duplicate ridge
-     make ridge sets in preparation for merging
-     remove qh_MERGEridge from neighbor set
-   for each duplicate ridge
-     restore the missing neighbor from the neighbor set that was qh_MERGEridge
-     add the missing ridge for this neighbor
-*/
-void qh_mark_dupridges(facetT *facetlist) {
-  facetT *facet, *neighbor, **neighborp;
-  int nummerge=0;
-  mergeT *merge, **mergep;
-
-
-  trace4((qh ferr, "qh_mark_dupridges: identify duplicate ridges\n"));
-  FORALLfacet_(facetlist) {
-    if (facet->dupridge) {
-      FOREACHneighbor_(facet) {
-        if (neighbor == qh_MERGEridge) {
-	  facet->mergeridge= True;
-	  continue;
-	}
-        if (neighbor->dupridge
-	&& !qh_setin (neighbor->neighbors, facet)) { /* qh_MERGEridge */
-	  qh_appendmergeset (facet, neighbor, MRGridge, NULL);
-	  facet->mergeridge2= True;
-	  facet->mergeridge= True;
-	  nummerge++;
-	}
-      }
-    }
-  }
-  if (!nummerge)
-    return;
-  FORALLfacet_(facetlist) {            /* gets rid of qh_MERGEridge */
-    if (facet->mergeridge && !facet->mergeridge2)
-      qh_makeridges (facet);
-  }
-  FOREACHmerge_(qh facet_mergeset) {   /* restore the missing neighbors */
-    if (merge->type == MRGridge) {
-      qh_setappend (&merge->facet2->neighbors, merge->facet1);
-      qh_makeridges (merge->facet1);   /* and the missing ridges */
-    }
-  }
-  trace1((qh ferr, "qh_mark_dupridges: found %d duplicated ridges\n",
-                nummerge));
-} /* mark_dupridges */
-
-/*---------------------------------
-
-  qh_maydropneighbor( facet )
-    drop neighbor relationship if no ridge between facet and neighbor
-
-  returns:
-    neighbor sets updated
-    appends degenerate facets to qh.facet_mergeset
-
-  notes:
-    won't cause redundant facets since vertex inclusion is the same
-    may drop vertex and neighbor if no ridge
-    uses qh.visit_id
-
-  design:
-    visit all neighbors with ridges
-    for each unvisited neighbor of facet
-      delete neighbor and facet from the neighbor sets
-      if neighbor becomes degenerate
-        append neighbor to qh.degen_mergeset
-    if facet is degenerate
-      append facet to qh.degen_mergeset
-*/
-void qh_maydropneighbor (facetT *facet) {
-  ridgeT *ridge, **ridgep;
-  realT angledegen= qh_ANGLEdegen;
-  facetT *neighbor, **neighborp;
-
-  qh visit_id++;
-  trace4((qh ferr, "qh_maydropneighbor: test f%d for no ridges to a neighbor\n",
-	  facet->id));
-  FOREACHridge_(facet->ridges) {
-    ridge->top->visitid= qh visit_id;
-    ridge->bottom->visitid= qh visit_id;
-  }
-  FOREACHneighbor_(facet) {
-    if (neighbor->visitid != qh visit_id) {
-      trace0((qh ferr, "qh_maydropneighbor: facets f%d and f%d are no longer neighbors during p%d\n",
-	    facet->id, neighbor->id, qh furthest_id));
-      zinc_(Zdropneighbor);
-      qh_setdel (facet->neighbors, neighbor);
-      neighborp--;  /* repeat, deleted a neighbor */
-      qh_setdel (neighbor->neighbors, facet);
-      if (qh_setsize (neighbor->neighbors) < qh hull_dim) {
-        zinc_(Zdropdegen);
-        qh_appendmergeset (neighbor, neighbor, MRGdegen, &angledegen);
-        trace2((qh ferr, "qh_maydropneighbors: f%d is degenerate.\n", neighbor->id));
-      }
-    }
-  }
-  if (qh_setsize (facet->neighbors) < qh hull_dim) {
-    zinc_(Zdropdegen);
-    qh_appendmergeset (facet, facet, MRGdegen, &angledegen);
-    trace2((qh ferr, "qh_maydropneighbors: f%d is degenerate.\n", facet->id));
-  }
-} /* maydropneighbor */
-
-
-/*---------------------------------
-
-  qh_merge_degenredundant()
-    merge all degenerate and redundant facets
-    qh.degen_mergeset contains merges from qh_degen_redundant_neighbors()
-
-  returns:
-    number of merges performed
-    resets facet->degenerate/redundant
-    if deleted (visible) facet has no neighbors
-      sets ->f.replace to NULL
-
-  notes:
-    redundant merges happen before degenerate ones
-    merging and renaming vertices can result in degen/redundant facets
-
-  design:
-    for each merge on qh.degen_mergeset
-      if redundant merge
-        if non-redundant facet merged into redundant facet
-          recheck facet for redundancy
-        else
-          merge redundant facet into other facet
-*/
-int qh_merge_degenredundant (void) {
-  int size;
-  mergeT *merge;
-  facetT *bestneighbor, *facet1, *facet2;
-  realT dist, mindist, maxdist;
-  vertexT *vertex, **vertexp;
-  int nummerges= 0;
-  mergeType mergetype;
-
-  while ((merge= (mergeT*)qh_setdellast (qh degen_mergeset))) {
-    facet1= merge->facet1;
-    facet2= merge->facet2;
-    mergetype= merge->type;
-    qh_memfree (merge, sizeof(mergeT));
-    if (facet1->visible)
-      continue;
-    facet1->degenerate= False;
-    facet1->redundant= False;
-    if (qh TRACEmerge-1 == zzval_(Ztotmerge))
-      qhmem.IStracing= qh IStracing= qh TRACElevel;
-    if (mergetype == MRGredundant) {
-      zinc_(Zneighbor);
-      while (facet2->visible) {
-        if (!facet2->f.replace) {
-          fprintf (qh ferr, "qhull internal error (qh_merge_degenredunant): f%d redundant but f%d has no replacement\n",
-	       facet1->id, facet2->id);
-          qh_errexit2 (qh_ERRqhull, facet1, facet2);
-        }
-        facet2= facet2->f.replace;
-      }
-      if (facet1 == facet2) {
-	qh_degen_redundant_facet (facet1); /* in case of others */
-	continue;
-      }
-      trace2((qh ferr, "qh_merge_degenredundant: facet f%d is contained in f%d, will merge\n",
-	    facet1->id, facet2->id));
-      qh_mergefacet(facet1, facet2, NULL, NULL, !qh_MERGEapex);
-      /* merge distance is already accounted for */
-      nummerges++;
-    }else {  /* mergetype == MRGdegen, other merges may have fixed */
-      if (!(size= qh_setsize (facet1->neighbors))) {
-        zinc_(Zdelfacetdup);
-        trace2((qh ferr, "qh_merge_degenredundant: facet f%d has no neighbors.  Deleted\n", facet1->id));
-        qh_willdelete (facet1, NULL);
-        FOREACHvertex_(facet1->vertices) {
-  	  qh_setdel (vertex->neighbors, facet1);
-	  if (!SETfirst_(vertex->neighbors)) {
-	    zinc_(Zdegenvertex);
-	    trace2((qh ferr, "qh_merge_degenredundant: deleted v%d because f%d has no neighbors\n",
-         	 vertex->id, facet1->id));
-	    vertex->deleted= True;
-	    qh_setappend (&qh del_vertices, vertex);
-	  }
-        }
-        nummerges++;
-      }else if (size < qh hull_dim) {
-        bestneighbor= qh_findbestneighbor(facet1, &dist, &mindist, &maxdist);
-        trace2((qh ferr, "qh_merge_degenredundant: facet f%d has %d neighbors, merge into f%d dist %2.2g\n",
-	      facet1->id, size, bestneighbor->id, dist));
-        qh_mergefacet(facet1, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
-        nummerges++;
-        if (qh PRINTstatistics) {
-	  zinc_(Zdegen);
-	  wmax_(Wdegenmax, dist);
-        }
-      }	/* else, another merge fixed the degeneracy and redundancy tested */
-    }
-  }
-  return nummerges;
-} /* merge_degenredundant */
-
-/*---------------------------------
-
-  qh_merge_nonconvex( facet1, facet2, mergetype )
-    remove non-convex ridge between facet1 into facet2
-    mergetype gives why the facet's are non-convex
-
-  returns:
-    merges one of the facets into the best neighbor
-
-  design:
-    if one of the facets is a new facet
-      prefer merging new facet into old facet
-    find best neighbors for both facets
-    merge the nearest facet into its best neighbor
-    update the statistics
-*/
-void qh_merge_nonconvex (facetT *facet1, facetT *facet2, mergeType mergetype) {
-  facetT *bestfacet, *bestneighbor, *neighbor;
-  realT dist, dist2, mindist, mindist2, maxdist, maxdist2;
-
-  if (qh TRACEmerge-1 == zzval_(Ztotmerge))
-    qhmem.IStracing= qh IStracing= qh TRACElevel;
-  trace3((qh ferr, "qh_merge_nonconvex: merge #%d for f%d and f%d type %d\n",
-      zzval_(Ztotmerge) + 1, facet1->id, facet2->id, mergetype));
-  /* concave or coplanar */
-  if (!facet1->newfacet) {
-    bestfacet= facet2;   /* avoid merging old facet if new is ok */
-    facet2= facet1;
-    facet1= bestfacet;
-  }else
-    bestfacet= facet1;
-  bestneighbor= qh_findbestneighbor(bestfacet, &dist, &mindist, &maxdist);
-  neighbor= qh_findbestneighbor(facet2, &dist2, &mindist2, &maxdist2);
-  if (dist < dist2) {
-    qh_mergefacet(bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
-  }else if (qh AVOIDold && !facet2->newfacet
-  && ((mindist >= -qh MAXcoplanar && maxdist <= qh max_outside)
-       || dist * 1.5 < dist2)) {
-    zinc_(Zavoidold);
-    wmax_(Wavoidoldmax, dist);
-    trace2((qh ferr, "qh_merge_nonconvex: avoid merging old facet f%d dist %2.2g.  Use f%d dist %2.2g instead\n",
-           facet2->id, dist2, facet1->id, dist2));
-    qh_mergefacet(bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
-  }else {
-    qh_mergefacet(facet2, neighbor, &mindist2, &maxdist2, !qh_MERGEapex);
-    dist= dist2;
-  }
-  if (qh PRINTstatistics) {
-    if (mergetype == MRGanglecoplanar) {
-      zinc_(Zacoplanar);
-      wmax_(Wacoplanarmax, dist);
-    }else if (mergetype == MRGconcave) {
-      zinc_(Zconcave);
-      wmax_(Wconcavemax, dist);
-    }else { /* MRGcoplanar */
-      zinc_(Zcoplanar);
-      wmax_(Wcoplanarmax, dist);
-    }
-  }
-} /* merge_nonconvex */
-
-/*---------------------------------
-
-  qh_mergecycle( samecycle, newfacet )
-    merge a cycle of facets starting at samecycle into a newfacet
-    newfacet is a horizon facet with ->normal
-    samecycle facets are simplicial from an apex
-
-  returns:
-    initializes vertex neighbors on first merge
-    samecycle deleted (placed on qh.visible_list)
-    newfacet at end of qh.facet_list
-    deleted vertices on qh.del_vertices
-
-  see:
-    qh_mergefacet()
-    called by qh_mergecycle_all() for multiple, same cycle facets
-
-  design:
-    make vertex neighbors if necessary
-    make ridges for newfacet
-    merge neighbor sets of samecycle into newfacet
-    merge ridges of samecycle into newfacet
-    merge vertex neighbors of samecycle into newfacet
-    make apex of samecycle the apex of newfacet
-    if newfacet wasn't a new facet
-      add its vertices to qh.newvertex_list
-    delete samecycle facets a make newfacet a newfacet
-*/
-void qh_mergecycle (facetT *samecycle, facetT *newfacet) {
-  int traceonce= False, tracerestore= 0;
-  vertexT *apex;
-#ifndef qh_NOtrace
-  facetT *same;
-#endif
-
-  if (newfacet->tricoplanar) {
-    if (!qh TRInormals) {
-      fprintf (qh ferr, "qh_mergecycle: does not work for tricoplanar facets.  Use option 'Q11'\n");
-      qh_errexit (qh_ERRqhull, newfacet, NULL);
-    }
-    newfacet->tricoplanar= False;
-    newfacet->keepcentrum= False;
-  }
-  if (!qh VERTEXneighbors)
-    qh_vertexneighbors();
-  zzinc_(Ztotmerge);
-  if (qh REPORTfreq2 && qh POSTmerging) {
-    if (zzval_(Ztotmerge) > qh mergereport + qh REPORTfreq2)
-      qh_tracemerging();
-  }
-#ifndef qh_NOtrace
-  if (qh TRACEmerge == zzval_(Ztotmerge))
-    qhmem.IStracing= qh IStracing= qh TRACElevel;
-  trace2((qh ferr, "qh_mergecycle: merge #%d for facets from cycle f%d into coplanar horizon f%d\n",
-        zzval_(Ztotmerge), samecycle->id, newfacet->id));
-  if (newfacet == qh tracefacet) {
-    tracerestore= qh IStracing;
-    qh IStracing= 4;
-    fprintf (qh ferr, "qh_mergecycle: ========= trace merge %d of samecycle %d into trace f%d, furthest is p%d\n",
-	       zzval_(Ztotmerge), samecycle->id, newfacet->id,  qh furthest_id);
-    traceonce= True;
-  }
-  if (qh IStracing >=4) {
-    fprintf (qh ferr, "  same cycle:");
-    FORALLsame_cycle_(samecycle)
-      fprintf(qh ferr, " f%d", same->id);
-    fprintf (qh ferr, "\n");
-  }
-  if (qh IStracing >=4)
-    qh_errprint ("MERGING CYCLE", samecycle, newfacet, NULL, NULL);
-#endif /* !qh_NOtrace */
-  apex= SETfirstt_(samecycle->vertices, vertexT);
-  qh_makeridges (newfacet);
-  qh_mergecycle_neighbors (samecycle, newfacet);
-  qh_mergecycle_ridges (samecycle, newfacet);
-  qh_mergecycle_vneighbors (samecycle, newfacet);
-  if (SETfirstt_(newfacet->vertices, vertexT) != apex)
-    qh_setaddnth (&newfacet->vertices, 0, apex);  /* apex has last id */
-  if (!newfacet->newfacet)
-    qh_newvertices (newfacet->vertices);
-  qh_mergecycle_facets (samecycle, newfacet);
-  qh_tracemerge (samecycle, newfacet);
-  /* check for degen_redundant_neighbors after qh_forcedmerges() */
-  if (traceonce) {
-    fprintf (qh ferr, "qh_mergecycle: end of trace facet\n");
-    qh IStracing= tracerestore;
-  }
-} /* mergecycle */
-
-/*---------------------------------
-
-  qh_mergecycle_all( facetlist, wasmerge )
-    merge all samecycles of coplanar facets into horizon
-    don't merge facets with ->mergeridge (these already have ->normal)
-    all facets are simplicial from apex
-    all facet->cycledone == False
-
-  returns:
-    all newfacets merged into coplanar horizon facets
-    deleted vertices on  qh.del_vertices
-    sets wasmerge if any merge
-
-  see:
-    calls qh_mergecycle for multiple, same cycle facets
-
-  design:
-    for each facet on facetlist
-      skip facets with duplicate ridges and normals
-      check that facet is in a samecycle (->mergehorizon)
-      if facet only member of samecycle
-	sets vertex->delridge for all vertices except apex
-        merge facet into horizon
-      else
-        mark all facets in samecycle
-        remove facets with duplicate ridges from samecycle
-        merge samecycle into horizon (deletes facets from facetlist)
-*/
-void qh_mergecycle_all (facetT *facetlist, boolT *wasmerge) {
-  facetT *facet, *same, *prev, *horizon;
-  facetT *samecycle= NULL, *nextfacet, *nextsame;
-  vertexT *apex, *vertex, **vertexp;
-  int cycles=0, total=0, facets, nummerge;
-
-  trace2((qh ferr, "qh_mergecycle_all: begin\n"));
-  for (facet= facetlist; facet && (nextfacet= facet->next); facet= nextfacet) {
-    if (facet->normal)
-      continue;
-    if (!facet->mergehorizon) {
-      fprintf (qh ferr, "qh_mergecycle_all: f%d without normal\n", facet->id);
-      qh_errexit (qh_ERRqhull, facet, NULL);
-    }
-    horizon= SETfirstt_(facet->neighbors, facetT);
-    if (facet->f.samecycle == facet) {
-      zinc_(Zonehorizon);
-      /* merge distance done in qh_findhorizon */
-      apex= SETfirstt_(facet->vertices, vertexT);
-      FOREACHvertex_(facet->vertices) {
-	if (vertex != apex)
-          vertex->delridge= True;
-      }
-      horizon->f.newcycle= NULL;
-      qh_mergefacet (facet, horizon, NULL, NULL, qh_MERGEapex);
-    }else {
-      samecycle= facet;
-      facets= 0;
-      prev= facet;
-      for (same= facet->f.samecycle; same;  /* FORALLsame_cycle_(facet) */
-	   same= (same == facet ? NULL :nextsame)) { /* ends at facet */
-	nextsame= same->f.samecycle;
-        if (same->cycledone || same->visible)
-          qh_infiniteloop (same);
-        same->cycledone= True;
-        if (same->normal) {
-          prev->f.samecycle= same->f.samecycle; /* unlink ->mergeridge */
-	  same->f.samecycle= NULL;
-        }else {
-          prev= same;
-	  facets++;
-	}
-      }
-      while (nextfacet && nextfacet->cycledone)  /* will delete samecycle */
-	nextfacet= nextfacet->next;
-      horizon->f.newcycle= NULL;
-      qh_mergecycle (samecycle, horizon);
-      nummerge= horizon->nummerge + facets;
-      if (nummerge > qh_MAXnummerge)
-      	horizon->nummerge= qh_MAXnummerge;
-      else
-        horizon->nummerge= nummerge;
-      zzinc_(Zcyclehorizon);
-      total += facets;
-      zmax_(Zcyclefacetmax, facets);
-    }
-    cycles++;
-  }
-  if (cycles)
-    *wasmerge= True;
-  trace1((qh ferr, "qh_mergecycle_all: merged %d same cycles or facets into coplanar horizons\n", cycles));
-} /* mergecycle_all */
-
-/*---------------------------------
-
-  qh_mergecycle_facets( samecycle, newfacet )
-    finish merge of samecycle into newfacet
-
-  returns:
-    samecycle prepended to visible_list for later deletion and partitioning
-      each facet->f.replace == newfacet
-
-    newfacet moved to end of qh.facet_list
-      makes newfacet a newfacet (get's facet1->id if it was old)
-      sets newfacet->newmerge
-      clears newfacet->center (unless merging into a large facet)
-      clears newfacet->tested and ridge->tested for facet1
-
-    adds neighboring facets to facet_mergeset if redundant or degenerate
-
-  design:
-    make newfacet a new facet and set its flags
-    move samecycle facets to qh.visible_list for later deletion
-    unless newfacet is large
-      remove its centrum
-*/
-void qh_mergecycle_facets (facetT *samecycle, facetT *newfacet) {
-  facetT *same, *next;
-
-  trace4((qh ferr, "qh_mergecycle_facets: make newfacet new and samecycle deleted\n"));
-  qh_removefacet(newfacet);  /* append as a newfacet to end of qh facet_list */
-  qh_appendfacet(newfacet);
-  newfacet->newfacet= True;
-  newfacet->simplicial= False;
-  newfacet->newmerge= True;
-
-  for (same= samecycle->f.samecycle; same; same= (same == samecycle ?  NULL : next)) {
-    next= same->f.samecycle;  /* reused by willdelete */
-    qh_willdelete (same, newfacet);
-  }
-  if (newfacet->center
-      && qh_setsize (newfacet->vertices) <= qh hull_dim + qh_MAXnewcentrum) {
-    qh_memfree (newfacet->center, qh normal_size);
-    newfacet->center= NULL;
-  }
-  trace3((qh ferr, "qh_mergecycle_facets: merged facets from cycle f%d into f%d\n",
-             samecycle->id, newfacet->id));
-} /* mergecycle_facets */
-
-/*---------------------------------
-
-  qh_mergecycle_neighbors( samecycle, newfacet )
-    add neighbors for samecycle facets to newfacet
-
-  returns:
-    newfacet with updated neighbors and vice-versa
-    newfacet has ridges
-    all neighbors of newfacet marked with qh.visit_id
-    samecycle facets marked with qh.visit_id-1
-    ridges updated for simplicial neighbors of samecycle with a ridge
-
-  notes:
-    assumes newfacet not in samecycle
-    usually, samecycle facets are new, simplicial facets without internal ridges
-      not so if horizon facet is coplanar to two different samecycles
-
-  see:
-    qh_mergeneighbors()
-
-  design:
-    check samecycle
-    delete neighbors from newfacet that are also in samecycle
-    for each neighbor of a facet in samecycle
-      if neighbor is simplicial
-        if first visit
-          move the neighbor relation to newfacet
-          update facet links for its ridges
-        else
-          make ridges for neighbor
-          remove samecycle reference
-      else
-        update neighbor sets
-*/
-void qh_mergecycle_neighbors(facetT *samecycle, facetT *newfacet) {
-  facetT *same, *neighbor, **neighborp;
-  int delneighbors= 0, newneighbors= 0;
-  unsigned int samevisitid;
-  ridgeT *ridge, **ridgep;
-
-  samevisitid= ++qh visit_id;
-  FORALLsame_cycle_(samecycle) {
-    if (same->visitid == samevisitid || same->visible)
-      qh_infiniteloop (samecycle);
-    same->visitid= samevisitid;
-  }
-  newfacet->visitid= ++qh visit_id;
-  trace4((qh ferr, "qh_mergecycle_neighbors: delete shared neighbors from newfacet\n"));
-  FOREACHneighbor_(newfacet) {
-    if (neighbor->visitid == samevisitid) {
-      SETref_(neighbor)= NULL;  /* samecycle neighbors deleted */
-      delneighbors++;
-    }else
-      neighbor->visitid= qh visit_id;
-  }
-  qh_setcompact (newfacet->neighbors);
-
-  trace4((qh ferr, "qh_mergecycle_neighbors: update neighbors\n"));
-  FORALLsame_cycle_(samecycle) {
-    FOREACHneighbor_(same) {
-      if (neighbor->visitid == samevisitid)
-	continue;
-      if (neighbor->simplicial) {
-	if (neighbor->visitid != qh visit_id) {
-	  qh_setappend (&newfacet->neighbors, neighbor);
-	  qh_setreplace (neighbor->neighbors, same, newfacet);
-	  newneighbors++;
-	  neighbor->visitid= qh visit_id;
-	  FOREACHridge_(neighbor->ridges) { /* update ridge in case of qh_makeridges */
-	    if (ridge->top == same) {
-	      ridge->top= newfacet;
-	      break;
-	    }else if (ridge->bottom == same) {
-	      ridge->bottom= newfacet;
-	      break;
-	    }
-	  }
-	}else {
-	  qh_makeridges (neighbor);
-	  qh_setdel (neighbor->neighbors, same);
-	  /* same can't be horizon facet for neighbor */
-	}
-      }else { /* non-simplicial neighbor */
-        qh_setdel (neighbor->neighbors, same);
-        if (neighbor->visitid != qh visit_id) {
-          qh_setappend (&neighbor->neighbors, newfacet);
-          qh_setappend (&newfacet->neighbors, neighbor);
-          neighbor->visitid= qh visit_id;
-          newneighbors++;
-        }
-      }
-    }
-  }
-  trace2((qh ferr, "qh_mergecycle_neighbors: deleted %d neighbors and added %d\n",
-             delneighbors, newneighbors));
-} /* mergecycle_neighbors */
-
-/*---------------------------------
-
-  qh_mergecycle_ridges( samecycle, newfacet )
-    add ridges/neighbors for facets in samecycle to newfacet
-    all new/old neighbors of newfacet marked with qh.visit_id
-    facets in samecycle marked with qh.visit_id-1
-    newfacet marked with qh.visit_id
-
-  returns:
-    newfacet has merged ridges
-
-  notes:
-    ridge already updated for simplicial neighbors of samecycle with a ridge
-
-  see:
-    qh_mergeridges()
-    qh_makeridges()
-
-  design:
-    remove ridges between newfacet and samecycle
-    for each facet in samecycle
-      for each ridge in facet
-        update facet pointers in ridge
-        skip ridges processed in qh_mergecycle_neighors
-        free ridges between newfacet and samecycle
-        free ridges between facets of samecycle (on 2nd visit)
-        append remaining ridges to newfacet
-      if simpilicial facet
-        for each neighbor of facet
-          if simplicial facet
-          and not samecycle facet or newfacet
-            make ridge between neighbor and newfacet
-*/
-void qh_mergecycle_ridges(facetT *samecycle, facetT *newfacet) {
-  facetT *same, *neighbor= NULL;
-  int numold=0, numnew=0;
-  int neighbor_i, neighbor_n;
-  unsigned int samevisitid;
-  ridgeT *ridge, **ridgep;
-  boolT toporient;
-  void **freelistp; /* used !qh_NOmem */
-
-  trace4((qh ferr, "qh_mergecycle_ridges: delete shared ridges from newfacet\n"));
-  samevisitid= qh visit_id -1;
-  FOREACHridge_(newfacet->ridges) {
-    neighbor= otherfacet_(ridge, newfacet);
-    if (neighbor->visitid == samevisitid)
-      SETref_(ridge)= NULL; /* ridge free'd below */
-  }
-  qh_setcompact (newfacet->ridges);
-
-  trace4((qh ferr, "qh_mergecycle_ridges: add ridges to newfacet\n"));
-  FORALLsame_cycle_(samecycle) {
-    FOREACHridge_(same->ridges) {
-      if (ridge->top == same) {
-        ridge->top= newfacet;
-	neighbor= ridge->bottom;
-      }else if (ridge->bottom == same) {
-	ridge->bottom= newfacet;
-	neighbor= ridge->top;
-      }else if (ridge->top == newfacet || ridge->bottom == newfacet) {
-        qh_setappend (&newfacet->ridges, ridge);
-        numold++;  /* already set by qh_mergecycle_neighbors */
-	continue;
-      }else {
-	fprintf (qh ferr, "qhull internal error (qh_mergecycle_ridges): bad ridge r%d\n", ridge->id);
-	qh_errexit (qh_ERRqhull, NULL, ridge);
-      }
-      if (neighbor == newfacet) {
-        qh_setfree(&(ridge->vertices));
-        qh_memfree_(ridge, sizeof(ridgeT), freelistp);
-        numold++;
-      }else if (neighbor->visitid == samevisitid) {
-	qh_setdel (neighbor->ridges, ridge);
-	qh_setfree(&(ridge->vertices));
-	qh_memfree_(ridge, sizeof(ridgeT), freelistp);
-	numold++;
-      }else {
-        qh_setappend (&newfacet->ridges, ridge);
-        numold++;
-      }
-    }
-    if (same->ridges)
-      qh_settruncate (same->ridges, 0);
-    if (!same->simplicial)
-      continue;
-    FOREACHneighbor_i_(same) {       /* note: !newfact->simplicial */
-      if (neighbor->visitid != samevisitid && neighbor->simplicial) {
-        ridge= qh_newridge();
-        ridge->vertices= qh_setnew_delnthsorted (same->vertices, qh hull_dim,
-  					                  neighbor_i, 0);
-        toporient= same->toporient ^ (neighbor_i & 0x1);
-        if (toporient) {
-          ridge->top= newfacet;
-          ridge->bottom= neighbor;
-        }else {
-          ridge->top= neighbor;
-          ridge->bottom= newfacet;
-        }
-        qh_setappend(&(newfacet->ridges), ridge);
-        qh_setappend(&(neighbor->ridges), ridge);
-        numnew++;
-      }
-    }
-  }
-
-  trace2((qh ferr, "qh_mergecycle_ridges: found %d old ridges and %d new ones\n",
-             numold, numnew));
-} /* mergecycle_ridges */
-
-/*---------------------------------
-
-  qh_mergecycle_vneighbors( samecycle, newfacet )
-    create vertex neighbors for newfacet from vertices of facets in samecycle
-    samecycle marked with visitid == qh.visit_id - 1
-
-  returns:
-    newfacet vertices with updated neighbors
-    marks newfacet with qh.visit_id-1
-    deletes vertices that are merged away
-    sets delridge on all vertices (faster here than in mergecycle_ridges)
-
-  see:
-    qh_mergevertex_neighbors()
-
-  design:
-    for each vertex of samecycle facet
-      set vertex->delridge
-      delete samecycle facets from vertex neighbors
-      append newfacet to vertex neighbors
-      if vertex only in newfacet
-        delete it from newfacet
-        add it to qh.del_vertices for later deletion
-*/
-void qh_mergecycle_vneighbors (facetT *samecycle, facetT *newfacet) {
-  facetT *neighbor, **neighborp;
-  unsigned int mergeid;
-  vertexT *vertex, **vertexp, *apex;
-  setT *vertices;
-
-  trace4((qh ferr, "qh_mergecycle_vneighbors: update vertex neighbors for newfacet\n"));
-  mergeid= qh visit_id - 1;
-  newfacet->visitid= mergeid;
-  vertices= qh_basevertices (samecycle); /* temp */
-  apex= SETfirstt_(samecycle->vertices, vertexT);
-  qh_setappend (&vertices, apex);
-  FOREACHvertex_(vertices) {
-    vertex->delridge= True;
-    FOREACHneighbor_(vertex) {
-      if (neighbor->visitid == mergeid)
-        SETref_(neighbor)= NULL;
-    }
-    qh_setcompact (vertex->neighbors);
-    qh_setappend (&vertex->neighbors, newfacet);
-    if (!SETsecond_(vertex->neighbors)) {
-      zinc_(Zcyclevertex);
-      trace2((qh ferr, "qh_mergecycle_vneighbors: deleted v%d when merging cycle f%d into f%d\n",
-        vertex->id, samecycle->id, newfacet->id));
-      qh_setdelsorted (newfacet->vertices, vertex);
-      vertex->deleted= True;
-      qh_setappend (&qh del_vertices, vertex);
-    }
-  }
-  qh_settempfree (&vertices);
-  trace3((qh ferr, "qh_mergecycle_vneighbors: merged vertices from cycle f%d into f%d\n",
-             samecycle->id, newfacet->id));
-} /* mergecycle_vneighbors */
-
-/*---------------------------------
-
-  qh_mergefacet( facet1, facet2, mindist, maxdist, mergeapex )
-    merges facet1 into facet2
-    mergeapex==qh_MERGEapex if merging new facet into coplanar horizon
-
-  returns:
-    qh.max_outside and qh.min_vertex updated
-    initializes vertex neighbors on first merge
-
-  returns:
-    facet2 contains facet1's vertices, neighbors, and ridges
-      facet2 moved to end of qh.facet_list
-      makes facet2 a newfacet
-      sets facet2->newmerge set
-      clears facet2->center (unless merging into a large facet)
-      clears facet2->tested and ridge->tested for facet1
-
-    facet1 prepended to visible_list for later deletion and partitioning
-      facet1->f.replace == facet2
-
-    adds neighboring facets to facet_mergeset if redundant or degenerate
-
-  notes:
-    mindist/maxdist may be NULL
-    traces merge if fmax_(maxdist,-mindist) > TRACEdist
-
-  see:
-    qh_mergecycle()
-
-  design:
-    trace merge and check for degenerate simplex
-    make ridges for both facets
-    update qh.max_outside, qh.max_vertex, qh.min_vertex
-    update facet2->maxoutside and keepcentrum
-    update facet2->nummerge
-    update tested flags for facet2
-    if facet1 is simplicial
-      merge facet1 into facet2
-    else
-      merge facet1's neighbors into facet2
-      merge facet1's ridges into facet2
-      merge facet1's vertices into facet2
-      merge facet1's vertex neighbors into facet2
-      add facet2's vertices to qh.new_vertexlist
-      unless qh_MERGEapex
-        test facet2 for degenerate or redundant neighbors
-      move facet1 to qh.visible_list for later deletion
-      move facet2 to end of qh.newfacet_list
-*/
-void qh_mergefacet(facetT *facet1, facetT *facet2, realT *mindist, realT *maxdist, boolT mergeapex) {
-  boolT traceonce= False;
-  vertexT *vertex, **vertexp;
-  int tracerestore=0, nummerge;
-
-  if (facet1->tricoplanar || facet2->tricoplanar) {
-    if (!qh TRInormals) {
-      fprintf (qh ferr, "qh_mergefacet: does not work for tricoplanar facets.  Use option 'Q11'\n");
-      qh_errexit2 (qh_ERRqhull, facet1, facet2);
-    }
-    if (facet2->tricoplanar) {
-      facet2->tricoplanar= False;
-      facet2->keepcentrum= False;
-    }
-  }
-  zzinc_(Ztotmerge);
-  if (qh REPORTfreq2 && qh POSTmerging) {
-    if (zzval_(Ztotmerge) > qh mergereport + qh REPORTfreq2)
-      qh_tracemerging();
-  }
-#ifndef qh_NOtrace
-  if (qh build_cnt >= qh RERUN) {
-    if (mindist && (-*mindist > qh TRACEdist || *maxdist > qh TRACEdist)) {
-      tracerestore= 0;
-      qh IStracing= qh TRACElevel;
-      traceonce= True;
-      fprintf (qh ferr, "qh_mergefacet: ========= trace wide merge #%d (%2.2g) for f%d into f%d, last point was p%d\n", zzval_(Ztotmerge),
-	     fmax_(-*mindist, *maxdist), facet1->id, facet2->id, qh furthest_id);
-    }else if (facet1 == qh tracefacet || facet2 == qh tracefacet) {
-      tracerestore= qh IStracing;
-      qh IStracing= 4;
-      traceonce= True;
-      fprintf (qh ferr, "qh_mergefacet: ========= trace merge #%d involving f%d, furthest is p%d\n",
-		 zzval_(Ztotmerge), qh tracefacet_id,  qh furthest_id);
-    }
-  }
-  if (qh IStracing >= 2) {
-    realT mergemin= -2;
-    realT mergemax= -2;
-
-    if (mindist) {
-      mergemin= *mindist;
-      mergemax= *maxdist;
-    }
-    fprintf (qh ferr, "qh_mergefacet: #%d merge f%d into f%d, mindist= %2.2g, maxdist= %2.2g\n",
-    zzval_(Ztotmerge), facet1->id, facet2->id, mergemin, mergemax);
-  }
-#endif /* !qh_NOtrace */
-  if (facet1 == facet2 || facet1->visible || facet2->visible) {
-    fprintf (qh ferr, "qhull internal error (qh_mergefacet): either f%d and f%d are the same or one is a visible facet\n",
-	     facet1->id, facet2->id);
-    qh_errexit2 (qh_ERRqhull, facet1, facet2);
-  }
-  if (qh num_facets - qh num_visible <= qh hull_dim + 1) {
-    fprintf(qh ferr, "\n\
-qhull precision error: Only %d facets remain.  Can not merge another\n\
-pair.  The input is too degenerate or the convexity constraints are\n\
-too strong.\n", qh hull_dim+1);
-    if (qh hull_dim >= 5 && !qh MERGEexact)
-      fprintf(qh ferr, "Option 'Qx' may avoid this problem.\n");
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  if (!qh VERTEXneighbors)
-    qh_vertexneighbors();
-  qh_makeridges(facet1);
-  qh_makeridges(facet2);
-  if (qh IStracing >=4)
-    qh_errprint ("MERGING", facet1, facet2, NULL, NULL);
-  if (mindist) {
-    maximize_(qh max_outside, *maxdist);
-    maximize_(qh max_vertex, *maxdist);
-#if qh_MAXoutside
-    maximize_(facet2->maxoutside, *maxdist);
-#endif
-    minimize_(qh min_vertex, *mindist);
-    if (!facet2->keepcentrum
-    && (*maxdist > qh WIDEfacet || *mindist < -qh WIDEfacet)) {
-      facet2->keepcentrum= True;
-      zinc_(Zwidefacet);
-    }
-  }
-  nummerge= facet1->nummerge + facet2->nummerge + 1;
-  if (nummerge >= qh_MAXnummerge)
-    facet2->nummerge= qh_MAXnummerge;
-  else
-    facet2->nummerge= nummerge;
-  facet2->newmerge= True;
-  facet2->dupridge= False;
-  qh_updatetested  (facet1, facet2);
-  if (qh hull_dim > 2 && qh_setsize (facet1->vertices) == qh hull_dim)
-    qh_mergesimplex (facet1, facet2, mergeapex);
-  else {
-    qh vertex_visit++;
-    FOREACHvertex_(facet2->vertices)
-      vertex->visitid= qh vertex_visit;
-    if (qh hull_dim == 2)
-      qh_mergefacet2d(facet1, facet2);
-    else {
-      qh_mergeneighbors(facet1, facet2);
-      qh_mergevertices(facet1->vertices, &facet2->vertices);
-    }
-    qh_mergeridges(facet1, facet2);
-    qh_mergevertex_neighbors(facet1, facet2);
-    if (!facet2->newfacet)
-      qh_newvertices (facet2->vertices);
-  }
-  if (!mergeapex)
-    qh_degen_redundant_neighbors (facet2, facet1);
-  if (facet2->coplanar || !facet2->newfacet) {
-    zinc_(Zmergeintohorizon);
-  }else if (!facet1->newfacet && facet2->newfacet) {
-    zinc_(Zmergehorizon);
-  }else {
-    zinc_(Zmergenew);
-  }
-  qh_willdelete (facet1, facet2);
-  qh_removefacet(facet2);  /* append as a newfacet to end of qh facet_list */
-  qh_appendfacet(facet2);
-  facet2->newfacet= True;
-  facet2->tested= False;
-  qh_tracemerge (facet1, facet2);
-  if (traceonce) {
-    fprintf (qh ferr, "qh_mergefacet: end of wide tracing\n");
-    qh IStracing= tracerestore;
-  }
-} /* mergefacet */
-
-
-/*---------------------------------
-
-  qh_mergefacet2d( facet1, facet2 )
-    in 2d, merges neighbors and vertices of facet1 into facet2
-
-  returns:
-    build ridges for neighbors if necessary
-    facet2 looks like a simplicial facet except for centrum, ridges
-      neighbors are opposite the corresponding vertex
-      maintains orientation of facet2
-
-  notes:
-    qh_mergefacet() retains non-simplicial structures
-      they are not needed in 2d, but later routines may use them
-    preserves qh.vertex_visit for qh_mergevertex_neighbors()
-
-  design:
-    get vertices and neighbors
-    determine new vertices and neighbors
-    set new vertices and neighbors and adjust orientation
-    make ridges for new neighbor if needed
-*/
-void qh_mergefacet2d (facetT *facet1, facetT *facet2) {
-  vertexT *vertex1A, *vertex1B, *vertex2A, *vertex2B, *vertexA, *vertexB;
-  facetT *neighbor1A, *neighbor1B, *neighbor2A, *neighbor2B, *neighborA, *neighborB;
-
-  vertex1A= SETfirstt_(facet1->vertices, vertexT);
-  vertex1B= SETsecondt_(facet1->vertices, vertexT);
-  vertex2A= SETfirstt_(facet2->vertices, vertexT);
-  vertex2B= SETsecondt_(facet2->vertices, vertexT);
-  neighbor1A= SETfirstt_(facet1->neighbors, facetT);
-  neighbor1B= SETsecondt_(facet1->neighbors, facetT);
-  neighbor2A= SETfirstt_(facet2->neighbors, facetT);
-  neighbor2B= SETsecondt_(facet2->neighbors, facetT);
-  if (vertex1A == vertex2A) {
-    vertexA= vertex1B;
-    vertexB= vertex2B;
-    neighborA= neighbor2A;
-    neighborB= neighbor1A;
-  }else if (vertex1A == vertex2B) {
-    vertexA= vertex1B;
-    vertexB= vertex2A;
-    neighborA= neighbor2B;
-    neighborB= neighbor1A;
-  }else if (vertex1B == vertex2A) {
-    vertexA= vertex1A;
-    vertexB= vertex2B;
-    neighborA= neighbor2A;
-    neighborB= neighbor1B;
-  }else { /* 1B == 2B */
-    vertexA= vertex1A;
-    vertexB= vertex2A;
-    neighborA= neighbor2B;
-    neighborB= neighbor1B;
-  }
-  /* vertexB always from facet2, neighborB always from facet1 */
-  if (vertexA->id > vertexB->id) {
-    SETfirst_(facet2->vertices)= vertexA;
-    SETsecond_(facet2->vertices)= vertexB;
-    if (vertexB == vertex2A)
-      facet2->toporient= !facet2->toporient;
-    SETfirst_(facet2->neighbors)= neighborA;
-    SETsecond_(facet2->neighbors)= neighborB;
-  }else {
-    SETfirst_(facet2->vertices)= vertexB;
-    SETsecond_(facet2->vertices)= vertexA;
-    if (vertexB == vertex2B)
-      facet2->toporient= !facet2->toporient;
-    SETfirst_(facet2->neighbors)= neighborB;
-    SETsecond_(facet2->neighbors)= neighborA;
-  }
-  qh_makeridges (neighborB);
-  qh_setreplace(neighborB->neighbors, facet1, facet2);
-  trace4((qh ferr, "qh_mergefacet2d: merged v%d and neighbor f%d of f%d into f%d\n",
-       vertexA->id, neighborB->id, facet1->id, facet2->id));
-} /* mergefacet2d */
-
-
-/*---------------------------------
-
-  qh_mergeneighbors( facet1, facet2 )
-    merges the neighbors of facet1 into facet2
-
-  see:
-    qh_mergecycle_neighbors()
-
-  design:
-    for each neighbor of facet1
-      if neighbor is also a neighbor of facet2
-        if neighbor is simpilicial
-          make ridges for later deletion as a degenerate facet
-        update its neighbor set
-      else
-        move the neighbor relation to facet2
-    remove the neighbor relation for facet1 and facet2
-*/
-void qh_mergeneighbors(facetT *facet1, facetT *facet2) {
-  facetT *neighbor, **neighborp;
-
-  trace4((qh ferr, "qh_mergeneighbors: merge neighbors of f%d and f%d\n",
-	  facet1->id, facet2->id));
-  qh visit_id++;
-  FOREACHneighbor_(facet2) {
-    neighbor->visitid= qh visit_id;
-  }
-  FOREACHneighbor_(facet1) {
-    if (neighbor->visitid == qh visit_id) {
-      if (neighbor->simplicial)    /* is degen, needs ridges */
-	qh_makeridges (neighbor);
-      if (SETfirstt_(neighbor->neighbors, facetT) != facet1) /*keep newfacet->horizon*/
-	qh_setdel (neighbor->neighbors, facet1);
-      else {
-        qh_setdel(neighbor->neighbors, facet2);
-        qh_setreplace(neighbor->neighbors, facet1, facet2);
-      }
-    }else if (neighbor != facet2) {
-      qh_setappend(&(facet2->neighbors), neighbor);
-      qh_setreplace(neighbor->neighbors, facet1, facet2);
-    }
-  }
-  qh_setdel(facet1->neighbors, facet2);  /* here for makeridges */
-  qh_setdel(facet2->neighbors, facet1);
-} /* mergeneighbors */
-
-
-/*---------------------------------
-
-  qh_mergeridges( facet1, facet2 )
-    merges the ridge set of facet1 into facet2
-
-  returns:
-    may delete all ridges for a vertex
-    sets vertex->delridge on deleted ridges
-
-  see:
-    qh_mergecycle_ridges()
-
-  design:
-    delete ridges between facet1 and facet2
-      mark (delridge) vertices on these ridges for later testing
-    for each remaining ridge
-      rename facet1 to facet2
-*/
-void qh_mergeridges(facetT *facet1, facetT *facet2) {
-  ridgeT *ridge, **ridgep;
-  vertexT *vertex, **vertexp;
-
-  trace4((qh ferr, "qh_mergeridges: merge ridges of f%d and f%d\n",
-	  facet1->id, facet2->id));
-  FOREACHridge_(facet2->ridges) {
-    if ((ridge->top == facet1) || (ridge->bottom == facet1)) {
-      FOREACHvertex_(ridge->vertices)
-        vertex->delridge= True;
-      qh_delridge(ridge);  /* expensive in high-d, could rebuild */
-      ridgep--; /*repeat*/
-    }
-  }
-  FOREACHridge_(facet1->ridges) {
-    if (ridge->top == facet1)
-      ridge->top= facet2;
-    else
-      ridge->bottom= facet2;
-    qh_setappend(&(facet2->ridges), ridge);
-  }
-} /* mergeridges */
-
-
-/*---------------------------------
-
-  qh_mergesimplex( facet1, facet2, mergeapex )
-    merge simplicial facet1 into facet2
-    mergeapex==qh_MERGEapex if merging samecycle into horizon facet
-      vertex id is latest (most recently created)
-    facet1 may be contained in facet2
-    ridges exist for both facets
-
-  returns:
-    facet2 with updated vertices, ridges, neighbors
-    updated neighbors for facet1's vertices
-    facet1 not deleted
-    sets vertex->delridge on deleted ridges
-
-  notes:
-    special case code since this is the most common merge
-    called from qh_mergefacet()
-
-  design:
-    if qh_MERGEapex
-      add vertices of facet2 to qh.new_vertexlist if necessary
-    else
-      for each ridge between facet1 and facet2
-        set vertex->delridge
-      determine the apex for facet1 (i.e., vertex to be merged)
-      unless apex already in facet2
-        insert apex into vertices for facet2
-      add vertices of facet2 to qh.new_vertexlist if necessary
-      add apex to qh.new_vertexlist if necessary
-      for each vertex of facet1
-        if apex
-          rename facet1 to facet2 in its vertex neighbors
-        else
-          delete facet1 from vertex neighors
-          if only in facet2
-            add vertex to qh.del_vertices for later deletion
-      for each ridge of facet1
-        delete ridges between facet1 and facet2
-        append other ridges to facet2 after renaming facet to facet2
-*/
-void qh_mergesimplex(facetT *facet1, facetT *facet2, boolT mergeapex) {
-  vertexT *vertex, **vertexp, *apex;
-  ridgeT *ridge, **ridgep;
-  boolT issubset= False;
-  int vertex_i= -1, vertex_n;
-  facetT *neighbor, **neighborp, *otherfacet;
-
-  if (mergeapex) {
-    if (!facet2->newfacet)
-      qh_newvertices (facet2->vertices);  /* apex is new */
-    apex= SETfirstt_(facet1->vertices, vertexT);
-    if (SETfirstt_(facet2->vertices, vertexT) != apex)
-      qh_setaddnth (&facet2->vertices, 0, apex);  /* apex has last id */
-    else
-      issubset= True;
-  }else {
-    zinc_(Zmergesimplex);
-    FOREACHvertex_(facet1->vertices)
-      vertex->seen= False;
-    FOREACHridge_(facet1->ridges) {
-      if (otherfacet_(ridge, facet1) == facet2) {
-	FOREACHvertex_(ridge->vertices) {
-	  vertex->seen= True;
-	  vertex->delridge= True;
-	}
-	break;
-      }
-    }
-    FOREACHvertex_(facet1->vertices) {
-      if (!vertex->seen)
-	break;  /* must occur */
-    }
-    apex= vertex;
-    trace4((qh ferr, "qh_mergesimplex: merge apex v%d of f%d into facet f%d\n",
-	  apex->id, facet1->id, facet2->id));
-    FOREACHvertex_i_(facet2->vertices) {
-      if (vertex->id < apex->id) {
-	break;
-      }else if (vertex->id == apex->id) {
-	issubset= True;
-	break;
-      }
-    }
-    if (!issubset)
-    if (!facet2->newfacet)
-      qh_newvertices (facet2->vertices);
-    else if (!apex->newlist) {
-      qh_removevertex (apex);
-      qh_appendvertex (apex);
-    }
-  }
-  trace4((qh ferr, "qh_mergesimplex: update vertex neighbors of f%d\n",
-	  facet1->id));
-  FOREACHvertex_(facet1->vertices) {
-    if (vertex == apex && !issubset)
-      qh_setreplace (vertex->neighbors, facet1, facet2);
-    else {
-      qh_setdel (vertex->neighbors, facet1);
-      if (!SETsecond_(vertex->neighbors))
-	qh_mergevertex_del (vertex, facet1, facet2);
-    }
-  }
-  trace4((qh ferr, "qh_mergesimplex: merge ridges and neighbors of f%d into f%d\n",
-	  facet1->id, facet2->id));
-  qh visit_id++;
-  FOREACHneighbor_(facet2)
-    neighbor->visitid= qh visit_id;
-  FOREACHridge_(facet1->ridges) {
-    otherfacet= otherfacet_(ridge, facet1);
-    if (otherfacet == facet2) {
-      qh_setdel (facet2->ridges, ridge);
-      qh_setfree(&(ridge->vertices));
-      qh_memfree (ridge, sizeof(ridgeT));
-      qh_setdel (facet2->neighbors, facet1);
-    }else {
-      qh_setappend (&facet2->ridges, ridge);
-      if (otherfacet->visitid != qh visit_id) {
-	qh_setappend (&facet2->neighbors, otherfacet);
-	qh_setreplace (otherfacet->neighbors, facet1, facet2);
-	otherfacet->visitid= qh visit_id;
-      }else {
-	if (otherfacet->simplicial)    /* is degen, needs ridges */
-	  qh_makeridges (otherfacet);
-	if (SETfirstt_(otherfacet->neighbors, facetT) != facet1)
-	  qh_setdel (otherfacet->neighbors, facet1);
-	else {   /*keep newfacet->neighbors->horizon*/
-	  qh_setdel(otherfacet->neighbors, facet2);
-	  qh_setreplace(otherfacet->neighbors, facet1, facet2);
-	}
-      }
-      if (ridge->top == facet1) /* wait until after qh_makeridges */
-	ridge->top= facet2;
-      else
-	ridge->bottom= facet2;
-    }
-  }
-  SETfirst_(facet1->ridges)= NULL; /* it will be deleted */
-  trace3((qh ferr, "qh_mergesimplex: merged simplex f%d apex v%d into facet f%d\n",
-	  facet1->id, getid_(apex), facet2->id));
-} /* mergesimplex */
-
-/*---------------------------------
-
-  qh_mergevertex_del( vertex, facet1, facet2 )
-    delete a vertex because of merging facet1 into facet2
-
-  returns:
-    deletes vertex from facet2
-    adds vertex to qh.del_vertices for later deletion
-*/
-void qh_mergevertex_del (vertexT *vertex, facetT *facet1, facetT *facet2) {
-
-  zinc_(Zmergevertex);
-  trace2((qh ferr, "qh_mergevertex_del: deleted v%d when merging f%d into f%d\n",
-          vertex->id, facet1->id, facet2->id));
-  qh_setdelsorted (facet2->vertices, vertex);
-  vertex->deleted= True;
-  qh_setappend (&qh del_vertices, vertex);
-} /* mergevertex_del */
-
-/*---------------------------------
-
-  qh_mergevertex_neighbors( facet1, facet2 )
-    merge the vertex neighbors of facet1 to facet2
-
-  returns:
-    if vertex is current qh.vertex_visit
-      deletes facet1 from vertex->neighbors
-    else
-      renames facet1 to facet2 in vertex->neighbors
-    deletes vertices if only one neighbor
-
-  notes:
-    assumes vertex neighbor sets are good
-*/
-void qh_mergevertex_neighbors(facetT *facet1, facetT *facet2) {
-  vertexT *vertex, **vertexp;
-
-  trace4((qh ferr, "qh_mergevertex_neighbors: merge vertex neighbors of f%d and f%d\n",
-	  facet1->id, facet2->id));
-  if (qh tracevertex) {
-    fprintf (qh ferr, "qh_mergevertex_neighbors: of f%d and f%d at furthest p%d f0= %p\n",
-	     facet1->id, facet2->id, qh furthest_id, qh tracevertex->neighbors->e[0].p);
-    qh_errprint ("TRACE", NULL, NULL, NULL, qh tracevertex);
-  }
-  FOREACHvertex_(facet1->vertices) {
-    if (vertex->visitid != qh vertex_visit)
-      qh_setreplace(vertex->neighbors, facet1, facet2);
-    else {
-      qh_setdel(vertex->neighbors, facet1);
-      if (!SETsecond_(vertex->neighbors))
-	qh_mergevertex_del (vertex, facet1, facet2);
-    }
-  }
-  if (qh tracevertex)
-    qh_errprint ("TRACE", NULL, NULL, NULL, qh tracevertex);
-} /* mergevertex_neighbors */
-
-
-/*---------------------------------
-
-  qh_mergevertices( vertices1, vertices2 )
-    merges the vertex set of facet1 into facet2
-
-  returns:
-    replaces vertices2 with merged set
-    preserves vertex_visit for qh_mergevertex_neighbors
-
-  design:
-    create a merged set of both vertices (in inverse id order)
-*/
-void qh_mergevertices(setT *vertices1, setT **vertices2) {
-  int newsize= qh_setsize(vertices1)+qh_setsize(*vertices2) - qh hull_dim + 1;
-  setT *mergedvertices;
-  vertexT *vertex, **vertexp, **vertex2= SETaddr_(*vertices2, vertexT);
-
-  mergedvertices= qh_settemp (newsize);
-  FOREACHvertex_(vertices1) {
-    if (!*vertex2 || vertex->id > (*vertex2)->id)
-      qh_setappend (&mergedvertices, vertex);
-    else {
-      while (*vertex2 && (*vertex2)->id > vertex->id)
-	qh_setappend (&mergedvertices, *vertex2++);
-      if (!*vertex2 || (*vertex2)->id < vertex->id)
-	qh_setappend (&mergedvertices, vertex);
-      else
-	qh_setappend (&mergedvertices, *vertex2++);
-    }
-  }
-  while (*vertex2)
-    qh_setappend (&mergedvertices, *vertex2++);
-  if (newsize < qh_setsize (mergedvertices)) {
-    fprintf (qh ferr, "qhull internal error (qh_mergevertices): facets did not share a ridge\n");
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }
-  qh_setfree(vertices2);
-  *vertices2= mergedvertices;
-  qh_settemppop ();
-} /* mergevertices */
-
-
-/*---------------------------------
-
-  qh_neighbor_intersections( vertex )
-    return intersection of all vertices in vertex->neighbors except for vertex
-
-  returns:
-    returns temporary set of vertices
-    does not include vertex
-    NULL if a neighbor is simplicial
-    NULL if empty set
-
-  notes:
-    used for renaming vertices
-
-  design:
-    initialize the intersection set with vertices of the first two neighbors
-    delete vertex from the intersection
-    for each remaining neighbor
-      intersect its vertex set with the intersection set
-      return NULL if empty
-    return the intersection set
-*/
-setT *qh_neighbor_intersections (vertexT *vertex) {
-  facetT *neighbor, **neighborp, *neighborA, *neighborB;
-  setT *intersect;
-  int neighbor_i, neighbor_n;
-
-  FOREACHneighbor_(vertex) {
-    if (neighbor->simplicial)
-      return NULL;
-  }
-  neighborA= SETfirstt_(vertex->neighbors, facetT);
-  neighborB= SETsecondt_(vertex->neighbors, facetT);
-  zinc_(Zintersectnum);
-  if (!neighborA)
-    return NULL;
-  if (!neighborB)
-    intersect= qh_setcopy (neighborA->vertices, 0);
-  else
-    intersect= qh_vertexintersect_new (neighborA->vertices, neighborB->vertices);
-  qh_settemppush (intersect);
-  qh_setdelsorted (intersect, vertex);
-  FOREACHneighbor_i_(vertex) {
-    if (neighbor_i >= 2) {
-      zinc_(Zintersectnum);
-      qh_vertexintersect (&intersect, neighbor->vertices);
-      if (!SETfirst_(intersect)) {
-        zinc_(Zintersectfail);
-        qh_settempfree (&intersect);
-        return NULL;
-      }
-    }
-  }
-  trace3((qh ferr, "qh_neighbor_intersections: %d vertices in neighbor intersection of v%d\n",
-          qh_setsize (intersect), vertex->id));
-  return intersect;
-} /* neighbor_intersections */
-
-/*---------------------------------
-
-  qh_newvertices( vertices )
-    add vertices to end of qh.vertex_list (marks as new vertices)
-
-  returns:
-    vertices on qh.newvertex_list
-    vertex->newlist set
-*/
-void qh_newvertices (setT *vertices) {
-  vertexT *vertex, **vertexp;
-
-  FOREACHvertex_(vertices) {
-    if (!vertex->newlist) {
-      qh_removevertex (vertex);
-      qh_appendvertex (vertex);
-    }
-  }
-} /* newvertices */
-
-/*---------------------------------
-
-  qh_reducevertices()
-    reduce extra vertices, shared vertices, and redundant vertices
-    facet->newmerge is set if merged since last call
-    if !qh.MERGEvertices, only removes extra vertices
-
-  returns:
-    True if also merged degen_redundant facets
-    vertices are renamed if possible
-    clears facet->newmerge and vertex->delridge
-
-  notes:
-    ignored if 2-d
-
-  design:
-    merge any degenerate or redundant facets
-    for each newly merged facet
-      remove extra vertices
-    if qh.MERGEvertices
-      for each newly merged facet
-        for each vertex
-          if vertex was on a deleted ridge
-            rename vertex if it is shared
-      remove delridge flag from new vertices
-*/
-boolT qh_reducevertices (void) {
-  int numshare=0, numrename= 0;
-  boolT degenredun= False;
-  facetT *newfacet;
-  vertexT *vertex, **vertexp;
-
-  if (qh hull_dim == 2)
-    return False;
-  if (qh_merge_degenredundant())
-    degenredun= True;
- LABELrestart:
-  FORALLnew_facets {
-    if (newfacet->newmerge) {
-      if (!qh MERGEvertices)
-        newfacet->newmerge= False;
-      qh_remove_extravertices (newfacet);
-    }
-  }
-  if (!qh MERGEvertices)
-    return False;
-  FORALLnew_facets {
-    if (newfacet->newmerge) {
-      newfacet->newmerge= False;
-      FOREACHvertex_(newfacet->vertices) {
-	if (vertex->delridge) {
-	  if (qh_rename_sharedvertex (vertex, newfacet)) {
-	    numshare++;
-	    vertexp--; /* repeat since deleted vertex */
-	  }
-        }
-      }
-    }
-  }
-  FORALLvertex_(qh newvertex_list) {
-    if (vertex->delridge && !vertex->deleted) {
-      vertex->delridge= False;
-      if (qh hull_dim >= 4 && qh_redundant_vertex (vertex)) {
-	numrename++;
-	if (qh_merge_degenredundant()) {
-	  degenredun= True;
-	  goto LABELrestart;
-	}
-      }
-    }
-  }
-  trace1((qh ferr, "qh_reducevertices: renamed %d shared vertices and %d redundant vertices. Degen? %d\n",
-	  numshare, numrename, degenredun));
-  return degenredun;
-} /* reducevertices */
-
-/*---------------------------------
-
-  qh_redundant_vertex( vertex )
-    detect and rename a redundant vertex
-    vertices have full vertex->neighbors
-
-  returns:
-    returns true if find a redundant vertex
-      deletes vertex (vertex->deleted)
-
-  notes:
-    only needed if vertex->delridge and hull_dim >= 4
-    may add degenerate facets to qh.facet_mergeset
-    doesn't change vertex->neighbors or create redundant facets
-
-  design:
-    intersect vertices of all facet neighbors of vertex
-    determine ridges for these vertices
-    if find a new vertex for vertex amoung these ridges and vertices
-      rename vertex to the new vertex
-*/
-vertexT *qh_redundant_vertex (vertexT *vertex) {
-  vertexT *newvertex= NULL;
-  setT *vertices, *ridges;
-
-  trace3((qh ferr, "qh_redundant_vertex: check if v%d can be renamed\n", vertex->id));
-  if ((vertices= qh_neighbor_intersections (vertex))) {
-    ridges= qh_vertexridges (vertex);
-    if ((newvertex= qh_find_newvertex (vertex, vertices, ridges)))
-      qh_renamevertex (vertex, newvertex, ridges, NULL, NULL);
-    qh_settempfree (&ridges);
-    qh_settempfree (&vertices);
-  }
-  return newvertex;
-} /* redundant_vertex */
-
-/*---------------------------------
-
-  qh_remove_extravertices( facet )
-    remove extra vertices from non-simplicial facets
-
-  returns:
-    returns True if it finds them
-
-  design:
-    for each vertex in facet
-      if vertex not in a ridge (i.e., no longer used)
-        delete vertex from facet
-        delete facet from vertice's neighbors
-        unless vertex in another facet
-          add vertex to qh.del_vertices for later deletion
-*/
-boolT qh_remove_extravertices (facetT *facet) {
-  ridgeT *ridge, **ridgep;
-  vertexT *vertex, **vertexp;
-  boolT foundrem= False;
-
-  trace4((qh ferr, "qh_remove_extravertices: test f%d for extra vertices\n",
-	  facet->id));
-  FOREACHvertex_(facet->vertices)
-    vertex->seen= False;
-  FOREACHridge_(facet->ridges) {
-    FOREACHvertex_(ridge->vertices)
-      vertex->seen= True;
-  }
-  FOREACHvertex_(facet->vertices) {
-    if (!vertex->seen) {
-      foundrem= True;
-      zinc_(Zremvertex);
-      qh_setdelsorted (facet->vertices, vertex);
-      qh_setdel (vertex->neighbors, facet);
-      if (!qh_setsize (vertex->neighbors)) {
-	vertex->deleted= True;
-	qh_setappend (&qh del_vertices, vertex);
-	zinc_(Zremvertexdel);
-	trace2((qh ferr, "qh_remove_extravertices: v%d deleted because it's lost all ridges\n", vertex->id));
-      }else
-	trace3((qh ferr, "qh_remove_extravertices: v%d removed from f%d because it's lost all ridges\n", vertex->id, facet->id));
-      vertexp--; /*repeat*/
-    }
-  }
-  return foundrem;
-} /* remove_extravertices */
-
-/*---------------------------------
-
-  qh_rename_sharedvertex( vertex, facet )
-    detect and rename if shared vertex in facet
-    vertices have full ->neighbors
-
-  returns:
-    newvertex or NULL
-    the vertex may still exist in other facets (i.e., a neighbor was pinched)
-    does not change facet->neighbors
-
-  notes:
-    a shared vertex for a facet is only in ridges to one neighbor
-    this may undo a pinched facet
-
-    it does not catch pinches involving multiple facets.  These appear
-      to be difficult to detect, since an exhaustive search is too expensive.
-
-  design:
-    if vertex only has two neighbors
-      determine the ridges that contain the vertex
-      determine the vertices shared by both neighbors
-      if can find a new vertex in this set
-        rename the vertex to the new vertex
-*/
-vertexT *qh_rename_sharedvertex (vertexT *vertex, facetT *facet) {
-  facetT *neighbor, **neighborp, *neighborA= NULL;
-  setT *vertices, *ridges;
-  vertexT *newvertex;
-
-  if (qh_setsize (vertex->neighbors) == 2) {
-    neighborA= SETfirstt_(vertex->neighbors, facetT);
-    if (neighborA == facet)
-      neighborA= SETsecondt_(vertex->neighbors, facetT);
-  }else if (qh hull_dim == 3)
-    return NULL;
-  else {
-    qh visit_id++;
-    FOREACHneighbor_(facet)
-      neighbor->visitid= qh visit_id;
-    FOREACHneighbor_(vertex) {
-      if (neighbor->visitid == qh visit_id) {
-        if (neighborA)
-          return NULL;
-        neighborA= neighbor;
-      }
-    }
-    if (!neighborA) {
-      fprintf (qh ferr, "qhull internal error (qh_rename_sharedvertex): v%d's neighbors not in f%d\n",
-        vertex->id, facet->id);
-      qh_errprint ("ERRONEOUS", facet, NULL, NULL, vertex);
-      qh_errexit (qh_ERRqhull, NULL, NULL);
-    }
-  }
-  /* the vertex is shared by facet and neighborA */
-  ridges= qh_settemp (qh TEMPsize);
-  neighborA->visitid= ++qh visit_id;
-  qh_vertexridges_facet (vertex, facet, &ridges);
-  trace2((qh ferr, "qh_rename_sharedvertex: p%d (v%d) is shared by f%d (%d ridges) and f%d\n",
-    qh_pointid(vertex->point), vertex->id, facet->id, qh_setsize (ridges), neighborA->id));
-  zinc_(Zintersectnum);
-  vertices= qh_vertexintersect_new (facet->vertices, neighborA->vertices);
-  qh_setdel (vertices, vertex);
-  qh_settemppush (vertices);
-  if ((newvertex= qh_find_newvertex (vertex, vertices, ridges)))
-    qh_renamevertex (vertex, newvertex, ridges, facet, neighborA);
-  qh_settempfree (&vertices);
-  qh_settempfree (&ridges);
-  return newvertex;
-} /* rename_sharedvertex */
-
-/*---------------------------------
-
-  qh_renameridgevertex( ridge, oldvertex, newvertex )
-    renames oldvertex as newvertex in ridge
-
-  returns:
-
-  design:
-    delete oldvertex from ridge
-    if newvertex already in ridge
-      copy ridge->noconvex to another ridge if possible
-      delete the ridge
-    else
-      insert newvertex into the ridge
-*/
-void qh_renameridgevertex(ridgeT *ridge, vertexT *oldvertex, vertexT *newvertex) {
-  int nth= 0, oldnth;
-  facetT *temp;
-  vertexT *vertex, **vertexp;
-
-  oldnth= qh_setindex (ridge->vertices, oldvertex);
-  qh_setdelnthsorted (ridge->vertices, oldnth);
-  FOREACHvertex_(ridge->vertices) {
-    if (vertex == newvertex) {
-      zinc_(Zdelridge);
-      if (ridge->nonconvex) /* only one ridge has nonconvex set */
-	qh_copynonconvex (ridge);
-      qh_delridge (ridge);
-      trace2((qh ferr, "qh_renameridgevertex: ridge r%d deleted.  It contained both v%d and v%d\n",
-        ridge->id, oldvertex->id, newvertex->id));
-      return;
-    }
-    if (vertex->id < newvertex->id)
-      break;
-    nth++;
-  }
-  if (abs(oldnth - nth)%2) {
-    trace3((qh ferr, "qh_renameridgevertex: swapped the top and bottom of ridge r%d\n",
-	    ridge->id));
-    temp= ridge->top;
-    ridge->top= ridge->bottom;
-    ridge->bottom= temp;
-  }
-} /* renameridgevertex */
-
-
-/*---------------------------------
-
-  qh_renamevertex( oldvertex, newvertex, ridges, oldfacet, neighborA )
-    renames oldvertex as newvertex in ridges
-    gives oldfacet/neighborA if oldvertex is shared between two facets
-
-  returns:
-    oldvertex may still exist afterwards
-
-
-  notes:
-    can not change neighbors of newvertex (since it's a subset)
-
-  design:
-    for each ridge in ridges
-      rename oldvertex to newvertex and delete degenerate ridges
-    if oldfacet not defined
-      for each neighbor of oldvertex
-        delete oldvertex from neighbor's vertices
-        remove extra vertices from neighbor
-    else if oldvertex only between oldfacet and neighborA
-      delete oldvertex from oldfacet and neighborA
-    else oldvertex is in oldfacet and neighborA and other facets (i.e., pinched)
-      delete oldvertex from oldfacet
-      delete oldfacet from oldvertice's neighbors
-      remove extra vertices (e.g., oldvertex) from neighborA
-*/
-void qh_renamevertex(vertexT *oldvertex, vertexT *newvertex, setT *ridges, facetT *oldfacet, facetT *neighborA) {
-  facetT *neighbor, **neighborp;
-  ridgeT *ridge, **ridgep;
-  boolT istrace= False;
-
-  if (qh IStracing >= 2 || oldvertex->id == qh tracevertex_id ||
-	newvertex->id == qh tracevertex_id)
-    istrace= True;
-  FOREACHridge_(ridges)
-    qh_renameridgevertex (ridge, oldvertex, newvertex);
-  if (!oldfacet) {
-    zinc_(Zrenameall);
-    if (istrace)
-      fprintf (qh ferr, "qh_renamevertex: renamed v%d to v%d in several facets\n",
-               oldvertex->id, newvertex->id);
-    FOREACHneighbor_(oldvertex) {
-      qh_maydropneighbor (neighbor);
-      qh_setdelsorted (neighbor->vertices, oldvertex);
-      if (qh_remove_extravertices (neighbor))
-        neighborp--; /* neighbor may be deleted */
-    }
-    if (!oldvertex->deleted) {
-      oldvertex->deleted= True;
-      qh_setappend (&qh del_vertices, oldvertex);
-    }
-  }else if (qh_setsize (oldvertex->neighbors) == 2) {
-    zinc_(Zrenameshare);
-    if (istrace)
-      fprintf (qh ferr, "qh_renamevertex: renamed v%d to v%d in oldfacet f%d\n",
-               oldvertex->id, newvertex->id, oldfacet->id);
-    FOREACHneighbor_(oldvertex)
-      qh_setdelsorted (neighbor->vertices, oldvertex);
-    oldvertex->deleted= True;
-    qh_setappend (&qh del_vertices, oldvertex);
-  }else {
-    zinc_(Zrenamepinch);
-    if (istrace || qh IStracing)
-      fprintf (qh ferr, "qh_renamevertex: renamed pinched v%d to v%d between f%d and f%d\n",
-               oldvertex->id, newvertex->id, oldfacet->id, neighborA->id);
-    qh_setdelsorted (oldfacet->vertices, oldvertex);
-    qh_setdel (oldvertex->neighbors, oldfacet);
-    qh_remove_extravertices (neighborA);
-  }
-} /* renamevertex */
-
-
-/*---------------------------------
-
-  qh_test_appendmerge( facet, neighbor )
-    tests facet/neighbor for convexity
-    appends to mergeset if non-convex
-    if pre-merging,
-      nop if qh.SKIPconvex, or qh.MERGEexact and coplanar
-
-  returns:
-    true if appends facet/neighbor to mergeset
-    sets facet->center as needed
-    does not change facet->seen
-
-  design:
-    if qh.cos_max is defined
-      if the angle between facet normals is too shallow
-        append an angle-coplanar merge to qh.mergeset
-        return True
-    make facet's centrum if needed
-    if facet's centrum is above the neighbor
-      set isconcave
-    else
-      if facet's centrum is not below the neighbor
-        set iscoplanar
-      make neighbor's centrum if needed
-      if neighbor's centrum is above the facet
-        set isconcave
-      else if neighbor's centrum is not below the facet
-        set iscoplanar
-   if isconcave or iscoplanar
-     get angle if needed
-     append concave or coplanar merge to qh.mergeset
-*/
-boolT qh_test_appendmerge (facetT *facet, facetT *neighbor) {
-  realT dist, dist2= -REALmax, angle= -REALmax;
-  boolT isconcave= False, iscoplanar= False, okangle= False;
-
-  if (qh SKIPconvex && !qh POSTmerging)
-    return False;
-  if ((!qh MERGEexact || qh POSTmerging) && qh cos_max < REALmax/2) {
-    angle= qh_getangle(facet->normal, neighbor->normal);
-    zinc_(Zangletests);
-    if (angle > qh cos_max) {
-      zinc_(Zcoplanarangle);
-      qh_appendmergeset(facet, neighbor, MRGanglecoplanar, &angle);
-      trace2((qh ferr, "qh_test_appendmerge: coplanar angle %4.4g between f%d and f%d\n",
-         angle, facet->id, neighbor->id));
-      return True;
-    }else
-      okangle= True;
-  }
-  if (!facet->center)
-    facet->center= qh_getcentrum (facet);
-  zzinc_(Zcentrumtests);
-  qh_distplane(facet->center, neighbor, &dist);
-  if (dist > qh centrum_radius)
-    isconcave= True;
-  else {
-    if (dist > -qh centrum_radius)
-      iscoplanar= True;
-    if (!neighbor->center)
-      neighbor->center= qh_getcentrum (neighbor);
-    zzinc_(Zcentrumtests);
-    qh_distplane(neighbor->center, facet, &dist2);
-    if (dist2 > qh centrum_radius)
-      isconcave= True;
-    else if (!iscoplanar && dist2 > -qh centrum_radius)
-      iscoplanar= True;
-  }
-  if (!isconcave && (!iscoplanar || (qh MERGEexact && !qh POSTmerging)))
-    return False;
-  if (!okangle && qh ANGLEmerge) {
-    angle= qh_getangle(facet->normal, neighbor->normal);
-    zinc_(Zangletests);
-  }
-  if (isconcave) {
-    zinc_(Zconcaveridge);
-    if (qh ANGLEmerge)
-      angle += qh_ANGLEconcave + 0.5;
-    qh_appendmergeset(facet, neighbor, MRGconcave, &angle);
-    trace0((qh ferr, "qh_test_appendmerge: concave f%d to f%d dist %4.4g and reverse dist %4.4g angle %4.4g during p%d\n",
-	   facet->id, neighbor->id, dist, dist2, angle, qh furthest_id));
-  }else /* iscoplanar */ {
-    zinc_(Zcoplanarcentrum);
-    qh_appendmergeset(facet, neighbor, MRGcoplanar, &angle);
-    trace2((qh ferr, "qh_test_appendmerge: coplanar f%d to f%d dist %4.4g, reverse dist %4.4g angle %4.4g\n",
-	      facet->id, neighbor->id, dist, dist2, angle));
-  }
-  return True;
-} /* test_appendmerge */
-
-/*---------------------------------
-
-  qh_test_vneighbors()
-    test vertex neighbors for convexity
-    tests all facets on qh.newfacet_list
-
-  returns:
-    true if non-convex vneighbors appended to qh.facet_mergeset
-    initializes vertex neighbors if needed
-
-  notes:
-    assumes all facet neighbors have been tested
-    this can be expensive
-    this does not guarantee that a centrum is below all facets
-      but it is unlikely
-    uses qh.visit_id
-
-  design:
-    build vertex neighbors if necessary
-    for all new facets
-      for all vertices
-        for each unvisited facet neighbor of the vertex
-          test new facet and neighbor for convexity
-*/
-boolT qh_test_vneighbors (void /* qh newfacet_list */) {
-  facetT *newfacet, *neighbor, **neighborp;
-  vertexT *vertex, **vertexp;
-  int nummerges= 0;
-
-  trace1((qh ferr, "qh_test_vneighbors: testing vertex neighbors for convexity\n"));
-  if (!qh VERTEXneighbors)
-    qh_vertexneighbors();
-  FORALLnew_facets
-    newfacet->seen= False;
-  FORALLnew_facets {
-    newfacet->seen= True;
-    newfacet->visitid= qh visit_id++;
-    FOREACHneighbor_(newfacet)
-      newfacet->visitid= qh visit_id;
-    FOREACHvertex_(newfacet->vertices) {
-      FOREACHneighbor_(vertex) {
-      	if (neighbor->seen || neighbor->visitid == qh visit_id)
-      	  continue;
-      	if (qh_test_appendmerge (newfacet, neighbor))
-          nummerges++;
-      }
-    }
-  }
-  trace1((qh ferr, "qh_test_vneighbors: found %d non-convex, vertex neighbors\n",
-           nummerges));
-  return (nummerges > 0);
-} /* test_vneighbors */
-
-/*---------------------------------
-
-  qh_tracemerge( facet1, facet2 )
-    print trace message after merge
-*/
-void qh_tracemerge (facetT *facet1, facetT *facet2) {
-  boolT waserror= False;
-
-#ifndef qh_NOtrace
-  if (qh IStracing >= 4)
-    qh_errprint ("MERGED", facet2, NULL, NULL, NULL);
-  if (facet2 == qh tracefacet || (qh tracevertex && qh tracevertex->newlist)) {
-    fprintf (qh ferr, "qh_tracemerge: trace facet and vertex after merge of f%d and f%d, furthest p%d\n", facet1->id, facet2->id, qh furthest_id);
-    if (facet2 != qh tracefacet)
-      qh_errprint ("TRACE", qh tracefacet,
-        (qh tracevertex && qh tracevertex->neighbors) ?
-           SETfirstt_(qh tracevertex->neighbors, facetT) : NULL,
-        NULL, qh tracevertex);
-  }
-  if (qh tracevertex) {
-    if (qh tracevertex->deleted)
-      fprintf (qh ferr, "qh_tracemerge: trace vertex deleted at furthest p%d\n",
-	    qh furthest_id);
-    else
-      qh_checkvertex (qh tracevertex);
-  }
-  if (qh tracefacet) {
-    qh_checkfacet (qh tracefacet, True, &waserror);
-    if (waserror)
-      qh_errexit (qh_ERRqhull, qh tracefacet, NULL);
-  }
-#endif /* !qh_NOtrace */
-  if (qh CHECKfrequently || qh IStracing >= 4) { /* can't check polygon here */
-    qh_checkfacet (facet2, True, &waserror);
-    if (waserror)
-      qh_errexit(qh_ERRqhull, NULL, NULL);
-  }
-} /* tracemerge */
-
-/*---------------------------------
-
-  qh_tracemerging()
-    print trace message during POSTmerging
-
-  returns:
-
-  notes:
-    called from qh_mergecycle() and qh_mergefacet()
-
-  see:
-    qh_buildtracing()
-*/
-void qh_tracemerging (void) {
-  realT cpu;
-  int total;
-  time_t timedata;
-  struct tm *tp;
-
-  qh mergereport= zzval_(Ztotmerge);
-  time (&timedata);
-  tp= localtime (&timedata);
-  cpu= qh_CPUclock;
-  cpu /= qh_SECticks;
-  total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
-  fprintf (qh ferr, "\n\
-At %d:%d:%d & %2.5g CPU secs, qhull has merged %d facets.  The hull\n\
-  contains %d facets and %d vertices.\n",
-      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu,
-      total, qh num_facets - qh num_visible,
-      qh num_vertices-qh_setsize (qh del_vertices));
-} /* tracemerging */
-
-/*---------------------------------
-
-  qh_updatetested( facet1, facet2 )
-    clear facet2->tested and facet1->ridge->tested for merge
-
-  returns:
-    deletes facet2->center unless it's already large
-      if so, clears facet2->ridge->tested
-
-  design:
-    clear facet2->tested
-    clear ridge->tested for facet1's ridges
-    if facet2 has a centrum
-      if facet2 is large
-        set facet2->keepcentrum
-      else if facet2 has 3 vertices due to many merges, or not large and post merging
-        clear facet2->keepcentrum
-      unless facet2->keepcentrum
-        clear facet2->center to recompute centrum later
-        clear ridge->tested for facet2's ridges
-*/
-void qh_updatetested (facetT *facet1, facetT *facet2) {
-  ridgeT *ridge, **ridgep;
-  int size;
-
-  facet2->tested= False;
-  FOREACHridge_(facet1->ridges)
-    ridge->tested= False;
-  if (!facet2->center)
-    return;
-  size= qh_setsize (facet2->vertices);
-  if (!facet2->keepcentrum) {
-    if (size > qh hull_dim + qh_MAXnewcentrum) {
-      facet2->keepcentrum= True;
-      zinc_(Zwidevertices);
-    }
-  }else if (size <= qh hull_dim + qh_MAXnewcentrum) {
-    /* center and keepcentrum was set */
-    if (size == qh hull_dim || qh POSTmerging)
-      facet2->keepcentrum= False; /* if many merges need to recompute centrum */
-  }
-  if (!facet2->keepcentrum) {
-    qh_memfree (facet2->center, qh normal_size);
-    facet2->center= NULL;
-    FOREACHridge_(facet2->ridges)
-      ridge->tested= False;
-  }
-} /* updatetested */
-
-/*---------------------------------
-
-  qh_vertexridges( vertex )
-    return temporary set of ridges adjacent to a vertex
-    vertex->neighbors defined
-
-  ntoes:
-    uses qh.visit_id
-    does not include implicit ridges for simplicial facets
-
-  design:
-    for each neighbor of vertex
-      add ridges that include the vertex to ridges
-*/
-setT *qh_vertexridges (vertexT *vertex) {
-  facetT *neighbor, **neighborp;
-  setT *ridges= qh_settemp (qh TEMPsize);
-  int size;
-
-  qh visit_id++;
-  FOREACHneighbor_(vertex)
-    neighbor->visitid= qh visit_id;
-  FOREACHneighbor_(vertex) {
-    if (*neighborp)   /* no new ridges in last neighbor */
-      qh_vertexridges_facet (vertex, neighbor, &ridges);
-  }
-  if (qh PRINTstatistics || qh IStracing) {
-    size= qh_setsize (ridges);
-    zinc_(Zvertexridge);
-    zmax_(Zvertexridgemax, size);
-    trace3((qh ferr, "qh_vertexridges: found %d ridges for v%d\n",
-             size, vertex->id));
-  }
-  return ridges;
-} /* vertexridges */
-
-/*---------------------------------
-
-  qh_vertexridges_facet( vertex, facet, ridges )
-    neighbor->visitid==qh.visit_id if it hasn't been visited
-
-  returns:
-    ridges updated
-    sets facet->visitid to qh.visit_id-1
-
-  design:
-    for each ridge of facet
-      if ridge of visited neighbor (i.e., unprocessed)
-        if vertex in ridge
-          append ridge to vertex
-    mark facet processed
-*/
-void qh_vertexridges_facet (vertexT *vertex, facetT *facet, setT **ridges) {
-  ridgeT *ridge, **ridgep;
-  facetT *neighbor;
-
-  FOREACHridge_(facet->ridges) {
-    neighbor= otherfacet_(ridge, facet);
-    if (neighbor->visitid == qh visit_id
-    && qh_setin (ridge->vertices, vertex))
-      qh_setappend (ridges, ridge);
-  }
-  facet->visitid= qh visit_id-1;
-} /* vertexridges_facet */
-
-/*---------------------------------
-
-  qh_willdelete( facet, replace )
-    moves facet to visible list
-    sets facet->f.replace to replace (may be NULL)
-
-  returns:
-    bumps qh.num_visible
-*/
-void qh_willdelete (facetT *facet, facetT *replace) {
-
-  qh_removefacet(facet);
-  qh_prependfacet (facet, &qh visible_list);
-  qh num_visible++;
-  facet->visible= True;
-  facet->f.replace= replace;
-} /* willdelete */
-
-#else /* qh_NOmerge */
-void qh_premerge (vertexT *apex, realT maxcentrum, realT maxangle) {
-}
-void qh_postmerge (char *reason, realT maxcentrum, realT maxangle,
-                      boolT vneighbors) {
-}
-boolT qh_checkzero (boolT testall) {
-   }
-#endif /* qh_NOmerge */
-
diff --git a/extern/qhull/src/merge.h b/extern/qhull/src/merge.h
deleted file mode 100644
index 7fc2afa5967..00000000000
--- a/extern/qhull/src/merge.h
+++ /dev/null
@@ -1,171 +0,0 @@
-/*  ---------------------------------
-
-   merge.h
-
-   see qh-merge.htm and merge.c
-
-   copyright (c) 1993-2002, The Geometry Center
-*/
-
-#ifndef qhDEFmerge
-#define qhDEFmerge 1
-
-
-/*============ -constants- ==============*/
-
-/*----------------------------------
-
-  qh_ANGLEredundant
-    indicates redundant merge in mergeT->angle
-*/
-#define qh_ANGLEredundant 6.0
-
-/*----------------------------------
-
-  qh_ANGLEdegen
-    indicates degenerate facet in mergeT->angle
-*/
-#define qh_ANGLEdegen     5.0
-
-/*----------------------------------
-
-  qh_ANGLEconcave
-    offset to indicate concave facets in mergeT->angle
-
-  notes:
-    concave facets are assigned the range of [2,4] in mergeT->angle
-    roundoff error may make the angle less than 2
-*/
-#define qh_ANGLEconcave  1.5
-
-/*----------------------------------
-
-  MRG... (mergeType)
-    indicates the type of a merge (mergeT->type)
-*/
-typedef enum {	/* in sort order for facet_mergeset */
-  MRGnone= 0,
-  MRGcoplanar,		/* centrum coplanar */
-  MRGanglecoplanar,	/* angle coplanar */
-  			/* could detect half concave ridges */
-  MRGconcave,		/* concave ridge */
-  MRGflip,		/* flipped facet. facet1 == facet2 */
-  MRGridge,		/* duplicate ridge (qh_MERGEridge) */
-                        /* degen and redundant go onto degen_mergeset */
-  MRGdegen,		/* degenerate facet (not enough neighbors) facet1 == facet2 */
-  MRGredundant,		/* redundant facet (vertex subset) */
-  			/* merge_degenredundant assumes degen < redundant */
-  MRGmirror,	        /* mirror facet from qh_triangulate */
-  ENDmrg
-} mergeType;
-
-/*----------------------------------
-
-  qh_MERGEapex
-    flag for qh_mergefacet() to indicate an apex merge
-*/
-#define qh_MERGEapex     True
-
-/*============ -structures- ====================*/
-
-/*----------------------------------
-
-  mergeT
-    structure used to merge facets
-*/
-
-typedef struct mergeT mergeT;
-struct mergeT {		/* initialize in qh_appendmergeset */
-  realT   angle;        /* angle between normals of facet1 and facet2 */
-  facetT *facet1; 	/* will merge facet1 into facet2 */
-  facetT *facet2;
-  mergeType type;
-};
-
-
-/*=========== -macros- =========================*/
-
-/*----------------------------------
-
-  FOREACHmerge_( merges ) {...}
-    assign 'merge' to each merge in merges
-
-  notes:
-    uses 'mergeT *merge, **mergep;'
-    if qh_mergefacet(),
-      restart since qh.facet_mergeset may change
-    see FOREACHsetelement_
-*/
-#define FOREACHmerge_( merges ) FOREACHsetelement_(mergeT, merges, merge)
-
-/*============ prototypes in alphabetical order after pre/postmerge =======*/
-
-void    qh_premerge (vertexT *apex, realT maxcentrum, realT maxangle);
-void    qh_postmerge (char *reason, realT maxcentrum, realT maxangle,
-             boolT vneighbors);
-void    qh_all_merges (boolT othermerge, boolT vneighbors);
-void    qh_appendmergeset(facetT *facet, facetT *neighbor, mergeType mergetype, realT *angle);
-setT   *qh_basevertices( facetT *samecycle);
-void    qh_checkconnect (void /* qh new_facets */);
-boolT   qh_checkzero (boolT testall);
-void    qh_copynonconvex (ridgeT *atridge);
-void    qh_degen_redundant_facet (facetT *facet);
-void   	qh_degen_redundant_neighbors (facetT *facet, facetT *delfacet);
-vertexT *qh_find_newvertex (vertexT *oldvertex, setT *vertices, setT *ridges);
-void    qh_findbest_test (boolT testcentrum, facetT *facet, facetT *neighbor,
-           facetT **bestfacet, realT *distp, realT *mindistp, realT *maxdistp);
-facetT *qh_findbestneighbor(facetT *facet, realT *distp, realT *mindistp, realT *maxdistp);
-void 	qh_flippedmerges(facetT *facetlist, boolT *wasmerge);
-void 	qh_forcedmerges( boolT *wasmerge);
-void	qh_getmergeset(facetT *facetlist);
-void 	qh_getmergeset_initial (facetT *facetlist);
-void    qh_hashridge (setT *hashtable, int hashsize, ridgeT *ridge, vertexT *oldvertex);
-ridgeT *qh_hashridge_find (setT *hashtable, int hashsize, ridgeT *ridge,
-              vertexT *vertex, vertexT *oldvertex, int *hashslot);
-void 	qh_makeridges(facetT *facet);
-void    qh_mark_dupridges(facetT *facetlist);
-void    qh_maydropneighbor (facetT *facet);
-int     qh_merge_degenredundant (void);
-void    qh_merge_nonconvex( facetT *facet1, facetT *facet2, mergeType mergetype);
-void    qh_mergecycle (facetT *samecycle, facetT *newfacet);
-void    qh_mergecycle_all (facetT *facetlist, boolT *wasmerge);
-void    qh_mergecycle_facets( facetT *samecycle, facetT *newfacet);
-void    qh_mergecycle_neighbors(facetT *samecycle, facetT *newfacet);
-void    qh_mergecycle_ridges(facetT *samecycle, facetT *newfacet);
-void    qh_mergecycle_vneighbors( facetT *samecycle, facetT *newfacet);
-void 	qh_mergefacet(facetT *facet1, facetT *facet2, realT *mindist, realT *maxdist, boolT mergeapex);
-void    qh_mergefacet2d (facetT *facet1, facetT *facet2);
-void 	qh_mergeneighbors(facetT *facet1, facetT *facet2);
-void 	qh_mergeridges(facetT *facet1, facetT *facet2);
-void    qh_mergesimplex(facetT *facet1, facetT *facet2, boolT mergeapex);
-void    qh_mergevertex_del (vertexT *vertex, facetT *facet1, facetT *facet2);
-void    qh_mergevertex_neighbors(facetT *facet1, facetT *facet2);
-void	qh_mergevertices(setT *vertices1, setT **vertices);
-setT   *qh_neighbor_intersections (vertexT *vertex);
-void    qh_newvertices (setT *vertices);
-boolT   qh_reducevertices (void);
-vertexT *qh_redundant_vertex (vertexT *vertex);
-boolT   qh_remove_extravertices (facetT *facet);
-vertexT *qh_rename_sharedvertex (vertexT *vertex, facetT *facet);
-void	qh_renameridgevertex(ridgeT *ridge, vertexT *oldvertex, vertexT *newvertex);
-void    qh_renamevertex(vertexT *oldvertex, vertexT *newvertex, setT *ridges,
-			facetT *oldfacet, facetT *neighborA);
-boolT 	qh_test_appendmerge (facetT *facet, facetT *neighbor);
-boolT   qh_test_vneighbors (void /* qh newfacet_list */);
-void    qh_tracemerge (facetT *facet1, facetT *facet2);
-void    qh_tracemerging (void);
-void    qh_updatetested( facetT *facet1, facetT *facet2);
-setT   *qh_vertexridges (vertexT *vertex);
-void    qh_vertexridges_facet (vertexT *vertex, facetT *facet, setT **ridges);
-void    qh_willdelete (facetT *facet, facetT *replace);
-
-#endif /* qhDEFmerge */
diff --git a/extern/qhull/src/poly.c b/extern/qhull/src/poly.c
deleted file mode 100644
index 6319e43d66a..00000000000
--- a/extern/qhull/src/poly.c
+++ /dev/null
@@ -1,1180 +0,0 @@
-/*  ---------------------------------
-
-   poly.c
-   implements polygons and simplices
-
-   see qh-poly.htm, poly.h and qhull.h
-
-   infrequent code is in poly2.c
-   (all but top 50 and their callers 12/3/95)
-
-   copyright (c) 1993-2002, The Geometry Center
-*/
-
-#include "qhull_a.h"
-
-/*======== functions in alphabetical order ==========*/
-
-/*---------------------------------
-
-  qh_appendfacet( facet )
-    appends facet to end of qh.facet_list,
-
-  returns:
-    increments qh.numfacets
-
-  notes:
-    assumes qh.facet_list/facet_tail is defined (createsimplex)
-
-  see:
-    qh_removefacet()
-
-*/
-void qh_appendfacet(facetT *facet) {
-  facetT *tail= qh facet_tail;
-
-  if (tail == qh newfacet_list)
-    qh newfacet_list= facet;
-  if (tail == qh facet_next)
-    qh facet_next= facet;
-  facet->previous= tail->previous;
-  facet->next= tail;
-  if (tail->previous)
-    tail->previous->next= facet;
-  else
-    qh facet_list= facet;
-  tail->previous= facet;
-  qh num_facets++;
-  trace4((qh ferr, "qh_appendfacet: append f%d to facet_list\n", facet->id));
-} /* appendfacet */
-
-
-/*---------------------------------
-
-  qh_appendvertex( vertex )
-    appends vertex to end of qh.vertex_list,
-
-  returns:
-    sets vertex->newlist
-    increments qh.num_vertices
-
-  notes:
-    assumes qh.vertex_list/vertex_tail is defined (createsimplex)
-
-*/
-void qh_appendvertex (vertexT *vertex) {
-  vertexT *tail= qh vertex_tail;
-
-  if (tail == qh newvertex_list)
-    qh newvertex_list= vertex;
-  vertex->newlist= True;
-  vertex->previous= tail->previous;
-  vertex->next= tail;
-  if (tail->previous)
-    tail->previous->next= vertex;
-  else
-    qh vertex_list= vertex;
-  tail->previous= vertex;
-  qh num_vertices++;
-  trace4((qh ferr, "qh_appendvertex: append v%d to vertex_list\n", vertex->id));
-} /* appendvertex */
-
-
-/*---------------------------------
-
-  qh_attachnewfacets( )
-    attach horizon facets to new facets in qh.newfacet_list
-    newfacets have neighbor and ridge links to horizon but not vice versa
-    only needed for qh.ONLYgood
-
-  returns:
-    set qh.NEWfacets
-    horizon facets linked to new facets
-      ridges changed from visible facets to new facets
-      simplicial ridges deleted
-    qh.visible_list, no ridges valid
-    facet->f.replace is a newfacet (if any)
-
-  design:
-    delete interior ridges and neighbor sets by
-      for each visible, non-simplicial facet
-        for each ridge
-          if last visit or if neighbor is simplicial
-            if horizon neighbor
-              delete ridge for horizon's ridge set
-            delete ridge
-        erase neighbor set
-    attach horizon facets and new facets by
-      for all new facets
-        if corresponding horizon facet is simplicial
-          locate corresponding visible facet {may be more than one}
-          link visible facet to new facet
-          replace visible facet with new facet in horizon
-        else it's non-simplicial
-          for all visible neighbors of the horizon facet
-            link visible neighbor to new facet
-            delete visible neighbor from horizon facet
-          append new facet to horizon's neighbors
-          the first ridge of the new facet is the horizon ridge
-          link the new facet into the horizon ridge
-*/
-void qh_attachnewfacets (void ) {
-  facetT *newfacet= NULL, *neighbor, **neighborp, *horizon, *visible;
-  ridgeT *ridge, **ridgep;
-
-  qh NEWfacets= True;
-  trace3((qh ferr, "qh_attachnewfacets: delete interior ridges\n"));
-  qh visit_id++;
-  FORALLvisible_facets {
-    visible->visitid= qh visit_id;
-    if (visible->ridges) {
-      FOREACHridge_(visible->ridges) {
-	neighbor= otherfacet_(ridge, visible);
-	if (neighbor->visitid == qh visit_id
-	    || (!neighbor->visible && neighbor->simplicial)) {
-	  if (!neighbor->visible)  /* delete ridge for simplicial horizon */
-	    qh_setdel (neighbor->ridges, ridge);
-	  qh_setfree (&(ridge->vertices)); /* delete on 2nd visit */
-	  qh_memfree (ridge, sizeof(ridgeT));
-	}
-      }
-      SETfirst_(visible->ridges)= NULL;
-    }
-    SETfirst_(visible->neighbors)= NULL;
-  }
-  trace1((qh ferr, "qh_attachnewfacets: attach horizon facets to new facets\n"));
-  FORALLnew_facets {
-    horizon= SETfirstt_(newfacet->neighbors, facetT);
-    if (horizon->simplicial) {
-      visible= NULL;
-      FOREACHneighbor_(horizon) {   /* may have more than one horizon ridge */
-	if (neighbor->visible) {
-	  if (visible) {
-	    if (qh_setequal_skip (newfacet->vertices, 0, horizon->vertices,
-				  SETindex_(horizon->neighbors, neighbor))) {
-	      visible= neighbor;
-	      break;
-	    }
-	  }else
-	    visible= neighbor;
-	}
-      }
-      if (visible) {
-	visible->f.replace= newfacet;
-	qh_setreplace (horizon->neighbors, visible, newfacet);
-      }else {
-	fprintf (qh ferr, "qhull internal error (qh_attachnewfacets): couldn't find visible facet for horizon f%d of newfacet f%d\n",
-		 horizon->id, newfacet->id);
-	qh_errexit2 (qh_ERRqhull, horizon, newfacet);
-      }
-    }else { /* non-simplicial, with a ridge for newfacet */
-      FOREACHneighbor_(horizon) {    /* may hold for many new facets */
-	if (neighbor->visible) {
-	  neighbor->f.replace= newfacet;
-	  qh_setdelnth (horizon->neighbors,
-			SETindex_(horizon->neighbors, neighbor));
-	  neighborp--; /* repeat */
-	}
-      }
-      qh_setappend (&horizon->neighbors, newfacet);
-      ridge= SETfirstt_(newfacet->ridges, ridgeT);
-      if (ridge->top == horizon)
-	ridge->bottom= newfacet;
-      else
-	ridge->top= newfacet;
-      }
-  } /* newfacets */
-  if (qh PRINTstatistics) {
-    FORALLvisible_facets {
-      if (!visible->f.replace)
-	zinc_(Zinsidevisible);
-    }
-  }
-} /* attachnewfacets */
-
-/*---------------------------------
-
-  qh_checkflipped( facet, dist, allerror )
-    checks facet orientation to interior point
-
-    if allerror set,
-      tests against qh.DISTround
-    else
-      tests against 0 since tested against DISTround before
-
-  returns:
-    False if it flipped orientation (sets facet->flipped)
-    distance if non-NULL
-*/
-boolT qh_checkflipped (facetT *facet, realT *distp, boolT allerror) {
-  realT dist;
-
-  if (facet->flipped && !distp)
-    return False;
-  zzinc_(Zdistcheck);
-  qh_distplane(qh interior_point, facet, &dist);
-  if (distp)
-    *distp= dist;
-  if ((allerror && dist > -qh DISTround)|| (!allerror && dist >= 0.0)) {
-    facet->flipped= True;
-    zzinc_(Zflippedfacets);
-    trace0((qh ferr, "qh_checkflipped: facet f%d is flipped, distance= %6.12g during p%d\n",
-              facet->id, dist, qh furthest_id));
-    qh_precision ("flipped facet");
-    return False;
-  }
-  return True;
-} /* checkflipped */
-
-/*---------------------------------
-
-  qh_delfacet( facet )
-    removes facet from facet_list and frees up its memory
-
-  notes:
-    assumes vertices and ridges already freed
-*/
-void qh_delfacet(facetT *facet) {
-  void **freelistp; /* used !qh_NOmem */
-
-  trace4((qh ferr, "qh_delfacet: delete f%d\n", facet->id));
-  if (facet == qh tracefacet)
-    qh tracefacet= NULL;
-  if (facet == qh GOODclosest)
-    qh GOODclosest= NULL;
-  qh_removefacet(facet);
-  if (!facet->tricoplanar || facet->keepcentrum) {
-    qh_memfree_(facet->normal, qh normal_size, freelistp);
-    if (qh CENTERtype == qh_ASvoronoi) {   /* uses macro calls */
-      qh_memfree_(facet->center, qh center_size, freelistp);
-    }else /* AScentrum */ {
-      qh_memfree_(facet->center, qh normal_size, freelistp);
-    }
-  }
-  qh_setfree(&(facet->neighbors));
-  if (facet->ridges)
-    qh_setfree(&(facet->ridges));
-  qh_setfree(&(facet->vertices));
-  if (facet->outsideset)
-    qh_setfree(&(facet->outsideset));
-  if (facet->coplanarset)
-    qh_setfree(&(facet->coplanarset));
-  qh_memfree_(facet, sizeof(facetT), freelistp);
-} /* delfacet */
-
-
-/*---------------------------------
-
-  qh_deletevisible()
-    delete visible facets and vertices
-
-  returns:
-    deletes each facet and removes from facetlist
-    at exit, qh.visible_list empty (== qh.newfacet_list)
-
-  notes:
-    horizon facets do not reference facets on qh.visible_list
-    new facets in qh.newfacet_list
-    uses   qh.visit_id;
-*/
-void qh_deletevisible (void /*qh visible_list*/) {
-  facetT *visible, *nextfacet;
-  vertexT *vertex, **vertexp;
-  int numvisible= 0, numdel= qh_setsize(qh del_vertices);
-
-  trace1((qh ferr, "qh_deletevisible: delete %d visible facets and %d vertices\n",
-         qh num_visible, numdel));
-  for (visible= qh visible_list; visible && visible->visible;
-                visible= nextfacet) { /* deleting current */
-    nextfacet= visible->next;
-    numvisible++;
-    qh_delfacet(visible);
-  }
-  if (numvisible != qh num_visible) {
-    fprintf (qh ferr, "qhull internal error (qh_deletevisible): qh num_visible %d is not number of visible facets %d\n",
-             qh num_visible, numvisible);
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }
-  qh num_visible= 0;
-  zmax_(Zvisfacetmax, numvisible);
-  zmax_(Zdelvertexmax, numdel);
-  FOREACHvertex_(qh del_vertices)
-    qh_delvertex (vertex);
-  qh_settruncate (qh del_vertices, 0);
-} /* deletevisible */
-
-/*---------------------------------
-
-  qh_facetintersect( facetA, facetB, skipa, skipB, prepend )
-    return vertices for intersection of two simplicial facets
-    may include 1 prepended entry (if more, need to settemppush)
-
-  returns:
-    returns set of qh.hull_dim-1 + prepend vertices
-    returns skipped index for each test and checks for exactly one
-
-  notes:
-    does not need settemp since set in quick memory
-
-    qh_vertexintersect and qh_vertexintersect_new
-    use qh_setnew_delnthsorted to get nth ridge (no skip information)
-
-  design:
-    locate skipped vertex by scanning facet A's neighbors
-    locate skipped vertex by scanning facet B's neighbors
-    intersect the vertex sets
-*/
-setT *qh_facetintersect (facetT *facetA, facetT *facetB,
-			 int *skipA,int *skipB, int prepend) {
-  setT *intersect;
-  int dim= qh hull_dim, i, j;
-  facetT **neighborsA, **neighborsB;
-
-  i= j= 0;
-  if (facetB == *neighborsA++)
-    *skipA= 0;
-  else if (facetB == *neighborsA++)
-    *skipA= 1;
-  else if (facetB == *neighborsA++)
-    *skipA= 2;
-  else {
-    for (i= 3; i < dim; i++) {
-      if (facetB == *neighborsA++) {
-        *skipA= i;
-        break;
-      }
-    }
-  }
-  if (facetA == *neighborsB++)
-    *skipB= 0;
-  else if (facetA == *neighborsB++)
-    *skipB= 1;
-  else if (facetA == *neighborsB++)
-    *skipB= 2;
-  else {
-    for (j= 3; j < dim; j++) {
-      if (facetA == *neighborsB++) {
-        *skipB= j;
-        break;
-      }
-    }
-  }
-  if (i >= dim || j >= dim) {
-    fprintf (qh ferr, "qhull internal error (qh_facetintersect): f%d or f%d not in others neighbors\n",
-            facetA->id, facetB->id);
-    qh_errexit2 (qh_ERRqhull, facetA, facetB);
-  }
-  intersect= qh_setnew_delnthsorted (facetA->vertices, qh hull_dim, *skipA, prepend);
-  trace4((qh ferr, "qh_facetintersect: f%d skip %d matches f%d skip %d\n",
-	  facetA->id, *skipA, facetB->id, *skipB));
-  return(intersect);
-} /* facetintersect */
-
-/*---------------------------------
-
-  qh_gethash( hashsize, set, size, firstindex, skipelem )
-    return hashvalue for a set with firstindex and skipelem
-
-  notes:
-    assumes at least firstindex+1 elements
-    assumes skipelem is NULL, in set, or part of hash
-
-    hashes memory addresses which may change over different runs of the same data
-    using sum for hash does badly in high d
-*/
-unsigned qh_gethash (int hashsize, setT *set, int size, int firstindex, void *skipelem) {
-  void **elemp= SETelemaddr_(set, firstindex, void);
-  ptr_intT hash = 0, elem;
-  int i;
-
-  switch (size-firstindex) {
-  case 1:
-    hash= (ptr_intT)(*elemp) - (ptr_intT) skipelem;
-    break;
-  case 2:
-    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] - (ptr_intT) skipelem;
-    break;
-  case 3:
-    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
-      - (ptr_intT) skipelem;
-    break;
-  case 4:
-    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
-      + (ptr_intT)elemp[3] - (ptr_intT) skipelem;
-    break;
-  case 5:
-    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
-      + (ptr_intT)elemp[3] + (ptr_intT)elemp[4] - (ptr_intT) skipelem;
-    break;
-  case 6:
-    hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
-      + (ptr_intT)elemp[3] + (ptr_intT)elemp[4]+ (ptr_intT)elemp[5]
-      - (ptr_intT) skipelem;
-    break;
-  default:
-    hash= 0;
-    i= 3;
-    do {     /* this is about 10% in 10-d */
-      if ((elem= (ptr_intT)*elemp++) != (ptr_intT)skipelem) {
-        hash ^= (elem << i) + (elem >> (32-i));
-	i += 3;
-	if (i >= 32)
-	  i -= 32;
-      }
-    }while(*elemp);
-    break;
-  }
-  hash %= (ptr_intT) hashsize;
-  /* hash= 0; for debugging purposes */
-  return hash;
-} /* gethash */
-
-/*---------------------------------
-
-  qh_makenewfacet( vertices, toporient, horizon )
-    creates a toporient? facet from vertices
-
-  returns:
-    returns newfacet
-      newfacet->vertices= vertices
-      if horizon
-        newfacet->neighbor= horizon, but not vice versa
-    newvertex_list updated with vertices
-*/
-facetT *qh_makenewfacet(setT *vertices, boolT toporient,facetT *horizon) {
-  facetT *newfacet;
-  vertexT *vertex, **vertexp;
-
-  FOREACHvertex_(vertices) {
-    if (!vertex->newlist) {
-      qh_removevertex (vertex);
-      qh_appendvertex (vertex);
-    }
-  }
-  newfacet= qh_newfacet();
-  newfacet->vertices= vertices;
-  newfacet->toporient= toporient;
-  if (horizon)
-    qh_setappend(&(newfacet->neighbors), horizon);
-  qh_appendfacet(newfacet);
-  return(newfacet);
-} /* makenewfacet */
-
-
-/*---------------------------------
-
-  qh_makenewplanes()
-    make new hyperplanes for facets on qh.newfacet_list
-
-  returns:
-    all facets have hyperplanes or are marked for   merging
-    doesn't create hyperplane if horizon is coplanar (will merge)
-
-  notes:
-    facet->f.samecycle is defined for facet->mergehorizon facets
-*/
-void qh_makenewplanes (void /* newfacet_list */) {
-  facetT *newfacet;
-
-  FORALLnew_facets {
-    if (!newfacet->mergehorizon)
-      qh_setfacetplane (newfacet);
-  }
-  if (qh JOGGLEmax < REALmax/2)
-    minimize_(qh min_vertex, -wwval_(Wnewvertexmax));
-} /* makenewplanes */
-
-/*---------------------------------
-
-  qh_makenew_nonsimplicial( visible, apex, numnew )
-    make new facets for ridges of a visible facet
-
-  returns:
-    first newfacet, bumps numnew as needed
-    attaches new facets if !qh.ONLYgood
-    marks ridge neighbors for simplicial visible
-    if (qh.ONLYgood)
-      ridges on newfacet, horizon, and visible
-    else
-      ridge and neighbors between newfacet and   horizon
-      visible facet's ridges are deleted
-
-  notes:
-    qh.visit_id if visible has already been processed
-    sets neighbor->seen for building f.samecycle
-      assumes all 'seen' flags initially false
-
-  design:
-    for each ridge of visible facet
-      get neighbor of visible facet
-      if neighbor was already processed
-        delete the ridge (will delete all visible facets later)
-      if neighbor is a horizon facet
-        create a new facet
-        if neighbor coplanar
-          adds newfacet to f.samecycle for later merging
-        else
-          (checks for non-simplicial facet with multiple ridges to visible facet)
-        (checks for simplicial neighbor to non-simplicial visible facet)
-	(deletes ridge if neighbor is simplicial)
-
-*/
-#ifndef qh_NOmerge
-facetT *qh_makenew_nonsimplicial (facetT *visible, vertexT *apex, int *numnew) {
-  void **freelistp; /* used !qh_NOmem */
-  ridgeT *ridge, **ridgep;
-  facetT *neighbor, *newfacet= NULL, *samecycle;
-  setT *vertices;
-  boolT toporient;
-  int ridgeid;
-
-  FOREACHridge_(visible->ridges) {
-    ridgeid= ridge->id;
-    neighbor= otherfacet_(ridge, visible);
-    if (neighbor->visible) {
-      if (!qh ONLYgood) {
-        if (neighbor->visitid == qh visit_id) {
-          qh_setfree (&(ridge->vertices));  /* delete on 2nd visit */
-	  qh_memfree_(ridge, sizeof(ridgeT), freelistp);
-	}
-      }
-    }else {  /* neighbor is an horizon facet */
-      toporient= (ridge->top == visible);
-      vertices= qh_setnew (qh hull_dim); /* makes sure this is quick */
-      qh_setappend (&vertices, apex);
-      qh_setappend_set (&vertices, ridge->vertices);
-      newfacet= qh_makenewfacet(vertices, toporient, neighbor);
-      (*numnew)++;
-      if (neighbor->coplanar) {
-	newfacet->mergehorizon= True;
-        if (!neighbor->seen) {
-          newfacet->f.samecycle= newfacet;
-          neighbor->f.newcycle= newfacet;
-        }else {
-          samecycle= neighbor->f.newcycle;
-          newfacet->f.samecycle= samecycle->f.samecycle;
-          samecycle->f.samecycle= newfacet;
-	}
-      }
-      if (qh ONLYgood) {
-        if (!neighbor->simplicial)
- 	  qh_setappend(&(newfacet->ridges), ridge);
-      }else {  /* qh_attachnewfacets */
-        if (neighbor->seen) {
-	  if (neighbor->simplicial) {
-	    fprintf (qh ferr, "qhull internal error (qh_makenew_nonsimplicial): simplicial f%d sharing two ridges with f%d\n",
-	           neighbor->id, visible->id);
-	    qh_errexit2 (qh_ERRqhull, neighbor, visible);
-	  }
-	  qh_setappend (&(neighbor->neighbors), newfacet);
-	}else
-          qh_setreplace (neighbor->neighbors, visible, newfacet);
-        if (neighbor->simplicial) {
-          qh_setdel (neighbor->ridges, ridge);
-          qh_setfree (&(ridge->vertices));
-	  qh_memfree (ridge, sizeof(ridgeT));
-	}else {
- 	  qh_setappend(&(newfacet->ridges), ridge);
- 	  if (toporient)
- 	    ridge->top= newfacet;
- 	  else
- 	    ridge->bottom= newfacet;
- 	}
-      trace4((qh ferr, "qh_makenew_nonsimplicial: created facet f%d from v%d and r%d of horizon f%d\n",
-	    newfacet->id, apex->id, ridgeid, neighbor->id));
-      }
-    }
-    neighbor->seen= True;
-  } /* for each ridge */
-  if (!qh ONLYgood)
-    SETfirst_(visible->ridges)= NULL;
-  return newfacet;
-} /* makenew_nonsimplicial */
-#else /* qh_NOmerge */
-facetT *qh_makenew_nonsimplicial (facetT *visible, vertexT *apex, int *numnew) {
-  return NULL;
-}
-#endif /* qh_NOmerge */
-
-/*---------------------------------
-
-  qh_makenew_simplicial( visible, apex, numnew )
-    make new facets for simplicial visible facet and apex
-
-  returns:
-    attaches new facets if (!qh.ONLYgood)
-      neighbors between newfacet and horizon
-
-  notes:
-    nop if neighbor->seen or neighbor->visible (see qh_makenew_nonsimplicial)
-
-  design:
-    locate neighboring horizon facet for visible facet
-    determine vertices and orientation
-    create new facet
-    if coplanar,
-      add new facet to f.samecycle
-    update horizon facet's neighbor list
-*/
-facetT *qh_makenew_simplicial (facetT *visible, vertexT *apex, int *numnew) {
-  facetT *neighbor, **neighborp, *newfacet= NULL;
-  setT *vertices;
-  boolT flip, toporient;
-  int horizonskip, visibleskip;
-
-  FOREACHneighbor_(visible) {
-    if (!neighbor->seen && !neighbor->visible) {
-      vertices= qh_facetintersect(neighbor,visible, &horizonskip, &visibleskip, 1);
-      SETfirst_(vertices)= apex;
-      flip= ((horizonskip & 0x1) ^ (visibleskip & 0x1));
-      if (neighbor->toporient)
-	toporient= horizonskip & 0x1;
-      else
-	toporient= (horizonskip & 0x1) ^ 0x1;
-      newfacet= qh_makenewfacet(vertices, toporient, neighbor);
-      (*numnew)++;
-      if (neighbor->coplanar && (qh PREmerge || qh MERGEexact)) {
-#ifndef qh_NOmerge
-	newfacet->f.samecycle= newfacet;
-	newfacet->mergehorizon= True;
-#endif
-      }
-      if (!qh ONLYgood)
-        SETelem_(neighbor->neighbors, horizonskip)= newfacet;
-      trace4((qh ferr, "qh_makenew_simplicial: create facet f%d top %d from v%d and horizon f%d skip %d top %d and visible f%d skip %d, flip? %d\n",
-	    newfacet->id, toporient, apex->id, neighbor->id, horizonskip,
-	      neighbor->toporient, visible->id, visibleskip, flip));
-    }
-  }
-  return newfacet;
-} /* makenew_simplicial */
-
-/*---------------------------------
-
-  qh_matchneighbor( newfacet, newskip, hashsize, hashcount )
-    either match subridge of newfacet with neighbor or add to hash_table
-
-  returns:
-    duplicate ridges are unmatched and marked by qh_DUPLICATEridge
-
-  notes:
-    ridge is newfacet->vertices w/o newskip vertex
-    do not allocate memory (need to free hash_table cleanly)
-    uses linear hash chains
-
-    qh_matchduplicates
-
-  design:
-    for each possible matching facet in qh.hash_table
-      if vertices match
-        set ismatch, if facets have opposite orientation
-        if ismatch and matching facet doesn't have a match
-          match the facets by updating their neighbor sets
-        else
-          indicate a duplicate ridge
-          set facet hyperplane for later testing
-          unless the other facet was already a duplicate ridge
-            mark both facets with a duplicate ridge
-            add other facet (if defined) to hash table
-*/
-void qh_matchneighbor (facetT *newfacet, int newskip, int hashsize, int *hashcount) {
-  boolT newfound= False;   /* True, if new facet is already in hash chain */
-  boolT same, ismatch;
-  int hash, scan;
-  facetT *facet, *matchfacet;
-  int skip, matchskip;
-
-  hash= (int)qh_gethash (hashsize, newfacet->vertices, qh hull_dim, 1,
-                     SETelem_(newfacet->vertices, newskip));
-  trace4((qh ferr, "qh_matchneighbor: newfacet f%d skip %d hash %d hashcount %d\n",
-	  newfacet->id, newskip, hash, *hashcount));
-  zinc_(Zhashlookup);
-  for (scan= hash; (facet= SETelemt_(qh hash_table, scan, facetT));
-       scan= (++scan >= hashsize ? 0 : scan)) {
-    if (facet == newfacet) {
-      newfound= True;
-      continue;
-    }
-    zinc_(Zhashtests);
-    if (qh_matchvertices (1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
-      if (SETelem_(newfacet->vertices, newskip) ==
-          SETelem_(facet->vertices, skip)) {
-        qh_precision ("two facets with the same vertices");
-        fprintf (qh ferr, "qhull precision error: Vertex sets are the same for f%d and f%d.  Can not force output.\n",
-          facet->id, newfacet->id);
-        qh_errexit2 (qh_ERRprec, facet, newfacet);
-      }
-      ismatch= (same == (newfacet->toporient ^ facet->toporient));
-      matchfacet= SETelemt_(facet->neighbors, skip, facetT);
-      if (ismatch && !matchfacet) {
-        SETelem_(facet->neighbors, skip)= newfacet;
-        SETelem_(newfacet->neighbors, newskip)= facet;
-        (*hashcount)--;
-        trace4((qh ferr, "qh_matchneighbor: f%d skip %d matched with new f%d skip %d\n",
-           facet->id, skip, newfacet->id, newskip));
-        return;
-      }
-      if (!qh PREmerge && !qh MERGEexact) {
-        qh_precision ("a ridge with more than two neighbors");
-	fprintf (qh ferr, "qhull precision error: facets f%d, f%d and f%d meet at a ridge with more than 2 neighbors.  Can not continue.\n",
-		 facet->id, newfacet->id, getid_(matchfacet));
-	qh_errexit2 (qh_ERRprec, facet, newfacet);
-      }
-      SETelem_(newfacet->neighbors, newskip)= qh_DUPLICATEridge;
-      newfacet->dupridge= True;
-      if (!newfacet->normal)
-	qh_setfacetplane (newfacet);
-      qh_addhash (newfacet, qh hash_table, hashsize, hash);
-      (*hashcount)++;
-      if (!facet->normal)
-	qh_setfacetplane (facet);
-      if (matchfacet != qh_DUPLICATEridge) {
-	SETelem_(facet->neighbors, skip)= qh_DUPLICATEridge;
-	facet->dupridge= True;
-	if (!facet->normal)
-	  qh_setfacetplane (facet);
-	if (matchfacet) {
-	  matchskip= qh_setindex (matchfacet->neighbors, facet);
-	  SETelem_(matchfacet->neighbors, matchskip)= qh_DUPLICATEridge;
-	  matchfacet->dupridge= True;
-	  if (!matchfacet->normal)
-	    qh_setfacetplane (matchfacet);
-	  qh_addhash (matchfacet, qh hash_table, hashsize, hash);
-	  *hashcount += 2;
-	}
-      }
-      trace4((qh ferr, "qh_matchneighbor: new f%d skip %d duplicates ridge for f%d skip %d matching f%d ismatch %d at hash %d\n",
-	   newfacet->id, newskip, facet->id, skip,
-	   (matchfacet == qh_DUPLICATEridge ? -2 : getid_(matchfacet)),
-	   ismatch, hash));
-      return; /* end of duplicate ridge */
-    }
-  }
-  if (!newfound)
-    SETelem_(qh hash_table, scan)= newfacet;  /* same as qh_addhash */
-  (*hashcount)++;
-  trace4((qh ferr, "qh_matchneighbor: no match for f%d skip %d at hash %d\n",
-           newfacet->id, newskip, hash));
-} /* matchneighbor */
-
-
-/*---------------------------------
-
-  qh_matchnewfacets()
-    match newfacets in qh.newfacet_list to their newfacet neighbors
-
-  returns:
-    qh.newfacet_list with full neighbor sets
-      get vertices with nth neighbor by deleting nth vertex
-    if qh.PREmerge/MERGEexact or qh.FORCEoutput
-      sets facet->flippped if flipped normal (also prevents point partitioning)
-    if duplicate ridges and qh.PREmerge/MERGEexact
-      sets facet->dupridge
-      missing neighbor links identifies extra ridges to be merging (qh_MERGEridge)
-
-  notes:
-    newfacets already have neighbor[0] (horizon facet)
-    assumes qh.hash_table is NULL
-    vertex->neighbors has not been updated yet
-    do not allocate memory after qh.hash_table (need to free it cleanly)
-
-  design:
-    delete neighbor sets for all new facets
-    initialize a hash table
-    for all new facets
-      match facet with neighbors
-    if unmatched facets (due to duplicate ridges)
-      for each new facet with a duplicate ridge
-        match it with a facet
-    check for flipped facets
-*/
-void qh_matchnewfacets (void /* qh newfacet_list */) {
-  int numnew=0, hashcount=0, newskip;
-  facetT *newfacet, *neighbor;
-  int dim= qh hull_dim, hashsize, neighbor_i, neighbor_n;
-  setT *neighbors;
-#ifndef qh_NOtrace
-  int facet_i, facet_n, numfree= 0;
-  facetT *facet;
-#endif
-
-  trace1((qh ferr, "qh_matchnewfacets: match neighbors for new facets.\n"));
-  FORALLnew_facets {
-    numnew++;
-    {  /* inline qh_setzero (newfacet->neighbors, 1, qh hull_dim); */
-      neighbors= newfacet->neighbors;
-      neighbors->e[neighbors->maxsize].i= dim+1; /*may be overwritten*/
-      memset ((char *)SETelemaddr_(neighbors, 1, void), 0, dim * SETelemsize);
-    }
-  }
-  qh_newhashtable (numnew*(qh hull_dim-1)); /* twice what is normally needed,
-                                     but every ridge could be DUPLICATEridge */
-  hashsize= qh_setsize (qh hash_table);
-  FORALLnew_facets {
-    for (newskip=1; newskipneighbors, k, facetT);
-	  if (!neighbor || neighbor == qh_DUPLICATEridge)
-	    count++;
-	}
-	if (facet == newfacet)
-	  break;
-      }
-      if (count != hashcount) {
-	fprintf (qh ferr, "qh_matchnewfacets: after adding facet %d, hashcount %d != count %d\n",
-		 newfacet->id, hashcount, count);
-	qh_errexit (qh_ERRqhull, newfacet, NULL);
-      }
-    }
-#endif  /* end of trap code */
-  }
-  if (hashcount) {
-    FORALLnew_facets {
-      if (newfacet->dupridge) {
-        FOREACHneighbor_i_(newfacet) {
-          if (neighbor == qh_DUPLICATEridge) {
-            qh_matchduplicates (newfacet, neighbor_i, hashsize, &hashcount);
-         	    /* this may report MERGEfacet */
-	  }
-        }
-      }
-    }
-  }
-  if (hashcount) {
-    fprintf (qh ferr, "qhull internal error (qh_matchnewfacets): %d neighbors did not match up\n",
-        hashcount);
-    qh_printhashtable (qh ferr);
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }
-#ifndef qh_NOtrace
-  if (qh IStracing >= 2) {
-    FOREACHfacet_i_(qh hash_table) {
-      if (!facet)
-        numfree++;
-    }
-    fprintf (qh ferr, "qh_matchnewfacets: %d new facets, %d unused hash entries .  hashsize %d\n",
-	     numnew, numfree, qh_setsize (qh hash_table));
-  }
-#endif /* !qh_NOtrace */
-  qh_setfree (&qh hash_table);
-  if (qh PREmerge || qh MERGEexact) {
-    if (qh IStracing >= 4)
-      qh_printfacetlist (qh newfacet_list, NULL, qh_ALL);
-    FORALLnew_facets {
-      if (newfacet->normal)
-	qh_checkflipped (newfacet, NULL, qh_ALL);
-    }
-  }else if (qh FORCEoutput)
-    qh_checkflipped_all (qh newfacet_list);  /* prints warnings for flipped */
-} /* matchnewfacets */
-
-
-/*---------------------------------
-
-  qh_matchvertices( firstindex, verticesA, skipA, verticesB, skipB, same )
-    tests whether vertices match with a single skip
-    starts match at firstindex since all new facets have a common vertex
-
-  returns:
-    true if matched vertices
-    skip index for each set
-    sets same iff vertices have the same orientation
-
-  notes:
-    assumes skipA is in A and both sets are the same size
-
-  design:
-    set up pointers
-    scan both sets checking for a match
-    test orientation
-*/
-boolT qh_matchvertices (int firstindex, setT *verticesA, int skipA,
-       setT *verticesB, int *skipB, boolT *same) {
-  vertexT **elemAp, **elemBp, **skipBp=NULL, **skipAp;
-
-  do if (elemAp != skipAp) {
-    while (*elemAp != *elemBp++) {
-      if (skipBp)
-        return False;
-      skipBp= elemBp;  /* one extra like FOREACH */
-    }
-  }while(*(++elemAp));
-  if (!skipBp)
-    skipBp= ++elemBp;
-  *skipB= SETindex_(verticesB, skipB);
-  *same= !(((ptr_intT)skipA & 0x1) ^ ((ptr_intT)*skipB & 0x1));
-  trace4((qh ferr, "qh_matchvertices: matched by skip %d (v%d) and skip %d (v%d) same? %d\n",
-	  skipA, (*skipAp)->id, *skipB, (*(skipBp-1))->id, *same));
-  return (True);
-} /* matchvertices */
-
-/*---------------------------------
-
-  qh_newfacet()
-    return a new facet
-
-  returns:
-    all fields initialized or cleared   (NULL)
-    preallocates neighbors set
-*/
-facetT *qh_newfacet(void) {
-  facetT *facet;
-  void **freelistp; /* used !qh_NOmem */
-
-  qh_memalloc_(sizeof(facetT), freelistp, facet, facetT);
-  memset ((char *)facet, 0, sizeof(facetT));
-  if (qh facet_id == qh tracefacet_id)
-    qh tracefacet= facet;
-  facet->id= qh facet_id++;
-  facet->neighbors= qh_setnew(qh hull_dim);
-#if !qh_COMPUTEfurthest
-  facet->furthestdist= 0.0;
-#endif
-#if qh_MAXoutside
-  if (qh FORCEoutput && qh APPROXhull)
-    facet->maxoutside= qh MINoutside;
-  else
-    facet->maxoutside= qh DISTround;
-#endif
-  facet->simplicial= True;
-  facet->good= True;
-  facet->newfacet= True;
-  trace4((qh ferr, "qh_newfacet: created facet f%d\n", facet->id));
-  return (facet);
-} /* newfacet */
-
-
-/*---------------------------------
-
-  qh_newridge()
-    return a new ridge
-*/
-ridgeT *qh_newridge(void) {
-  ridgeT *ridge;
-  void **freelistp;   /* used !qh_NOmem */
-
-  qh_memalloc_(sizeof(ridgeT), freelistp, ridge, ridgeT);
-  memset ((char *)ridge, 0, sizeof(ridgeT));
-  zinc_(Ztotridges);
-  if (qh ridge_id == 0xFFFFFF) {
-    fprintf(qh ferr, "\
-qhull warning: more than %d ridges.  ID field overflows and two ridges\n\
-may have the same identifier.  Otherwise output ok.\n", 0xFFFFFF);
-  }
-  ridge->id= qh ridge_id++;
-  trace4((qh ferr, "qh_newridge: created ridge r%d\n", ridge->id));
-  return (ridge);
-} /* newridge */
-
-
-/*---------------------------------
-
-  qh_pointid(  )
-    return id for a point,
-    returns -3 if null, -2 if interior, or -1 if not known
-
-  alternative code:
-    unsigned long id;
-    id= ((unsigned long)point - (unsigned long)qh.first_point)/qh.normal_size;
-
-  notes:
-    if point not in point array
-      the code does a comparison of unrelated pointers.
-*/
-int qh_pointid (pointT *point) {
-  long offset, id;
-
-  if (!point)
-    id= -3;
-  else if (point == qh interior_point)
-    id= -2;
-  else if (point >= qh first_point
-  && point < qh first_point + qh num_points * qh hull_dim) {
-    offset= point - qh first_point;
-    id= offset / qh hull_dim;
-  }else if ((id= qh_setindex (qh other_points, point)) != -1)
-    id += qh num_points;
-  else
-    id= -1;
-  return (int) id;
-} /* pointid */
-
-/*---------------------------------
-
-  qh_removefacet( facet )
-
-  returns:
-    updates qh.facet_list .newfacet_list .facet_next visible_list
-    decrements qh.num_facets
-
-  see:
-    qh_appendfacet
-*/
-void qh_removefacet(facetT *facet) {
-  facetT *next= facet->next, *previous= facet->previous;
-
-  if (facet == qh newfacet_list)
-    qh newfacet_list= next;
-  if (facet == qh facet_next)
-    qh facet_next= next;
-  if (facet == qh visible_list)
-    qh visible_list= next;
-  if (previous) {
-    previous->next= next;
-    next->previous= previous;
-  }else {  /* 1st facet in qh facet_list */
-    qh facet_list= next;
-    qh facet_list->previous= NULL;
-  }
-  qh num_facets--;
-  trace4((qh ferr, "qh_removefacet: remove f%d from facet_list\n", facet->id));
-} /* removefacet */
-
-
-/*---------------------------------
-
-  qh_removevertex( vertex )
-
-  returns:
-    decrements qh.num_vertices
-*/
-void qh_removevertex(vertexT *vertex) {
-  vertexT *next= vertex->next, *previous= vertex->previous;
-
-  if (vertex == qh newvertex_list)
-    qh newvertex_list= next;
-  if (previous) {
-    previous->next= next;
-    next->previous= previous;
-  }else {  /* 1st vertex in qh vertex_list */
-    qh vertex_list= vertex->next;
-    qh vertex_list->previous= NULL;
-  }
-  qh num_vertices--;
-  trace4((qh ferr, "qh_removevertex: remove v%d from vertex_list\n", vertex->id));
-} /* removevertex */
-
-
-/*---------------------------------
-
-  qh_updatevertices()
-    update vertex neighbors and delete interior vertices
-
-  returns:
-    if qh.VERTEXneighbors, updates neighbors for each vertex
-      if qh.newvertex_list,
-         removes visible neighbors  from vertex neighbors
-      if qh.newfacet_list
-         adds new facets to vertex neighbors
-    if qh.visible_list
-       interior vertices added to qh.del_vertices for later partitioning
-
-  design:
-    if qh.VERTEXneighbors
-      deletes references to visible facets from vertex neighbors
-      appends new facets to the neighbor list for each vertex
-      checks all vertices of visible facets
-        removes visible facets from neighbor lists
-        marks unused vertices for deletion
-*/
-void qh_updatevertices (void /*qh newvertex_list, newfacet_list, visible_list*/) {
-  facetT *newfacet= NULL, *neighbor, **neighborp, *visible;
-  vertexT *vertex, **vertexp;
-
-  trace3((qh ferr, "qh_updatevertices: delete interior vertices and update vertex->neighbors\n"));
-  if (qh VERTEXneighbors) {
-    FORALLvertex_(qh newvertex_list) {
-      FOREACHneighbor_(vertex) {
-	if (neighbor->visible)
-	  SETref_(neighbor)= NULL;
-      }
-      qh_setcompact (vertex->neighbors);
-    }
-    FORALLnew_facets {
-      FOREACHvertex_(newfacet->vertices)
-        qh_setappend (&vertex->neighbors, newfacet);
-    }
-    FORALLvisible_facets {
-      FOREACHvertex_(visible->vertices) {
-        if (!vertex->newlist && !vertex->deleted) {
-  	  FOREACHneighbor_(vertex) { /* this can happen under merging */
-	    if (!neighbor->visible)
-	      break;
-	  }
-	  if (neighbor)
-	    qh_setdel (vertex->neighbors, visible);
-	  else {
-	    vertex->deleted= True;
-	    qh_setappend (&qh del_vertices, vertex);
-	    trace2((qh ferr, "qh_updatevertices: delete vertex p%d (v%d) in f%d\n",
-		  qh_pointid(vertex->point), vertex->id, visible->id));
-  	  }
-        }
-      }
-    }
-  }else {  /* !VERTEXneighbors */
-    FORALLvisible_facets {
-      FOREACHvertex_(visible->vertices) {
-        if (!vertex->newlist && !vertex->deleted) {
-          vertex->deleted= True;
-	  qh_setappend (&qh del_vertices, vertex);
-	  trace2((qh ferr, "qh_updatevertices: delete vertex p%d (v%d) in f%d\n",
-		  qh_pointid(vertex->point), vertex->id, visible->id));
-  	}
-      }
-    }
-  }
-} /* updatevertices */
-
-
-
diff --git a/extern/qhull/src/poly.h b/extern/qhull/src/poly.h
deleted file mode 100644
index 294ec9527fc..00000000000
--- a/extern/qhull/src/poly.h
+++ /dev/null
@@ -1,290 +0,0 @@
-/*  ---------------------------------
-
-   poly.h
-   header file for poly.c and poly2.c
-
-   see qh-poly.htm, qhull.h and poly.c
-
-   copyright (c) 1993-2002, The Geometry Center
-*/
-
-#ifndef qhDEFpoly
-#define qhDEFpoly 1
-
-/*===============   constants ========================== */
-
-/*----------------------------------
-
-  ALGORITHMfault
-*/
-#define qh_ALGORITHMfault 0
-
-/*----------------------------------
-
-  DATAfault
-*/
-#define qh_DATAfault 1
-
-/*----------------------------------
-
-  DUPLICATEridge
-    special value for facet->neighbor to indicate a duplicate ridge
-
-  notes:
-    set by matchneighbor, used by matchmatch and mark_dupridge
-*/
-#define qh_DUPLICATEridge ( facetT * ) 1L
-
-/*----------------------------------
-
-  MERGEridge       flag in facet
-    special value for facet->neighbor to indicate a merged ridge
-
-  notes:
-    set by matchneighbor, used by matchmatch and mark_dupridge
-*/
-#define qh_MERGEridge ( facetT * ) 2L
-
-
-/*============ -structures- ====================*/
-
-/*=========== -macros- =========================*/
-
-/*----------------------------------
-
-  FORALLfacet_( facetlist ) { ... }
-    assign 'facet' to each facet in facetlist
-
-  notes:
-    uses 'facetT *facet;'
-    assumes last facet is a sentinel
-
-  see:
-    FORALLfacets
-*/
-#define FORALLfacet_( facetlist ) if ( facetlist ) for( facet=( facetlist );facet && facet->next;facet=facet->next )
-
-/*----------------------------------
-
-  FORALLnew_facets { ... }
-    assign 'newfacet' to each facet in qh.newfacet_list
-
-  notes:
-    uses 'facetT *newfacet;'
-    at exit, newfacet==NULL
-*/
-#define FORALLnew_facets for( newfacet=qh newfacet_list;newfacet && newfacet->next;newfacet=newfacet->next )
-
-/*----------------------------------
-
-  FORALLvertex_( vertexlist ) { ... }
-    assign 'vertex' to each vertex in vertexlist
-
-  notes:
-    uses 'vertexT *vertex;'
-    at exit, vertex==NULL
-*/
-#define FORALLvertex_( vertexlist ) for ( vertex=( vertexlist );vertex && vertex->next;vertex= vertex->next )
-
-/*----------------------------------
-
-  FORALLvisible_facets { ... }
-    assign 'visible' to each visible facet in qh.visible_list
-
-  notes:
-    uses 'vacetT *visible;'
-    at exit, visible==NULL
-*/
-#define FORALLvisible_facets for (visible=qh visible_list; visible && visible->visible; visible= visible->next)
-
-/*----------------------------------
-
-  FORALLsame_( newfacet ) { ... }
-    assign 'same' to each facet in newfacet->f.samecycle
-
-  notes:
-    uses 'facetT *same;'
-    stops when it returns to newfacet
-*/
-#define FORALLsame_(newfacet) for (same= newfacet->f.samecycle; same != newfacet; same= same->f.samecycle)
-
-/*----------------------------------
-
-  FORALLsame_cycle_( newfacet ) { ... }
-    assign 'same' to each facet in newfacet->f.samecycle
-
-  notes:
-    uses 'facetT *same;'
-    at exit, same == NULL
-*/
-#define FORALLsame_cycle_(newfacet) \
-     for (same= newfacet->f.samecycle; \
-         same; same= (same == newfacet ?  NULL : same->f.samecycle))
-
-/*----------------------------------
-
-  FOREACHneighborA_( facet ) { ... }
-    assign 'neighborA' to each neighbor in facet->neighbors
-
-  FOREACHneighborA_( vertex ) { ... }
-    assign 'neighborA' to each neighbor in vertex->neighbors
-
-  declare:
-    facetT *neighborA, **neighborAp;
-
-  see:
-    FOREACHsetelement_
-*/
-#define FOREACHneighborA_(facet)  FOREACHsetelement_(facetT, facet->neighbors, neighborA)
-
-/*----------------------------------
-
-  FOREACHvisible_( facets ) { ... }
-    assign 'visible' to each facet in facets
-
-  notes:
-    uses 'facetT *facet, *facetp;'
-    see FOREACHsetelement_
-*/
-#define FOREACHvisible_(facets) FOREACHsetelement_(facetT, facets, visible)
-
-/*----------------------------------
-
-  FOREACHnewfacet_( facets ) { ... }
-    assign 'newfacet' to each facet in facets
-
-  notes:
-    uses 'facetT *newfacet, *newfacetp;'
-    see FOREACHsetelement_
-*/
-#define FOREACHnewfacet_(facets) FOREACHsetelement_(facetT, facets, newfacet)
-
-/*----------------------------------
-
-  FOREACHvertexA_( vertices ) { ... }
-    assign 'vertexA' to each vertex in vertices
-
-  notes:
-    uses 'vertexT *vertexA, *vertexAp;'
-    see FOREACHsetelement_
-*/
-#define FOREACHvertexA_(vertices) FOREACHsetelement_(vertexT, vertices, vertexA)
-
-/*----------------------------------
-
-  FOREACHvertexreverse12_( vertices ) { ... }
-    assign 'vertex' to each vertex in vertices
-    reverse order of first two vertices
-
-  notes:
-    uses 'vertexT *vertex, *vertexp;'
-    see FOREACHsetelement_
-*/
-#define FOREACHvertexreverse12_(vertices) FOREACHsetelementreverse12_(vertexT, vertices, vertex)
-
-
-/*=============== prototypes poly.c in alphabetical order ================*/
-
-void    qh_appendfacet(facetT *facet);
-void    qh_appendvertex(vertexT *vertex);
-void 	qh_attachnewfacets (void);
-boolT   qh_checkflipped (facetT *facet, realT *dist, boolT allerror);
-void	qh_delfacet(facetT *facet);
-void 	qh_deletevisible(void /*qh visible_list, qh horizon_list*/);
-setT   *qh_facetintersect (facetT *facetA, facetT *facetB, int *skipAp,int *skipBp, int extra);
-unsigned qh_gethash (int hashsize, setT *set, int size, int firstindex, void *skipelem);
-facetT *qh_makenewfacet(setT *vertices, boolT toporient, facetT *facet);
-void    qh_makenewplanes ( void /* newfacet_list */);
-facetT *qh_makenew_nonsimplicial (facetT *visible, vertexT *apex, int *numnew);
-facetT *qh_makenew_simplicial (facetT *visible, vertexT *apex, int *numnew);
-void    qh_matchneighbor (facetT *newfacet, int newskip, int hashsize,
-			  int *hashcount);
-void	qh_matchnewfacets (void);
-boolT   qh_matchvertices (int firstindex, setT *verticesA, int skipA,
-			  setT *verticesB, int *skipB, boolT *same);
-facetT *qh_newfacet(void);
-ridgeT *qh_newridge(void);
-int     qh_pointid (pointT *point);
-void 	qh_removefacet(facetT *facet);
-void 	qh_removevertex(vertexT *vertex);
-void    qh_updatevertices (void);
-
-
-/*========== -prototypes poly2.c in alphabetical order ===========*/
-
-void    qh_addhash (void* newelem, setT *hashtable, int hashsize, unsigned hash);
-void 	qh_check_bestdist (void);
-void    qh_check_maxout (void);
-void    qh_check_output (void);
-void    qh_check_point (pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2);
-void   	qh_check_points(void);
-void 	qh_checkconvex(facetT *facetlist, int fault);
-void    qh_checkfacet(facetT *facet, boolT newmerge, boolT *waserrorp);
-void 	qh_checkflipped_all (facetT *facetlist);
-void 	qh_checkpolygon(facetT *facetlist);
-void    qh_checkvertex (vertexT *vertex);
-void 	qh_clearcenters (qh_CENTER type);
-void 	qh_createsimplex(setT *vertices);
-void 	qh_delridge(ridgeT *ridge);
-void    qh_delvertex (vertexT *vertex);
-setT   *qh_facet3vertex (facetT *facet);
-facetT *qh_findbestfacet (pointT *point, boolT bestoutside,
-           realT *bestdist, boolT *isoutside);
-facetT *qh_findfacet_all (pointT *point, realT *bestdist, boolT *isoutside,
-			  int *numpart);
-int 	qh_findgood (facetT *facetlist, int goodhorizon);
-void 	qh_findgood_all (facetT *facetlist);
-void    qh_furthestnext (void /* qh facet_list */);
-void    qh_furthestout (facetT *facet);
-void    qh_infiniteloop (facetT *facet);
-void 	qh_initbuild(void);
-void 	qh_initialhull(setT *vertices);
-setT   *qh_initialvertices(int dim, setT *maxpoints, pointT *points, int numpoints);
-vertexT *qh_isvertex (pointT *point, setT *vertices);
-vertexT *qh_makenewfacets (pointT *point /*horizon_list, visible_list*/);
-void    qh_matchduplicates (facetT *atfacet, int atskip, int hashsize, int *hashcount);
-void    qh_nearcoplanar ( void /* qh.facet_list */);
-vertexT *qh_nearvertex (facetT *facet, pointT *point, realT *bestdistp);
-int 	qh_newhashtable(int newsize);
-vertexT *qh_newvertex(pointT *point);
-ridgeT *qh_nextridge3d (ridgeT *atridge, facetT *facet, vertexT **vertexp);
-void    qh_outcoplanar (void /* facet_list */);
-pointT *qh_point (int id);
-void 	qh_point_add (setT *set, pointT *point, void *elem);
-setT   *qh_pointfacet (void /*qh facet_list*/);
-setT   *qh_pointvertex (void /*qh facet_list*/);
-void 	qh_prependfacet(facetT *facet, facetT **facetlist);
-void	qh_printhashtable(FILE *fp);
-void    qh_printlists (void);
-void    qh_resetlists (boolT stats, boolT resetVisible /*qh newvertex_list newfacet_list visible_list*/);
-void    qh_setvoronoi_all (void);
-void	qh_triangulate (void /*qh facet_list*/);
-void    qh_triangulate_facet (facetT *facetA, vertexT **first_vertex);
-void    qh_triangulate_link (facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB);
-void	qh_triangulate_mirror (facetT *facetA, facetT *facetB);
-void    qh_triangulate_null (facetT *facetA);
-void    qh_vertexintersect(setT **vertexsetA,setT *vertexsetB);
-setT   *qh_vertexintersect_new(setT *vertexsetA,setT *vertexsetB);
-void    qh_vertexneighbors (void /*qh facet_list*/);
-boolT 	qh_vertexsubset(setT *vertexsetA, setT *vertexsetB);
-
-
-#endif /* qhDEFpoly */
diff --git a/extern/qhull/src/poly2.c b/extern/qhull/src/poly2.c
deleted file mode 100644
index 713faab8bed..00000000000
--- a/extern/qhull/src/poly2.c
+++ /dev/null
@@ -1,3070 +0,0 @@
-/*  ---------------------------------
-
-   poly2.c
-   implements polygons and simplices
-
-   see qh-poly.htm, poly.h and qhull.h
-
-   frequently used code is in poly.c
-
-   copyright (c) 1993-2002, The Geometry Center
-*/
-
-#include "qhull_a.h"
-
-/*======== functions in alphabetical order ==========*/
-
-/*---------------------------------
-
-  qh_addhash( newelem, hashtable, hashsize, hash )
-    add newelem to linear hash table at hash if not already there
-*/
-void qh_addhash (void* newelem, setT *hashtable, int hashsize, unsigned hash) {
-  int scan;
-  void *elem;
-
-  for (scan= (int)hash; (elem= SETelem_(hashtable, scan));
-       scan= (++scan >= hashsize ? 0 : scan)) {
-    if (elem == newelem)
-      break;
-  }
-  /* loop terminates because qh_HASHfactor >= 1.1 by qh_initbuffers */
-  if (!elem)
-    SETelem_(hashtable, scan)= newelem;
-
-/*---------------------------------
-
-  qh_check_bestdist()
-    check that all points are within max_outside of the nearest facet
-    if qh.ONLYgood,
-      ignores !good facets
-
-  see:
-    qh_check_maxout(), qh_outerinner()
-
-  notes:
-    only called from qh_check_points()
-      seldom used since qh.MERGING is almost always set
-    if notverified>0 at end of routine
-      some points were well inside the hull.  If the hull contains
-      a lens-shaped component, these points were not verified.  Use
-      options 'Qi Tv' to verify all points.  (Exhaustive check also verifies)
-
-  design:
-    determine facet for each point (if any)
-    for each point
-      find the best facet for the point and check all coplanar facets
-      error if point is outside of facet
-*/
-void qh_check_bestdist (void) {
-  boolT waserror= False, unassigned;
-  facetT *facet, *bestfacet, *errfacet1= NULL, *errfacet2= NULL;
-  facetT *facetlist;
-  realT dist, maxoutside, maxdist= -REALmax;
-  pointT *point;
-  int numpart= 0, facet_i, facet_n, notgood= 0, notverified= 0;
-  setT *facets;
-
-  trace1((qh ferr, "qh_check_bestdist: check points below nearest facet.  Facet_list f%d\n",
-      qh facet_list->id));
-  maxoutside= qh_maxouter();
-  maxoutside += qh DISTround;
-  /* one more qh.DISTround for check computation */
-  trace1((qh ferr, "qh_check_bestdist: check that all points are within %2.2g of best facet\n", maxoutside));
-  facets= qh_pointfacet (/*qh facet_list*/);
-  if (!qh_QUICKhelp && qh PRINTprecision)
-    fprintf (qh ferr, "\n\
-qhull output completed.  Verifying that %d points are\n\
-below %2.2g of the nearest %sfacet.\n",
-	     qh_setsize(facets), maxoutside, (qh ONLYgood ?  "good " : ""));
-  FOREACHfacet_i_(facets) {  /* for each point with facet assignment */
-    if (facet)
-      unassigned= False;
-    else {
-      unassigned= True;
-      facet= qh facet_list;
-    }
-    point= qh_point(facet_i);
-    if (point == qh GOODpointp)
-      continue;
-    qh_distplane(point, facet, &dist);
-    numpart++;
-    bestfacet= qh_findbesthorizon (!qh_IScheckmax, point, facet, qh_NOupper, &dist, &numpart);
-    /* occurs after statistics reported */
-    maximize_(maxdist, dist);
-    if (dist > maxoutside) {
-      if (qh ONLYgood && !bestfacet->good
-	  && !((bestfacet= qh_findgooddist (point, bestfacet, &dist, &facetlist))
-	       && dist > maxoutside))
-	notgood++;
-      else {
-	waserror= True;
-	fprintf(qh ferr, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
-		facet_i, bestfacet->id, dist, maxoutside);
-	if (errfacet1 != bestfacet) {
-	  errfacet2= errfacet1;
-	  errfacet1= bestfacet;
-	}
-      }
-    }else if (unassigned && dist < -qh MAXcoplanar)
-      notverified++;
-  }
-  qh_settempfree (&facets);
-  if (notverified && !qh DELAUNAY && !qh_QUICKhelp && qh PRINTprecision)
-    fprintf(qh ferr, "\n%d points were well inside the hull.  If the hull contains\n\
-a lens-shaped component, these points were not verified.  Use\n\
-options 'Qci Tv' to verify all points.\n", notverified);
-  if (maxdist > qh outside_err) {
-    fprintf( qh ferr, "qhull precision error (qh_check_bestdist): a coplanar point is %6.2g from convex hull.  The maximum value (qh.outside_err) is %6.2g\n",
-              maxdist, qh outside_err);
-    qh_errexit2 (qh_ERRprec, errfacet1, errfacet2);
-  }else if (waserror && qh outside_err > REALmax/2)
-    qh_errexit2 (qh_ERRprec, errfacet1, errfacet2);
-  else if (waserror)
-    ;                       /* the error was logged to qh.ferr but does not effect the output */
-  trace0((qh ferr, "qh_check_bestdist: max distance outside %2.2g\n", maxdist));
-} /* check_bestdist */
-
-/*---------------------------------
-
-  qh_check_maxout()
-    updates qh.max_outside by checking all points against bestfacet
-    if qh.ONLYgood, ignores !good facets
-
-  returns:
-    sets qh.maxoutdone
-    if printing qh.min_vertex (qh_outerinner),
-      it is updated to the current vertices
-    removes inside/coplanar points from coplanarset as needed
-
-  notes:
-    defines coplanar as min_vertex instead of MAXcoplanar
-    may not need to check near-inside points because of qh.MAXcoplanar
-      and qh.KEEPnearinside (before it was -DISTround)
-
-    qh_check_bestdist()
-
-  design:
-    if qh.min_vertex is needed
-      for all neighbors of all vertices
-        test distance from vertex to neighbor
-    determine facet for each point (if any)
-    for each point with an assigned facet
-      find the best facet for the point and check all coplanar facets
-    remove near-inside points from coplanar sets
-*/
-#ifndef qh_NOmerge
-void qh_check_maxout (void) {
-  facetT *facet, *bestfacet, *neighbor, **neighborp, *facetlist;
-  realT dist, maxoutside, minvertex, old_maxoutside;
-  pointT *point;
-  int numpart= 0, facet_i, facet_n, notgood= 0;
-  setT *facets, *vertices;
-  vertexT *vertex;
-
-  trace1((qh ferr, "qh_check_maxout: check and update maxoutside for each facet.\n"));
-  maxoutside= minvertex= 0;
-  if (qh VERTEXneighbors
-  && (qh PRINTsummary || qh KEEPinside || qh KEEPcoplanar
-	|| qh TRACElevel || qh PRINTstatistics
-	|| qh PRINTout[0] == qh_PRINTsummary || qh PRINTout[0] == qh_PRINTnone)) {
-    trace1((qh ferr, "qh_check_maxout: determine actual maxoutside and minvertex\n"));
-    vertices= qh_pointvertex (/*qh facet_list*/);
-    FORALLvertices {
-      FOREACHneighbor_(vertex) {
-        zinc_(Zdistvertex);  /* distance also computed by main loop below */
-	qh_distplane (vertex->point, neighbor, &dist);
-	minimize_(minvertex, dist);
-	if (-dist > qh TRACEdist || dist > qh TRACEdist
-	|| neighbor == qh tracefacet || vertex == qh tracevertex)
-	  fprintf (qh ferr, "qh_check_maxout: p%d (v%d) is %.2g from f%d\n",
-		    qh_pointid (vertex->point), vertex->id, dist, neighbor->id);
-      }
-    }
-    if (qh MERGING) {
-      wmin_(Wminvertex, qh min_vertex);
-    }
-    qh min_vertex= minvertex;
-    qh_settempfree (&vertices);
-  }
-  facets= qh_pointfacet (/*qh facet_list*/);
-  do {
-    old_maxoutside= fmax_(qh max_outside, maxoutside);
-    FOREACHfacet_i_(facets) {     /* for each point with facet assignment */
-      if (facet) {
-	point= qh_point(facet_i);
-	if (point == qh GOODpointp)
-	  continue;
-	zinc_(Ztotcheck);
-	qh_distplane(point, facet, &dist);
-	numpart++;
-	bestfacet= qh_findbesthorizon (qh_IScheckmax, point, facet, !qh_NOupper, &dist, &numpart);
-	if (bestfacet && dist > maxoutside) {
-	  if (qh ONLYgood && !bestfacet->good
-	  && !((bestfacet= qh_findgooddist (point, bestfacet, &dist, &facetlist))
-	       && dist > maxoutside))
-	    notgood++;
-	  else
-	    maxoutside= dist;
-	}
-	if (dist > qh TRACEdist || (bestfacet && bestfacet == qh tracefacet))
-	  fprintf (qh ferr, "qh_check_maxout: p%d is %.2g above f%d\n",
-		     qh_pointid (point), dist, bestfacet->id);
-      }
-    }
-  }while
-    (maxoutside > 2*old_maxoutside);
-    /* if qh.maxoutside increases substantially, qh_SEARCHdist is not valid
-          e.g., RBOX 5000 s Z1 G1e-13 t1001200614 | qhull */
-  qh_settempfree (&facets);
-  wval_(Wmaxout)= maxoutside - qh max_outside;
-  wmax_(Wmaxoutside, qh max_outside);
-  qh max_outside= maxoutside;
-  qh_nearcoplanar (/*qh.facet_list*/);
-  qh maxoutdone= True;
-  trace1((qh ferr, "qh_check_maxout: maxoutside %2.2g, min_vertex %2.2g, outside of not good %d\n",
-       maxoutside, qh min_vertex, notgood));
-} /* check_maxout */
-#else /* qh_NOmerge */
-void qh_check_maxout (void) {
-}
-#endif
-
-/*---------------------------------
-
-  qh_check_output()
-    performs the checks at the end of qhull algorithm
-    Maybe called after voronoi output.  Will recompute otherwise centrums are Voronoi centers instead
-*/
-void qh_check_output (void) {
-  int i;
-
-  if (qh STOPcone)
-    return;
-  if (qh VERIFYoutput | qh IStracing | qh CHECKfrequently) {
-    qh_checkpolygon (qh facet_list);
-    qh_checkflipped_all (qh facet_list);
-    qh_checkconvex (qh facet_list, qh_ALGORITHMfault);
-  }else if (!qh MERGING && qh_newstats (qhstat precision, &i)) {
-    qh_checkflipped_all (qh facet_list);
-    qh_checkconvex (qh facet_list, qh_ALGORITHMfault);
-  }
-} /* check_output */
-
-
-
-/*---------------------------------
-
-  qh_check_point( point, facet, maxoutside, maxdist, errfacet1, errfacet2 )
-    check that point is less than maxoutside from facet
-*/
-void qh_check_point (pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2) {
-  realT dist;
-
-  /* occurs after statistics reported */
-  qh_distplane(point, facet, &dist);
-  if (dist > *maxoutside) {
-    if (*errfacet1 != facet) {
-      *errfacet2= *errfacet1;
-      *errfacet1= facet;
-    }
-    fprintf(qh ferr, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
-	      qh_pointid(point), facet->id, dist, *maxoutside);
-  }
-  maximize_(*maxdist, dist);
-} /* qh_check_point */
-
-
-/*---------------------------------
-
-  qh_check_points()
-    checks that all points are inside all facets
-
-  notes:
-    if many points and qh_check_maxout not called (i.e., !qh.MERGING),
-       calls qh_findbesthorizon (seldom done).
-    ignores flipped facets
-    maxoutside includes 2 qh.DISTrounds
-      one qh.DISTround for the computed distances in qh_check_points
-    qh_printafacet and qh_printsummary needs only one qh.DISTround
-    the computation for qh.VERIFYdirect does not account for qh.other_points
-
-  design:
-    if many points
-      use qh_check_bestdist()
-    else
-      for all facets
-        for all points
-          check that point is inside facet
-*/
-void qh_check_points (void) {
-  facetT *facet, *errfacet1= NULL, *errfacet2= NULL;
-  realT total, maxoutside, maxdist= -REALmax;
-  pointT *point, **pointp, *pointtemp;
-  boolT testouter;
-
-  maxoutside= qh_maxouter();
-  maxoutside += qh DISTround;
-  /* one more qh.DISTround for check computation */
-  trace1((qh ferr, "qh_check_points: check all points below %2.2g of all facet planes\n",
-	  maxoutside));
-  if (qh num_good)   /* miss counts other_points and !good facets */
-     total= (float) qh num_good * qh num_points;
-  else
-     total= (float) qh num_facets * qh num_points;
-  if (total >= qh_VERIFYdirect && !qh maxoutdone) {
-    if (!qh_QUICKhelp && qh SKIPcheckmax && qh MERGING)
-      fprintf (qh ferr, "\n\
-qhull input warning: merging without checking outer planes ('Q5' or 'Po').\n\
-Verify may report that a point is outside of a facet.\n");
-    qh_check_bestdist();
-  }else {
-    if (qh_MAXoutside && qh maxoutdone)
-      testouter= True;
-    else
-      testouter= False;
-    if (!qh_QUICKhelp) {
-      if (qh MERGEexact)
-	fprintf (qh ferr, "\n\
-qhull input warning: exact merge ('Qx').  Verify may report that a point\n\
-is outside of a facet.  See qh-optq.htm#Qx\n");
-      else if (qh SKIPcheckmax || qh NOnearinside)
-	fprintf (qh ferr, "\n\
-qhull input warning: no outer plane check ('Q5') or no processing of\n\
-near-inside points ('Q8').  Verify may report that a point is outside\n\
-of a facet.\n");
-    }
-    if (qh PRINTprecision) {
-      if (testouter)
-	fprintf (qh ferr, "\n\
-Output completed.  Verifying that all points are below outer planes of\n\
-all %sfacets.  Will make %2.0f distance computations.\n",
-	      (qh ONLYgood ?  "good " : ""), total);
-      else
-	fprintf (qh ferr, "\n\
-Output completed.  Verifying that all points are below %2.2g of\n\
-all %sfacets.  Will make %2.0f distance computations.\n",
-	      maxoutside, (qh ONLYgood ?  "good " : ""), total);
-    }
-    FORALLfacets {
-      if (!facet->good && qh ONLYgood)
-        continue;
-      if (facet->flipped)
-        continue;
-      if (!facet->normal) {
-	fprintf( qh ferr, "qhull warning (qh_check_points): missing normal for facet f%d\n", facet->id);
-        continue;
-      }
-      if (testouter) {
-#if qh_MAXoutside
-	maxoutside= facet->maxoutside + 2* qh DISTround;
-	/* one DISTround to actual point and another to computed point */
-#endif
-      }
-      FORALLpoints {
-	if (point != qh GOODpointp)
-	  qh_check_point (point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
-      }
-      FOREACHpoint_(qh other_points) {
-	if (point != qh GOODpointp)
-	  qh_check_point (point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
-      }
-    }
-    if (maxdist > qh outside_err) {
-      fprintf( qh ferr, "qhull precision error (qh_check_points): a coplanar point is %6.2g from convex hull.  The maximum value (qh.outside_err) is %6.2g\n",
-                maxdist, qh outside_err );
-      qh_errexit2( qh_ERRprec, errfacet1, errfacet2 );
-    }else if (errfacet1 && qh outside_err > REALmax/2)
-        qh_errexit2( qh_ERRprec, errfacet1, errfacet2 );
-    else if (errfacet1)
-        ;  /* the error was logged to qh.ferr but does not effect the output */
-    trace0((qh ferr, "qh_check_points: max distance outside %2.2g\n", maxdist));
-  }
-} /* check_points */
-
-
-/*---------------------------------
-
-  qh_checkconvex( facetlist, fault )
-    check that each ridge in facetlist is convex
-    fault = qh_DATAfault if reporting errors
-          = qh_ALGORITHMfault otherwise
-
-  returns:
-    counts Zconcaveridges and Zcoplanarridges
-    errors if concaveridge or if merging an coplanar ridge
-
-  note:
-    if not merging,
-      tests vertices for neighboring simplicial facets
-    else if ZEROcentrum,
-      tests vertices for neighboring simplicial   facets
-    else
-      tests centrums of neighboring facets
-
-  design:
-    for all facets
-      report flipped facets
-      if ZEROcentrum and simplicial neighbors
-        test vertices for neighboring simplicial facets
-      else
-        test centrum against all neighbors
-*/
-void qh_checkconvex(facetT *facetlist, int fault) {
-  facetT *facet, *neighbor, **neighborp, *errfacet1=NULL, *errfacet2=NULL;
-  vertexT *vertex;
-  realT dist;
-  pointT *centrum;
-  boolT waserror= False, centrum_warning= False, tempcentrum= False, allsimplicial;
-  int neighbor_i;
-
-  trace1((qh ferr, "qh_checkconvex: check all ridges are convex\n"));
-  if (!qh RERUN) {
-    zzval_(Zconcaveridges)= 0;
-    zzval_(Zcoplanarridges)= 0;
-  }
-  FORALLfacet_(facetlist) {
-    if (facet->flipped) {
-      qh_precision ("flipped facet");
-      fprintf (qh ferr, "qhull precision error: f%d is flipped (interior point is outside)\n",
-	       facet->id);
-      errfacet1= facet;
-      waserror= True;
-      continue;
-    }
-    if (qh MERGING && (!qh ZEROcentrum || !facet->simplicial || facet->tricoplanar))
-      allsimplicial= False;
-    else {
-      allsimplicial= True;
-      neighbor_i= 0;
-      FOREACHneighbor_(facet) {
-        vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
-	if (!neighbor->simplicial || neighbor->tricoplanar) {
-	  allsimplicial= False;
-	  continue;
-	}
-        qh_distplane (vertex->point, neighbor, &dist);
-        if (dist > -qh DISTround) {
-	  if (fault == qh_DATAfault) {
-            qh_precision ("coplanar or concave ridge");
-	    fprintf (qh ferr, "qhull precision error: initial simplex is not convex. Distance=%.2g\n", dist);
-	    qh_errexit(qh_ERRsingular, NULL, NULL);
-	  }
-          if (dist > qh DISTround) {
-            zzinc_(Zconcaveridges);
-            qh_precision ("concave ridge");
-            fprintf (qh ferr, "qhull precision error: f%d is concave to f%d, since p%d (v%d) is %6.4g above\n",
-              facet->id, neighbor->id, qh_pointid(vertex->point), vertex->id, dist);
-            errfacet1= facet;
-            errfacet2= neighbor;
-            waserror= True;
-          }else if (qh ZEROcentrum) {
-            if (dist > 0) {     /* qh_checkzero checks that dist < - qh DISTround */
-              zzinc_(Zcoplanarridges);
-              qh_precision ("coplanar ridge");
-              fprintf (qh ferr, "qhull precision error: f%d is clearly not convex to f%d, since p%d (v%d) is %6.4g above\n",
-                facet->id, neighbor->id, qh_pointid(vertex->point), vertex->id, dist);
-              errfacet1= facet;
-              errfacet2= neighbor;
-              waserror= True;
-	    }
-	  }else {
-            zzinc_(Zcoplanarridges);
-            qh_precision ("coplanar ridge");
-            trace0((qh ferr, "qhull precision error: f%d may be coplanar to f%d, since p%d (v%d) is within %6.4g during p%d\n",
-              facet->id, neighbor->id, qh_pointid(vertex->point), vertex->id, dist, qh furthest_id));
-          }
-        }
-      }
-    }
-    if (!allsimplicial) {
-      if (qh CENTERtype == qh_AScentrum) {
-        if (!facet->center)
-          facet->center= qh_getcentrum (facet);
-        centrum= facet->center;
-      }else {
-	if (!centrum_warning && (!facet->simplicial || facet->tricoplanar)) {
-	   centrum_warning= True;
-	   fprintf (qh ferr, "qhull note: recomputing centrums for convexity test.  This may lead to false, precision errors.\n");
-	}
-        centrum= qh_getcentrum(facet);
-        tempcentrum= True;
-      }
-      FOREACHneighbor_(facet) {
-	if (qh ZEROcentrum && facet->simplicial && neighbor->simplicial)
-	  continue;
-	if (facet->tricoplanar || neighbor->tricoplanar)
-	  continue;
-        zzinc_(Zdistconvex);
-        qh_distplane (centrum, neighbor, &dist);
-        if (dist > qh DISTround) {
-          zzinc_(Zconcaveridges);
-          qh_precision ("concave ridge");
-          fprintf (qh ferr, "qhull precision error: f%d is concave to f%d.  Centrum of f%d is %6.4g above f%d\n",
-            facet->id, neighbor->id, facet->id, dist, neighbor->id);
-          errfacet1= facet;
-          errfacet2= neighbor;
-          waserror= True;
-	}else if (dist >= 0.0) {   /* if arithmetic always rounds the same,
-          zzinc_(Zcoplanarridges);
-          qh_precision ("coplanar ridge");
-          fprintf (qh ferr, "qhull precision error: f%d is coplanar or concave to f%d.  Centrum of f%d is %6.4g above f%d\n",
-            facet->id, neighbor->id, facet->id, dist, neighbor->id);
-	  errfacet1= facet;
-	  errfacet2= neighbor;
-	  waserror= True;
-        }
-      }
-      if (tempcentrum)
-        qh_memfree(centrum, qh normal_size);
-    }
-  }
-  if (waserror && !qh FORCEoutput)
-    qh_errexit2 (qh_ERRprec, errfacet1, errfacet2);
-} /* checkconvex */
-
-
-/*---------------------------------
-
-  qh_checkfacet( facet, newmerge, waserror )
-    checks for consistency errors in facet
-    newmerge set if from merge.c
-
-  returns:
-    sets waserror if any error occurs
-
-  checks:
-    vertex ids are inverse sorted
-    unless newmerge, at least hull_dim neighbors and vertices (exactly if simplicial)
-    if non-simplicial, at least as many ridges as neighbors
-    neighbors are not duplicated
-    ridges are not duplicated
-    in 3-d, ridges=verticies
-    (qh.hull_dim-1) ridge vertices
-    neighbors are reciprocated
-    ridge neighbors are facet neighbors and a ridge for every neighbor
-    simplicial neighbors match facetintersect
-    vertex intersection matches vertices of common ridges
-    vertex neighbors and facet vertices agree
-    all ridges have distinct vertex sets
-
-  notes:
-    uses neighbor->seen
-
-  design:
-    check sets
-    check vertices
-    check sizes of neighbors and vertices
-    check for qh_MERGEridge and qh_DUPLICATEridge flags
-    check neighbor set
-    check ridge set
-    check ridges, neighbors, and vertices
-*/
-void qh_checkfacet(facetT *facet, boolT newmerge, boolT *waserrorp) {
-  facetT *neighbor, **neighborp, *errother=NULL;
-  ridgeT *ridge, **ridgep, *errridge= NULL, *ridge2;
-  vertexT *vertex, **vertexp;
-  unsigned previousid= INT_MAX;
-  int numneighbors, numvertices, numridges=0, numRvertices=0;
-  boolT waserror= False;
-  int skipA, skipB, ridge_i, ridge_n, i;
-  setT *intersection;
-
-  if (facet->visible) {
-    fprintf (qh ferr, "qhull internal error (qh_checkfacet): facet f%d is on the visible_list\n",
-      facet->id);
-    qh_errexit (qh_ERRqhull, facet, NULL);
-  }
-  if (!facet->normal) {
-    fprintf (qh ferr, "qhull internal error (qh_checkfacet): facet f%d does not have  a normal\n",
-      facet->id);
-    waserror= True;
-  }
-  qh_setcheck (facet->vertices, "vertices for f", facet->id);
-  qh_setcheck (facet->ridges, "ridges for f", facet->id);
-  qh_setcheck (facet->outsideset, "outsideset for f", facet->id);
-  qh_setcheck (facet->coplanarset, "coplanarset for f", facet->id);
-  qh_setcheck (facet->neighbors, "neighbors for f", facet->id);
-  FOREACHvertex_(facet->vertices) {
-    if (vertex->deleted) {
-      fprintf(qh ferr, "qhull internal error (qh_checkfacet): deleted vertex v%d in f%d\n", vertex->id, facet->id);
-      qh_errprint ("ERRONEOUS", NULL, NULL, NULL, vertex);
-      waserror= True;
-    }
-    if (vertex->id >= previousid) {
-      fprintf(qh ferr, "qhull internal error (qh_checkfacet): vertices of f%d are not in descending id order at v%d\n", facet->id, vertex->id);
-      waserror= True;
-      break;
-    }
-    previousid= vertex->id;
-  }
-  numneighbors= qh_setsize(facet->neighbors);
-  numvertices= qh_setsize(facet->vertices);
-  numridges= qh_setsize(facet->ridges);
-  if (facet->simplicial) {
-    if (numvertices+numneighbors != 2*qh hull_dim
-    && !facet->degenerate && !facet->redundant) {
-      fprintf(qh ferr, "qhull internal error (qh_checkfacet): for simplicial facet f%d, #vertices %d + #neighbors %d != 2*qh hull_dim\n",
-                facet->id, numvertices, numneighbors);
-      qh_setprint (qh ferr, "", facet->neighbors);
-      waserror= True;
-    }
-  }else { /* non-simplicial */
-    if (!newmerge
-    &&(numvertices < qh hull_dim || numneighbors < qh hull_dim)
-    && !facet->degenerate && !facet->redundant) {
-      fprintf(qh ferr, "qhull internal error (qh_checkfacet): for facet f%d, #vertices %d or #neighbors %d < qh hull_dim\n",
-         facet->id, numvertices, numneighbors);
-       waserror= True;
-    }
-    /* in 3-d, can get a vertex twice in an edge list, e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv TP624 TW1e-13 T4 */
-    if (numridges < numneighbors
-    ||(qh hull_dim == 3 && numvertices > numridges && !qh NEWfacets)
-    ||(qh hull_dim == 2 && numridges + numvertices + numneighbors != 6)) {
-      if (!facet->degenerate && !facet->redundant) {
-	fprintf(qh ferr, "qhull internal error (qh_checkfacet): for facet f%d, #ridges %d < #neighbors %d or (3-d) > #vertices %d or (2-d) not all 2\n",
-	    facet->id, numridges, numneighbors, numvertices);
-	waserror= True;
-      }
-    }
-  }
-  FOREACHneighbor_(facet) {
-    if (neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge) {
-      fprintf(qh ferr, "qhull internal error (qh_checkfacet): facet f%d still has a MERGE or DUP neighbor\n", facet->id);
-      qh_errexit (qh_ERRqhull, facet, NULL);
-    }
-    neighbor->seen= True;
-  }
-  FOREACHneighbor_(facet) {
-    if (!qh_setin(neighbor->neighbors, facet)) {
-      fprintf(qh ferr, "qhull internal error (qh_checkfacet): facet f%d has neighbor f%d, but f%d does not have neighbor f%d\n",
-	      facet->id, neighbor->id, neighbor->id, facet->id);
-      errother= neighbor;
-      waserror= True;
-    }
-    if (!neighbor->seen) {
-      fprintf(qh ferr, "qhull internal error (qh_checkfacet): facet f%d has a duplicate neighbor f%d\n",
-	      facet->id, neighbor->id);
-      errother= neighbor;
-      waserror= True;
-    }
-    neighbor->seen= False;
-  }
-  FOREACHridge_(facet->ridges) {
-    qh_setcheck (ridge->vertices, "vertices for r", ridge->id);
-    ridge->seen= False;
-  }
-  FOREACHridge_(facet->ridges) {
-    if (ridge->seen) {
-      fprintf(qh ferr, "qhull internal error (qh_checkfacet): facet f%d has a duplicate ridge r%d\n",
-	      facet->id, ridge->id);
-      errridge= ridge;
-      waserror= True;
-    }
-    ridge->seen= True;
-    numRvertices= qh_setsize(ridge->vertices);
-    if (numRvertices != qh hull_dim - 1) {
-      fprintf(qh ferr, "qhull internal error (qh_checkfacet): ridge between f%d and f%d has %d vertices\n",
-                ridge->top->id, ridge->bottom->id, numRvertices);
-      errridge= ridge;
-      waserror= True;
-    }
-    neighbor= otherfacet_(ridge, facet);
-    neighbor->seen= True;
-    if (!qh_setin(facet->neighbors, neighbor)) {
-      fprintf(qh ferr, "qhull internal error (qh_checkfacet): for facet f%d, neighbor f%d of ridge r%d not in facet\n",
-           facet->id, neighbor->id, ridge->id);
-      errridge= ridge;
-      waserror= True;
-    }
-  }
-  if (!facet->simplicial) {
-    FOREACHneighbor_(facet) {
-      if (!neighbor->seen) {
-        fprintf(qh ferr, "qhull internal error (qh_checkfacet): facet f%d does not have a ridge for neighbor f%d\n",
-	      facet->id, neighbor->id);
-	errother= neighbor;
-        waserror= True;
-      }
-      intersection= qh_vertexintersect_new(facet->vertices, neighbor->vertices);
-      qh_settemppush (intersection);
-      FOREACHvertex_(facet->vertices) {
-	vertex->seen= False;
-	vertex->seen2= False;
-      }
-      FOREACHvertex_(intersection)
-	vertex->seen= True;
-      FOREACHridge_(facet->ridges) {
-	if (neighbor != otherfacet_(ridge, facet))
-	    continue;
-	FOREACHvertex_(ridge->vertices) {
-	  if (!vertex->seen) {
-	    fprintf (qh ferr, "qhull internal error (qh_checkfacet): vertex v%d in r%d not in f%d intersect f%d\n",
-  	          vertex->id, ridge->id, facet->id, neighbor->id);
-	    qh_errexit (qh_ERRqhull, facet, ridge);
-	  }
-	  vertex->seen2= True;
-	}
-      }
-      if (!newmerge) {
-	FOREACHvertex_(intersection) {
-	  if (!vertex->seen2) {
-	    if (qh IStracing >=3 || !qh MERGING) {
-	      fprintf (qh ferr, "qhull precision error (qh_checkfacet): vertex v%d in f%d intersect f%d but\n\
- not in a ridge.  This is ok under merging.  Last point was p%d\n",
-		     vertex->id, facet->id, neighbor->id, qh furthest_id);
-	      if (!qh FORCEoutput && !qh MERGING) {
-		qh_errprint ("ERRONEOUS", facet, neighbor, NULL, vertex);
-		if (!qh MERGING)
-		  qh_errexit (qh_ERRqhull, NULL, NULL);
-	      }
-	    }
-	  }
-	}
-      }
-      qh_settempfree (&intersection);
-    }
-  }else { /* simplicial */
-    FOREACHneighbor_(facet) {
-      if (neighbor->simplicial) {
-	skipA= SETindex_(facet->neighbors, neighbor);
-	skipB= qh_setindex (neighbor->neighbors, facet);
-	if (!qh_setequal_skip (facet->vertices, skipA, neighbor->vertices, skipB)) {
-	  fprintf (qh ferr, "qhull internal error (qh_checkfacet): facet f%d skip %d and neighbor f%d skip %d do not match \n",
-		   facet->id, skipA, neighbor->id, skipB);
-	  errother= neighbor;
-	  waserror= True;
-	}
-      }
-    }
-  }
-  if (qh hull_dim < 5 && (qh IStracing > 2 || qh CHECKfrequently)) {
-    FOREACHridge_i_(facet->ridges) {           /* expensive */
-      for (i= ridge_i+1; i < ridge_n; i++) {
-	ridge2= SETelemt_(facet->ridges, i, ridgeT);
-	if (qh_setequal (ridge->vertices, ridge2->vertices)) {
-	  fprintf (qh ferr, "qh_checkfacet: ridges r%d and r%d have the same vertices\n",
-		  ridge->id, ridge2->id);
-	  errridge= ridge;
-	  waserror= True;
-	}
-      }
-    }
-  }
-  if (waserror) {
-    qh_errprint("ERRONEOUS", facet, errother, errridge, NULL);
-    *waserrorp= True;
-  }
-} /* checkfacet */
-
-
-/*---------------------------------
-
-  qh_checkflipped_all( facetlist )
-    checks orientation of facets in list against interior point
-*/
-void qh_checkflipped_all (facetT *facetlist) {
-  facetT *facet;
-  boolT waserror= False;
-  realT dist;
-
-  if (facetlist == qh facet_list)
-    zzval_(Zflippedfacets)= 0;
-  FORALLfacet_(facetlist) {
-    if (facet->normal && !qh_checkflipped (facet, &dist, !qh_ALL)) {
-      fprintf(qh ferr, "qhull precision error: facet f%d is flipped, distance= %6.12g\n",
-	      facet->id, dist);
-      if (!qh FORCEoutput) {
-	qh_errprint("ERRONEOUS", facet, NULL, NULL, NULL);
-	waserror= True;
-      }
-    }
-  }
-  if (waserror) {
-    fprintf (qh ferr, "\n\
-A flipped facet occurs when its distance to the interior point is\n\
-greater than %2.2g, the maximum roundoff error.\n", -qh DISTround);
-    qh_errexit(qh_ERRprec, NULL, NULL);
-  }
-} /* checkflipped_all */
-
-/*---------------------------------
-
-  qh_checkpolygon( facetlist )
-    checks the correctness of the structure
-
-  notes:
-    call with either qh.facet_list or qh.newfacet_list
-    checks num_facets and num_vertices if qh.facet_list
-
-  design:
-    for each facet
-      checks facet and outside set
-    initializes vertexlist
-    for each facet
-      checks vertex set
-    if checking all facets (qh.facetlist)
-      check facet count
-      if qh.VERTEXneighbors
-        check vertex neighbors and count
-      check vertex count
-*/
-void qh_checkpolygon(facetT *facetlist) {
-  facetT *facet;
-  vertexT *vertex, **vertexp, *vertexlist;
-  int numfacets= 0, numvertices= 0, numridges= 0;
-  int totvneighbors= 0, totvertices= 0;
-  boolT waserror= False, nextseen= False, visibleseen= False;
-
-  trace1((qh ferr, "qh_checkpolygon: check all facets from f%d\n", facetlist->id));
-  if (facetlist != qh facet_list || qh ONLYgood)
-    nextseen= True;
-  FORALLfacet_(facetlist) {
-    if (facet == qh visible_list)
-      visibleseen= True;
-    if (!facet->visible) {
-      if (!nextseen) {
-	if (facet == qh facet_next)
-	  nextseen= True;
-	else if (qh_setsize (facet->outsideset)) {
-	  if (!qh NARROWhull
-#if !qh_COMPUTEfurthest
-	       || facet->furthestdist >= qh MINoutside
-#endif
-			) {
-	    fprintf (qh ferr, "qhull internal error (qh_checkpolygon): f%d has outside points before qh facet_next\n",
-		     facet->id);
-	    qh_errexit (qh_ERRqhull, facet, NULL);
-	  }
-	}
-      }
-      numfacets++;
-      qh_checkfacet(facet, False, &waserror);
-    }
-  }
-  if (qh visible_list && !visibleseen && facetlist == qh facet_list) {
-    fprintf (qh ferr, "qhull internal error (qh_checkpolygon): visible list f%d no longer on facet list\n", qh visible_list->id);
-    qh_printlists();
-    qh_errexit (qh_ERRqhull, qh visible_list, NULL);
-  }
-  if (facetlist == qh facet_list)
-    vertexlist= qh vertex_list;
-  else if (facetlist == qh newfacet_list)
-    vertexlist= qh newvertex_list;
-  else
-    vertexlist= NULL;
-  FORALLvertex_(vertexlist) {
-    vertex->seen= False;
-    vertex->visitid= 0;
-  }
-  FORALLfacet_(facetlist) {
-    if (facet->visible)
-      continue;
-    if (facet->simplicial)
-      numridges += qh hull_dim;
-    else
-      numridges += qh_setsize (facet->ridges);
-    FOREACHvertex_(facet->vertices) {
-      vertex->visitid++;
-      if (!vertex->seen) {
-	vertex->seen= True;
-	numvertices++;
-	if (qh_pointid (vertex->point) == -1) {
-	  fprintf (qh ferr, "qhull internal error (qh_checkpolygon): unknown point %p for vertex v%d first_point %p\n",
-		   vertex->point, vertex->id, qh first_point);
-	  waserror= True;
-	}
-      }
-    }
-  }
-  qh vertex_visit += numfacets;
-  if (facetlist == qh facet_list) {
-    if (numfacets != qh num_facets - qh num_visible) {
-      fprintf(qh ferr, "qhull internal error (qh_checkpolygon): actual number of facets is %d, cumulative facet count is %d - %d visible facets\n",
-	      numfacets, qh num_facets, qh num_visible);
-      waserror= True;
-    }
-    qh vertex_visit++;
-    if (qh VERTEXneighbors) {
-      FORALLvertices {
-	qh_setcheck (vertex->neighbors, "neighbors for v", vertex->id);
-	if (vertex->deleted)
-	  continue;
-	totvneighbors += qh_setsize (vertex->neighbors);
-      }
-      FORALLfacet_(facetlist)
-	totvertices += qh_setsize (facet->vertices);
-      if (totvneighbors != totvertices) {
-	fprintf(qh ferr, "qhull internal error (qh_checkpolygon): vertex neighbors inconsistent.  Totvneighbors %d, totvertices %d\n",
-		totvneighbors, totvertices);
-	waserror= True;
-      }
-    }
-    if (numvertices != qh num_vertices - qh_setsize(qh del_vertices)) {
-      fprintf(qh ferr, "qhull internal error (qh_checkpolygon): actual number of vertices is %d, cumulative vertex count is %d\n",
-	      numvertices, qh num_vertices - qh_setsize(qh del_vertices));
-      waserror= True;
-    }
-    if (qh hull_dim == 2 && numvertices != numfacets) {
-      fprintf (qh ferr, "qhull internal error (qh_checkpolygon): #vertices %d != #facets %d\n",
-        numvertices, numfacets);
-      waserror= True;
-    }
-    if (qh hull_dim == 3 && numvertices + numfacets - numridges/2 != 2) {
-      fprintf (qh ferr, "qhull warning: #vertices %d + #facets %d - #edges %d != 2\n\
-	A vertex appears twice in a edge list.  May occur during merging.",
-        numvertices, numfacets, numridges/2);
-      /* occurs if lots of merging and a vertex ends up twice in an edge list.  e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv */
-    }
-  }
-  if (waserror)
-    qh_errexit(qh_ERRqhull, NULL, NULL);
-} /* checkpolygon */
-
-
-/*---------------------------------
-
-  qh_checkvertex( vertex )
-    check vertex for consistency
-    checks vertex->neighbors
-
-  notes:
-    neighbors checked efficiently in checkpolygon
-*/
-void qh_checkvertex (vertexT *vertex) {
-  boolT waserror= False;
-  facetT *neighbor, **neighborp, *errfacet=NULL;
-
-  if (qh_pointid (vertex->point) == -1) {
-    fprintf (qh ferr, "qhull internal error (qh_checkvertex): unknown point id %p\n", vertex->point);
-    waserror= True;
-  }
-  if (vertex->id >= qh vertex_id) {
-    fprintf (qh ferr, "qhull internal error (qh_checkvertex): unknown vertex id %d\n", vertex->id);
-    waserror= True;
-  }
-  if (!waserror && !vertex->deleted) {
-    if (qh_setsize (vertex->neighbors)) {
-      FOREACHneighbor_(vertex) {
-        if (!qh_setin (neighbor->vertices, vertex)) {
-          fprintf (qh ferr, "qhull internal error (qh_checkvertex): neighbor f%d does not contain v%d\n", neighbor->id, vertex->id);
-	  errfacet= neighbor;
-	  waserror= True;
-	}
-      }
-    }
-  }
-  if (waserror) {
-    qh_errprint ("ERRONEOUS", NULL, NULL, NULL, vertex);
-    qh_errexit (qh_ERRqhull, errfacet, NULL);
-  }
-} /* checkvertex */
-
-/*---------------------------------
-
-  qh_clearcenters( type )
-    clear old data from facet->center
-
-  notes:
-    sets new centertype
-    nop if CENTERtype is the same
-*/
-void qh_clearcenters (qh_CENTER type) {
-  facetT *facet;
-
-  if (qh CENTERtype != type) {
-    FORALLfacets {
-      if (qh CENTERtype == qh_ASvoronoi){
-        if (facet->center) {
-          qh_memfree (facet->center, qh center_size);
-          facet->center= NULL;
-        }
-      }else /* qh CENTERtype == qh_AScentrum */ {
-        if (facet->center) {
-          qh_memfree (facet->center, qh normal_size);
-	  facet->center= NULL;
-        }
-      }
-    }
-    qh CENTERtype= type;
-  }
-  trace2((qh ferr, "qh_clearcenters: switched to center type %d\n", type));
-} /* clearcenters */
-
-/*---------------------------------
-
-  qh_createsimplex( vertices )
-    creates a simplex from a set of vertices
-
-  returns:
-    initializes qh.facet_list to the simplex
-    initializes qh.newfacet_list, .facet_tail
-    initializes qh.vertex_list, .newvertex_list, .vertex_tail
-
-  design:
-    initializes lists
-    for each vertex
-      create a new facet
-    for each new facet
-      create its neighbor set
-*/
-void qh_createsimplex(setT *vertices) {
-  facetT *facet= NULL, *newfacet;
-  boolT toporient= True;
-  int vertex_i, vertex_n, nth;
-  setT *newfacets= qh_settemp (qh hull_dim+1);
-  vertexT *vertex;
-
-  qh facet_list= qh newfacet_list= qh facet_tail= qh_newfacet();
-  qh num_facets= qh num_vertices= qh num_visible= 0;
-  qh vertex_list= qh newvertex_list= qh vertex_tail= qh_newvertex(NULL);
-  FOREACHvertex_i_(vertices) {
-    newfacet= qh_newfacet();
-    newfacet->vertices= qh_setnew_delnthsorted (vertices, vertex_n,
-						vertex_i, 0);
-    newfacet->toporient= toporient;
-    qh_appendfacet(newfacet);
-    newfacet->newfacet= True;
-    qh_appendvertex (vertex);
-    qh_setappend (&newfacets, newfacet);
-    toporient ^= True;
-  }
-  FORALLnew_facets {
-    nth= 0;
-    FORALLfacet_(qh newfacet_list) {
-      if (facet != newfacet)
-        SETelem_(newfacet->neighbors, nth++)= facet;
-    }
-    qh_settruncate (newfacet->neighbors, qh hull_dim);
-  }
-  qh_settempfree (&newfacets);
-  trace1((qh ferr, "qh_createsimplex: created simplex\n"));
-} /* createsimplex */
-
-/*---------------------------------
-
-  qh_delridge( ridge )
-    deletes ridge from data structures it belongs to
-    frees up its memory
-
-  notes:
-    in merge.c, caller sets vertex->delridge for each vertex
-    ridges also freed in qh_freeqhull
-*/
-void qh_delridge(ridgeT *ridge) {
-  void **freelistp; /* used !qh_NOmem */
-
-  qh_setdel(ridge->top->ridges, ridge);
-  qh_setdel(ridge->bottom->ridges, ridge);
-  qh_setfree(&(ridge->vertices));
-  qh_memfree_(ridge, sizeof(ridgeT), freelistp);
-} /* delridge */
-
-
-/*---------------------------------
-
-  qh_delvertex( vertex )
-    deletes a vertex and frees its memory
-
-  notes:
-    assumes vertex->adjacencies have been updated if needed
-*/
-void qh_delvertex (vertexT *vertex) {
-
-  if (vertex == qh tracevertex)
-    qh tracevertex= NULL;
-  qh_removevertex (vertex);
-  qh_setfree (&vertex->neighbors);
-  qh_memfree(vertex, sizeof(vertexT));
-} /* delvertex */
-
-
-/*---------------------------------
-
-  qh_facet3vertex(  )
-    return temporary set of 3-d vertices in qh_ORIENTclock order
-
-  design:
-    if simplicial facet
-      build set from facet->vertices with facet->toporient
-    else
-      for each ridge in order
-        build set from ridge's vertices
-*/
-setT *qh_facet3vertex (facetT *facet) {
-  ridgeT *ridge, *firstridge;
-  vertexT *vertex;
-  int cntvertices, cntprojected=0;
-  setT *vertices;
-
-  cntvertices= qh_setsize(facet->vertices);
-  vertices= qh_settemp (cntvertices);
-  if (facet->simplicial) {
-    if (cntvertices != 3) {
-      fprintf (qh ferr, "qhull internal error (qh_facet3vertex): only %d vertices for simplicial facet f%d\n",
-                  cntvertices, facet->id);
-      qh_errexit(qh_ERRqhull, facet, NULL);
-    }
-    qh_setappend (&vertices, SETfirst_(facet->vertices));
-    if (facet->toporient ^ qh_ORIENTclock)
-      qh_setappend (&vertices, SETsecond_(facet->vertices));
-    else
-    qh_setappend (&vertices, SETelem_(facet->vertices, 2));
-  }else {
-    ridge= firstridge= SETfirstt_(facet->ridges, ridgeT);   /* no infinite */
-    while ((ridge= qh_nextridge3d (ridge, facet, &vertex))) {
-      qh_setappend (&vertices, vertex);
-      if (++cntprojected > cntvertices || ridge == firstridge)
-        break;
-    }
-    if (!ridge || cntprojected != cntvertices) {
-      fprintf (qh ferr, "qhull internal error (qh_facet3vertex): ridges for facet %d don't match up.  got at least %d\n",
-                  facet->id, cntprojected);
-      qh_errexit(qh_ERRqhull, facet, ridge);
-    }
-  }
-  return vertices;
-} /* facet3vertex */
-
-/*---------------------------------
-
-  qh_findbestfacet( point, bestoutside, bestdist, isoutside )
-    find facet that is furthest below a point
-
-    for Delaunay triangulations,
-      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
-      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
-
-  returns:
-    if bestoutside is set (e.g., qh_ALL)
-      returns best facet that is not upperdelaunay
-      if Delaunay and inside, point is outside circumsphere of bestfacet
-    else
-      returns first facet below point
-      if point is inside, returns nearest, !upperdelaunay facet
-    distance to facet
-    isoutside set if outside of facet
-
-  notes:
-    this works for all distributions
-    if inside, qh_findbestfacet performs an exhaustive search
-       this may be too conservative.  Sometimes it is clearly required.
-    qh_findbestfacet is not used by qhull.
-    uses qh.visit_id and qh.coplanarset
-
-  see:
-    qh_findbest
-*/
-facetT *qh_findbestfacet (pointT *point, boolT bestoutside,
-           realT *bestdist, boolT *isoutside) {
-  facetT *bestfacet= NULL;
-  int numpart, totpart= 0;
-
-  bestfacet= qh_findbest (point, qh facet_list,
-			    bestoutside, !qh_ISnewfacets, bestoutside /* qh_NOupper */,
-			    bestdist, isoutside, &totpart);
-  if (*bestdist < -qh DISTround) {
-    bestfacet= qh_findfacet_all (point, bestdist, isoutside, &numpart);
-    totpart += numpart;
-    if ((isoutside && bestoutside)
-    || (!isoutside && bestfacet->upperdelaunay)) {
-      bestfacet= qh_findbest (point, bestfacet,
-			    bestoutside, False, bestoutside,
-			    bestdist, isoutside, &totpart);
-      totpart += numpart;
-    }
-  }
-  trace3((qh ferr, "qh_findbestfacet: f%d dist %2.2g isoutside %d totpart %d\n",
-	  bestfacet->id, *bestdist, *isoutside, totpart));
-  return bestfacet;
-} /* findbestfacet */
-
-/*---------------------------------
-
-  qh_findfacet_all( point, bestdist, isoutside, numpart )
-    exhaustive search for facet below a point
-
-    for Delaunay triangulations,
-      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
-      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
-
-  returns:
-    returns first facet below point
-    if point is inside,
-      returns nearest facet
-    distance to facet
-    isoutside if point is outside of the hull
-    number of distance tests
-*/
-facetT *qh_findfacet_all (pointT *point, realT *bestdist, boolT *isoutside,
-			  int *numpart) {
-  facetT *bestfacet= NULL, *facet;
-  realT dist;
-  int totpart= 0;
-
-  *bestdist= REALmin;
-  *isoutside= False;
-  FORALLfacets {
-    if (facet->flipped || !facet->normal)
-      continue;
-    totpart++;
-    qh_distplane (point, facet, &dist);
-    if (dist > *bestdist) {
-      *bestdist= dist;
-      bestfacet= facet;
-      if (dist > qh MINoutside) {
-        *isoutside= True;
-        break;
-      }
-    }
-  }
-  *numpart= totpart;
-  trace3((qh ferr, "qh_findfacet_all: f%d dist %2.2g isoutside %d totpart %d\n",
-	  getid_(bestfacet), *bestdist, *isoutside, totpart));
-  return bestfacet;
-} /* findfacet_all */
-
-/*---------------------------------
-
-  qh_findgood( facetlist, goodhorizon )
-    identify good facets for qh.PRINTgood
-    if qh.GOODvertex>0
-      facet includes point as vertex
-      if !match, returns goodhorizon
-      inactive if qh.MERGING
-    if qh.GOODpoint
-      facet is visible or coplanar (>0) or not visible (<0)
-    if qh.GOODthreshold
-      facet->normal matches threshold
-    if !goodhorizon and !match,
-      selects facet with closest angle
-      sets GOODclosest
-
-  returns:
-    number of new, good facets found
-    determines facet->good
-    may update qh.GOODclosest
-
-  notes:
-    qh_findgood_all further reduces the good region
-
-  design:
-    count good facets
-    mark good facets for qh.GOODpoint
-    mark good facets for qh.GOODthreshold
-    if necessary
-      update qh.GOODclosest
-*/
-int qh_findgood (facetT *facetlist, int goodhorizon) {
-  facetT *facet, *bestfacet= NULL;
-  realT angle, bestangle= REALmax, dist;
-  int  numgood=0;
-
-  FORALLfacet_(facetlist) {
-    if (facet->good)
-      numgood++;
-  }
-  if (qh GOODvertex>0 && !qh MERGING) {
-    FORALLfacet_(facetlist) {
-      if (!qh_isvertex (qh GOODvertexp, facet->vertices)) {
-        facet->good= False;
-        numgood--;
-      }
-    }
-  }
-  if (qh GOODpoint && numgood) {
-    FORALLfacet_(facetlist) {
-      if (facet->good && facet->normal) {
-        zinc_(Zdistgood);
-        qh_distplane (qh GOODpointp, facet, &dist);
-        if ((qh GOODpoint > 0) ^ (dist > 0.0)) {
-          facet->good= False;
-          numgood--;
-        }
-      }
-    }
-  }
-  if (qh GOODthreshold && (numgood || goodhorizon || qh GOODclosest)) {
-    FORALLfacet_(facetlist) {
-      if (facet->good && facet->normal) {
-        if (!qh_inthresholds (facet->normal, &angle)) {
-          facet->good= False;
-          numgood--;
-          if (angle < bestangle) {
-            bestangle= angle;
-            bestfacet= facet;
-          }
-        }
-      }
-    }
-    if (!numgood && (!goodhorizon || qh GOODclosest)) {
-      if (qh GOODclosest) {
-	if (qh GOODclosest->visible)
-	  qh GOODclosest= NULL;
-	else {
-	  qh_inthresholds (qh GOODclosest->normal, &angle);
-	  if (angle < bestangle)
-	    bestfacet= qh GOODclosest;
-	}
-      }
-      if (bestfacet && bestfacet != qh GOODclosest) {
-	if (qh GOODclosest)
-	  qh GOODclosest->good= False;
-	qh GOODclosest= bestfacet;
-	bestfacet->good= True;
-	numgood++;
-	trace2((qh ferr, "qh_findgood: f%d is closest (%2.2g) to thresholds\n",
-           bestfacet->id, bestangle));
-	return numgood;
-      }
-    }else if (qh GOODclosest) { /* numgood > 0 */
-      qh GOODclosest->good= False;
-      qh GOODclosest= NULL;
-    }
-  }
-  trace2((qh ferr, "qh_findgood: found %d good facets with %d good horizon\n",
-               numgood, goodhorizon));
-  if (!numgood && qh GOODvertex>0 && !qh MERGING)
-    return goodhorizon;
-  return numgood;
-} /* findgood */
-
-/*---------------------------------
-
-  qh_findgood_all( facetlist )
-    apply other constraints for good facets (used by qh.PRINTgood)
-    if qh.GOODvertex
-      facet includes (>0) or doesn't include (<0) point as vertex
-      if last good facet and ONLYgood, prints warning and continues
-    if qh.SPLITthresholds
-      facet->normal matches threshold, or if none, the closest one
-    calls qh_findgood
-    nop if good not used
-
-  returns:
-    clears facet->good if not good
-    sets qh.num_good
-
-  notes:
-    this is like qh_findgood but more restrictive
-
-  design:
-    uses qh_findgood to mark good facets
-    marks facets for qh.GOODvertex
-    marks facets for qh.SPLITthreholds
-*/
-void qh_findgood_all (facetT *facetlist) {
-  facetT *facet, *bestfacet=NULL;
-  realT angle, bestangle= REALmax;
-  int  numgood=0, startgood;
-
-  if (!qh GOODvertex && !qh GOODthreshold && !qh GOODpoint
-  && !qh SPLITthresholds)
-    return;
-  if (!qh ONLYgood)
-    qh_findgood (qh facet_list, 0);
-  FORALLfacet_(facetlist) {
-    if (facet->good)
-      numgood++;
-  }
-  if (qh GOODvertex <0 || (qh GOODvertex > 0 && qh MERGING)) {
-    FORALLfacet_(facetlist) {
-      if (facet->good && ((qh GOODvertex > 0) ^ !!qh_isvertex (qh GOODvertexp, facet->vertices))) {
-        if (!--numgood) {
-	  if (qh ONLYgood) {
-            fprintf (qh ferr, "qhull warning: good vertex p%d does not match last good facet f%d.  Ignored.\n",
-               qh_pointid(qh GOODvertexp), facet->id);
-	    return;
-	  }else if (qh GOODvertex > 0)
-            fprintf (qh ferr, "qhull warning: point p%d is not a vertex ('QV%d').\n",
-		qh GOODvertex-1, qh GOODvertex-1);
-	  else
-            fprintf (qh ferr, "qhull warning: point p%d is a vertex for every facet ('QV-%d').\n",
-	        -qh GOODvertex - 1, -qh GOODvertex - 1);
-        }
-        facet->good= False;
-      }
-    }
-  }
-  startgood= numgood;
-  if (qh SPLITthresholds) {
-    FORALLfacet_(facetlist) {
-      if (facet->good) {
-        if (!qh_inthresholds (facet->normal, &angle)) {
-          facet->good= False;
-          numgood--;
-          if (angle < bestangle) {
-            bestangle= angle;
-            bestfacet= facet;
-          }
-        }
-      }
-    }
-    if (!numgood && bestfacet) {
-      bestfacet->good= True;
-      numgood++;
-      trace0((qh ferr, "qh_findgood_all: f%d is closest (%2.2g) to thresholds\n",
-           bestfacet->id, bestangle));
-      return;
-    }
-  }
-  qh num_good= numgood;
-  trace0((qh ferr, "qh_findgood_all: %d good facets remain out of %d facets\n",
-        numgood, startgood));
-} /* findgood_all */
-
-/*---------------------------------
-
-  qh_furthestnext()
-    set qh.facet_next to facet with furthest of all furthest points
-    searches all facets on qh.facet_list
-
-  notes:
-    this may help avoid precision problems
-*/
-void qh_furthestnext (void /* qh facet_list */) {
-  facetT *facet, *bestfacet= NULL;
-  realT dist, bestdist= -REALmax;
-
-  FORALLfacets {
-    if (facet->outsideset) {
-#if qh_COMPUTEfurthest
-      pointT *furthest;
-      furthest= (pointT*)qh_setlast (facet->outsideset);
-      zinc_(Zcomputefurthest);
-      qh_distplane (furthest, facet, &dist);
-#else
-      dist= facet->furthestdist;
-#endif
-      if (dist > bestdist) {
-	bestfacet= facet;
-	bestdist= dist;
-      }
-    }
-  }
-  if (bestfacet) {
-    qh_removefacet (bestfacet);
-    qh_prependfacet (bestfacet, &qh facet_next);
-    trace1((qh ferr, "qh_furthestnext: made f%d next facet (dist %.2g)\n",
-	    bestfacet->id, bestdist));
-  }
-} /* furthestnext */
-
-/*---------------------------------
-
-  qh_furthestout( facet )
-    make furthest outside point the last point of outsideset
-
-  returns:
-    clears facet->notfurthest
-    sets facet->furthestdist
-
-  design:
-    determine best point of outsideset
-    make it the last point of outsideset
-*/
-void qh_furthestout (facetT *facet) {
-  pointT *point, **pointp, *bestpoint= NULL;
-  realT dist, bestdist= -REALmax;
-
-  FOREACHpoint_(facet->outsideset) {
-    qh_distplane (point, facet, &dist);
-    zinc_(Zcomputefurthest);
-    if (dist > bestdist) {
-      bestpoint= point;
-      bestdist= dist;
-    }
-  }
-  if (bestpoint) {
-    qh_setdel (facet->outsideset, point);
-    qh_setappend (&facet->outsideset, point);
-#if !qh_COMPUTEfurthest
-    facet->furthestdist= bestdist;
-#endif
-  }
-  facet->notfurthest= False;
-  trace3((qh ferr, "qh_furthestout: p%d is furthest outside point of f%d\n",
-	  qh_pointid (point), facet->id));
-} /* furthestout */
-
-
-/*---------------------------------
-
-  qh_infiniteloop( facet )
-    report infinite loop error due to facet
-*/
-void qh_infiniteloop (facetT *facet) {
-
-  fprintf (qh ferr, "qhull internal error (qh_infiniteloop): potential infinite loop detected\n");
-  qh_errexit (qh_ERRqhull, facet, NULL);
-} /* qh_infiniteloop */
-
-/*---------------------------------
-
-  qh_initbuild()
-    initialize hull and outside sets with point array
-    qh.FIRSTpoint/qh.NUMpoints is point array
-    if qh.GOODpoint
-      adds qh.GOODpoint to initial hull
-
-  returns:
-    qh_facetlist with initial hull
-    points partioned into outside sets, coplanar sets, or inside
-    initializes qh.GOODpointp, qh.GOODvertexp,
-
-  design:
-    initialize global variables used during qh_buildhull
-    determine precision constants and points with max/min coordinate values
-      if qh.SCALElast, scale last coordinate (for 'd')
-    build initial simplex
-    partition input points into facets of initial simplex
-    set up lists
-    if qh.ONLYgood
-      check consistency
-*/
-void qh_initbuild( void) {
-  setT *maxpoints, *vertices;
-  facetT *facet;
-  int i, numpart;
-  realT dist;
-  boolT isoutside;
-
-  qh furthest_id= -1;
-  qh lastreport= 0;
-  qh facet_id= qh vertex_id= qh ridge_id= 0;
-  qh visit_id= qh vertex_visit= 0;
-  qh maxoutdone= False;
-
-  if (qh GOODpoint > 0)
-    qh GOODpointp= qh_point (qh GOODpoint-1);
-  else if (qh GOODpoint < 0)
-    qh GOODpointp= qh_point (-qh GOODpoint-1);
-  if (qh GOODvertex > 0)
-    qh GOODvertexp= qh_point (qh GOODvertex-1);
-  else if (qh GOODvertex < 0)
-    qh GOODvertexp= qh_point (-qh GOODvertex-1);
-  if ((qh GOODpoint
-       && (qh GOODpointp < qh first_point  /* also catches !GOODpointp */
-	   || qh GOODpointp > qh_point (qh num_points-1)))
-    || (qh GOODvertex
-	&& (qh GOODvertexp < qh first_point  /* also catches !GOODvertexp */
-	    || qh GOODvertexp > qh_point (qh num_points-1)))) {
-    fprintf (qh ferr, "qhull input error: either QGn or QVn point is > p%d\n",
-	     qh num_points-1);
-    qh_errexit (qh_ERRinput, NULL, NULL);
-  }
-  maxpoints= qh_maxmin(qh first_point, qh num_points, qh hull_dim);
-  if (qh SCALElast)
-    qh_scalelast (qh first_point, qh num_points, qh hull_dim,
-               qh MINlastcoord, qh MAXlastcoord, qh MAXwidth);
-  qh_detroundoff();
-  if (qh DELAUNAY && qh upper_threshold[qh hull_dim-1] > REALmax/2
-                  && qh lower_threshold[qh hull_dim-1] < -REALmax/2) {
-    for (i= qh_PRINTEND; i--; ) {
-      if (qh PRINTout[i] == qh_PRINTgeom && qh DROPdim < 0
- 	  && !qh GOODthreshold && !qh SPLITthresholds)
-	break;  /* in this case, don't set upper_threshold */
-    }
-    if (i < 0) {
-      if (qh UPPERdelaunay) { /* matches qh.upperdelaunay in qh_setfacetplane */
-	qh lower_threshold[qh hull_dim-1]= qh ANGLEround * qh_ZEROdelaunay;
-	qh GOODthreshold= True;
-      }else {
-	qh upper_threshold[qh hull_dim-1]= -qh ANGLEround * qh_ZEROdelaunay;
-        if (!qh GOODthreshold)
-	  qh SPLITthresholds= True; /* build upper-convex hull even if Qg */
-          /* qh_initqhull_globals errors if Qg without Pdk/etc. */
-      }
-    }
-  }
-  vertices= qh_initialvertices(qh hull_dim, maxpoints, qh first_point, qh num_points);
-  qh_initialhull (vertices);  /* initial qh facet_list */
-  qh_partitionall (vertices, qh first_point, qh num_points);
-  if (qh PRINToptions1st || qh TRACElevel || qh IStracing) {
-    if (qh TRACElevel || qh IStracing)
-      fprintf (qh ferr, "\nTrace level %d for %s | %s\n",
-         qh IStracing ? qh IStracing : qh TRACElevel, qh rbox_command, qh qhull_command);
-    fprintf (qh ferr, "Options selected for Qhull %s:\n%s\n", qh_VERSION, qh qhull_options);
-  }
-  qh_resetlists (False, qh_RESETvisible /*qh visible_list newvertex_list newfacet_list */);
-  qh facet_next= qh facet_list;
-  qh_furthestnext (/* qh facet_list */);
-  if (qh PREmerge) {
-    qh cos_max= qh premerge_cos;
-  }
-  if (qh ONLYgood) {
-    if (qh GOODvertex > 0 && qh MERGING) {
-      fprintf (qh ferr, "qhull input error: 'Qg QVn' (only good vertex) does not work with merging.\nUse 'QJ' to joggle the input or 'Q0' to turn off merging.\n");
-      qh_errexit (qh_ERRinput, NULL, NULL);
-    }
-    if (!(qh GOODthreshold || qh GOODpoint
-         || (!qh MERGEexact && !qh PREmerge && qh GOODvertexp))) {
-      fprintf (qh ferr, "qhull input error: 'Qg' (ONLYgood) needs a good threshold ('Pd0D0'), a\n\
-good point (QGn or QG-n), or a good vertex with 'QJ' or 'Q0' (QVn).\n");
-      qh_errexit (qh_ERRinput, NULL, NULL);
-    }
-    if (qh GOODvertex > 0  && !qh MERGING  /* matches qh_partitionall */
-	&& !qh_isvertex (qh GOODvertexp, vertices)) {
-      facet= qh_findbestnew (qh GOODvertexp, qh facet_list,
-			  &dist, !qh_ALL, &isoutside, &numpart);
-      if (!isoutside) {
-        fprintf (qh ferr, "qhull input error: point for QV%d is inside initial simplex.  It can not be made a vertex.\n",
-	       qh_pointid(qh GOODvertexp));
-        qh_errexit (qh_ERRinput, NULL, NULL);
-      }
-      if (!qh_addpoint (qh GOODvertexp, facet, False)) {
-	qh_settempfree(&vertices);
-	qh_settempfree(&maxpoints);
-	return;
-      }
-    }
-    qh_findgood (qh facet_list, 0);
-  }
-  qh_settempfree(&vertices);
-  qh_settempfree(&maxpoints);
-  trace1((qh ferr, "qh_initbuild: initial hull created and points partitioned\n"));
-} /* initbuild */
-
-/*---------------------------------
-
-  qh_initialhull( vertices )
-    constructs the initial hull as a DIM3 simplex of vertices
-
-  design:
-    creates a simplex (initializes lists)
-    determines orientation of simplex
-    sets hyperplanes for facets
-    doubles checks orientation (in case of axis-parallel facets with Gaussian elimination)
-    checks for flipped facets and qh.NARROWhull
-    checks the result
-*/
-void qh_initialhull(setT *vertices) {
-  facetT *facet, *firstfacet, *neighbor, **neighborp;
-  realT dist, angle, minangle= REALmax;
-#ifndef qh_NOtrace
-  int k;
-#endif
-
-  qh_createsimplex(vertices);  /* qh facet_list */
-  qh_resetlists (False, qh_RESETvisible);
-  qh facet_next= qh facet_list;      /* advance facet when processed */
-  qh interior_point= qh_getcenter(vertices);
-  firstfacet= qh facet_list;
-  qh_setfacetplane(firstfacet);
-  zinc_(Znumvisibility); /* needs to be in printsummary */
-  qh_distplane(qh interior_point, firstfacet, &dist);
-  if (dist > 0) {
-    FORALLfacets
-      facet->toporient ^= True;
-  }
-  FORALLfacets
-    qh_setfacetplane(facet);
-  FORALLfacets {
-    if (!qh_checkflipped (facet, NULL, qh_ALL)) {/* due to axis-parallel facet */
-      trace1((qh ferr, "qh_initialhull: initial orientation incorrect.  Correct all facets\n"));
-      facet->flipped= False;
-      FORALLfacets {
-	facet->toporient ^= True;
-	qh_orientoutside (facet);
-      }
-      break;
-    }
-  }
-  FORALLfacets {
-    if (!qh_checkflipped (facet, NULL, !qh_ALL)) {  /* can happen with 'R0.1' */
-      qh_precision ("initial facet is coplanar with interior point");
-      fprintf (qh ferr, "qhull precision error: initial facet %d is coplanar with the interior point\n",
-                   facet->id);
-      qh_errexit (qh_ERRsingular, facet, NULL);
-    }
-    FOREACHneighbor_(facet) {
-      angle= qh_getangle (facet->normal, neighbor->normal);
-      minimize_( minangle, angle);
-    }
-  }
-  if (minangle < qh_MAXnarrow && !qh NOnarrow) {
-    realT diff= 1.0 + minangle;
-
-    qh NARROWhull= True;
-    qh_option ("_narrow-hull", NULL, &diff);
-    if (minangle < qh_WARNnarrow && !qh RERUN && qh PRINTprecision)
-      fprintf (qh ferr, "qhull precision warning: \n\
-The initial hull is narrow (cosine of min. angle is %.16f).\n\
-A coplanar point may lead to a wide facet.  Options 'QbB' (scale to unit box)\n\
-or 'Qbb' (scale last coordinate) may remove this warning.  Use 'Pp' to skip\n\
-this warning.  See 'Limitations' in qh-impre.htm.\n",
-          -minangle);   /* convert from angle between normals to angle between facets */
-  }
-  zzval_(Zprocessed)= qh hull_dim+1;
-  qh_checkpolygon (qh facet_list);
-  qh_checkconvex(qh facet_list,   qh_DATAfault);
-#ifndef qh_NOtrace
-  if (qh IStracing >= 1) {
-    fprintf(qh ferr, "qh_initialhull: simplex constructed, interior point:");
-    for (k=0; k < qh hull_dim; k++)
-      fprintf (qh ferr, " %6.4g", qh interior_point[k]);
-    fprintf (qh ferr, "\n");
-  }
-#endif
-} /* initialhull */
-
-/*---------------------------------
-
-  qh_initialvertices( dim, maxpoints, points, numpoints )
-    determines a non-singular set of initial vertices
-    maxpoints may include duplicate points
-
-  returns:
-    temporary set of dim+1 vertices in descending order by vertex id
-    if qh.RANDOMoutside && !qh.ALLpoints
-      picks random points
-    if dim >= qh_INITIALmax,
-      uses min/max x and max points with non-zero determinants
-
-  notes:
-    unless qh.ALLpoints,
-      uses maxpoints as long as determinate is non-zero
-*/
-setT *qh_initialvertices(int dim, setT *maxpoints, pointT *points, int numpoints) {
-  pointT *point, **pointp;
-  setT *vertices, *simplex, *tested;
-  realT randr;
-  int index, point_i, point_n, k;
-  boolT nearzero= False;
-
-  vertices= qh_settemp (dim + 1);
-  simplex= qh_settemp (dim+1);
-  if (qh ALLpoints)
-    qh_maxsimplex (dim, NULL, points, numpoints, &simplex);
-  else if (qh RANDOMoutside) {
-    while (qh_setsize (simplex) != dim+1) {
-      randr= qh_RANDOMint;
-      randr= randr/(qh_RANDOMmax+1);
-      index= (int)floor(qh num_points * randr);
-      while (qh_setin (simplex, qh_point (index))) {
-	index++; /* in case qh_RANDOMint always returns the same value */
-        index= index < qh num_points ? index : 0;
-      }
-      qh_setappend (&simplex, qh_point (index));
-    }
-  }else if (qh hull_dim >= qh_INITIALmax) {
-    tested= qh_settemp (dim+1);
-    qh_setappend (&simplex, SETfirst_(maxpoints));   /* max and min X coord */
-    qh_setappend (&simplex, SETsecond_(maxpoints));
-    qh_maxsimplex (fmin_(qh_INITIALsearch, dim), maxpoints, points, numpoints, &simplex);
-    k= qh_setsize (simplex);
-    FOREACHpoint_i_(maxpoints) {
-      if (point_i & 0x1) {     /* first pick up max. coord. points */
-      	if (!qh_setin (simplex, point) && !qh_setin (tested, point)){
-	  qh_detsimplex(point, simplex, k, &nearzero);
-          if (nearzero)
-            qh_setappend (&tested, point);
-          else {
-            qh_setappend (&simplex, point);
-            if (++k == dim)  /* use search for last point */
-	      break;
-	  }
-	}
-      }
-    }
-    while (k != dim && (point= (pointT*)qh_setdellast (maxpoints))) {
-      if (!qh_setin (simplex, point) && !qh_setin (tested, point)){
-        qh_detsimplex (point, simplex, k, &nearzero);
-        if (nearzero)
-          qh_setappend (&tested, point);
-        else {
-          qh_setappend (&simplex, point);
-          k++;
-	}
-      }
-    }
-    index= 0;
-    while (k != dim && (point= qh_point (index++))) {
-      if (!qh_setin (simplex, point) && !qh_setin (tested, point)){
-        qh_detsimplex (point, simplex, k, &nearzero);
-        if (!nearzero){
-          qh_setappend (&simplex, point);
-          k++;
-	}
-      }
-    }
-    qh_settempfree (&tested);
-    qh_maxsimplex (dim, maxpoints, points, numpoints, &simplex);
-  }else
-    qh_maxsimplex (dim, maxpoints, points, numpoints, &simplex);
-  FOREACHpoint_(simplex)
-    qh_setaddnth (&vertices, 0, qh_newvertex(point)); /* descending order */
-  qh_settempfree (&simplex);
-  return vertices;
-} /* initialvertices */
-
-
-/*---------------------------------
-
-  qh_isvertex(  )
-    returns vertex if point is in vertex set, else returns NULL
-
-  notes:
-    for qh.GOODvertex
-*/
-vertexT *qh_isvertex (pointT *point, setT *vertices) {
-  vertexT *vertex, **vertexp;
-
-  FOREACHvertex_(vertices) {
-    if (vertex->point == point)
-      return vertex;
-  }
-  return NULL;
-} /* isvertex */
-
-/*---------------------------------
-
-  qh_makenewfacets( point )
-    make new facets from point and qh.visible_list
-
-  returns:
-    qh.newfacet_list= list of new facets with hyperplanes and ->newfacet
-    qh.newvertex_list= list of vertices in new facets with ->newlist set
-
-    if (qh.ONLYgood)
-      newfacets reference horizon facets, but not vice versa
-      ridges reference non-simplicial horizon ridges, but not vice versa
-      does not change existing facets
-    else
-      sets qh.NEWfacets
-      new facets attached to horizon facets and ridges
-      for visible facets,
-        visible->r.replace is corresponding new facet
-
-    qh_makenewplanes() -- make hyperplanes for facets
-    qh_attachnewfacets() -- attachnewfacets if not done here (qh ONLYgood)
-    qh_matchnewfacets() -- match up neighbors
-    qh_updatevertices() -- update vertex neighbors and delvertices
-    qh_deletevisible() -- delete visible facets
-    qh_checkpolygon() --check the result
-    qh_triangulate() -- triangulate a non-simplicial facet
-
-  design:
-    for each visible facet
-      make new facets to its horizon facets
-      update its f.replace
-      clear its neighbor set
-*/
-vertexT *qh_makenewfacets (pointT *point /*visible_list*/) {
-  facetT *visible, *newfacet= NULL, *newfacet2= NULL, *neighbor, **neighborp;
-  vertexT *apex;
-  int numnew=0;
-
-  qh newfacet_list= qh facet_tail;
-  qh newvertex_list= qh vertex_tail;
-  apex= qh_newvertex(point);
-  qh_appendvertex (apex);
-  qh visit_id++;
-  if (!qh ONLYgood)
-    qh NEWfacets= True;
-  FORALLvisible_facets {
-    FOREACHneighbor_(visible)
-      neighbor->seen= False;
-    if (visible->ridges) {
-      visible->visitid= qh visit_id;
-      newfacet2= qh_makenew_nonsimplicial (visible, apex, &numnew);
-    }
-    if (visible->simplicial)
-      newfacet= qh_makenew_simplicial (visible, apex, &numnew);
-    if (!qh ONLYgood) {
-      if (newfacet2)  /* newfacet is null if all ridges defined */
-        newfacet= newfacet2;
-      if (newfacet)
-      	visible->f.replace= newfacet;
-      else
-        zinc_(Zinsidevisible);
-      SETfirst_(visible->neighbors)= NULL;
-    }
-  }
-  trace1((qh ferr, "qh_makenewfacets: created %d new facets from point p%d to horizon\n",
-	  numnew, qh_pointid(point)));
-  if (qh IStracing >= 4)
-    qh_printfacetlist (qh newfacet_list, NULL, qh_ALL);
-  return apex;
-} /* makenewfacets */
-
-/*---------------------------------
-
-  qh_matchduplicates( atfacet, atskip, hashsize, hashcount )
-    match duplicate ridges in qh.hash_table for atfacet/atskip
-    duplicates marked with ->dupridge and qh_DUPLICATEridge
-
-  returns:
-    picks match with worst merge (min distance apart)
-
-    qh_matchneighbor
-
-  notes:
-
-  design:
-    compute hash value for atfacet and atskip
-    repeat twice -- once to make best matches, once to match the rest
-      for each possible facet in qh.hash_table
-        if it is a matching facet and pass 2
-          make match
-	  unless tricoplanar, mark match for merging (qh_MERGEridge)
-          [e.g., tricoplanar RBOX s 1000 t993602376 | QHULL C-1e-3 d Qbb FA Qt]
-        if it is a matching facet and pass 1
-          test if this is a better match
-      if pass 1,
-        make best match (it will not be merged)
-*/
-#ifndef qh_NOmerge
-void qh_matchduplicates (facetT *atfacet, int atskip, int hashsize, int *hashcount) {
-  boolT same, ismatch;
-  int hash, scan;
-  facetT *facet, *newfacet, *maxmatch= NULL, *maxmatch2= NULL, *nextfacet;
-  int skip, newskip, nextskip= 0, maxskip= 0, maxskip2= 0, makematch;
-  realT maxdist= -REALmax, mindist, dist2, low, high;
-
-  hash= (int)qh_gethash (hashsize, atfacet->vertices, qh hull_dim, 1,
-                     SETelem_(atfacet->vertices, atskip));
-  trace2((qh ferr, "qh_matchduplicates: find duplicate matches for f%d skip %d hash %d hashcount %d\n",
-	  atfacet->id, atskip, hash, *hashcount));
-  for (makematch= 0; makematch < 2; makematch++) {
-    qh visit_id++;
-    for (newfacet= atfacet, newskip= atskip; newfacet; newfacet= nextfacet, newskip= nextskip) {
-      zinc_(Zhashlookup);
-      nextfacet= NULL;
-      newfacet->visitid= qh visit_id;
-      for (scan= hash; (facet= SETelemt_(qh hash_table, scan, facetT));
-	   scan= (++scan >= hashsize ? 0 : scan)) {
-	if (!facet->dupridge || facet->visitid == qh visit_id)
-	  continue;
-	zinc_(Zhashtests);
-	if (qh_matchvertices (1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
-	  ismatch= (same == (newfacet->toporient ^ facet->toporient));
-	  if (SETelemt_(facet->neighbors, skip, facetT) != qh_DUPLICATEridge) {
-	    if (!makematch) {
-	      fprintf (qh ferr, "qhull internal error (qh_matchduplicates): missing dupridge at f%d skip %d for new f%d skip %d hash %d\n",
-		     facet->id, skip, newfacet->id, newskip, hash);
-	      qh_errexit2 (qh_ERRqhull, facet, newfacet);
-	    }
-	  }else if (ismatch && makematch) {
-	    if (SETelemt_(newfacet->neighbors, newskip, facetT) == qh_DUPLICATEridge) {
-	      SETelem_(facet->neighbors, skip)= newfacet;
-	      if (newfacet->tricoplanar)
-  		SETelem_(newfacet->neighbors, newskip)= facet;
-	      else
-		SETelem_(newfacet->neighbors, newskip)= qh_MERGEridge;
-	      *hashcount -= 2; /* removed two unmatched facets */
-	      trace4((qh ferr, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d merge\n",
-		    facet->id, skip, newfacet->id, newskip));
-	    }
-	  }else if (ismatch) {
-	    mindist= qh_getdistance (facet, newfacet, &low, &high);
-	    dist2= qh_getdistance (newfacet, facet, &low, &high);
-	    minimize_(mindist, dist2);
-	    if (mindist > maxdist) {
-	      maxdist= mindist;
-	      maxmatch= facet;
-	      maxskip= skip;
-	      maxmatch2= newfacet;
-	      maxskip2= newskip;
-	    }
-	    trace3((qh ferr, "qh_matchduplicates: duplicate f%d skip %d new f%d skip %d at dist %2.2g, max is now f%d f%d\n",
-		    facet->id, skip, newfacet->id, newskip, mindist,
-		    maxmatch->id, maxmatch2->id));
-	  }else { /* !ismatch */
-	    nextfacet= facet;
-	    nextskip= skip;
-	  }
-	}
-	if (makematch && !facet
-        && SETelemt_(facet->neighbors, skip, facetT) == qh_DUPLICATEridge) {
-	  fprintf (qh ferr, "qhull internal error (qh_matchduplicates): no MERGEridge match for duplicate f%d skip %d at hash %d\n",
-		     newfacet->id, newskip, hash);
-	  qh_errexit (qh_ERRqhull, newfacet, NULL);
-	}
-      }
-    } /* end of for each new facet at hash */
-    if (!makematch) {
-      if (!maxmatch) {
-	fprintf (qh ferr, "qhull internal error (qh_matchduplicates): no maximum match at duplicate f%d skip %d at hash %d\n",
-		     atfacet->id, atskip, hash);
-	qh_errexit (qh_ERRqhull, atfacet, NULL);
-      }
-      SETelem_(maxmatch->neighbors, maxskip)= maxmatch2;
-      SETelem_(maxmatch2->neighbors, maxskip2)= maxmatch;
-      *hashcount -= 2; /* removed two unmatched facets */
-      zzinc_(Zmultiridge);
-      trace0((qh ferr, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d keep\n",
-	      maxmatch->id, maxskip, maxmatch2->id, maxskip2));
-      qh_precision ("ridge with multiple neighbors");
-      if (qh IStracing >= 4)
-	qh_errprint ("DUPLICATED/MATCH", maxmatch, maxmatch2, NULL, NULL);
-    }
-  }
-} /* matchduplicates */
-
-/*---------------------------------
-
-  qh_nearcoplanar()
-    for all facets, remove near-inside points from facet->coplanarset
-    coplanar points defined by innerplane from qh_outerinner()
-
-  returns:
-    if qh KEEPcoplanar && !qh KEEPinside
-      facet->coplanarset only contains coplanar points
-    if qh.JOGGLEmax
-      drops inner plane by another qh.JOGGLEmax diagonal since a
-        vertex could shift out while a coplanar point shifts in
-
-  notes:
-    used for qh.PREmerge and qh.JOGGLEmax
-    must agree with computation of qh.NEARcoplanar in qh_detroundoff()
-  design:
-    if not keeping coplanar or inside points
-      free all coplanar sets
-    else if not keeping both coplanar and inside points
-      remove !coplanar or !inside points from coplanar sets
-*/
-void qh_nearcoplanar ( void /* qh.facet_list */) {
-  facetT *facet;
-  pointT *point, **pointp;
-  int numpart;
-  realT dist, innerplane;
-
-  if (!qh KEEPcoplanar && !qh KEEPinside) {
-    FORALLfacets {
-      if (facet->coplanarset)
-        qh_setfree( &facet->coplanarset);
-    }
-  }else if (!qh KEEPcoplanar || !qh KEEPinside) {
-    qh_outerinner (NULL, NULL, &innerplane);
-    if (qh JOGGLEmax < REALmax/2)
-      innerplane -= qh JOGGLEmax * sqrt (qh hull_dim);
-    numpart= 0;
-    FORALLfacets {
-      if (facet->coplanarset) {
-        FOREACHpoint_(facet->coplanarset) {
-          numpart++;
-	  qh_distplane (point, facet, &dist);
-  	  if (dist < innerplane) {
-	    if (!qh KEEPinside)
-              SETref_(point)= NULL;
-          }else if (!qh KEEPcoplanar)
-            SETref_(point)= NULL;
-        }
-	qh_setcompact (facet->coplanarset);
-      }
-    }
-  }
-} /* nearcoplanar */
-
-/*---------------------------------
-
-  qh_nearvertex( facet, point, bestdist )
-    return nearest vertex in facet to point
-
-  returns:
-    vertex and its distance
-
-  notes:
-    if qh.DELAUNAY
-      distance is measured in the input set
-    searches neighboring tricoplanar facets (requires vertexneighbors)
-      Slow implementation.  Recomputes vertex set for each point.
-    The vertex set could be stored in the qh.keepcentrum facet.
-*/
-vertexT *qh_nearvertex (facetT *facet, pointT *point, realT *bestdistp) {
-  realT bestdist= REALmax, dist;
-  vertexT *bestvertex= NULL, *vertex, **vertexp, *apex;
-  coordT *center;
-  facetT *neighbor, **neighborp;
-  setT *vertices;
-  int dim= qh hull_dim;
-
-  if (qh DELAUNAY)
-    dim--;
-  if (facet->tricoplanar) {
-    if (!qh VERTEXneighbors || !facet->center) {
-      fprintf(qh ferr, "qhull internal error (qh_nearvertex): qh.VERTEXneighbors and facet->center required for tricoplanar facets\n");
-      qh_errexit(qh_ERRqhull, NULL, NULL);
-    }
-    vertices= qh_settemp (qh TEMPsize);
-    apex= SETfirst_(facet->vertices);
-    center= facet->center;
-    FOREACHneighbor_(apex) {
-      if (neighbor->center == center) {
-	FOREACHvertex_(neighbor->vertices)
-	  qh_setappend(&vertices, vertex);
-      }
-    }
-  }else
-    vertices= facet->vertices;
-  FOREACHvertex_(vertices) {
-    dist= qh_pointdist (vertex->point, point, -dim);
-    if (dist < bestdist) {
-      bestdist= dist;
-      bestvertex= vertex;
-    }
-  }
-  if (facet->tricoplanar)
-    qh_settempfree (&vertices);
-  *bestdistp= sqrt (bestdist);
-  return bestvertex;
-} /* nearvertex */
-
-/*---------------------------------
-
-  qh_newhashtable( newsize )
-    returns size of qh.hash_table of at least newsize slots
-
-  notes:
-    assumes qh.hash_table is NULL
-    qh_HASHfactor determines the number of extra slots
-    size is not divisible by 2, 3, or 5
-*/
-int qh_newhashtable(int newsize) {
-  int size;
-
-  size= ((newsize+1)*qh_HASHfactor) | 0x1;  /* odd number */
-  while (True) {
-    if ((size%3) && (size%5))
-      break;
-    size += 2;
-    /* loop terminates because there is an infinite number of primes */
-  }
-  qh hash_table= qh_setnew (size);
-  qh_setzero (qh hash_table, 0, size);
-  return size;
-} /* newhashtable */
-
-/*---------------------------------
-
-  qh_newvertex( point )
-    returns a new vertex for point
-*/
-vertexT *qh_newvertex(pointT *point) {
-  vertexT *vertex;
-
-  zinc_(Ztotvertices);
-  vertex= (vertexT *)qh_memalloc(sizeof(vertexT));
-  memset ((char *) vertex, 0, sizeof (vertexT));
-  if (qh vertex_id == 0xFFFFFF) {
-    fprintf(qh ferr, "qhull input error: more than %d vertices.  ID field overflows and two vertices\n\
-may have the same identifier.  Vertices not sorted correctly.\n", 0xFFFFFF);
-    qh_errexit(qh_ERRinput, NULL, NULL);
-  }
-  if (qh vertex_id == qh tracevertex_id)
-    qh tracevertex= vertex;
-  vertex->id= qh vertex_id++;
-  vertex->point= point;
-  trace4((qh ferr, "qh_newvertex: vertex p%d (v%d) created\n", qh_pointid(vertex->point),
-	  vertex->id));
-  return (vertex);
-} /* newvertex */
-
-/*---------------------------------
-
-  qh_nextridge3d( atridge, facet, vertex )
-    return next ridge and vertex for a 3d facet
-
-  notes:
-    in qh_ORIENTclock order
-    this is a O(n^2) implementation to trace all ridges
-    be sure to stop on any 2nd visit
-
-  design:
-    for each ridge
-      exit if it is the ridge after atridge
-*/
-ridgeT *qh_nextridge3d (ridgeT *atridge, facetT *facet, vertexT **vertexp) {
-  vertexT *atvertex, *vertex, *othervertex;
-  ridgeT *ridge, **ridgep;
-
-  if ((atridge->top == facet) ^ qh_ORIENTclock)
-    atvertex= SETsecondt_(atridge->vertices, vertexT);
-  else
-    atvertex= SETfirstt_(atridge->vertices, vertexT);
-  FOREACHridge_(facet->ridges) {
-    if (ridge == atridge)
-      continue;
-    if ((ridge->top == facet) ^ qh_ORIENTclock) {
-      othervertex= SETsecondt_(ridge->vertices, vertexT);
-      vertex= SETfirstt_(ridge->vertices, vertexT);
-    }else {
-      vertex= SETsecondt_(ridge->vertices, vertexT);
-      othervertex= SETfirstt_(ridge->vertices, vertexT);
-    }
-    if (vertex == atvertex) {
-      if (vertexp)
-        *vertexp= othervertex;
-      return ridge;
-    }
-  }
-  return NULL;
-} /* nextridge3d */
-#else /* qh_NOmerge */
-void qh_matchduplicates (facetT *atfacet, int atskip, int hashsize, int *hashcount) {
-}
-ridgeT *qh_nextridge3d (ridgeT *atridge, facetT *facet, vertexT **vertexp) {
-
-  return NULL;
-}
-#endif /* qh_NOmerge */
-
-/*---------------------------------
-
-  qh_outcoplanar()
-    move points from all facets' outsidesets to their coplanarsets
-
-  notes:
-    for post-processing under qh.NARROWhull
-
-  design:
-    for each facet
-      for each outside point for facet
-        partition point into coplanar set
-*/
-void qh_outcoplanar (void /* facet_list */) {
-  pointT *point, **pointp;
-  facetT *facet;
-  realT dist;
-
-  trace1((qh ferr, "qh_outcoplanar: move outsideset to coplanarset for qh NARROWhull\n"));
-  FORALLfacets {
-    FOREACHpoint_(facet->outsideset) {
-      qh num_outside--;
-      if (qh KEEPcoplanar || qh KEEPnearinside) {
-	qh_distplane (point, facet, &dist);
-        zinc_(Zpartition);
-	qh_partitioncoplanar (point, facet, &dist);
-      }
-    }
-    qh_setfree (&facet->outsideset);
-  }
-} /* outcoplanar */
-
-/*---------------------------------
-
-  qh_point( id )
-    return point for a point id, or NULL if unknown
-
-  alternative code:
-    return ((pointT *)((unsigned   long)qh.first_point
-           + (unsigned long)((id)*qh.normal_size)));
-*/
-pointT *qh_point (int id) {
-
-  if (id < 0)
-    return NULL;
-  if (id < qh num_points)
-    return qh first_point + id * qh hull_dim;
-  id -= qh num_points;
-  if (id < qh_setsize (qh other_points))
-    return SETelemt_(qh other_points, id, pointT);
-  return NULL;
-} /* point */
-
-/*---------------------------------
-
-  qh_point_add( set, point, elem )
-    stores elem at set[point.id]
-
-  returns:
-    access function for qh_pointfacet and qh_pointvertex
-
-  notes:
-    checks point.id
-*/
-void qh_point_add (setT *set, pointT *point, void *elem) {
-  int id, size;
-
-  SETreturnsize_(set, size);
-  if ((id= qh_pointid(point)) < 0)
-    fprintf (qh ferr, "qhull internal warning (point_add): unknown point %p id %d\n",
-      point, id);
-  else if (id >= size) {
-    fprintf (qh ferr, "qhull internal errror (point_add): point p%d is out of bounds (%d)\n",
-	     id, size);
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }else
-    SETelem_(set, id)= elem;
-
-
-/*---------------------------------
-
-  qh_pointfacet()
-    return temporary set of facet for each point
-    the set is indexed by point id
-
-  notes:
-    vertices assigned to one of the facets
-    coplanarset assigned to the facet
-    outside set assigned to the facet
-    NULL if no facet for point (inside)
-      includes qh.GOODpointp
-
-  access:
-    FOREACHfacet_i_(facets) { ... }
-    SETelem_(facets, i)
-
-  design:
-    for each facet
-*/
-setT *qh_pointfacet (void /*qh facet_list*/) {
-  int numpoints= qh num_points + qh_setsize (qh other_points);
-  setT *facets;
-  facetT *facet;
-  vertexT *vertex, **vertexp;
-  pointT *point, **pointp;
-
-  facets= qh_settemp (numpoints);
-  qh_setzero (facets, 0, numpoints);
-  qh vertex_visit++;
-  FORALLfacets {
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->visitid != qh vertex_visit) {
-        vertex->visitid= qh vertex_visit;
-      }
-    }
-    FOREACHpoint_(facet->coplanarset)
-    FOREACHpoint_(facet->outsideset)
-  }
-  return facets;
-} /* pointfacet */
-
-/*---------------------------------
-
-  qh_pointvertex(  )
-    return temporary set of vertices indexed by point id
-    entry is NULL if no vertex for a point
-      this will include qh.GOODpointp
-
-  access:
-    FOREACHvertex_i_(vertices) { ... }
-    SETelem_(vertices, i)
-*/
-setT *qh_pointvertex (void /*qh facet_list*/) {
-  int numpoints= qh num_points + qh_setsize (qh other_points);
-  setT *vertices;
-  vertexT *vertex;
-
-  vertices= qh_settemp (numpoints);
-  qh_setzero (vertices, 0, numpoints);
-  FORALLvertices
-  return vertices;
-} /* pointvertex */
-
-
-/*---------------------------------
-
-  qh_prependfacet( facet, facetlist )
-    prepend facet to the start of a facetlist
-
-  returns:
-    increments qh.numfacets
-
-  notes:
-    be careful of prepending since it can lose a pointer.
-      e.g., can lose _next by deleting and then prepending before _next
-*/
-void qh_prependfacet(facetT *facet, facetT **facetlist) {
-  facetT *prevfacet, *list;
-
-
-  trace4((qh ferr, "qh_prependfacet: prepend f%d before f%d\n",
-	  facet->id, getid_(*facetlist)));
-  if (!*facetlist)
-    (*facetlist)= qh facet_tail;
-  list= *facetlist;
-  prevfacet= list->previous;
-  facet->previous= prevfacet;
-  if (prevfacet)
-    prevfacet->next= facet;
-  list->previous= facet;
-  facet->next= *facetlist;
-  if (qh facet_list == list)  /* this may change *facetlist */
-    qh facet_list= facet;
-  if (qh facet_next == list)
-    qh facet_next= facet;
-  *facetlist= facet;
-  qh num_facets++;
-} /* prependfacet */
-
-
-/*---------------------------------
-
-  qh_printhashtable( fp )
-    print hash table to fp
-
-  notes:
-    not in I/O to avoid bringing io.c in
-
-  design:
-    for each hash entry
-      if defined
-        if unmatched or will merge (NULL, qh_MERGEridge, qh_DUPLICATEridge)
-          print entry and neighbors
-*/
-void qh_printhashtable(FILE *fp) {
-  facetT *facet, *neighbor;
-  int id, facet_i, facet_n, neighbor_i= 0, neighbor_n= 0;
-  vertexT *vertex, **vertexp;
-
-  FOREACHfacet_i_(qh hash_table) {
-    if (facet) {
-      FOREACHneighbor_i_(facet) {
-        if (!neighbor || neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge)
-          break;
-      }
-      if (neighbor_i == neighbor_n)
-        continue;
-      fprintf (fp, "hash %d f%d ", facet_i, facet->id);
-      FOREACHvertex_(facet->vertices)
-        fprintf (fp, "v%d ", vertex->id);
-      fprintf (fp, "\n neighbors:");
-      FOREACHneighbor_i_(facet) {
-	if (neighbor == qh_MERGEridge)
-	  id= -3;
-	else if (neighbor == qh_DUPLICATEridge)
-	  id= -2;
-	else
-	  id= getid_(neighbor);
-        fprintf (fp, " %d", id);
-      }
-      fprintf (fp, "\n");
-    }
-  }
-} /* printhashtable */
-
-
-/*---------------------------------
-
-  qh_printlists( fp )
-    print out facet and vertex list for debugging (without 'f/v' tags)
-*/
-void qh_printlists (void) {
-  facetT *facet;
-  vertexT *vertex;
-  int count= 0;
-
-  fprintf (qh ferr, "qh_printlists: facets:");
-  FORALLfacets {
-    if (++count % 100 == 0)
-      fprintf (qh ferr, "\n     ");
-    fprintf (qh ferr, " %d", facet->id);
-  }
-  fprintf (qh ferr, "\n  new facets %d visible facets %d next facet for qh_addpoint %d\n  vertices (new %d):",
-     getid_(qh newfacet_list), getid_(qh visible_list), getid_(qh facet_next),
-     getid_(qh newvertex_list));
-  count = 0;
-  FORALLvertices {
-    if (++count % 100 == 0)
-      fprintf (qh ferr, "\n     ");
-    fprintf (qh ferr, " %d", vertex->id);
-  }
-  fprintf (qh ferr, "\n");
-} /* printlists */
-
-/*---------------------------------
-
-  qh_resetlists( stats, qh_RESETvisible )
-    reset newvertex_list, newfacet_list, visible_list
-    if stats,
-      maintains statistics
-
-  returns:
-    visible_list is empty if qh_deletevisible was called
-*/
-void qh_resetlists (boolT stats, boolT resetVisible /*qh newvertex_list newfacet_list visible_list*/) {
-  vertexT *vertex;
-  facetT *newfacet, *visible;
-  int totnew=0, totver=0;
-
-  if (stats) {
-    FORALLvertex_(qh newvertex_list)
-      totver++;
-    FORALLnew_facets
-      totnew++;
-    zmax_(Zvisvertexmax, totver);
-    zmax_(Znewfacetmax, totnew);
-  }
-  FORALLvertex_(qh newvertex_list)
-    vertex->newlist= False;
-  qh newvertex_list= NULL;
-  FORALLnew_facets
-    newfacet->newfacet= False;
-  qh newfacet_list= NULL;
-  if (resetVisible) {
-    FORALLvisible_facets {
-      visible->f.replace= NULL;
-      visible->visible= False;
-    }
-    qh num_visible= 0;
-  }
-  qh visible_list= NULL; /* may still have visible facets via qh_triangulate */
-  qh NEWfacets= False;
-} /* resetlists */
-
-/*---------------------------------
-
-  qh_setvoronoi_all()
-    compute Voronoi centers for all facets
-    includes upperDelaunay facets if qh.UPPERdelaunay ('Qu')
-
-  returns:
-    facet->center is the Voronoi center
-
-  notes:
-    this is unused/untested code
-
-  use:
-    FORALLvertices {...} to locate the vertex for a point.
-    FOREACHneighbor_(vertex) {...} to visit the Voronoi centers for a Voronoi cell.
-*/
-void qh_setvoronoi_all (void) {
-  facetT *facet;
-
-  qh_clearcenters (qh_ASvoronoi);
-  qh_vertexneighbors();
-
-  FORALLfacets {
-    if (!facet->normal || !facet->upperdelaunay || qh UPPERdelaunay) {
-      if (!facet->center)
-        facet->center= qh_facetcenter (facet->vertices);
-    }
-  }
-} /* setvoronoi_all */
-
-#ifndef qh_NOmerge
-
-/*---------------------------------
-
-  qh_triangulate()
-    triangulate non-simplicial facets on qh.facet_list,
-    if qh.CENTERtype=qh_ASvoronoi, sets Voronoi centers of non-simplicial facets
-
-  returns:
-    all facets simplicial
-    each tricoplanar facet has ->f.triowner == owner of ->center,normal,etc.
-
-  notes:
-    call after qh_check_output since may switch to Voronoi centers
-    Output may overwrite ->f.triowner with ->f.area
-*/
-void qh_triangulate (void /*qh facet_list*/) {
-  facetT *facet, *nextfacet, *owner;
-  int onlygood= qh ONLYgood;
-  facetT *neighbor, *visible= NULL, *facet1, *facet2, *new_facet_list= NULL;
-  facetT *orig_neighbor= NULL, *otherfacet;
-  vertexT *new_vertex_list= NULL;
-  mergeT *merge;
-  mergeType mergetype;
-  int neighbor_i, neighbor_n;
-
-  trace1((qh ferr, "qh_triangulate: triangulate non-simplicial facets\n"));
-  if (qh hull_dim == 2)
-    return;
-  if (qh VORONOI) {  /* otherwise lose Voronoi centers [could rebuild vertex set from tricoplanar] */
-    qh_clearcenters (qh_ASvoronoi);
-    qh_vertexneighbors();
-  }
-  qh ONLYgood= False; /* for makenew_nonsimplicial */
-  qh visit_id++;
-  qh NEWfacets= True;
-  qh degen_mergeset= qh_settemp (qh TEMPsize);
-  qh newvertex_list= qh vertex_tail;
-  for (facet= qh facet_list; facet && facet->next; facet= nextfacet) { /* non-simplicial facets moved to end */
-    nextfacet= facet->next;
-    if (facet->visible || facet->simplicial)
-      continue;
-    /* triangulate all non-simplicial facets, otherwise merging does not work, e.g., RBOX c P-0.1 P+0.1 P+0.1 D3 | QHULL d Qt Tv */
-    if (!new_facet_list)
-      new_facet_list= facet;  /* will be moved to end */
-    qh_triangulate_facet (facet, &new_vertex_list);
-  }
-  trace2((qh ferr, "qh_triangulate: delete null facets from f%d -- apex same as second vertex\n", getid_(new_facet_list)));
-  for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* null facets moved to end */
-    nextfacet= facet->next;
-    if (facet->visible)
-      continue;
-    if (facet->ridges) {
-      if (qh_setsize(facet->ridges) > 0) {
-	fprintf( qh ferr, "qhull error (qh_triangulate): ridges still defined for f%d\n", facet->id);
-	qh_errexit (qh_ERRqhull, facet, NULL);
-      }
-      qh_setfree (&facet->ridges);
-    }
-    if (SETfirst_(facet->vertices) == SETsecond_(facet->vertices)) {
-      zinc_(Ztrinull);
-      qh_triangulate_null (facet);
-    }
-  }
-  trace2((qh ferr, "qh_triangulate: delete %d or more mirror facets -- same vertices and neighbors\n", qh_setsize(qh degen_mergeset)));
-  qh visible_list= qh facet_tail;
-  while ((merge= (mergeT*)qh_setdellast (qh degen_mergeset))) {
-    facet1= merge->facet1;
-    facet2= merge->facet2;
-    mergetype= merge->type;
-    qh_memfree (merge, sizeof(mergeT));
-    if (mergetype == MRGmirror) {
-      zinc_(Ztrimirror);
-      qh_triangulate_mirror (facet1, facet2);
-    }
-  }
-  qh_settempfree(&qh degen_mergeset);
-  trace2((qh ferr, "qh_triangulate: update neighbor lists for vertices from v%d\n", getid_(new_vertex_list)));
-  qh newvertex_list= new_vertex_list;  /* all vertices of new facets */
-  qh visible_list= NULL;
-  qh_updatevertices(/*qh newvertex_list, empty newfacet_list and visible_list*/);
-  qh_resetlists (False, !qh_RESETvisible /*qh newvertex_list, empty newfacet_list and visible_list*/);
-
-  trace2((qh ferr, "qh_triangulate: identify degenerate tricoplanar facets from f%d\n", getid_(new_facet_list)));
-  trace2((qh ferr, "qh_triangulate: and replace facet->f.triowner with tricoplanar facets that own center, normal, etc.\n"));
-  FORALLfacet_(new_facet_list) {
-    if (facet->tricoplanar && !facet->visible) {
-      FOREACHneighbor_i_(facet) {
-	if (neighbor_i == 0) {  /* first iteration */
-	  if (neighbor->tricoplanar)
-            orig_neighbor= neighbor->f.triowner;
-	  else
-	    orig_neighbor= neighbor;
-	}else {
-	  if (neighbor->tricoplanar)
-  	    otherfacet= neighbor->f.triowner;
-	  else
-	    otherfacet= neighbor;
-	  if (orig_neighbor == otherfacet) {
-	    zinc_(Ztridegen);
-	    facet->degenerate= True;
-	    break;
-	  }
-	}
-      }
-    }
-  }
-
-  trace2((qh ferr, "qh_triangulate: delete visible facets -- non-simplicial, null, and mirrored facets\n"));
-  owner= NULL;
-  visible= NULL;
-  for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* may delete facet */
-    nextfacet= facet->next;
-    if (facet->visible) {
-      if (facet->tricoplanar) { /* a null or mirrored facet */
-	qh_delfacet(facet);
-	qh num_visible--;
-      }else {  /* a non-simplicial facet followed by its tricoplanars */
-	if (visible && !owner) {
-	  /*  RBOX 200 s D5 t1001471447 | QHULL Qt C-0.01 Qx Qc Tv Qt -- f4483 had 6 vertices/neighbors and 8 ridges */
-	  trace2((qh ferr, "qh_triangulate: all tricoplanar facets degenerate for non-simplicial facet f%d\n",
-		       visible->id));
-	  qh_delfacet(visible);
-	  qh num_visible--;
-	}
-	visible= facet;
-	owner= NULL;
-      }
-    }else if (facet->tricoplanar) {
-      if (facet->f.triowner != visible) {
-	fprintf( qh ferr, "qhull error (qh_triangulate): tricoplanar facet f%d not owned by its visible, non-simplicial facet f%d\n", facet->id, getid_(visible));
-	qh_errexit2 (qh_ERRqhull, facet, visible);
-      }
-      if (owner)
-	facet->f.triowner= owner;
-      else if (!facet->degenerate) {
-	owner= facet;
-	nextfacet= visible->next; /* rescan tricoplanar facets with owner */
-	facet->keepcentrum= True;  /* one facet owns ->normal, etc. */
-	facet->coplanarset= visible->coplanarset;
-	facet->outsideset= visible->outsideset;
-  	visible->coplanarset= NULL;
-	visible->outsideset= NULL;
-        if (!qh TRInormals) { /* center and normal copied to tricoplanar facets */
-	  visible->center= NULL;
-	  visible->normal= NULL;
-	}
-	qh_delfacet(visible);
-	qh num_visible--;
-      }
-    }
-  }
-  if (visible && !owner) {
-    trace2((qh ferr, "qh_triangulate: all tricoplanar facets degenerate for last non-simplicial facet f%d\n",
-	         visible->id));
-    qh_delfacet(visible);
-    qh num_visible--;
-  }
-  qh NEWfacets= False;
-  qh ONLYgood= onlygood; /* restore value */
-  if (qh CHECKfrequently)
-    qh_checkpolygon (qh facet_list);
-} /* triangulate */
-
-
-/*---------------------------------
-
-  qh_triangulate_facet (facetA)
-    triangulate a non-simplicial facet
-      if qh.CENTERtype=qh_ASvoronoi, sets its Voronoi center
-  returns:
-    qh.newfacet_list == simplicial facets
-      facet->tricoplanar set and ->keepcentrum false
-      facet->degenerate set if duplicated apex
-      facet->f.trivisible set to facetA
-      facet->center copied from facetA (created if qh_ASvoronoi)
-	qh_eachvoronoi, qh_detvridge, qh_detvridge3 assume centers copied
-      facet->normal,offset,maxoutside copied from facetA
-
-  notes:
-      qh_makenew_nonsimplicial uses neighbor->seen for the same
-
-      qh_makenewfacets() -- construct a cone of facets for a new vertex
-
-  design:
-      if qh_ASvoronoi,
-	 compute Voronoi center (facet->center)
-      select first vertex (highest ID to preserve ID ordering of ->vertices)
-      triangulate from vertex to ridges
-      copy facet->center, normal, offset
-      update vertex neighbors
-*/
-void qh_triangulate_facet (facetT *facetA, vertexT **first_vertex) {
-  facetT *newfacet;
-  facetT *neighbor, **neighborp;
-  vertexT *apex;
-  int numnew=0;
-
-  trace3((qh ferr, "qh_triangulate_facet: triangulate facet f%d\n", facetA->id));
-
-  if (qh IStracing >= 4)
-    qh_printfacet (qh ferr, facetA);
-  FOREACHneighbor_(facetA) {
-    neighbor->seen= False;
-    neighbor->coplanar= False;
-  }
-  if (qh CENTERtype == qh_ASvoronoi && !facetA->center  /* matches upperdelaunay in qh_setfacetplane() */
-        && fabs_(facetA->normal[qh hull_dim -1]) >= qh ANGLEround * qh_ZEROdelaunay) {
-    facetA->center= qh_facetcenter (facetA->vertices);
-  }
-  qh_willdelete (facetA, NULL);
-  qh newfacet_list= qh facet_tail;
-  facetA->visitid= qh visit_id;
-  apex= SETfirst_(facetA->vertices);
-  qh_makenew_nonsimplicial (facetA, apex, &numnew);
-  SETfirst_(facetA->neighbors)= NULL;
-  FORALLnew_facets {
-    newfacet->tricoplanar= True;
-    newfacet->f.trivisible= facetA;
-    newfacet->degenerate= False;
-    newfacet->upperdelaunay= facetA->upperdelaunay;
-    newfacet->good= facetA->good;
-    if (qh TRInormals) {
-      newfacet->keepcentrum= True;
-      newfacet->normal= qh_copypoints (facetA->normal, 1, qh hull_dim);
-      if (qh CENTERtype == qh_AScentrum)
-	newfacet->center= qh_getcentrum (newfacet);
-      else
-	newfacet->center= qh_copypoints (facetA->center, 1, qh hull_dim);
-    }else {
-      newfacet->keepcentrum= False;
-      newfacet->normal= facetA->normal;
-      newfacet->center= facetA->center;
-    }
-    newfacet->offset= facetA->offset;
-#if qh_MAXoutside
-    newfacet->maxoutside= facetA->maxoutside;
-#endif
-  }
-  qh_matchnewfacets(/*qh newfacet_list*/);
-  zinc_(Ztricoplanar);
-  zmax_(Ztricoplanarmax, numnew);
-  qh visible_list= NULL;
-  if (!(*first_vertex))
-    (*first_vertex)= qh newvertex_list;
-  qh newvertex_list= NULL;
-  qh_updatevertices(/*qh newfacet_list, empty visible_list and newvertex_list*/);
-  qh_resetlists (False, !qh_RESETvisible /*qh newfacet_list, empty visible_list and newvertex_list*/);
-} /* triangulate_facet */
-
-/*---------------------------------
-
-  qh_triangulate_link (oldfacetA, facetA, oldfacetB, facetB)
-    relink facetA to facetB via oldfacets
-  returns:
-    adds mirror facets to qh degen_mergeset (4-d and up only)
-  design:
-    if they are already neighbors, the opposing neighbors become MRGmirror facets
-*/
-void qh_triangulate_link (facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB) {
-  int errmirror= False;
-
-  trace3((qh ferr, "qh_triangulate_link: relink old facets f%d and f%d between neighbors f%d and f%d\n",
-         oldfacetA->id, oldfacetB->id, facetA->id, facetB->id));
-  if (qh_setin (facetA->neighbors, facetB)) {
-    if (!qh_setin (facetB->neighbors, facetA))
-      errmirror= True;
-    else
-      qh_appendmergeset (facetA, facetB, MRGmirror, NULL);
-  }else if (qh_setin (facetB->neighbors, facetA))
-    errmirror= True;
-  if (errmirror) {
-    fprintf( qh ferr, "qhull error (qh_triangulate_link): mirror facets f%d and f%d do not match for old facets f%d and f%d\n",
-       facetA->id, facetB->id, oldfacetA->id, oldfacetB->id);
-    qh_errexit2 (qh_ERRqhull, facetA, facetB);
-  }
-  qh_setreplace (facetB->neighbors, oldfacetB, facetA);
-  qh_setreplace (facetA->neighbors, oldfacetA, facetB);
-
-/*---------------------------------
-
-  qh_triangulate_mirror (facetA, facetB)
-    delete mirrored facets from qh_triangulate_null() and qh_triangulate_mirror
-      a mirrored facet shares the same vertices of a logical ridge
-  design:
-    since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
-    if they are already neighbors, the opposing neighbors become MRGmirror facets
-*/
-void qh_triangulate_mirror (facetT *facetA, facetT *facetB) {
-  facetT *neighbor, *neighborB;
-  int neighbor_i, neighbor_n;
-
-  trace3((qh ferr, "qh_triangulate_mirror: delete mirrored facets f%d and f%d\n",
-         facetA->id, facetB->id));
-  FOREACHneighbor_i_(facetA) {
-    neighborB= SETelemt_(facetB->neighbors, neighbor_i, facetT);
-    if (neighbor == neighborB)
-      continue; /* occurs twice */
-    qh_triangulate_link (facetA, neighbor, facetB, neighborB);
-  }
-  qh_willdelete (facetA, NULL);
-  qh_willdelete (facetB, NULL);
-} /* triangulate_mirror */
-
-/*---------------------------------
-
-  qh_triangulate_null (facetA)
-    remove null facetA from qh_triangulate_facet()
-      a null facet has vertex #1 (apex) == vertex #2
-  returns:
-    adds facetA to ->visible for deletion after qh_updatevertices
-    qh degen_mergeset contains mirror facets (4-d and up only)
-  design:
-    since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
-    if they are already neighbors, the opposing neighbors become MRGmirror facets
-*/
-void qh_triangulate_null (facetT *facetA) {
-  facetT *neighbor, *otherfacet;
-
-  trace3((qh ferr, "qh_triangulate_null: delete null facet f%d\n", facetA->id));
-  neighbor= SETfirst_(facetA->neighbors);
-  otherfacet= SETsecond_(facetA->neighbors);
-  qh_triangulate_link (facetA, neighbor, facetA, otherfacet);
-  qh_willdelete (facetA, NULL);
-} /* triangulate_null */
-
-#else /* qh_NOmerge */
-void qh_triangulate (void) {
-}
-#endif /* qh_NOmerge */
-
-   /*---------------------------------
-
-  qh_vertexintersect( vertexsetA, vertexsetB )
-    intersects two vertex sets (inverse id ordered)
-    vertexsetA is a temporary set at the top of qhmem.tempstack
-
-  returns:
-    replaces vertexsetA with the intersection
-
-  notes:
-    could overwrite vertexsetA if currently too slow
-*/
-void qh_vertexintersect(setT **vertexsetA,setT *vertexsetB) {
-  setT *intersection;
-
-  intersection= qh_vertexintersect_new (*vertexsetA, vertexsetB);
-  qh_settempfree (vertexsetA);
-  *vertexsetA= intersection;
-  qh_settemppush (intersection);
-} /* vertexintersect */
-
-/*---------------------------------
-
-  qh_vertexintersect_new(  )
-    intersects two vertex sets (inverse id ordered)
-
-  returns:
-    a new set
-*/
-setT *qh_vertexintersect_new (setT *vertexsetA,setT *vertexsetB) {
-  setT *intersection= qh_setnew (qh hull_dim - 1);
-
-  while (*vertexA && *vertexB) {
-    if (*vertexA  == *vertexB) {
-      qh_setappend(&intersection, *vertexA);
-      vertexA++; vertexB++;
-    }else {
-      if ((*vertexA)->id > (*vertexB)->id)
-        vertexA++;
-      else
-        vertexB++;
-    }
-  }
-  return intersection;
-} /* vertexintersect_new */
-
-/*---------------------------------
-
-  qh_vertexneighbors()
-    for each vertex in qh.facet_list,
-      determine its neighboring facets
-
-  returns:
-    sets qh.VERTEXneighbors
-      nop if qh.VERTEXneighbors already set
-
-  notes:
-    assumes all vertex->neighbors are NULL
-
-  design:
-    for each facet
-      for each vertex
-        append facet to vertex->neighbors
-*/
-void qh_vertexneighbors (void /*qh facet_list*/) {
-  facetT *facet;
-  vertexT *vertex, **vertexp;
-
-  if (qh VERTEXneighbors)
-    return;
-  trace1((qh ferr, "qh_vertexneighbors: determing neighboring facets for each vertex\n"));
-  qh vertex_visit++;
-  FORALLfacets {
-    if (facet->visible)
-      continue;
-    FOREACHvertex_(facet->vertices) {
-      if (vertex->visitid != qh vertex_visit) {
-        vertex->visitid= qh vertex_visit;
-        vertex->neighbors= qh_setnew (qh hull_dim);
-      }
-      qh_setappend (&vertex->neighbors, facet);
-    }
-  }
-  qh VERTEXneighbors= True;
-} /* vertexneighbors */
-
-/*---------------------------------
-
-  qh_vertexsubset( vertexsetA, vertexsetB )
-    returns True if vertexsetA is a subset of vertexsetB
-    assumes vertexsets are sorted
-
-  note:
-    empty set is a subset of any other set
-*/
-boolT qh_vertexsubset(setT *vertexsetA, setT *vertexsetB) {
-  vertexT **vertexA= (vertexT **) SETaddr_(vertexsetA, vertexT);
-  vertexT **vertexB= (vertexT **) SETaddr_(vertexsetB, vertexT);
-
-  while (True) {
-    if (!*vertexA)
-      return True;
-    if (!*vertexB)
-      return False;
-    if ((*vertexA)->id > (*vertexB)->id)
-      return False;
-    if (*vertexA  == *vertexB)
-      vertexA++;
-    vertexB++;
-  }
-  return False; /* avoid warnings */
-} /* vertexsubset */
diff --git a/extern/qhull/src/qconvex.c b/extern/qhull/src/qconvex.c
deleted file mode 100644
index 67b78646e50..00000000000
--- a/extern/qhull/src/qconvex.c
+++ /dev/null
@@ -1,334 +0,0 @@
-/*  ---------------------------------
-
-   qconvex.c
-      compute convex hulls using qhull
-
-   see unix.c for full interface
-
-   copyright (c) 1993-2002, The Geometry Center
-*/
-
-#include
-#include
-#include
-#include
-#include
-#include "qhull.h"
-#include "mem.h"
-#include "qset.h"
-
-#if __MWERKS__ && __POWERPC__
-#include
-#include
-#include
-#include
-
-#elif __cplusplus
-extern "C" {
-  int isatty (int);
-}
-
-#elif _MSC_VER
-#include
-#define isatty _isatty
-
-#else
-int isatty (int);  /* returns 1 if stdin is a tty
-		   if "Undefined symbol" this can be deleted along with call in main() */
-#endif
-
-/*---------------------------------
-
-  qh_prompt
-    long prompt for qconvex
-
-  notes:
-    restricted version of qhull.c
-
-  see:
-    concise prompt below
-*/
-
-/* duplicated in qconvex.htm */
-char hidden_options[]=" d v H Qbb Qf Qg Qm Qr Qu Qv Qx Qz TR E V Fp Gt Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
-
-char qh_prompta[]= "\n\
-qconvex- compute the convex hull\n\
-    http://www.geom.umn.edu/software/qhull  %s\n\
-\n\
-input (stdin):\n\
-    first lines: dimension and number of points (or vice-versa).\n\
-    other lines: point coordinates, best if one point per line\n\
-\n\
-options:\n\
-    Qt   - triangulated output\n\
-    QJ   - joggled input instead of merged facets\n\
-    Qc   - keep coplanar points with nearest facet\n\
-    Qi   - keep interior points with nearest facet\n\
-\n\
-Qhull control options:\n\
-    Qbk:n   - scale coord k so that low bound is n\n\
-      QBk:n - scale coord k so that upper bound is n (QBk is %2.2g)\n\
-    QbB  - scale input to unit cube centered at the origin\n\
-    Qbk:0Bk:0 - remove k-th coordinate from input\n\
-    QJn  - randomly joggle input in range [-n,n]\n\
-    QRn  - random rotation (n=seed, n=0 time, n=-1 time/no rotate)\n\
-%s%s%s%s";  /* split up qh_prompt for Visual C++ */
-char qh_promptb[]= "\
-    Qs   - search all points for the initial simplex\n\
-    QGn  - good facet if visible from point n, -n for not visible\n\
-    QVn  - good facet if it includes point n, -n if not\n\
-\n\
-";
-char qh_promptc[]= "\
-Trace options:\n\
-    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
-    Tc   - check frequently during execution\n\
-    Ts   - print statistics\n\
-    Tv   - verify result: structure, convexity, and point inclusion\n\
-    Tz   - send all output to stdout\n\
-    TFn  - report summary when n or more facets created\n\
-    TI file - input data from file, no spaces or single quotes\n\
-    TO file - output results to file, may be enclosed in single quotes\n\
-    TPn  - turn on tracing when point n added to hull\n\
-     TMn - turn on tracing at merge n\n\
-     TWn - trace merge facets when width > n\n\
-    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
-     TCn - stop qhull after building cone for point n (see TVn)\n\
-\n\
-Precision options:\n\
-    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
-     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
-           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
-    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
-    Un   - max distance below plane for a new, coplanar point\n\
-    Wn   - min facet width for outside point (before roundoff)\n\
-\n\
-Output formats (may be combined; if none, produces a summary to stdout):\n\
-    f    - facet dump\n\
-    G    - Geomview output (see below)\n\
-    i    - vertices incident to each facet\n\
-    m    - Mathematica output (2-d and 3-d)\n\
-    n    - normals with offsets\n\
-    o    - OFF file format (dim, points and facets; Voronoi regions)\n\
-    p    - point coordinates \n\
-    s    - summary (stderr)\n\
-\n\
-";
-char qh_promptd[]= "\
-More formats:\n\
-    Fa   - area for each facet\n\
-    FA   - compute total area and volume for option 's'\n\
-    Fc   - count plus coplanar points for each facet\n\
-           use 'Qc' (default) for coplanar and 'Qi' for interior\n\
-    FC   - centrum for each facet\n\
-    Fd   - use cdd format for input (homogeneous with offset first)\n\
-    FD   - use cdd format for numeric output (offset first)\n\
-    FF   - facet dump without ridges\n\
-    Fi   - inner plane for each facet\n\
-    FI   - ID for each facet\n\
-    Fm   - merge count for each facet (511 max)\n\
-    Fn   - count plus neighboring facets for each facet\n\
-    FN   - count plus neighboring facets for each point\n\
-    Fo   - outer plane (or max_outside) for each facet\n\
-    FO   - options and precision constants\n\
-    FP   - nearest vertex for each coplanar point\n\
-    FQ   - command used for qconvex\n\
-    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
-                      for output: #vertices, #facets,\n\
-                                  #coplanar points, #non-simplicial facets\n\
-                    #real (2), max outer plane, min vertex\n\
-    FS   - sizes:   #int (0) \n\
-                    #real(2) tot area, tot volume\n\
-    Ft   - triangulation with centrums for non-simplicial facets (OFF format)\n\
-    Fv   - count plus vertices for each facet\n\
-    FV   - average of vertices (a feasible point for 'H')\n\
-    Fx   - extreme points (in order for 2-d)\n\
-\n\
-";
-char qh_prompte[]= "\
-Geomview output (2-d, 3-d, and 4-d)\n\
-    Ga   - all points as dots\n\
-     Gp  -  coplanar points and vertices as radii\n\
-     Gv  -  vertices as spheres\n\
-    Gi   - inner planes only\n\
-     Gn  -  no planes\n\
-     Go  -  outer planes only\n\
-    Gc   - centrums\n\
-    Gh   - hyperplane intersections\n\
-    Gr   - ridges\n\
-    GDn  - drop dimension n in 3-d and 4-d output\n\
-\n\
-Print options:\n\
-    PAn  - keep n largest facets by area\n\
-    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
-    PDk:n - drop facet if normal[k] >= n\n\
-    Pg   - print good facets (needs 'QGn' or 'QVn')\n\
-    PFn  - keep facets whose area is at least n\n\
-    PG   - print neighbors of good facets\n\
-    PMn  - keep n facets with most merges\n\
-    Po   - force output.  If error, output neighborhood of facet\n\
-    Pp   - do not report precision problems\n\
-\n\
-    .    - list of all options\n\
-    -    - one line descriptions of all options\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt2
-    synopsis for qhull
-*/
-char qh_prompt2[]= "\n\
-qconvex- compute the convex hull.  Qhull %s\n\
-    input (stdin): dimension, number of points, point coordinates\n\
-\n\
-options (qconvex.htm):\n\
-    Qt   - triangulated output\n\
-    QJ   - joggled input instead of merged facets\n\
-    Tv   - verify result: structure, convexity, and point inclusion\n\
-    .    - concise list of all options\n\
-    -    - one-line description of all options\n\
-\n\
-output options (subset):\n\
-    s    - summary of results (default)\n\
-    i    - vertices incident to each facet\n\
-    n    - normals with offsets\n\
-    p    - vertex coordinates (includes coplanar points if 'Qc')\n\
-    Fx   - extreme points (convex hull vertices)\n\
-    FA   - compute total area and volume\n\
-    o    - OFF format (dim, n, points, facets)\n\
-    G    - Geomview output (2-d, 3-d, and 4-d)\n\
-    m    - Mathematica output (2-d and 3-d)\n\
-    QVn  - print facets that include point n, -n if not\n\
-    TO file- output results to file, may be enclosed in single quotes\n\
-\n\
-examples:\n\
-    rbox c D2 | qconvex s n                    rbox c D2 | qconvex i\n\
-    rbox c D2 | qconvex o                      rbox 1000 s | qconvex s Tv FA\n\
-    rbox c d D2 | qconvex s Qc Fx              rbox y 1000 W0 | qconvex s n\n\
-    rbox y 1000 W0 | qconvex s QJ              rbox d G1 D12 | qconvex QR0 FA Pp\n\
-    rbox c D7 | qconvex FA TF1000\n\
-\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt3
-    concise prompt for qhull
-*/
-char qh_prompt3[]= "\n\
-Qhull %s.\n\
-Except for 'F.' and 'PG', upper-case options take an argument.\n\
-\n\
- incidences     mathematica    normals        OFF_format     points\n\
- summary        facet_dump\n\
-\n\
- Farea          FArea_total    Fcoplanars     FCentrums      Fd_cdd_in\n\
- FD_cdd_out     FFacet_xridge  Finner         FIDs           Fmerges\n\
- Fneighbors     FNeigh_vertex  Fouter         FOptions       FPoint_near\n\
- FQhull         Fsummary       FSize          Fvertices      FVertex_ave\n\
- Fxtremes\n\
-\n\
- Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
- Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
-\n\
- PArea_keep     Pdrop d0:0D0   PFacet_area_keep Pgood        PGood_neighbors\n\
- PMerge_keep    Poutput_forced Pprecision_not\n\
-\n\
- QbBound 0:0.5  QbB_scale_box  Qcoplanar      QGood_point    Qinterior\n\
- QJoggle        Qrandom        QRotate        Qsearch_1st    Qtriangulate\n\
- QVertex_good\n\
-\n\
- T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
- TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
- TWide_trace    TVertex_stop   TCone_stop\n\
-\n\
- Angle_max      Centrum_size   Random_dist    Ucoplanar_max  Wide_outside\n\
-";
-
-/*---------------------------------
-
-  main( argc, argv )
-    processes the command line, calls qhull() to do the work, and exits
-
-  design:
-    initializes data structures
-    finishes initialization
-    computes convex hull and other structures
-    checks the result
-    writes the output
-    frees memory
-*/
-int main(int argc, char *argv[]) {
-  int curlong, totlong; /* used !qh_NOmem */
-  int exitcode, numpoints, dim;
-  coordT *points;
-  boolT ismalloc;
-
-#if __MWERKS__ && __POWERPC__
-  char inBuf[BUFSIZ], outBuf[BUFSIZ], errBuf[BUFSIZ];
-  SIOUXSettings.showstatusline= false;
-  SIOUXSettings.tabspaces= 1;
-  SIOUXSettings.rows= 40;
-  if (setvbuf (stdin, inBuf, _IOFBF, sizeof(inBuf)) < 0   /* w/o, SIOUX I/O is slow*/
-  || setvbuf (stdout, outBuf, _IOFBF, sizeof(outBuf)) < 0
-  || (stdout != stderr && setvbuf (stderr, errBuf, _IOFBF, sizeof(errBuf)) < 0))
-    fprintf (stderr, "qhull internal warning (main): could not change stdio to fully buffered.\n");
-  argc= ccommand(&argv);
-#endif
-
-  if ((argc == 1) && isatty( 0 /*stdin*/)) {
-    fprintf(stdout, qh_prompt2, qh_VERSION);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompta, qh_VERSION, qh_DEFAULTbox,
-		qh_promptb, qh_promptc, qh_promptd, qh_prompte);
-    exit(qh_ERRnone);
-  }
-  if (argc >1 && *argv[1] == '.' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompt3, qh_VERSION);
-    exit(qh_ERRnone);
-  }
-  qh_init_A (stdin, stdout, stderr, argc, argv);  /* sets qh qhull_command */
-  exitcode= setjmp (qh errexit); /* simple statement for CRAY J916 */
-  if (!exitcode) {
-    qh_checkflags (qh qhull_command, hidden_options);
-    qh_initflags (qh qhull_command);
-    points= qh_readpoints (&numpoints, &dim, &ismalloc);
-    if (dim >= 5) {
-      qh_option ("Qxact_merge", NULL, NULL);
-      qh MERGEexact= True; /* 'Qx' always */
-    }
-    qh_init_B (points, numpoints, dim, ismalloc);
-    qh_qhull();
-    qh_check_output();
-    qh_produce_output();
-    if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
-      qh_check_points();
-    exitcode= qh_ERRnone;
-  }
-  qh NOerrexit= True;  /* no more setjmp */
-#ifdef qh_NOmem
-  qh_freeqhull( True);
-#else
-  qh_freeqhull( False);
-  qh_memfreeshort (&curlong, &totlong);
-  if (curlong || totlong)
-    fprintf (stderr, "qhull internal warning (main): did not free %d bytes of long memory (%d pieces)\n",
-       totlong, curlong);
-#endif
-  return exitcode;
-} /* main */
-
diff --git a/extern/qhull/src/qdelaun.c b/extern/qhull/src/qdelaun.c
deleted file mode 100644
index 0e49d9c381e..00000000000
--- a/extern/qhull/src/qdelaun.c
+++ /dev/null
@@ -1,323 +0,0 @@
-/*  ---------------------------------
-
-   qdelaun.c
-     compute Delaunay triangulations and furthest-point Delaunay
-     triangulations using qhull
-
-   see unix.c for full interface
-
-   copyright (c) 1993-2002, The Geometry Center
-*/
-
-#include
-#include
-#include
-#include
-#include
-#include "qhull.h"
-#include "mem.h"
-#include "qset.h"
-
-#if __MWERKS__ && __POWERPC__
-#include
-#include
-#include
-#include
-
-#elif __cplusplus
-extern "C" {
-  int isatty (int);
-}
-
-#elif _MSC_VER
-#include
-#define isatty _isatty
-
-#else
-int isatty (int);  /* returns 1 if stdin is a tty
-		   if "Undefined symbol" this can be deleted along with call in main() */
-#endif
-
-/*---------------------------------
-
-  qh_prompt
-    long prompt for qhull
-
-  notes:
-    restricted version of qhull.c
-
-  see:
-    concise prompt below
-*/
-
-/* duplicated in qdelau_f.htm and qdelaun.htm */
-char hidden_options[]=" d n v H U Qb QB Qc Qf Qg Qi Qm Qr QR Qv Qx TR E V FC Fi Fo Ft Fp FV Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
-
-char qh_prompta[]= "\n\
-qdelaunay- compute the Delaunay triangulation\n\
-    http://www.geom.umn.edu/software/qhull  %s\n\
-\n\
-input (stdin):\n\
-    first lines: dimension and number of points (or vice-versa).\n\
-    other lines: point coordinates, best if one point per line\n\
-\n\
-options:\n\
-    Qu   - compute furthest-site Delaunay triangulation\n\
-    Qt   - triangulated output\n\
-    QJ   - joggled input instead of merged facets\n\
-\n\
-Qhull control options:\n\
-    QJn  - randomly joggle input in range [-n,n]\n\
-%s%s%s%s";  /* split up qh_prompt for Visual C++ */
-char qh_promptb[]= "\
-    Qs   - search all points for the initial simplex\n\
-    Qz   - add point-at-infinity to Delaunay triangulation\n\
-    QGn  - print Delaunay region if visible from point n, -n if not\n\
-    QVn  - print Delaunay regions that include point n, -n if not\n\
-\n\
-";
-char qh_promptc[]= "\
-Trace options:\n\
-    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
-    Tc   - check frequently during execution\n\
-    Ts   - print statistics\n\
-    Tv   - verify result: structure, convexity, and in-circle test\n\
-    Tz   - send all output to stdout\n\
-    TFn  - report summary when n or more facets created\n\
-    TI file - input data from file, no spaces or single quotes\n\
-    TO file - output results to file, may be enclosed in single quotes\n\
-    TPn  - turn on tracing when point n added to hull\n\
-     TMn - turn on tracing at merge n\n\
-     TWn - trace merge facets when width > n\n\
-    TVn  - stop qhull after adding point n, -n for before (see TCn)\n\
-     TCn - stop qhull after building cone for point n (see TVn)\n\
-\n\
-Precision options:\n\
-    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
-     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
-           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
-    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
-    Wn   - min facet width for outside point (before roundoff)\n\
-\n\
-Output formats (may be combined; if none, produces a summary to stdout):\n\
-    f    - facet dump\n\
-    G    - Geomview output (see below)\n\
-    i    - vertices incident to each Delaunay region\n\
-    m    - Mathematica output (2-d only, lifted to a paraboloid)\n\
-    o    - OFF format (dim, points, and facets as a paraboloid)\n\
-    p    - point coordinates (lifted to a paraboloid)\n\
-    s    - summary (stderr)\n\
-\n\
-";
-char qh_promptd[]= "\
-More formats:\n\
-    Fa   - area for each Delaunay region\n\
-    FA   - compute total area for option 's'\n\
-    Fc   - count plus coincident points for each Delaunay region\n\
-    Fd   - use cdd format for input (homogeneous with offset first)\n\
-    FD   - use cdd format for numeric output (offset first)\n\
-    FF   - facet dump without ridges\n\
-    FI   - ID of each Delaunay region\n\
-    Fm   - merge count for each Delaunay region (511 max)\n\
-    Fn   - count plus neighboring region for each Delaunay region\n\
-    FN   - count plus neighboring region for each point\n\
-    FO   - options and precision constants\n\
-    FP   - nearest point and distance for each coincident point\n\
-    FQ   - command used for qdelaunay\n\
-    Fs   - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
-                    for output: #vertices, #Delaunay regions,\n\
-                                #coincident points, #non-simplicial regions\n\
-                    #real (2), max outer plane, min vertex\n\
-    FS   - sizes:   #int (0)\n\
-                    #real(2) tot area, 0\n\
-    Fv   - count plus vertices for each Delaunay region\n\
-    Fx   - extreme points of Delaunay triangulation (on convex hull)\n\
-\n\
-";
-char qh_prompte[]= "\
-Geomview options (2-d and 3-d)\n\
-    Ga   - all points as dots\n\
-     Gp  -  coplanar points and vertices as radii\n\
-     Gv  -  vertices as spheres\n\
-    Gi   - inner planes only\n\
-     Gn  -  no planes\n\
-     Go  -  outer planes only\n\
-    Gc	   - centrums\n\
-    Gh   - hyperplane intersections\n\
-    Gr   - ridges\n\
-    GDn  - drop dimension n in 3-d and 4-d output\n\
-    Gt   - transparent outer ridges to view 3-d Delaunay\n\
-\n\
-Print options:\n\
-    PAn  - keep n largest Delaunay regions by area\n\
-    Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
-    PDk:n - drop facet if normal[k] >= n\n\
-    Pg   - print good Delaunay regions (needs 'QGn' or 'QVn')\n\
-    PFn  - keep Delaunay regions whose area is at least n\n\
-    PG   - print neighbors of good regions (needs 'QGn' or 'QVn')\n\
-    PMn  - keep n Delaunay regions with most merges\n\
-    Po   - force output.  If error, output neighborhood of facet\n\
-    Pp   - do not report precision problems\n\
-\n\
-    .    - list of all options\n\
-    -    - one line descriptions of all options\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt2
-    synopsis for qhull
-*/
-char qh_prompt2[]= "\n\
-qdelaunay- compute the Delaunay triangulation. Qhull %s\n\
-    input (stdin): dimension, number of points, point coordinates\n\
-\n\
-options (qdelaun.htm):\n\
-    Qu   - furthest-site Delaunay triangulation\n\
-    Qt   - triangulated output\n\
-    QJ   - joggled input instead of merged facets\n\
-    Tv   - verify result: structure, convexity, and in-circle test\n\
-    .    - concise list of all options\n\
-    -    - one-line description of all options\n\
-\n\
-output options (subset):\n\
-    s    - summary of results (default)\n\
-    i    - vertices incident to each Delaunay region\n\
-    Fx   - extreme points (vertices of the convex hull)\n\
-    o    - OFF format (shows the points lifted to a paraboloid)\n\
-    G    - Geomview output (2-d and 3-d points lifted to a paraboloid)\n\
-    m    - Mathematica output (2-d inputs lifted to a paraboloid)\n\
-    QVn  - print Delaunay regions that include point n, -n if not\n\
-    TO file- output results to file, may be enclosed in single quotes\n\
-\n\
-examples:\n\
-    rbox c P0 D2 | qdelaunay s o          rbox c P0 D2 | qdelaunay i\n\
-    rbox c P0 D2 | qdelaunay Fv           rbox c P0 D2 | qdelaunay s Qu Fv\n\
-    rbox c G1 d D2 | qdelaunay s i        rbox c G1 d D2 | qdelaunay Qt\n\
-    rbox M3,4 z 100 D2 | qdelaunay s      rbox M3,4 z 100 D2 | qdelaunay s Qt\n\
-\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt3
-    concise prompt for qhull
-*/
-char qh_prompt3[]= "\n\
-Qhull %s.\n\
-Except for 'F.' and 'PG', upper-case options take an argument.\n\
-\n\
- incidences     mathematica    OFF_format     points_lifted  summary\n\
- facet_dump\n\
-\n\
- Farea          FArea_total    Fcoincident    Fd_cdd_in      FD_cdd_out\n\
- FF_dump_xridge FIDs           Fmerges        Fneighbors     FNeigh_vertex\n\
- FOptions       FPoint_near    FQdelaun       Fsummary       FSize\n\
- Fvertices      Fxtremes\n\
-\n\
- Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
- Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
- Gtransparent\n\
-\n\
- PArea_keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
- PGood_neighbors PMerge_keep   Poutput_forced Pprecision_not\n\
-\n\
- QGood_point    QJoggle        Qsearch_1st    Qtriangulate   QupperDelaunay\n\
- QVertex_good   Qzinfinite\n\
-\n\
- T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
- TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
- TWide_trace    TVertex_stop   TCone_stop\n\
-\n\
- Angle_max      Centrum_size   Random_dist    Wide_outside\n\
-";
-
-/*---------------------------------
-
-  main( argc, argv )
-    processes the command line, calls qhull() to do the work, and exits
-
-  design:
-    initializes data structures
-    finishes initialization
-    computes convex hull and other structures
-    checks the result
-    writes the output
-    frees memory
-*/
-int main(int argc, char *argv[]) {
-  int curlong, totlong; /* used !qh_NOmem */
-  int exitcode, numpoints, dim;
-  coordT *points;
-  boolT ismalloc;
-
-#if __MWERKS__ && __POWERPC__
-  char inBuf[BUFSIZ], outBuf[BUFSIZ], errBuf[BUFSIZ];
-  SIOUXSettings.showstatusline= false;
-  SIOUXSettings.tabspaces= 1;
-  SIOUXSettings.rows= 40;
-  if (setvbuf (stdin, inBuf, _IOFBF, sizeof(inBuf)) < 0   /* w/o, SIOUX I/O is slow*/
-  || setvbuf (stdout, outBuf, _IOFBF, sizeof(outBuf)) < 0
-  || (stdout != stderr && setvbuf (stderr, errBuf, _IOFBF, sizeof(errBuf)) < 0))
-    fprintf (stderr, "qhull internal warning (main): could not change stdio to fully buffered.\n");
-  argc= ccommand(&argv);
-#endif
-
-  if ((argc == 1) && isatty( 0 /*stdin*/)) {
-    fprintf(stdout, qh_prompt2, qh_VERSION);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompta, qh_VERSION,
-		qh_promptb, qh_promptc, qh_promptd, qh_prompte);
-    exit(qh_ERRnone);
-  }
-  if (argc >1 && *argv[1] == '.' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompt3, qh_VERSION);
-    exit(qh_ERRnone);
-  }
-  qh_init_A (stdin, stdout, stderr, argc, argv);  /* sets qh qhull_command */
-  exitcode= setjmp (qh errexit); /* simple statement for CRAY J916 */
-  if (!exitcode) {
-    qh_option ("delaunay  Qbbound-last", NULL, NULL);
-    qh DELAUNAY= True;     /* 'd'   */
-    qh SCALElast= True;    /* 'Qbb' */
-    qh KEEPcoplanar= True; /* 'Qc', to keep coplanars in 'p' */
-    qh_checkflags (qh qhull_command, hidden_options);
-    qh_initflags (qh qhull_command);
-    points= qh_readpoints (&numpoints, &dim, &ismalloc);
-    if (dim >= 5) {
-      qh_option ("Qxact_merge", NULL, NULL);
-      qh MERGEexact= True; /* 'Qx' always */
-    }
-    qh_init_B (points, numpoints, dim, ismalloc);
-    qh_qhull();
-    qh_check_output();
-    qh_produce_output();
-    if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
-      qh_check_points();
-    exitcode= qh_ERRnone;
-  }
-  qh NOerrexit= True;  /* no more setjmp */
-#ifdef qh_NOmem
-  qh_freeqhull( True);
-#else
-  qh_freeqhull( False);
-  qh_memfreeshort (&curlong, &totlong);
-  if (curlong || totlong)
-    fprintf (stderr, "qhull internal warning (main): did not free %d bytes of long memory (%d pieces)\n",
-       totlong, curlong);
-#endif
-  return exitcode;
-} /* main */
-
diff --git a/extern/qhull/src/qhalf.c b/extern/qhull/src/qhalf.c
deleted file mode 100644
index a2b3875dd7f..00000000000
--- a/extern/qhull/src/qhalf.c
+++ /dev/null
@@ -1,324 +0,0 @@
-/*  ---------------------------------
-
-   qhalf.c
-     compute the intersection of halfspaces about a point
-
-   see unix.c for full interface
-
-   copyright (c) 1993-2002, The Geometry Center
-*/
-
-#include
-#include
-#include
-#include
-#include
-#include "qhull.h"
-#include "mem.h"
-#include "qset.h"
-
-#if __MWERKS__ && __POWERPC__
-#include
-#include
-#include
-#include
-
-#elif __cplusplus
-extern "C" {
-  int isatty (int);
-}
-
-#elif _MSC_VER
-#include
-#define isatty _isatty
-
-#else
-int isatty (int);  /* returns 1 if stdin is a tty
-		   if "Undefined symbol" this can be deleted along with call in main() */
-#endif
-
-/*---------------------------------
-
-  qh_prompt
-    long prompt for qhull
-
-  notes:
-    restricted version of qhull.c
-
-  see:
-    concise prompt below
-*/
-
-/* duplicated in qhalf.htm */
-char hidden_options[]=" d n v Qbb QbB Qf Qg Qm Qr QR Qv Qx Qz TR E V Fa FA FC FD FS Ft FV Gt Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
-
-char qh_prompta[]= "\n\
-qhalf- compute the intersection of halfspaces about a point\n\
-    http://www.geom.umn.edu/software/qhull  %s\n\
-\n\
-input (stdin):\n\
-    optional interior point: dimension, 1, coordinates\n\
-    first lines: dimension+1 and number of halfspaces\n\
-    other lines: halfspace coefficients followed by offset\n\
-\n\
-options:\n\
-    Hn,n - specify coordinates of interior point\n\
-    Qt   - triangulated output\n\
-    QJ   - joggled input instead of merged facets\n\
-    Qc   - keep coplanar halfspaces\n\
-    Qi   - keep other redundant halfspaces\n\
-\n\
-Qhull control options:\n\
-    QJn  - randomly joggle input in range [-n,n]\n\
-%s%s%s%s";  /* split up qh_prompt for Visual C++ */
-char qh_promptb[]= "\
-    Qbk:0Bk:0 - remove k-th coordinate from input\n\
-    Qs   - search all halfspaces for the initial simplex\n\
-    QGn  - print intersection if visible to halfspace n, -n for not\n\
-    QVn  - print intersections for halfspace n, -n if not\n\
-\n\
-";
-char qh_promptc[]= "\
-Trace options:\n\
-    T4   - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
-    Tc   - check frequently during execution\n\
-    Ts   - print statistics\n\
-    Tv   - verify result: structure, convexity, and redundancy\n\
-    Tz   - send all output to stdout\n\
-    TFn  - report summary when n or more facets created\n\
-    TI file - input data from file, no spaces or single quotes\n\
-    TO file - output results to file, may be enclosed in single quotes\n\
-    TPn  - turn on tracing when halfspace n added to intersection\n\
-    TMn  - turn on tracing at merge n\n\
-    TWn  - trace merge facets when width > n\n\
-    TVn  - stop qhull after adding halfspace n, -n for before (see TCn)\n\
-    TCn  - stop qhull after building cone for halfspace n (see TVn)\n\
-\n\
-Precision options:\n\
-    Cn   - radius of centrum (roundoff added).  Merge facets if non-convex\n\
-     An  - cosine of maximum angle.  Merge facets if cosine > n or non-convex\n\
-           C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
-    Rn   - randomly perturb computations by a factor of [1-n,1+n]\n\
-    Un   - max distance below plane for a new, coplanar halfspace\n\
-    Wn   - min facet width for outside halfspace (before roundoff)\n\
-\n\
-Output formats (may be combined; if none, produces a summary to stdout):\n\
-    f    - facet dump\n\
-    G    - Geomview output (dual convex hull)\n\
-    i    - non-redundant halfspaces incident to each intersection\n\
-    m    - Mathematica output (dual convex hull)\n\
-    o    - OFF format (dual convex hull: dimension, points, and facets)\n\
-    p    - vertex coordinates of dual convex hull (coplanars if 'Qc' or 'Qi')\n\
-    s    - summary (stderr)\n\
-\n\
-";
-char qh_promptd[]= "\
-More formats:\n\
-    Fc   - count plus redundant halfspaces for each intersection\n\
-         -   Qc (default) for coplanar and Qi for other redundant\n\
-    Fd   - use cdd format for input (homogeneous with offset first)\n\
-    FF   - facet dump without ridges\n\
-    FI   - ID of each intersection\n\
-    Fm   - merge count for each intersection (511 max)\n\
-    Fn   - count plus neighboring intersections for each intersection\n\
-    FN   - count plus intersections for each non-redundant halfspace\n\
-    FO   - options and precision constants\n\
-    Fp   - dim, count, and intersection coordinates\n\
-    FP   - nearest halfspace and distance for each redundant halfspace\n\
-    FQ   - command used for qhalf\n\
-    Fs   - summary: #int (8), dim, #halfspaces, #non-redundant, #intersections\n\
-                      for output: #non-redundant, #intersections, #coplanar\n\
-                                  halfspaces, #non-simplicial intersections\n\
-                    #real (2), max outer plane, min vertex\n\
-    Fv   - count plus non-redundant halfspaces for each intersection\n\
-    Fx   - non-redundant halfspaces\n\
-\n\
-";
-char qh_prompte[]= "\
-Geomview output (2-d, 3-d and 4-d; dual convex hull)\n\
-    Ga   - all points (i.e., transformed halfspaces) as dots\n\
-     Gp  -  coplanar points and vertices as radii\n\
-     Gv  -  vertices (i.e., non-redundant halfspaces) as spheres\n\
-    Gi   - inner planes (i.e., halfspace intersections) only\n\
-     Gn  -  no planes\n\
-     Go  -  outer planes only\n\
-    Gc	 - centrums\n\
-    Gh   - hyperplane intersections\n\
-    Gr   - ridges\n\
-    GDn  - drop dimension n in 3-d and 4-d output\n\
-\n\
-Print options:\n\
-    PAn  - keep n largest facets (i.e., intersections) by area\n\
-    Pdk:n- drop facet if normal[k] <= n (default 0.0)\n\
-    PDk:n- drop facet if normal[k] >= n\n\
-    Pg   - print good facets (needs 'QGn' or 'QVn')\n\
-    PFn  - keep facets whose area is at least n\n\
-    PG   - print neighbors of good facets\n\
-    PMn  - keep n facets with most merges\n\
-    Po   - force output.  If error, output neighborhood of facet\n\
-    Pp   - do not report precision problems\n\
-\n\
-    .    - list of all options\n\
-    -    - one line descriptions of all options\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt2
-    synopsis for qhull
-*/
-char qh_prompt2[]= "\n\
-qhalf- halfspace intersection about a point. Qhull %s\n\
-    input (stdin): [dim, 1, interior point], dim+1, n, coefficients+offset\n\
-\n\
-options (qhalf.htm):\n\
-    Hn,n - specify coordinates of interior point\n\
-    Qt   - triangulated output\n\
-    QJ   - joggled input instead of merged facets\n\
-    Tv   - verify result: structure, convexity, and redundancy\n\
-    .    - concise list of all options\n\
-    -    - one-line description of all options\n\
-\n\
-output options (subset):\n\
-    s    - summary of results (default)\n\
-    Fp   - intersection coordinates\n\
-    Fv   - non-redundant halfspaces incident to each intersection\n\
-    Fx   - non-redundant halfspaces\n\
-    o    - OFF file format (dual convex hull)\n\
-    G    - Geomview output (dual convex hull)\n\
-    m    - Mathematica output (dual convex hull)\n\
-    QVn  - print intersections for halfspace n, -n if not\n\
-    TO file - output results to file, may be enclosed in single quotes\n\
-\n\
-examples:\n\
-    rbox d | qconvex FQ n | qhalf s H0,0,0 Fp\n\
-    rbox c | qconvex FQ FV n | qhalf s i\n\
-    rbox c | qconvex FQ FV n | qhalf s o\n\
-\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*---------------------------------
-
-  qh_prompt3
-    concise prompt for qhull
-*/
-char qh_prompt3[]= "\n\
-Qhull %s.\n\
-Except for 'F.' and 'PG', upper_case options take an argument.\n\
-\n\
- incidences     Geomview       mathematica    OFF_format     point_dual\n\
- summary        facet_dump\n\
-\n\
- Fc_redundant   Fd_cdd_in      FF_dump_xridge FIDs           Fmerges\n\
- Fneighbors     FN_intersect   FOptions       Fp_coordinates FP_nearest\n\
- FQhalf         Fsummary       Fv_halfspace   Fx_non_redundant\n\
-\n\
- Gvertices      Gpoints        Gall_points    Gno_planes     Ginner\n\
- Gcentrums      Ghyperplanes   Gridges        Gouter         GDrop_dim\n\
-\n\
- PArea_keep     Pdrop d0:0D0   Pgood          PFacet_area_keep\n\
- PGood_neighbors PMerge_keep   Poutput_forced Pprecision_not\n\
-\n\
- Qbk:0Bk:0_drop Qcoplanar      QG_half_good   Qi_redundant   QJoggle\n\
- Qsearch_1st    Qtriangulate   QVertex_good\n\
-\n\
- T4_trace       Tcheck_often   Tstatistics    Tverify        Tz_stdout\n\
- TFacet_log     TInput_file    TPoint_trace   TMerge_trace   TOutput_file\n\
- TWide_trace    TVertex_stop   TCone_stop\n\
-\n\
- Angle_max      Centrum_size   Random_dist    Ucoplanar_max  Wide_outside\n\
-";
-
-/*---------------------------------
-
-  main( argc, argv )
-    processes the command line, calls qhull() to do the work, and exits
-
-  design:
-    initializes data structures
-    finishes initialization
-    computes convex hull and other structures
-    checks the result
-    writes the output
-    frees memory
-*/
-int main(int argc, char *argv[]) {
-  int curlong, totlong; /* used !qh_NOmem */
-  int exitcode, numpoints, dim;
-  coordT *points;
-  boolT ismalloc;
-
-#if __MWERKS__ && __POWERPC__
-  char inBuf[BUFSIZ], outBuf[BUFSIZ], errBuf[BUFSIZ];
-  SIOUXSettings.showstatusline= false;
-  SIOUXSettings.tabspaces= 1;
-  SIOUXSettings.rows= 40;
-  if (setvbuf (stdin, inBuf, _IOFBF, sizeof(inBuf)) < 0   /* w/o, SIOUX I/O is slow*/
-  || setvbuf (stdout, outBuf, _IOFBF, sizeof(outBuf)) < 0
-  || (stdout != stderr && setvbuf (stderr, errBuf, _IOFBF, sizeof(errBuf)) < 0))
-    fprintf (stderr, "qhull internal warning (main): could not change stdio to fully buffered.\n");
-  argc= ccommand(&argv);
-#endif
-
-  if ((argc == 1) && isatty( 0 /*stdin*/)) {
-    fprintf(stdout, qh_prompt2, qh_VERSION);
-    exit(qh_ERRnone);
-  }
-  if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompta, qh_VERSION,
-        qh_promptb, qh_promptc, qh_promptd, qh_prompte);
-    exit(qh_ERRnone);
-  }
-  if (argc >1 && *argv[1] == '.' && !*(argv[1]+1)) {
-    fprintf(stdout, qh_prompt3, qh_VERSION);
-    exit(qh_ERRnone);
-  }
-  qh_init_A (stdin, stdout, stderr, argc, argv);  /* sets qh qhull_command */
-  exitcode= setjmp (qh errexit); /* simple statement for CRAY J916 */
-  if (!exitcode) {
-    qh_option ("Halfspace", NULL, NULL);
-    qh HALFspace= True;    /* 'H'   */
-    qh_checkflags (qh qhull_command, hidden_options);
-    qh_initflags (qh qhull_command);
-    if (qh SCALEinput) {
-      fprintf(qh ferr, "\
-qhull error: options 'Qbk:n' and 'QBk:n' are not used with qhalf.\n\
-             Use 'Qbk:0Bk:0 to drop dimension k.\n");
-      qh_errexit(qh_ERRinput, NULL, NULL);
-    }
-    points= qh_readpoints (&numpoints, &dim, &ismalloc);
-    if (dim >= 5) {
-      qh_option ("Qxact_merge", NULL, NULL);
-      qh MERGEexact= True; /* 'Qx' always */
-    }
-    qh_init_B (points, numpoints, dim, ismalloc);
-    qh_qhull();
-    qh_check_output();
-    qh_produce_output();
-    if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
-      qh_check_points();
-    exitcode= qh_ERRnone;
-  }
-  qh NOerrexit= True;  /* no more setjmp */
-#ifdef qh_NOmem
-  qh_freeqhull( True);
-#else
-  qh_freeqhull( False);
-  qh_memfreeshort (&curlong, &totlong);
-  if (curlong || totlong)
-    fprintf (stderr, "qhull internal warning (main): did not free %d bytes of long memory (%d pieces)\n",
-       totlong, curlong);
-#endif
-  return exitcode;
-} /* main */
-
diff --git a/extern/qhull/src/qhull.c b/extern/qhull/src/qhull.c
deleted file mode 100644
index dc835bb4f28..00000000000
--- a/extern/qhull/src/qhull.c
+++ /dev/null
@@ -1,1395 +0,0 @@
-/*  ---------------------------------
-
-   qhull.c
-   Quickhull algorithm for convex hulls
-
-   qhull() and top-level routines
-
-   see qh-qhull.htm, qhull.h, unix.c
-
-   see qhull_a.h for internal functions
-
-   copyright (c) 1993-2002 The Geometry Center
-*/
-
-#include "qhull_a.h"
-
-/*============= functions in alphabetic order after qhull() =======*/
-
-/*---------------------------------
-
-  qh_qhull()
-    compute DIM3 convex hull of qh.num_points starting at qh.first_point
-    qh contains all global options and variables
-
-  returns:
-    returns polyhedron
-      qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices,
-
-    returns global variables
-      qh.hulltime, qh.max_outside, qh.interior_point, qh.max_vertex, qh.min_vertex
-
-    returns precision constants
-      qh.ANGLEround, centrum_radius, cos_max, DISTround, MAXabs_coord, ONEmerge
-
-  notes:
-    unless needed for output
-      qh.max_vertex and qh.min_vertex are max/min due to merges
-
-  see:
-    to add individual points to either qh.num_points
-
-    if qh.GETarea
-      qh_produceoutput() returns qh.totarea and qh.totvol via qh_getarea()
-
-  design:
-    record starting time
-    initialize hull and partition points
-    build convex hull
-    unless early termination
-      update facet->maxoutside for vertices, coplanar, and near-inside points
-    error if temporary sets exist
-    record end time
-*/
-void qh_qhull (void) {
-  int numoutside;
-
-  qh hulltime= qh_CPUclock;
-  if (qh RERUN || qh JOGGLEmax < REALmax/2)
-    qh_build_withrestart();
-  else {
-    qh_initbuild();
-    qh_buildhull();
-  }
-  if (!qh STOPpoint && !qh STOPcone) {
-    if (qh ZEROall_ok && !qh TESTvneighbors && qh MERGEexact)
-      qh_checkzero( qh_ALL);
-    if (qh ZEROall_ok && !qh TESTvneighbors && !qh WAScoplanar) {
-      trace2((qh ferr, "qh_qhull: all facets are clearly convex and no coplanar points.  Post-merging and check of maxout not needed.\n"));
-      qh DOcheckmax= False;
-    }else {
-      if (qh MERGEexact || (qh hull_dim > qh_DIMreduceBuild && qh PREmerge))
-        qh_postmerge ("First post-merge", qh premerge_centrum, qh premerge_cos,
-             (qh POSTmerge ? False : qh TESTvneighbors));
-      else if (!qh POSTmerge && qh TESTvneighbors)
-        qh_postmerge ("For testing vertex neighbors", qh premerge_centrum,
-             qh premerge_cos, True);
-      if (qh POSTmerge)
-        qh_postmerge ("For post-merging", qh postmerge_centrum,
-             qh postmerge_cos, qh TESTvneighbors);
-      if (qh visible_list == qh facet_list) { /* i.e., merging done */
-        qh findbestnew= True;
-        qh_partitionvisible (/*visible_list, newfacet_list*/ !qh_ALL, &numoutside);
-        qh findbestnew= False;
-        qh_deletevisible (/*qh visible_list*/);
-        qh_resetlists (False, qh_RESETvisible /*qh visible_list newvertex_list newfacet_list */);
-      }
-    }
-    if (qh DOcheckmax){
-      if (qh REPORTfreq) {
-	qh_buildtracing (NULL, NULL);
-	fprintf (qh ferr, "\nTesting all coplanar points.\n");
-      }
-      qh_check_maxout();
-    }
-    if (qh KEEPnearinside && !qh maxoutdone)
-      qh_nearcoplanar();
-  }
-  if (qh_setsize ((setT*)qhmem.tempstack) != 0) {
-    fprintf (qh ferr, "qhull internal error (qh_qhull): temporary sets not empty (%d)\n",
-	     qh_setsize ((setT*)qhmem.tempstack));
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }
-  qh hulltime= qh_CPUclock - qh hulltime;
-  qh QHULLfinished= True;
-  trace1((qh ferr, "qh_qhull: algorithm completed\n"));
-} /* qhull */
-
-/*---------------------------------
-
-  qh_addpoint( furthest, facet, checkdist )
-    add point (usually furthest point) above facet to hull
-    if checkdist,
-      check that point is above facet.
-      if point is not outside of the hull, uses qh_partitioncoplanar()
-      assumes that facet is defined by qh_findbestfacet()
-    else if facet specified,
-      assumes that point is above facet (major damage if below)
-    for Delaunay triangulations,
-      Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
-      Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
-
-  returns:
-    returns False if user requested an early termination
-     qh.visible_list, newfacet_list, delvertex_list, NEWfacets may be defined
-    updates qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices
-    clear qh.maxoutdone (will need to call qh_check_maxout() for facet->maxoutside)
-    if unknown point, adds a pointer to qh.other_points
-      do not deallocate the point's coordinates
-
-  notes:
-    assumes point is near its best facet and not at a local minimum of a lens
-      distributions.  Use qh_findbestfacet to avoid this case.
-    uses qh.visible_list, qh.newfacet_list, qh.delvertex_list, qh.NEWfacets
-
-    qh_triangulate() -- triangulate non-simplicial facets
-
-  design:
-    check point in qh.first_point/.num_points
-    if checkdist
-      if point not above facet
-        partition coplanar point
-        exit
-    exit if pre STOPpoint requested
-    find horizon and visible facets for point
-    make new facets for point to horizon
-    make hyperplanes for point
-    compute balance statistics
-    match neighboring new facets
-    update vertex neighbors and delete interior vertices
-    exit if STOPcone requested
-    merge non-convex new facets
-    if merge found, many merges, or 'Qf'
-       use qh_findbestnew() instead of qh_findbest()
-    partition outside points from visible facets
-    delete visible facets
-    check polyhedron if requested
-    exit if post STOPpoint requested
-    reset working lists of facets and vertices
-*/
-boolT qh_addpoint (pointT *furthest, facetT *facet, boolT checkdist) {
-  int goodvisible, goodhorizon;
-  vertexT *vertex;
-  facetT *newfacet;
-  realT dist, newbalance, pbalance;
-  boolT isoutside= False;
-  int numpart, numpoints, numnew, firstnew;
-
-  qh maxoutdone= False;
-  if (qh_pointid (furthest) == -1)
-    qh_setappend (&qh other_points, furthest);
-  if (!facet) {
-    fprintf (qh ferr, "qh_addpoint: NULL facet.  Need to call qh_findbestfacet first\n");
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }
-  if (checkdist) {
-    facet= qh_findbest (furthest, facet, !qh_ALL, !qh_ISnewfacets, !qh_NOupper,
-			&dist, &isoutside, &numpart);
-    if (!isoutside) {
-      zinc_(Znotmax);  /* last point of outsideset is no longer furthest. */
-      facet->notfurthest= True;
-      qh_partitioncoplanar (furthest, facet, &dist);
-      return True;
-    }
-  }
-  qh_buildtracing (furthest, facet);
-  if (qh STOPpoint < 0 && qh furthest_id == -qh STOPpoint-1) {
-    facet->notfurthest= True;
-    return False;
-  }
-  qh_findhorizon (furthest, facet, &goodvisible, &goodhorizon);
-  if (qh ONLYgood && !(goodvisible+goodhorizon) && !qh GOODclosest) {
-    zinc_(Znotgood);
-    facet->notfurthest= True;
-    /* last point of outsideset is no longer furthest.  This is ok
-       since all points of the outside are likely to be bad */
-    qh_resetlists (False, qh_RESETvisible /*qh visible_list newvertex_list newfacet_list */);
-    return True;
-  }
-  zzinc_(Zprocessed);
-  firstnew= qh facet_id;
-  vertex= qh_makenewfacets (furthest /*visible_list, attaches if !ONLYgood */);
-  qh_makenewplanes (/* newfacet_list */);
-  numnew= qh facet_id - firstnew;
-  newbalance= numnew - (realT) (qh num_facets-qh num_visible)
-                         * qh hull_dim/qh num_vertices;
-  if (qh ONLYgood
-  && !qh_findgood (qh newfacet_list, goodhorizon) && !qh GOODclosest) {
-    FORALLnew_facets
-      qh_delfacet (newfacet);
-    qh_delvertex (vertex);
-    qh_resetlists (True, qh_RESETvisible /*qh visible_list newvertex_list newfacet_list */);
-    zinc_(Znotgoodnew);
-    facet->notfurthest= True;
-    return True;
-  }
-  if (qh ONLYgood)
-    qh_attachnewfacets(/*visible_list*/);
-  qh_matchnewfacets();
-  qh_updatevertices();
-  if (qh STOPcone && qh furthest_id == qh STOPcone-1) {
-    facet->notfurthest= True;
-    return False;  /* visible_list etc. still defined */
-  }
-  qh findbestnew= False;
-  if (qh PREmerge || qh MERGEexact) {
-    qh_premerge (vertex, qh premerge_centrum, qh premerge_cos);
-    if (qh_USEfindbestnew)
-      qh findbestnew= True;
-    else {
-      FORALLnew_facets {
-	if (!newfacet->simplicial) {
-	  qh findbestnew= True;  /* use qh_findbestnew instead of qh_findbest*/
-	  break;
-	}
-      }
-    }
-  }else if (qh BESToutside)
-    qh findbestnew= True;
-  qh_partitionvisible (/*visible_list, newfacet_list*/ !qh_ALL, &numpoints);
-  qh findbestnew= False;
-  qh findbest_notsharp= False;
-  zinc_(Zpbalance);
-  pbalance= numpoints - (realT) qh hull_dim /* assumes all points extreme */
-                * (qh num_points - qh num_vertices)/qh num_vertices;
-  qh_deletevisible (/*qh visible_list*/);
-  zmax_(Zmaxvertex, qh num_vertices);
-  qh NEWfacets= False;
-  if (qh IStracing >= 4) {
-    if (qh num_facets < 2000)
-      qh_printlists();
-    qh_printfacetlist (qh newfacet_list, NULL, True);
-    qh_checkpolygon (qh facet_list);
-  }else if (qh CHECKfrequently) {
-    if (qh num_facets < 50)
-      qh_checkpolygon (qh facet_list);
-    else
-      qh_checkpolygon (qh newfacet_list);
-  }
-  if (qh STOPpoint > 0 && qh furthest_id == qh STOPpoint-1)
-    return False;
-  qh_resetlists (True, qh_RESETvisible /*qh visible_list newvertex_list newfacet_list */);
-  /* qh_triangulate(); to test qh.TRInormals */
-  trace2((qh ferr, "qh_addpoint: added p%d new facets %d new balance %2.2g point balance %2.2g\n",
-    qh_pointid (furthest), numnew, newbalance, pbalance));
-  return True;
-
-/*---------------------------------
-
-  qh_build_withrestart()
-    allow restarts due to qh.JOGGLEmax while calling qh_buildhull()
-    qh.FIRSTpoint/qh.NUMpoints is point array
-        it may be moved by qh_joggleinput()
-*/
-void qh_build_withrestart (void) {
-  int restart;
-
-  qh ALLOWrestart= True;
-  while (True) {
-    restart= setjmp (qh restartexit); /* simple statement for CRAY J916 */
-    if (restart) {       /* only from qh_precision() */
-      zzinc_(Zretry);
-      wmax_(Wretrymax, qh JOGGLEmax);
-      qh ERREXITcalled= False;
-      qh STOPcone= True; /* if break, prevents normal output */
-    }
-    if (!qh RERUN && qh JOGGLEmax < REALmax/2) {
-      if (qh build_cnt > qh_JOGGLEmaxretry) {
-	fprintf(qh ferr, "\n\
-qhull precision error: %d attempts to construct a convex hull\n\
-        with joggled input.  Increase joggle above 'QJ%2.2g'\n\
-	or modify qh_JOGGLE... parameters in user.h\n",
-	   qh build_cnt, qh JOGGLEmax);
-	qh_errexit (qh_ERRqhull, NULL, NULL);
-      }
-      if (qh build_cnt && !restart)
-	break;
-    }else if (qh build_cnt && qh build_cnt >= qh RERUN)
-      break;
-    qh STOPcone= False;
-    qh_freebuild (True);  /* first call is a nop */
-    qh build_cnt++;
-    if (!qh qhull_optionsiz)
-      qh qhull_optionsiz= strlen (qh qhull_options);
-    else {
-      qh qhull_options [qh qhull_optionsiz]= '\0';
-      qh qhull_optionlen= 80;
-    }
-    qh_option("_run", &qh build_cnt, NULL);
-    if (qh build_cnt == qh RERUN) {
-      qh IStracing= qh TRACElastrun;  /* duplicated from qh_initqhull_globals */
-      if (qh TRACEpoint != -1 || qh TRACEdist < REALmax/2 || qh TRACEmerge) {
-        qh TRACElevel= (qh IStracing? qh IStracing : 3);
-        qh IStracing= 0;
-      }
-      qhmem.IStracing= qh IStracing;
-    }
-    if (qh JOGGLEmax < REALmax/2)
-      qh_joggleinput();
-    qh_initbuild();
-    qh_buildhull();
-    if (qh JOGGLEmax < REALmax/2 && !qh MERGING)
-      qh_checkconvex (qh facet_list, qh_ALGORITHMfault);
-  }
-  qh ALLOWrestart= False;
-} /* qh_build_withrestart */
-
-/*---------------------------------
-
-  qh_buildhull()
-    construct a convex hull by adding outside points one at a time
-
-  returns:
-
-  notes:
-    may be called multiple times
-    checks facet and vertex lists for incorrect flags
-    to recover from STOPcone, call qh_deletevisible and qh_resetlists
-
-  design:
-    check visible facet and newfacet flags
-    check newlist vertex flags and qh.STOPcone/STOPpoint
-    for each facet with a furthest outside point
-      exit if qh.STOPcone or qh.STOPpoint requested
-    if qh.NARROWhull for initial simplex
-      partition remaining outside points to coplanar sets
-*/
-void qh_buildhull(void) {
-  facetT *facet;
-  pointT *furthest;
-  vertexT *vertex;
-  int id;
-
-  trace1((qh ferr, "qh_buildhull: start build hull\n"));
-  FORALLfacets {
-    if (facet->visible || facet->newfacet) {
-      fprintf (qh ferr, "qhull internal error (qh_buildhull): visible or new facet f%d in facet list\n",
-                   facet->id);
-      qh_errexit (qh_ERRqhull, facet, NULL);
-    }
-  }
-  FORALLvertices {
-    if (vertex->newlist) {
-      fprintf (qh ferr, "qhull internal error (qh_buildhull): new vertex f%d in vertex list\n",
-                   vertex->id);
-      qh_errprint ("ERRONEOUS", NULL, NULL, NULL, vertex);
-      qh_errexit (qh_ERRqhull, NULL, NULL);
-    }
-    id= qh_pointid (vertex->point);
-    if ((qh STOPpoint>0 && id == qh STOPpoint-1) ||
-	(qh STOPpoint<0 && id == -qh STOPpoint-1) ||
-	(qh STOPcone>0 && id == qh STOPcone-1)) {
-      trace1((qh ferr,"qh_buildhull: stop point or cone P%d in initial hull\n", id));
-      return;
-    }
-  }
-  qh facet_next= qh facet_list;      /* advance facet when processed */
-  while ((furthest= qh_nextfurthest (&facet))) {
-    qh num_outside--;  /* if ONLYmax, furthest may not be outside */
-    if (!qh_addpoint (furthest, facet, qh ONLYmax))
-      break;
-  }
-  if (qh NARROWhull) /* move points from outsideset to coplanarset */
-    qh_outcoplanar( /* facet_list */ );
-  if (qh num_outside && !furthest) {
-    fprintf (qh ferr, "qhull internal error (qh_buildhull): %d outside points were never processed.\n", qh num_outside);
-    qh_errexit (qh_ERRqhull, NULL, NULL);
-  }
-  trace1((qh ferr, "qh_buildhull: completed the hull construction\n"));
-} /* buildhull */
-
-
-/*---------------------------------
-
-  qh_buildtracing( furthest, facet )
-    trace an iteration of qh_buildhull() for furthest point and facet
-    if !furthest, prints progress message
-
-  returns:
-    tracks progress with qh.lastreport
-    updates qh.furthest_id (-3 if furthest is NULL)
-    also resets visit_id, vertext_visit on wrap around
-
-  see:
-    qh_tracemerging()
-
-  design:
-    if !furthest
-      print progress message
-      exit
-    if 'TFn' iteration
-      print progress message
-    else if tracing
-      trace furthest point and facet
-    reset qh.visit_id and qh.vertex_visit if overflow may occur
-    set qh.furthest_id for tracing
-*/
-void qh_buildtracing (pointT *furthest, facetT *facet) {
-  realT dist= 0;
-  float cpu;
-  int total, furthestid;
-  time_t timedata;
-  struct tm *tp;
-  vertexT *vertex;
-
-  qh old_randomdist= qh RANDOMdist;
-  qh RANDOMdist= False;
-  if (!furthest) {
-    time (&timedata);
-    tp= localtime (&timedata);
-    cpu= qh_CPUclock - qh hulltime;
-    cpu /= qh_SECticks;
-    total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
-    fprintf (qh ferr, "\n\
-At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
- The current hull contains %d facets and %d vertices.  Last point was p%d\n",
-      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh facet_id -1,
-      total, qh num_facets, qh num_vertices, qh furthest_id);
-    return;
-  }
-  furthestid= qh_pointid (furthest);
-  if (qh TRACEpoint == furthestid) {
-    qh IStracing= qh TRACElevel;
-    qhmem.IStracing= qh TRACElevel;
-  }else if (qh TRACEpoint != -1 && qh TRACEdist < REALmax/2) {
-    qh IStracing= 0;
-    qhmem.IStracing= 0;
-  }
-  if (qh REPORTfreq && (qh facet_id-1 > qh lastreport+qh REPORTfreq)) {
-    qh lastreport= qh facet_id-1;
-    time (&timedata);
-    tp= localtime (&timedata);
-    cpu= qh_CPUclock - qh hulltime;
-    cpu /= qh_SECticks;
-    total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
-    zinc_(Zdistio);
-    qh_distplane (furthest, facet, &dist);
-    fprintf (qh ferr, "\n\
-At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
- The current hull contains %d facets and %d vertices.  There are %d\n\
- outside points.  Next is point p%d (v%d), %2.2g above f%d.\n",
-      tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh facet_id -1,
-      total, qh num_facets, qh num_vertices, qh num_outside+1,
-      furthestid, qh vertex_id, dist, getid_(facet));
-  }else if (qh IStracing >=1) {
-    cpu= qh_CPUclock - qh hulltime;
-    cpu /= qh_SECticks;
-    qh_distplane (furthest, facet, &dist);
-    fprintf (qh ferr, "qh_addpoint: add p%d (v%d) to hull of %d facets (%2.2g above f%d) and %d outside at %4.4g CPU secs.  Previous was p%d.\n",
-      furthestid, qh vertex_id, qh num_facets, dist,
-      getid_(facet), qh num_outside+1, cpu, qh furthest_id);
-  }
-  if (qh visit_id > (unsigned) INT_MAX) {
-    qh visit_id= 0;
-    FORALLfacets
-      facet->visitid= qh visit_id;
-  }
-  if (qh vertex_visit > (unsigned) INT_MAX) {
-    qh vertex_visit= 0;
-    FORALLvertices
-      vertex->visitid= qh vertex_visit;
-  }
-  qh furthest_id= furthestid;
-  qh RANDOMdist= qh old_randomdist;
-} /* buildtracing */
-
-/*---------------------------------
-
-  qh_errexit2( exitcode, facet, otherfacet )
-    return exitcode to system after an error
-    report two facets
-
-  returns:
-    assumes exitcode non-zero
-
-  see:
-    normally use qh_errexit() in user.c (reports a facet and a ridge)
-*/
-void qh_errexit2(int exitcode, facetT *facet, facetT *otherfacet) {
-
-  qh_errprint("ERRONEOUS", facet, otherfacet, NULL, NULL);
-  qh_errexit (exitcode, NULL, NULL);
-} /* errexit2 */
-
-
-/*---------------------------------
-
-  qh_findhorizon( point, facet, goodvisible, goodhorizon )
-    given a visible facet, find the point's horizon and visible facets
-    for all facets, !facet-visible
-
-  returns:
-    returns qh.visible_list/num_visible with all visible facets
-      marks visible facets with ->visible
-    updates count of good visible and good horizon facets
-
-  see:
-    similar to qh_delpoint()
-
-  design:
-    move facet to qh.visible_list at end of qh.facet_list
-    for all visible facets
-     for each unvisited neighbor of a visible facet
-       compute distance of point to neighbor
-       if point above neighbor
-         move neighbor to end of qh.visible_list
-       else if point is coplanar with neighbor
-         update qh.max_outside, qh.max_vertex, neighbor->maxoutside
-         mark neighbor coplanar (will create a samecycle later)
-         update horizon statistics
-*/
-void qh_findhorizon(pointT *point, facetT *facet, int *goodvisible, int *goodhorizon) {
-  facetT *neighbor, **neighborp, *visible;
-  int numhorizon= 0, coplanar= 0;
-  realT dist;
-
-  trace1((qh ferr,"qh_findhorizon: find horizon for point p%d facet f%d\n",qh_pointid(point),facet->id));
-  *goodvisible= *goodhorizon= 0;
-  zinc_(Ztotvisible);
-  qh_removefacet(facet);  /* visible_list at end of qh facet_list */
-  qh_appendfacet(facet);
-  qh num_visible= 1;
-  if (facet->good)
-    (*goodvisible)++;
-  qh visible_list= facet;
-  facet->visible= True;
-  facet->f.replace= NULL;
-  if (qh IStracing >=4)
-    qh_errprint ("visible", facet, NULL, NULL, NULL);
-  qh visit_id++;
-  FORALLvisible_facets {
-    if (visible->tricoplanar && !qh TRInormals) {
-      fprintf (qh ferr, "qh_findhorizon: does not work for tricoplanar facets.  Use option 'Q11'\n");
-      qh_errexit (qh_ERRqhull, visible, NULL);
-    }
-    visible->visitid= qh visit_id;
-    FOREACHneighbor_(visible) {
-      if (neighbor->visitid == qh visit_id)
-        continue;
-      neighbor->visitid= qh visit_id;
-      zzinc_(Znumvisibility);
-      qh_distplane(point, neighbor, &dist);
-      if (dist > qh MINvisible) {
-        zinc_(Ztotvisible);
-	qh_removefacet(neighbor);  /* append to end of qh visible_list */
-	qh_appendfacet(neighbor);
-	neighbor->visible= True;
-        neighbor->f.replace= NULL;
-	qh num_visible++;
-	if (neighbor->good)
-	  (*goodvisible)++;
-        if (qh IStracing >=4)
-          qh_errprint ("visible", neighbor, NULL, NULL, NULL);
-      }else {
- 	if (dist > - qh MAXcoplanar) {
-    	  neighbor->coplanar= True;
-          zzinc_(Zcoplanarhorizon);
-          qh_precision ("coplanar horizon");
-	  coplanar++;
-	  if (qh MERGING) {
-	    if (dist > 0) {
-	      maximize_(qh max_outside, dist);
-	      maximize_(qh max_vertex, dist);
-#if qh_MAXoutside
-	      maximize_(neighbor->maxoutside, dist);
-#endif
-	    }else
-	      minimize_(qh min_vertex, dist);  /* due to merge later */
-	  }
-      	  trace2((qh ferr, "qh_findhorizon: point p%d is coplanar to horizon f%d, dist=%2.7g < qh MINvisible (%2.7g)\n",
-	      qh_pointid(point), neighbor->id, dist, qh MINvisible));
-	}else
-    	  neighbor->coplanar= False;
-    	zinc_(Ztothorizon);
-        numhorizon++;
-	if (neighbor->good)
-	  (*goodhorizon)++;
-        if (qh IStracing >=4)
-          qh_errprint ("horizon", neighbor, NULL, NULL, NULL);
-      }
-    }
-  }
-  if (!numhorizon) {
-    qh_precision ("empty horizon");
-    fprintf(qh ferr, "qhull precision error (qh_findhorizon): empty horizon\n\
-Point p%d was above all facets.\n", qh_pointid(point));
-    qh_printfacetlist (qh facet_list, NULL, True);
-    qh_errexit(qh_ERRprec, NULL, NULL);
-  }
-  trace1((qh ferr, "qh_findhorizon: %d horizon facets (good %d), %d visible (good %d), %d coplanar\n",
-       numhorizon, *goodhorizon, qh num_visible, *goodvisible, coplanar));
-  if (qh IStracing >= 4 && qh num_facets < 50)
-    qh_printlists ();
-} /* findhorizon */
-
-/*---------------------------------
-
-  qh_nextfurthest( visible )
-    returns next furthest point and visible facet for qh_addpoint()
-    starts search at qh.facet_next
-
-  returns:
-    removes furthest point from outside set
-    NULL if none available
-    advances qh.facet_next over facets with empty outside sets
-
-  design:
-    for each facet from qh.facet_next
-      if empty outside set
-      else if qh.NARROWhull
-        determine furthest outside point
-        if furthest point is not outside
-          advance qh.facet_next (point will be coplanar)
-    remove furthest point from outside set
-*/
-pointT *qh_nextfurthest (facetT **visible) {
-  facetT *facet;
-  int size, index;
-  realT randr, dist;
-  pointT *furthest;
-
-  while ((facet= qh facet_next) != qh facet_tail) {
-    if (!facet->outsideset) {
-      qh facet_next= facet->next;
-      continue;
-    }
-    SETreturnsize_(facet->outsideset, size);
-    if (!size) {
-      qh_setfree (&facet->outsideset);
-      qh facet_next= facet->next;
-      continue;
-    }
-    if (qh NARROWhull) {
-      if (facet->notfurthest)
-	qh_furthestout (facet);
-      furthest= (pointT*)qh_setlast (facet->outsideset);
-#if qh_COMPUTEfurthest
-      qh_distplane (furthest, facet, &dist);
-      zinc_(Zcomputefurthest);
-#else
-      dist= facet->furthestdist;
-#endif
-      if (dist < qh MINoutside) { /* remainder of outside set is coplanar for qh_outcoplanar */
-	qh facet_next= facet->next;
-	continue;
-      }
-    }
-    if (!qh RANDOMoutside && !qh VIRTUALmemory) {
-      if (qh PICKfurthest) {
-	qh_furthestnext (/* qh facet_list */);
-	facet= qh facet_next;
-      }
-      *visible= facet;
-      return ((pointT*)qh_setdellast (facet->outsideset));
-    }
-    if (qh RANDOMoutside) {
-      int outcoplanar = 0;
-      if (qh NARROWhull) {
-        FORALLfacets {
-	  if (facet == qh facet_next)
-	    break;
-	  if (facet->outsideset)
-  	    outcoplanar += qh_setsize( facet->outsideset);
-	}
-      }
-      randr= qh_RANDOMint;
-      randr= randr/(qh_RANDOMmax+1);
-      index= (int)floor((qh num_outside - outcoplanar) * randr);
-      FORALLfacet_(qh facet_next) {
-        if (facet->outsideset) {
-          SETreturnsize_(facet->outsideset, size);
-          if (!size)
-            qh_setfree (&facet->outsideset);
-          else if (size > index) {
-            *visible= facet;
-            return ((pointT*)qh_setdelnth (facet->outsideset, index));
-          }else
-            index -= size;
-        }
-      }
-      fprintf (qh ferr, "qhull internal error (qh_nextfurthest): num_outside %d is too low\nby at least %d, or a random real %g >= 1.0\n",
-              qh num_outside, index+1, randr);
-      qh_errexit (qh_ERRqhull, NULL, NULL);
-    }else { /* VIRTUALmemory */
-      facet= qh facet_tail->previous;
-      if (!(furthest= (pointT*)qh_setdellast(facet->outsideset))) {
-        if (facet->outsideset)
-          qh_setfree (&facet->outsideset);
-        qh_removefacet (facet);
-        qh_prependfacet (facet, &qh facet_list);
-        continue;
-      }
-      *visible= facet;
-      return furthest;
-    }
-  }
-  return NULL;
-} /* nextfurthest */
-
-/*---------------------------------
-
-  qh_partitionall( vertices, points, numpoints )
-    partitions all points in points/numpoints to the outsidesets of facets
-    vertices= vertices in qh.facet_list (not partitioned)
-
-  returns:
-    builds facet->outsideset
-    does not partition qh.GOODpoint
-    if qh.ONLYgood && !qh.MERGING,
-      does not partition qh.GOODvertex
-
-  notes:
-    faster if qh.facet_list sorted by anticipated size of outside set
-
-  design:
-    initialize pointset with all points
-    remove vertices from pointset
-    remove qh.GOODpointp from pointset (unless it's qh.STOPcone or qh.STOPpoint)
-    for all facets
-      for all remaining points in pointset
-        compute distance from point to facet
-        if point is outside facet
-          remove point from pointset (by not reappending)
-          update bestpoint
-          append point or old bestpoint to facet's outside set
-      append bestpoint to facet's outside set (furthest)
-    for all points remaining in pointset
-      partition point into facets' outside sets and coplanar sets
-*/
-void qh_partitionall(setT *vertices, pointT *points, int numpoints){
-  setT *pointset;
-  vertexT *vertex, **vertexp;
-  pointT *point, **pointp, *bestpoint;
-  int size, point_i, point_n, point_end, remaining, i, id;
-  facetT *facet;
-  realT bestdist= -REALmax, dist, distoutside;
-
-  trace1((qh ferr, "qh_partitionall: partition all points into outside sets\n"));
-  pointset= qh_settemp (numpoints);
-  qh num_outside= 0;
-  for (i=numpoints, point= points; i--; point += qh hull_dim)
-    *(pointp++)= point;
-  qh_settruncate (pointset, numpoints);
-  FOREACHvertex_(vertices) {
-    if ((id= qh_pointid(vertex->point)) >= 0)
-      SETelem_(pointset, id)= NULL;
-  }
-  id= qh_pointid (qh GOODpointp);
-  if (id >=0 && qh STOPcone-1 != id && -qh STOPpoint-1 != id)
-    SETelem_(pointset, id)= NULL;
-  if (qh GOODvertexp && qh ONLYgood && !qh MERGING) { /* matches qhull()*/
-    if ((id= qh_pointid(qh GOODvertexp)) >= 0)
-      SETelem_(pointset, id)= NULL;
-  }
-  if (!qh BESToutside) {  /* matches conditional for qh_partitionpoint below */
-    distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user.h */
-    zval_(Ztotpartition)= qh num_points - qh hull_dim - 1; /*misses GOOD... */
-    remaining= qh num_facets;
-    point_end= numpoints;
-    FORALLfacets {
-      size= point_end/(remaining--) + 100;
-      facet->outsideset= qh_setnew (size);
-      bestpoint= NULL;
-      point_end= 0;
-      FOREACHpoint_i_(pointset) {
-        if (point) {
-          zzinc_(Zpartitionall);
-          qh_distplane (point, facet, &dist);
-          if (dist < distoutside)
-            SETelem_(pointset, point_end++)= point;
-          else {
-	    qh num_outside++;
-            if (!bestpoint) {
-              bestpoint= point;
-              bestdist= dist;
-            }else if (dist > bestdist) {
-              qh_setappend (&facet->outsideset, bestpoint);
-              bestpoint= point;
-              bestdist= dist;
-            }else
-              qh_setappend (&facet->outsideset, point);
-          }
-        }
-      }
-      if (bestpoint) {
-        qh_setappend (&facet->outsideset, bestpoint);
-#if !qh_COMPUTEfurthest
-	facet->furthestdist= bestdist;
-#endif
-      }else
-        qh_setfree (&facet->outsideset);
-      qh_settruncate (pointset, point_end);
-    }
-  }
-  /* if !qh BESToutside, pointset contains points not assigned to outsideset */
-  if (qh BESToutside || qh MERGING || qh KEEPcoplanar || qh KEEPinside) {
-    qh findbestnew= True;
-    FOREACHpoint_i_(pointset) {
-      if (point)
-        qh_partitionpoint(point, qh facet_list);
-    }
-    qh findbestnew= False;
-  }
-  zzval_(Zpartition)= 0;
-  qh_settempfree(&pointset);
-  if (qh IStracing >= 4)
-    qh_printfacetlist (qh facet_list, NULL, True);
-} /* partitionall */
-
-
-/*---------------------------------
-
-  qh_partitioncoplanar( point, facet, dist )
-    partition coplanar point to a facet
-    dist is distance from point to facet
-    if dist NULL,
-      searches for bestfacet and does nothing if inside
-    if qh.findbestnew set,
-      searches new facets instead of using qh_findbest()
-
-  returns:
-    qh.max_ouside updated
-    if qh.KEEPcoplanar or qh.KEEPinside
-      point assigned to best coplanarset
-
-  notes:
-    facet->maxoutside is updated at end by qh_check_maxout
-
-  design:
-    if dist undefined
-      find best facet for point
-      if point sufficiently below facet (depends on qh.NEARinside and qh.KEEPinside)
-        exit
-    if keeping coplanar/nearinside/inside points
-      if point is above furthest coplanar point
-        append point to coplanar set (it is the new furthest)
-        update qh.max_outside
-      else
-        append point one before end of coplanar set
-    else if point is clearly outside of qh.max_outside and bestfacet->coplanarset
-    and bestfacet is more than perpendicular to facet
-      repartition the point using qh_findbest() -- it may be put on an outsideset
-    else
-      update qh.max_outside
-*/
-void qh_partitioncoplanar (pointT *point, facetT *facet, realT *dist) {
-  facetT *bestfacet;
-  pointT *oldfurthest;
-  realT bestdist, dist2, angle;
-  int numpart= 0, oldfindbest;
-  boolT isoutside;
-
-  qh WAScoplanar= True;
-  if (!dist) {
-    if (qh findbestnew)
-      bestfacet= qh_findbestnew (point, facet, &bestdist, qh_ALL, &isoutside, &numpart);
-    else
-      bestfacet= qh_findbest (point, facet, qh_ALL, !qh_ISnewfacets, qh DELAUNAY,
-                          &bestdist, &isoutside, &numpart);
-    zinc_(Ztotpartcoplanar);
-    if (!qh DELAUNAY && !qh KEEPinside) { /*  for 'd', bestdist skips upperDelaunay facets */
-      if (qh KEEPnearinside) {
-        if (bestdist < -qh NEARinside) {
-          zinc_(Zcoplanarinside);
-	  trace4((qh ferr, "qh_partitioncoplanar: point p%d is more than near-inside facet f%d dist %2.2g findbestnew %d\n",
-		  qh_pointid(point), bestfacet->id, bestdist, qh findbestnew));
-          return;
-        }
-      }else if (bestdist < -qh MAXcoplanar) {
-	  trace4((qh ferr, "qh_partitioncoplanar: point p%d is inside facet f%d dist %2.2g findbestnew %d\n",
-		  qh_pointid(point), bestfacet->id, bestdist, qh findbestnew));
-        zinc_(Zcoplanarinside);
-        return;
-      }
-    }
-  }else {
-    bestfacet= facet;
-    bestdist= *dist;
-  }
-  if (bestdist > qh max_outside) {
-    if (!dist && facet != bestfacet) {
-      zinc_(Zpartangle);
-      angle= qh_getangle(facet->normal, bestfacet->normal);
-      if (angle < 0) {
-	/* typically due to deleted vertex and coplanar facets, e.g.,
-	     RBOX 1000 s Z1 G1e-13 t1001185205 | QHULL Tv */
-	zinc_(Zpartflip);
-	trace2((qh ferr, "qh_partitioncoplanar: repartition point p%d from f%d.  It is above flipped facet f%d dist %2.2g\n",
-		qh_pointid(point), facet->id, bestfacet->id, bestdist));
-	oldfindbest= qh findbestnew;
-        qh findbestnew= False;
-	qh_partitionpoint(point, bestfacet);
-        qh findbestnew= oldfindbest;
-	return;
-      }
-    }
-    qh max_outside= bestdist;
-    if (bestdist > qh TRACEdist) {
-      fprintf (qh ferr, "qh_partitioncoplanar: ====== p%d from f%d increases max_outside to %2.2g of f%d last p%d\n",
-		     qh_pointid(point), facet->id, bestdist, bestfacet->id, qh furthest_id);
-      qh_errprint ("DISTANT", facet, bestfacet, NULL, NULL);
-    }
-  }
-  if (qh KEEPcoplanar + qh KEEPinside + qh KEEPnearinside) {
-    oldfurthest= (pointT*)qh_setlast (bestfacet->coplanarset);
-    if (oldfurthest) {
-      zinc_(Zcomputefurthest);
-      qh_distplane (oldfurthest, bestfacet, &dist2);
-    }
-    if (!oldfurthest || dist2 < bestdist)
-      qh_setappend(&bestfacet->coplanarset, point);
-    else
-      qh_setappend2ndlast(&bestfacet->coplanarset, point);
-  }
-  trace4((qh ferr, "qh_partitioncoplanar: point p%d is coplanar with facet f%d (or inside) dist %2.2g\n",
-	  qh_pointid(point), bestfacet->id, bestdist));
-} /* partitioncoplanar */
-
-/*---------------------------------
-
-  qh_partitionpoint( point, facet )
-    assigns point to an outside set, coplanar set, or inside set (i.e., dropt)
-    if qh.findbestnew
-      uses qh_findbestnew() to search all new facets
-    else
-      uses qh_findbest()
-
-  notes:
-    after qh_distplane(), this and qh_findbest() are most expensive in 3-d
-
-  design:
-    find best facet for point
-      (either exhaustive search of new facets or directed search from facet)
-    if qh.NARROWhull
-      retain coplanar and nearinside points as outside points
-    if point is outside bestfacet
-      if point above furthest point for bestfacet
-        append point to outside set (it becomes the new furthest)
-        if outside set was empty
-          move bestfacet to end of qh.facet_list (i.e., after qh.facet_next)
-        update bestfacet->furthestdist
-      else
-        append point one before end of outside set
-    else if point is coplanar to bestfacet
-      if keeping coplanar points or need to update qh.max_outside
-        partition coplanar point into bestfacet
-    else if near-inside point
-      partition as coplanar point into bestfacet
-    else is an inside point
-      if keeping inside points
-        partition as coplanar point into bestfacet
-*/
-void qh_partitionpoint (pointT *point, facetT *facet) {
-  realT bestdist;
-  boolT isoutside;
-  facetT *bestfacet;
-  int numpart;
-#if qh_COMPUTEfurthest
-  realT dist;
-#endif
-
-  if (qh findbestnew)
-    bestfacet= qh_findbestnew (point, facet, &bestdist, qh BESToutside, &isoutside, &numpart);
-  else
-    bestfacet= qh_findbest (point, facet, qh BESToutside, qh_ISnewfacets, !qh_NOupper,
-			  &bestdist, &isoutside, &numpart);
-  zinc_(Ztotpartition);
-  if (qh NARROWhull) {
-    if (qh DELAUNAY && !isoutside && bestdist >= -qh MAXcoplanar)
-      qh_precision ("nearly incident point (narrow hull)");
-    if (qh KEEPnearinside) {
-      if (bestdist >= -qh NEARinside)
-	isoutside= True;
-    }else if (bestdist >= -qh MAXcoplanar)
-      isoutside= True;
-  }
-
-  if (isoutside) {
-    if (!bestfacet->outsideset
-    || !qh_setlast (bestfacet->outsideset)) {
-      qh_setappend(&(bestfacet->outsideset), point);
-      if (!bestfacet->newfacet) {
-        qh_removefacet (bestfacet);  /* make sure it's after qh facet_next */
-        qh_appendfacet (bestfacet);
-      }
-#if !qh_COMPUTEfurthest
-      bestfacet->furthestdist= bestdist;
-#endif
-    }else {
-#if qh_COMPUTEfurthest
-      zinc_(Zcomputefurthest);
-      qh_distplane (oldfurthest, bestfacet, &dist);
-      if (dist < bestdist)
-	qh_setappend(&(bestfacet->outsideset), point);
-      else
-	qh_setappend2ndlast(&(bestfacet->outsideset), point);
-#else
-      if (bestfacet->furthestdist < bestdist) {
-	qh_setappend(&(bestfacet->outsideset), point);
-	bestfacet->furthestdist= bestdist;
-      }else
-	qh_setappend2ndlast(&(bestfacet->outsideset), point);
-#endif
-    }
-    qh num_outside++;
-    trace4((qh ferr, "qh_partitionpoint: point p%d is outside facet f%d new? %d(or narrowhull)\n",
-	  qh_pointid(point), bestfacet->id, bestfacet->newfacet));
-  }else if (qh DELAUNAY || bestdist >= -qh MAXcoplanar) { /* for 'd', bestdist skips upperDelaunay facets */
-    zzinc_(Zcoplanarpart);
-    if (qh DELAUNAY)
-      qh_precision ("nearly incident point");
-    if ((qh KEEPcoplanar + qh KEEPnearinside) || bestdist > qh max_outside)
-      qh_partitioncoplanar (point, bestfacet, &bestdist);
-    else {
-      trace4((qh ferr, "qh_partitionpoint: point p%d is coplanar to facet f%d (dropped)\n",
-	  qh_pointid(point), bestfacet->id));
-    }
-  }else if (qh KEEPnearinside && bestdist > -qh NEARinside) {
-    zinc_(Zpartnear);
-    qh_partitioncoplanar (point, bestfacet, &bestdist);
-  }else {
-    zinc_(Zpartinside);
-    trace4((qh ferr, "qh_partitionpoint: point p%d is inside all facets, closest to f%d dist %2.2g\n",
-	  qh_pointid(point), bestfacet->id, bestdist));
-    if (qh KEEPinside)
-      qh_partitioncoplanar (point, bestfacet, &bestdist);
-  }
-} /* partitionpoint */
-
-/*---------------------------------
-
-  qh_partitionvisible( allpoints, numoutside )
-    partitions points in visible facets to qh.newfacet_list
-    qh.visible_list= visible facets
-    for visible facets
-      1st neighbor (if any) points to a horizon facet or a new facet
-    if allpoints (not used),
-      repartitions coplanar points
-
-  returns:
-    updates outside sets and coplanar sets of qh.newfacet_list
-    updates qh.num_outside (count of outside points)
-
-  notes:
-    qh.findbest_notsharp should be clear (extra work if set)
-
-  design:
-    for all visible facets with outside set or coplanar set
-      select a newfacet for visible facet
-      if outside set
-        partition outside set into new facets
-      if coplanar set and keeping coplanar/near-inside/inside points
-        if allpoints
-          partition coplanar set into new facets, may be assigned outside
-        else
-          partition coplanar set into coplanar sets of new facets
-    for each deleted vertex
-      if allpoints
-        partition vertex into new facets, may be assigned outside
-      else
-        partition vertex into coplanar sets of new facets
-*/
-void qh_partitionvisible(/*visible_list*/ boolT allpoints, int *numoutside) {
-  facetT *visible, *newfacet;
-  pointT *point, **pointp;
-  int coplanar=0, size;
-  unsigned count;
-  vertexT *vertex, **vertexp;
-
-  if (qh ONLYmax)
-    maximize_(qh MINoutside, qh max_vertex);
-  *numoutside= 0;
-  FORALLvisible_facets {
-    if (!visible->outsideset && !visible->coplanarset)
-      continue;
-    newfacet= visible->f.replace;
-    count= 0;
-    while (newfacet && newfacet->visible) {
-      newfacet= newfacet->f.replace;
-      if (count++ > qh facet_id)
-	qh_infiniteloop (visible);
-    }
-    if (!newfacet)
-      newfacet= qh newfacet_list;
-    if (newfacet == qh facet_tail) {
-      fprintf (qh ferr, "qhull precision error (qh_partitionvisible): all new facets deleted as\n        degenerate facets. Can not continue.\n");
-      qh_errexit (qh_ERRprec, NULL, NULL);
-    }
-    if (visible->outsideset) {
-      size= qh_setsize (visible->outsideset);
-      *numoutside += size;
-      qh num_outside -= size;
-      FOREACHpoint_(visible->outsideset)
-        qh_partitionpoint (point, newfacet);
-    }
-    if (visible->coplanarset && (qh KEEPcoplanar + qh KEEPinside + qh KEEPnearinside)) {
-      size= qh_setsize (visible->coplanarset);
-      coplanar += size;
-      FOREACHpoint_(visible->coplanarset) {
-        if (allpoints) /* not used */
-          qh_partitionpoint (point, newfacet);
-        else
-          qh_partitioncoplanar (point, newfacet, NULL);
-      }
-    }
-  }
-  FOREACHvertex_(qh del_vertices) {
-    if (vertex->point) {
-      if (allpoints) /* not used */
-        qh_partitionpoint (vertex->point, qh newfacet_list);
-      else
-        qh_partitioncoplanar (vertex->point, qh newfacet_list, NULL);
-    }
-  }
-  trace1((qh ferr,"qh_partitionvisible: partitioned %d points from outsidesets and %d points from coplanarsets\n", *numoutside, coplanar));
-} /* partitionvisible */
-
-
-
-/*---------------------------------
-
-  qh_precision( reason )
-    restart on precision errors if not merging and if 'QJn'
-*/
-void qh_precision (char *reason) {
-
-  if (qh ALLOWrestart && !qh PREmerge && !qh MERGEexact) {
-    if (qh JOGGLEmax < REALmax/2) {
-      trace0((qh ferr, "qh_precision: qhull restart because of %s\n", reason));
-      longjmp(qh restartexit, qh_ERRprec);
-    }
-  }
-} /* qh_precision */
-
-/*---------------------------------
-
-  qh_printsummary( fp )
-    prints summary to fp
-
-  notes:
-    not in io.c so that user_eg.c can prevent io.c from loading
-    qh_printsummary and qh_countfacets must match counts
-
-  design:
-    determine number of points, vertices, and coplanar points
-    print summary
-*/
-void qh_printsummary(FILE *fp) {
-  realT ratio, outerplane, innerplane;
-  float cpu;
-  int size, id, nummerged, numvertices, numcoplanars= 0, nonsimplicial=0;
-  int goodused;
-  facetT *facet;
-  char *s;
-  int numdel= zzval_(Zdelvertextot);
-  int numtricoplanars= 0;
-
-  size= qh num_points + qh_setsize (qh other_points);
-  numvertices= qh num_vertices - qh_setsize (qh del_vertices);
-  id= qh_pointid (qh GOODpointp);
-  FORALLfacets {
-    if (facet->coplanarset)
-      numcoplanars += qh_setsize( facet->coplanarset);
-    if (facet->good) {
-      if (facet->simplicial) {
-	if (facet->keepcentrum && facet->tricoplanar)
-	  numtricoplanars++;
-      }else if (qh_setsize(facet->vertices) != qh hull_dim)
-	nonsimplicial++;
-    }
-  }
-  if (id >=0 && qh STOPcone-1 != id && -qh STOPpoint-1 != id)
-    size--;
-  if (qh STOPcone || qh STOPpoint)
-      fprintf (fp, "\nAt a premature exit due to 'TVn', 'TCn', 'TRn', or precision error.");
-  if (qh UPPERdelaunay)
-    goodused= qh GOODvertex + qh GOODpoint + qh SPLITthresholds;
-  else if (qh DELAUNAY)
-    goodused= qh GOODvertex + qh GOODpoint + qh GOODthreshold;
-  else
-    goodused= qh num_good;
-  nummerged= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
-  if (qh VORONOI) {
-    if (qh UPPERdelaunay)
-      fprintf (fp, "\n\
-Furthest-site Voronoi vertices by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
-    else
-      fprintf (fp, "\n\
-Voronoi diagram by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
-    fprintf(fp, "  Number of Voronoi regions%s: %d\n",
-              qh ATinfinity ? " and at-infinity" : "", numvertices);
-    if (numdel)
-      fprintf(fp, "  Total number of deleted points due to merging: %d\n", numdel);
-    if (numcoplanars - numdel > 0)
-      fprintf(fp, "  Number of nearly incident points: %d\n", numcoplanars - numdel);
-    else if (size - numvertices - numdel > 0)
-      fprintf(fp, "  Total number of nearly incident points: %d\n", size - numvertices - numdel);
-    fprintf(fp, "  Number of%s Voronoi vertices: %d\n",
-              goodused ? " 'good'" : "", qh num_good);
-    if (nonsimplicial)
-      fprintf(fp, "  Number of%s non-simplicial Voronoi vertices: %d\n",
-              goodused ? " 'good'" : "", nonsimplicial);
-  }else if (qh DELAUNAY) {
-    if (qh UPPERdelaunay)
-      fprintf (fp, "\n\
-Furthest-site Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
-    else
-      fprintf (fp, "\n\
-Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
-    fprintf(fp, "  Number of input sites%s: %d\n",
-              qh ATinfinity ? " and at-infinity" : "", numvertices);
-    if (numdel)
-      fprintf(fp, "  Total number of deleted points due to merging: %d\n", numdel);
-    if (numcoplanars - numdel > 0)
-      fprintf(fp, "  Number of nearly incident points: %d\n", numcoplanars - numdel);
-    else if (size - numvertices - numdel > 0)
-      fprintf(fp, "  Total number of nearly incident points: %d\n", size - numvertices - numdel);
-    fprintf(fp, "  Number of%s Delaunay regions: %d\n",
-              goodused ? " 'good'" : "", qh num_good);
-    if (nonsimplicial)
-      fprintf(fp, "  Number of%s non-simplicial Delaunay regions: %d\n",
-              goodused ? " 'good'" : "", nonsimplicial);
-  }else if (qh HALFspace) {
-    fprintf (fp, "\n\
-Halfspace intersection by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
-    fprintf(fp, "  Number of halfspaces: %d\n", size);
-    fprintf(fp, "  Number of non-redundant halfspaces: %d\n", numvertices);
-    if (numcoplanars) {
-      if (qh KEEPinside && qh KEEPcoplanar)
-      	s= "similar and redundant";
-      else if (qh KEEPinside)
-        s= "redundant";
-      else
-        s= "similar";
-      fprintf(fp, "  Number of %s halfspaces: %d\n", s, numcoplanars);
-    }
-    fprintf(fp, "  Number of intersection points: %d\n", qh num_facets - qh num_visible);
-    if (goodused)
-      fprintf(fp, "  Number of 'good' intersection points: %d\n", qh num_good);
-    if (nonsimplicial)
-      fprintf(fp, "  Number of%s non-simplicial intersection points: %d\n",
-              goodused ? " 'good'" : "", nonsimplicial);
-  }else {
-    fprintf (fp, "\n\
-Convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
-    fprintf(fp, "  Number of vertices: %d\n", numvertices);
-    if (numcoplanars) {
-      if (qh KEEPinside && qh KEEPcoplanar)
-      	s= "coplanar and interior";
-      else if (qh KEEPinside)
-        s= "interior";
-      else
-        s= "coplanar";
-      fprintf(fp, "  Number of %s points: %d\n", s, numcoplanars);
-    }
-    fprintf(fp, "  Number of facets: %d\n", qh num_facets - qh num_visible);
-    if (goodused)
-      fprintf(fp, "  Number of 'good' facets: %d\n", qh num_good);
-    if (nonsimplicial)
-      fprintf(fp, "  Number of%s non-simplicial facets: %d\n",
-              goodused ? " 'good'" : "", nonsimplicial);
-  }
-  if (numtricoplanars)
-      fprintf(fp, "  Number of triangulated facets: %d\n", numtricoplanars);
-  fprintf(fp, "\nStatistics for: %s | %s",
-                      qh rbox_command, qh qhull_command);
-  if (qh ROTATErandom != INT_MIN)
-    fprintf(fp, " QR%d\n\n", qh ROTATErandom);
-  else
-    fprintf(fp, "\n\n");
-  fprintf(fp, "  Number of points processed: %d\n", zzval_(Zprocessed));
-  fprintf(fp, "  Number of hyperplanes created: %d\n", zzval_(Zsetplane));
-  if (qh DELAUNAY)
-    fprintf(fp, "  Number of facets in hull: %d\n", qh num_facets - qh num_visible);
-  fprintf(fp, "  Number of distance tests for qhull: %d\n", zzval_(Zpartition)+
-      zzval_(Zpartitionall)+zzval_(Znumvisibility)+zzval_(Zpartcoplanar));
-#if 0  /* NOTE: must print before printstatistics() */
-  {realT stddev, ave;
-  fprintf(fp, "  average new facet balance: %2.2g\n",
-	  wval_(Wnewbalance)/zval_(Zprocessed));
-  stddev= qh_stddev (zval_(Zprocessed), wval_(Wnewbalance),
-                                 wval_(Wnewbalance2), &ave);
-  fprintf(fp, "  new facet standard deviation: %2.2g\n", stddev);
-  fprintf(fp, "  average partition balance: %2.2g\n",
-	  wval_(Wpbalance)/zval_(Zpbalance));
-  stddev= qh_stddev (zval_(Zpbalance), wval_(Wpbalance),
-                                 wval_(Wpbalance2), &ave);
-  fprintf(fp, "  partition standard deviation: %2.2g\n", stddev);
-  }
-#endif
-  if (nummerged) {
-    fprintf(fp,"  Number of distance tests for merging: %d\n",zzval_(Zbestdist)+
-          zzval_(Zcentrumtests)+zzval_(Zdistconvex)+zzval_(Zdistcheck)+
-          zzval_(Zdistzero));
-    fprintf(fp,"  Number of distance tests for checking: %d\n",zzval_(Zcheckpart));
-    fprintf(fp,"  Number of merged facets: %d\n", nummerged);
-  }
-  if (!qh RANDOMoutside && qh QHULLfinished) {
-    cpu= qh hulltime;
-    cpu /= qh_SECticks;
-    wval_(Wcpu)= cpu;
-    fprintf (fp, "  CPU seconds to compute hull (after input): %2.4g\n", cpu);
-  }
-  if (qh RERUN) {
-    if (!qh PREmerge && !qh MERGEexact)
-      fprintf(fp, "  Percentage of runs with precision errors: %4.1f\n",
-	   zzval_(Zretry)*100.0/qh build_cnt);  /* careful of order */
-  }else if (qh JOGGLEmax < REALmax/2) {
-    if (zzval_(Zretry))
-      fprintf(fp, "  After %d retries, input joggled by: %2.2g\n",
-         zzval_(Zretry), qh JOGGLEmax);
-    else
-      fprintf(fp, "  Input joggled by: %2.2g\n", qh JOGGLEmax);
-  }
-  if (qh totarea != 0.0)
-    fprintf(fp, "  %s facet area:   %2.8g\n",
-	    zzval_(Ztotmerge) ? "Approximate" : "Total", qh totarea);
-  if (qh totvol != 0.0)
-    fprintf(fp, "  %s volume:       %2.8g\n",
-	    zzval_(Ztotmerge) ? "Approximate" : "Total", qh totvol);
-  if (qh MERGING) {
-    qh_outerinner (NULL, &outerplane, &innerplane);
-    if (outerplane > 2 * qh DISTround) {
-      fprintf(fp, "  Maximum distance of %spoint above facet: %2.2g",
-	    (qh QHULLfinished ? "" : "merged "), outerplane);
-      ratio= outerplane/(qh ONEmerge + qh DISTround);
-      /* don't report ratio if MINoutside is large */
-      if (ratio > 0.05 && 2* qh ONEmerge > qh MINoutside && qh JOGGLEmax > REALmax/2)
-        fprintf (fp, " (%.1fx)\n", ratio);
-      else
-        fprintf (fp, "\n");
-    }
-    if (innerplane < -2 * qh DISTround) {
-      fprintf(fp, "  Maximum distance of %svertex below facet: %2.2g",
-	    (qh QHULLfinished ? "" : "merged "), innerplane);
-      ratio= -innerplane/(qh ONEmerge+qh DISTround);
-      if (ratio > 0.05 && qh JOGGLEmax > REALmax/2)
-        fprintf (fp, " (%.1fx)\n", ratio);
-      else
-        fprintf (fp, "\n");
-    }
-  }
-  fprintf(fp, "\n");
-} /* printsummary */
-
-
diff --git a/extern/qhull/src/qhull.h b/extern/qhull/src/qhull.h
deleted file mode 100644
index 896ec1e9c18..00000000000
--- a/extern/qhull/src/qhull.h
+++ /dev/null
@@ -1,1048 +0,0 @@
-/*  ---------------------------------
-
-   qhull.h
-   user-level header file for using qhull.a library
-
-   see qh-qhull.htm, qhull_a.h
-
-   copyright (c) 1993-2002, The Geometry Center
-
-   NOTE: access to qh_qh is via the 'qh' macro.  This allows
-   qh_qh to be either a pointer or a structure.  An example
-   of using qh is "qh DROPdim" which accesses the DROPdim
-   the 'qhstat' macro.
-
-   includes function prototypes for qhull.c, geom.c, global.c, io.c, user.c
-
-   use mem.h for mem.c
-   use qset.h for qset.c
-
-   see unix.c for an example of using qhull.h
-
-   recompile qhull if you change this file
-*/
-
-#ifndef qhDEFqhull
-#define qhDEFqhull 1
-
-/*=========================== -included files ==============*/
-
-#include
-#include
-#include
-
-#if __MWERKS__ && __POWERPC__
-#include
-#include
-#include
-#endif
-
-#ifndef __STDC__
-#ifndef __cplusplus
-#if     !_MSC_VER
-#error  Neither __STDC__ nor __cplusplus is defined.  Please use strict ANSI C or C++ to compile
-#error  Qhull.  You may need to turn off compiler extensions in your project configuration.  If
-#error  your compiler is a standard C compiler, you can delete this warning from qhull.h
-#endif
-#endif
-#endif
-
-#include "user.h"      /* user defineable constants */
-
-/*============ constants and basic types ====================*/
-
-/*----------------------------------
-
-  qh_VERSION
-    version string by year and date
-
-    the revision increases on code changes only
-
-  notes:
-    change date:    Changes.txt, Announce.txt, README.txt, qhull.man
-                    qhull-news.html, Eudora signatures,
-    change version: README.txt, qhull.html, file_id.diz, Makefile
-    change year:    Copying.txt
-    recompile user_eg.c, rbox.c, qhull.c, qconvex.c, qdelaun.c qvoronoi.c, qhalf.c
-    make copy of qhull-news.html as qh-news.htm
-*/
-
-#define qh_VERSION "2002.1 2002/8/20"
-
-/*----------------------------------
-
-  coordT
-    coordinates and coefficients are stored as realT (i.e., double)
-
-  notes:
-    could use 'float' for data and 'double' for calculations (realT vs. coordT)
-      This requires many type casts, and adjusted error bounds.
-      Also C compilers may do expressions in double anyway.
-*/
-#define coordT realT
-
-/*----------------------------------
-
-  pointT
-    a point is an array of DIM3 coordinates
-*/
-#define pointT coordT
-
-/*----------------------------------
-
-  flagT
-    Boolean flag as a bit
-*/
-#define flagT unsigned int
-
-/*----------------------------------
-
-  boolT
-    boolean value, either True or False
-
-  notes:
-    needed for portability
-*/
-#define boolT unsigned int
-#ifdef False
-#undef False
-#endif
-#ifdef True
-#undef True
-#endif
-#define False 0
-#define True 1
-
-/*----------------------------------
-
-  qh_CENTER
-    to distinguish facet->center
-*/
-typedef enum
-{
-    qh_ASnone = 0, qh_ASvoronoi, qh_AScentrum
-}
-qh_CENTER;
-
-/*----------------------------------
-
-  qh_PRINT
-    output formats for printing (qh.PRINTout).
-    'Fa' 'FV' 'Fc' 'FC'
-
-
-   notes:
-   some of these names are similar to qh names.  The similar names are only
-   used in switch statements in qh_printbegin() etc.
-*/
-typedef enum {qh_PRINTnone= 0,
-  qh_PRINTarea, qh_PRINTaverage,           /* 'Fa' 'FV' 'Fc' 'FC' */
-  qh_PRINTcoplanars, qh_PRINTcentrums,
-  qh_PRINTfacets, qh_PRINTfacets_xridge,   /* 'f' 'FF' 'G' 'FI' 'Fi' 'Fn' */
-  qh_PRINTgeom, qh_PRINTids, qh_PRINTinner, qh_PRINTneighbors,
-  qh_PRINTnormals, qh_PRINTouter,          /* 'n' 'Fo' 'i' 'm' 'Fm' 'o' */
-  qh_PRINTincidences, qh_PRINTmathematica, qh_PRINTmerges, qh_PRINToff,
-  qh_PRINToptions, qh_PRINTpointintersect, /* 'FO' 'Fp' 'FP' 'p' 'FQ' 'FS' */
-  qh_PRINTpointnearest, qh_PRINTpoints, qh_PRINTqhull, qh_PRINTsize,
-  qh_PRINTsummary, qh_PRINTtriangles,      /* 'Fs' 'Ft' 'Fv' 'FN' 'Fx' */
-  qh_PRINTvertices, qh_PRINTvneighbors, qh_PRINTextremes,
-  qh_PRINTEND} qh_PRINT;
-
-/*----------------------------------
-
-  qh_ALL
-    argument flag for selecting everything
-*/
-#define qh_ALL      True
-#define qh_NOupper  True     /* argument for qh_findbest */
-#define qh_IScheckmax  True     /* argument for qh_findbesthorizon */
-#define qh_ISnewfacets  True     /* argument for qh_findbest */
-#define qh_RESETvisible  True     /* argument for qh_resetlists */
-
-/*----------------------------------
-
-  qh_ERR
-    Qhull exit codes, for indicating errors
-*/
-#define qh_ERRnone  0    /* no error occurred during qhull */
-#define qh_ERRinput 1    /* input inconsistency */
-#define qh_ERRsingular 2 /* singular input data */
-#define qh_ERRprec  3    /* precision error */
-#define qh_ERRmem   4    /* insufficient memory, matches mem.h */
-#define qh_ERRqhull 5    /* internal error detected, matches mem.h */
-
-/* ============ -structures- ====================
-   each of the following structures is defined by a typedef
-   all realT and coordT fields occur at the beginning of a structure
-        (otherwise space may be wasted due to alignment)
-   define all flags together and pack into 32-bit number
-*/
-
-typedef struct vertexT vertexT;
-typedef struct ridgeT ridgeT;
-typedef struct facetT facetT;
-#ifndef DEFsetT
-#define DEFsetT 1
-typedef struct setT setT;          /* defined in qset.h */
-#endif
-
-/*----------------------------------
-
-  facetT
-    defines a facet
-
-  notes:
-   qhull() generates the hull as a list of facets.
-
-  topological information:
-    f.previous,next     doubly-linked list of facets
-    f.vertices          set of vertices
-    f.ridges            set of ridges
-    f.neighbors         set of neighbors
-    f.toporient         True if facet has top-orientation (else bottom)
-
-  geometric information:
-    f.offset,normal     hyperplane equation
-    f.maxoutside        offset to outer plane -- all points inside
-    f.center            centrum for testing convexity
-    f.simplicial        True if facet is simplicial
-    f.flipped           True if facet does not include qh.interior_point
-
-  for constructing hull:
-    f.visible           True if facet on list of visible facets (will be deleted)
-    f.newfacet          True if facet on list of newly created facets
-    f.coplanarset       set of points coplanar with this facet
-                        (includes near-inside points for later testing)
-    f.outsideset        set of points outside of this facet
-    f.furthestdist      distance to furthest point of outside set
-    f.visitid           marks visited facets during a loop
-    f.replace           replacement facet for to-be-deleted, visible facets
-    f.samecycle,newcycle cycle of facets for merging into horizon facet
-
-  see below for other flags and fields
-*/
-struct facetT {
-#if !qh_COMPUTEfurthest
-  coordT   furthestdist;/* distance to furthest point of outsideset */
-#endif
-#if qh_MAXoutside
-  coordT   maxoutside;  /* max computed distance of point to facet
-  			Before QHULLfinished this is an approximation
-  			since maxdist not always set for mergefacet
-			Actual outer plane is +DISTround and
-			computed outer plane is +2*DISTround */
-#endif
-  coordT   offset;      /* exact offset of hyperplane from origin */
-  coordT  *normal;      /* normal of hyperplane, hull_dim coefficients */
-			/*   if tricoplanar, shared with a neighbor */
-  union {               /* in order of testing */
-   realT   area;        /* area of facet, only in io.c if  ->isarea */
-   facetT *replace;	/*  replacement facet if ->visible and NEWfacets
-  			     is NULL only if qh_mergedegen_redundant or interior */
-   facetT *samecycle;   /*  cycle of facets from the same visible/horizon intersection,
-   			     if ->newfacet */
-   facetT *newcycle;    /*  in horizon facet, current samecycle of new facets */
-   facetT *trivisible;  /* visible facet for ->tricoplanar facets during qh_triangulate() */
-   facetT *triowner;    /* owner facet for ->tricoplanar, !isarea facets w/ ->keepcentrum */
-  }f;
-  coordT  *center;      /*  centrum for convexity, qh CENTERtype == qh_AScentrum */
-      			/*  Voronoi center, qh CENTERtype == qh_ASvoronoi */
-			/*   if tricoplanar, shared with a neighbor */
-  facetT  *previous;    /* previous facet in the facet_list */
-  facetT  *next;        /* next facet in the facet_list */
-  setT    *vertices;    /* vertices for this facet, inverse sorted by ID
-                           if simplicial, 1st vertex was apex/furthest */
-  setT    *ridges;      /* explicit ridges for nonsimplicial facets.
-  			   for simplicial facets, neighbors defines ridge */
-  setT    *neighbors;   /* neighbors of the facet.  If simplicial, the kth
-			   neighbor is opposite the kth vertex, and the first
-			   neighbor is the horizon facet for the first vertex*/
-  setT    *outsideset;  /* set of points outside this facet
-		           if non-empty, last point is furthest
-			   if NARROWhull, includes coplanars for partitioning*/
-  setT    *coplanarset; /* set of points coplanar with this facet
-  			   > qh.min_vertex and <= facet->max_outside
-                           a point is assigned to the furthest facet
-		           if non-empty, last point is furthest away */
-  unsigned visitid;     /* visit_id, for visiting all neighbors,
-			   all uses are independent */
-  unsigned id;	        /* unique identifier from qh facet_id */
-  unsigned nummerge:9;  /* number of merges */
-#define qh_MAXnummerge 511 /*     2^9-1, 32 flags total, see "flags:" in io.c */
-  flagT    tricoplanar:1; /* True if TRIangulate and simplicial and coplanar with a neighbor */
-			  /*   all tricoplanars share the same ->center, ->normal, ->offset, ->maxoutside */
-			  /*   all tricoplanars share the same apex */
-                          /*   if ->degenerate, does not span facet (one logical ridge) */
-                          /*   one tricoplanar has ->keepcentrum and ->coplanarset */
-                          /*   during qh_triangulate, f.trivisible points to original facet */
-  flagT	   newfacet:1;  /* True if facet on qh newfacet_list (new or merged) */
-  flagT	   visible:1;   /* True if visible facet (will be deleted) */
-  flagT    toporient:1; /* True if created with top orientation
-			   after merging, use ridge orientation */
-  flagT    simplicial:1;/* True if simplicial facet, ->ridges may be implicit */
-  flagT    seen:1;      /* used to perform operations only once, like visitid */
-  flagT    seen2:1;     /* used to perform operations only once, like visitid */
-  flagT	   flipped:1;   /* True if facet is flipped */
-  flagT    upperdelaunay:1; /* True if facet is upper envelope of Delaunay triangulation */
-  flagT    notfurthest:1; /* True if last point of outsideset is not furthest*/
-
-/*-------- flags primarily for output ---------*/
-  flagT	   good:1;      /* True if a facet marked good for output */
-  flagT    isarea:1;    /* True if facet->f.area is defined */
-
-/*-------- flags for merging ------------------*/
-  flagT    dupridge:1;  /* True if duplicate ridge in facet */
-  flagT    mergeridge:1; /* True if facet or neighbor contains a qh_MERGEridge
-                            ->normal defined (also defined for mergeridge2) */
-  flagT    mergeridge2:1; /* True if neighbor contains a qh_MERGEridge (mark_dupridges */
-  flagT    coplanar:1;  /* True if horizon facet is coplanar at last use */
-  flagT     mergehorizon:1; /* True if will merge into horizon (->coplanar) */
-  flagT	    cycledone:1;/* True if mergecycle_all already done */
-  flagT    tested:1;    /* True if facet convexity has been tested (false after merge */
-  flagT    keepcentrum:1; /* True if keep old centrum after a merge, or marks owner for ->tricoplanar */
-  flagT	   newmerge:1;  /* True if facet is newly merged for reducevertices */
-  flagT	   degenerate:1; /* True if facet is degenerate (degen_mergeset or ->tricoplanar) */
-  flagT	   redundant:1;  /* True if facet is redundant (degen_mergeset) */
-};
-
-
-/*----------------------------------
-
-  ridgeT
-    defines a ridge
-
-  notes:
-  a ridge is DIM3-1 simplex between two neighboring facets.  If the
-  facets are non-simplicial, there may be more than one ridge between
-  two facets.  E.G. a 4-d hypercube has two triangles between each pair
-  of neighboring facets.
-
-  topological information:
-    vertices            a set of vertices
-    top,bottom          neighboring facets with orientation
-
-  geometric information:
-    tested              True if ridge is clearly convex
-    nonconvex           True if ridge is non-convex
-*/
-struct ridgeT {
-  setT    *vertices;    /* vertices belonging to this ridge, inverse sorted by ID
-                           NULL if a degen ridge (matchsame) */
-  facetT  *top;         /* top facet this ridge is part of */
-  facetT  *bottom;      /* bottom facet this ridge is part of */
-  unsigned id:24;       /* unique identifier, =>room for 8 flags */
-  flagT    seen:1;      /* used to perform operations only once */
-  flagT    tested:1;    /* True when ridge is tested for convexity */
-  flagT    nonconvex:1; /* True if getmergeset detected a non-convex neighbor
-			   only one ridge between neighbors may have nonconvex */
-};
-
-/*----------------------------------
-
-  vertexT
-     defines a vertex
-
-  topological information:
-    next,previous       doubly-linked list of all vertices
-    neighbors           set of adjacent facets (only if qh.VERTEXneighbors)
-
-  geometric information:
-    point               array of DIM3 coordinates
-*/
-struct vertexT {
-  vertexT *next;        /* next vertex in vertex_list */
-  vertexT *previous;    /* previous vertex in vertex_list */
-  pointT  *point;       /* hull_dim coordinates (coordT) */
-  setT    *neighbors;   /* neighboring facets of vertex, qh_vertexneighbors()
-			   inits in io.c or after first merge */
-  unsigned visitid; /* for use with qh vertex_visit */
-  unsigned id:24;   /* unique identifier, =>room for 8 flags */
-  flagT    seen:1;      /* used to perform operations only once */
-  flagT    seen2:1;     /* another seen flag */
-  flagT    delridge:1;  /* vertex was part of a deleted ridge */
-  flagT	   deleted:1;   /* true if vertex on qh del_vertices */
-  flagT    newlist:1;   /* true if vertex on qh newvertex_list */
-};
-
-/*======= -global variables -qh ============================*/
-
-/*----------------------------------
-
-  qh
-   all global variables for qhull are in qh, qhmem, and qhstat
-
-  notes:
-   qhmem is defined in mem.h and qhstat is defined in stat.h
-   access to qh_qh is via the "qh" macro.  See qh_QHpointer in user.h
-*/
-typedef struct qhT qhT;
-#if qh_QHpointer
-#define qh qh_qh->
-extern qhT *qh_qh;     /* allocated in global.c */
-#else
-#define qh qh_qh.
-extern qhT qh_qh;
-#endif
-
-struct qhT {
-
-/*----------------------------------
-
-  qh constants
-    configuration flags and constants for Qhull
-
-  notes:
-    The user configures Qhull by defining flags.  They are
-    copied into qh by qh_setflags().  qh-quick.htm#options defines the flags.
-*/
-  boolT ALLpoints;        /* true 'Qs' if search all points for initial simplex */
-  boolT ANGLEmerge;	  /* true 'Qa' if sort potential merges by angle */
-  boolT APPROXhull;       /* true 'Wn' if MINoutside set */
-  realT MINoutside;       /*   'Wn' min. distance for an outside point */
-  boolT ATinfinity;       /* true 'Qz' if point num_points-1 is "at-infinity"
-                             for improving precision in Delaunay triangulations */
-  boolT AVOIDold;         /* true 'Q4' if avoid old->new merges */
-  boolT BESToutside;      /* true 'Qf' if partition points into best outsideset */
-  boolT CDDinput;         /* true 'Pc' if input uses CDD format (1.0/offset first) */
-  boolT CDDoutput;        /* true 'PC' if print normals in CDD format (offset first) */
-  boolT CHECKfrequently;  /* true 'Tc' if checking frequently */
-  realT premerge_cos;     /*   'A-n'   cos_max when pre merging */
-  realT postmerge_cos;    /*   'An'    cos_max when post merging */
-  boolT DELAUNAY;         /* true 'd' if computing DELAUNAY triangulation */
-  boolT DOintersections;  /* true 'Gh' if print hyperplane intersections */
-  int   DROPdim;          /* drops dim 'GDn' for 4-d -> 3-d output */
-  boolT FORCEoutput;      /* true 'Po' if forcing output despite degeneracies */
-  int   GOODpoint;        /* 1+n for 'QGn', good facet if visible/not(-) from point n*/
-  pointT *GOODpointp;     /*   the actual point */
-  boolT GOODthreshold;    /* true if qh lower_threshold/upper_threshold defined
-  			     false if qh SPLITthreshold */
-  int   GOODvertex;       /* 1+n, good facet if vertex for point n */
-  pointT *GOODvertexp;     /*   the actual point */
-  boolT HALFspace;        /* true 'Hn,n,n' if halfspace intersection */
-  int   IStracing;        /* trace execution, 0=none, 1=least, 4=most, -1=events */
-  int   KEEParea;         /* 'PAn' number of largest facets to keep */
-  boolT KEEPcoplanar;     /* true 'Qc' if keeping nearest facet for coplanar points */
-  boolT KEEPinside;       /* true 'Qi' if keeping nearest facet for inside points
-			      set automatically if 'd Qc' */
-  int   KEEPmerge;        /* 'PMn' number of facets to keep with most merges */
-  realT KEEPminArea;      /* 'PFn' minimum facet area to keep */
-  realT MAXcoplanar;      /* 'Un' max distance below a facet to be coplanar*/
-  boolT MERGEexact;	  /* true 'Qx' if exact merges (coplanar, degen, dupridge, flipped) */
-  boolT MERGEindependent; /* true 'Q2' if merging independent sets */
-  boolT MERGING;          /* true if exact-, pre- or post-merging, with angle and centrum tests */
-  realT   premerge_centrum;  /*   'C-n' centrum_radius when pre merging.  Default is round-off */
-  realT   postmerge_centrum; /*   'Cn' centrum_radius when post merging.  Default is round-off */
-  boolT MERGEvertices;	  /* true 'Q3' if merging redundant vertices */
-  realT MINvisible;       /* 'Vn' min. distance for a facet to be visible */
-  boolT NOnarrow;         /* true 'Q10' if no special processing for narrow distributions */
-  boolT NOnearinside;     /* true 'Q8' if ignore near-inside points when partitioning */
-  boolT NOpremerge;       /* true 'Q0' if no defaults for C-0 or Qx */
-  boolT ONLYgood; 	  /* true 'Qg' if process points with good visible or horizon facets */
-  boolT ONLYmax; 	  /* true 'Qm' if only process points that increase max_outside */
-  boolT PICKfurthest;     /* true 'Q9' if process furthest of furthest points*/
-  boolT POSTmerge;        /* true if merging after buildhull (Cn or An) */
-  boolT PREmerge;         /* true if merging during buildhull (C-n or A-n) */
-  			/* NOTE: some of these names are similar to qh_PRINT names */
-  boolT PRINTcentrums;	  /* true 'Gc' if printing centrums */
-  boolT PRINTcoplanar;    /* true 'Gp' if printing coplanar points */
-  int	PRINTdim;      	  /* print dimension for Geomview output */
-  boolT PRINTdots;        /```