source/blender/blenkernel/intern/curve.c

   1 /*
   2  * ***** BEGIN GPL LICENSE BLOCK *****
   3  *
   4  * This program is free software; you can redistribute it and/or
   5  * modify it under the terms of the GNU General Public License
   6  * as published by the Free Software Foundation; either version 2
   7  * of the License, or (at your option) any later version.
   8  *
   9  * This program is distributed in the hope that it will be useful,
  10  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  11  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  12  * GNU General Public License for more details.
  13  *
  14  * You should have received a copy of the GNU General Public License
  15  * along with this program; if not, write to the Free Software Foundation,
  16  * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
  17  *
  18  * The Original Code is Copyright (C) 2001-2002 by NaN Holding BV.
  19  * All rights reserved.
  20  *
  21  * The Original Code is: all of this file.
  22  *
  23  * Contributor(s): none yet.
  24  *
  25  * ***** END GPL LICENSE BLOCK *****
  26  */
  27
  28 /** \file blender/blenkernel/intern/curve.c
  29  *  \ingroup bke
  30  */
  31
  32
  33 #include <math.h>  // floor
  34 #include <string.h>
  35 #include <stdlib.h>
  36
  37 #include "MEM_guardedalloc.h"
  38
  39 #include "BLI_blenlib.h"
  40 #include "BLI_math.h"
  41 #include "BLI_utildefines.h"
  42 #include "BLI_ghash.h"
  43
  44 #include "DNA_curve_types.h"
  45 #include "DNA_material_types.h"
  46
  47 /* for dereferencing pointers */
  48 #include "DNA_key_types.h"
  49 #include "DNA_scene_types.h"
  50 #include "DNA_vfont_types.h"
  51 #include "DNA_object_types.h"
  52
  53 #include "BKE_animsys.h"
  54 #include "BKE_anim.h"
  55 #include "BKE_curve.h"
  56 #include "BKE_displist.h"
  57 #include "BKE_font.h"
  58 #include "BKE_global.h"
  59 #include "BKE_key.h"
  60 #include "BKE_library.h"
  61 #include "BKE_main.h"
  62 #include "BKE_object.h"
  63 #include "BKE_material.h"
  64
  65 /* globals */
  66
  67 /* local */
  68 static int cu_isectLL(const float v1[3], const float v2[3], const float v3[3], const float v4[3],
  69                       short cox, short coy,
  70                       float *lambda, float *mu, float vec[3]);
  71
  72 void BKE_curve_unlink(Curve *cu)
  73 {
  74         int a;
  75
  76         for (a = 0; a < cu->totcol; a++) {
  77                 if (cu->mat[a]) cu->mat[a]->id.us--;
  78                 cu->mat[a] = NULL;
  79         }
  80         if (cu->vfont)
  81                 cu->vfont->id.us--;
  82         cu->vfont = NULL;
  83
  84         if (cu->vfontb)
  85                 cu->vfontb->id.us--;
  86         cu->vfontb = NULL;
  87
  88         if (cu->vfonti)
  89                 cu->vfonti->id.us--;
  90         cu->vfonti = NULL;
  91
  92         if (cu->vfontbi)
  93                 cu->vfontbi->id.us--;
  94         cu->vfontbi = NULL;
  95
  96         if (cu->key)
  97                 cu->key->id.us--;
  98         cu->key = NULL;
  99 }
 100
 101 /* frees editcurve entirely */
 102 void BKE_curve_editfont_free(Curve *cu)
 103 {
 104         if (cu->editfont) {
 105                 EditFont *ef = cu->editfont;
 106
 107                 if (ef->textbuf)
 108                         MEM_freeN(ef->textbuf);
 109                 if (ef->textbufinfo)
 110                         MEM_freeN(ef->textbufinfo);
 111                 if (ef->copybuf)
 112                         MEM_freeN(ef->copybuf);
 113                 if (ef->copybufinfo)
 114                         MEM_freeN(ef->copybufinfo);
 115                 if (ef->selboxes)
 116                         MEM_freeN(ef->selboxes);
 117
 118                 MEM_freeN(ef);
 119                 cu->editfont = NULL;
 120         }
 121 }
 122
 123 void BKE_curve_editNurb_keyIndex_free(EditNurb *editnurb)
 124 {
 125         if (!editnurb->keyindex) {
 126                 return;
 127         }
 128         BLI_ghash_free(editnurb->keyindex, NULL, MEM_freeN);
 129         editnurb->keyindex = NULL;
 130 }
 131
 132 void BKE_curve_editNurb_free(Curve *cu)
 133 {
 134         if (cu->editnurb) {
 135                 BKE_nurbList_free(&cu->editnurb->nurbs);
 136                 BKE_curve_editNurb_keyIndex_free(cu->editnurb);
 137                 MEM_freeN(cu->editnurb);
 138                 cu->editnurb = NULL;
 139         }
 140 }
 141
 142 /* don't free curve itself */
 143 void BKE_curve_free(Curve *cu)
 144 {
 145         BKE_nurbList_free(&cu->nurb);
 146         BKE_curve_editfont_free(cu);
 147
 148         BKE_curve_editNurb_free(cu);
 149         BKE_curve_unlink(cu);
 150         BKE_free_animdata((ID *)cu);
 151
 152         if (cu->mat)
 153                 MEM_freeN(cu->mat);
 154         if (cu->str)
 155                 MEM_freeN(cu->str);
 156         if (cu->strinfo)
 157                 MEM_freeN(cu->strinfo);
 158         if (cu->bb)
 159                 MEM_freeN(cu->bb);
 160         if (cu->tb)
 161                 MEM_freeN(cu->tb);
 162 }
 163
 164 Curve *BKE_curve_add(Main *bmain, const char *name, int type)
 165 {
 166         Curve *cu;
 167
 168         cu = BKE_libblock_alloc(bmain, ID_CU, name);
 169         copy_v3_fl(cu->size, 1.0f);
 170         cu->flag = CU_FRONT | CU_BACK | CU_DEFORM_BOUNDS_OFF | CU_PATH_RADIUS;
 171         cu->pathlen = 100;
 172         cu->resolu = cu->resolv = (type == OB_SURF) ? 4 : 12;
 173         cu->width = 1.0;
 174         cu->wordspace = 1.0;
 175         cu->spacing = cu->linedist = 1.0;
 176         cu->fsize = 1.0;
 177         cu->ulheight = 0.05;
 178         cu->texflag = CU_AUTOSPACE;
 179         cu->smallcaps_scale = 0.75f;
 180         /* XXX: this one seems to be the best one in most cases, at least for curve deform... */
 181         cu->twist_mode = CU_TWIST_MINIMUM;
 182         cu->type = type;
 183         cu->bevfac1 = 0.0f;
 184         cu->bevfac2 = 1.0f;
 185         cu->bevfac1_mapping = CU_BEVFAC_MAP_RESOLU;
 186         cu->bevfac2_mapping = CU_BEVFAC_MAP_RESOLU;
 187
 188         cu->bb = BKE_boundbox_alloc_unit();
 189
 190         if (type == OB_FONT) {
 191                 cu->vfont = cu->vfontb = cu->vfonti = cu->vfontbi = BKE_vfont_builtin_get();
 192                 cu->vfont->id.us += 4;
 193                 cu->str = MEM_mallocN(12, "str");
 194                 BLI_strncpy(cu->str, "Text", 12);
 195                 cu->len = cu->len_wchar = cu->pos = 4;
 196                 cu->strinfo = MEM_callocN(12 * sizeof(CharInfo), "strinfo new");
 197                 cu->totbox = cu->actbox = 1;
 198                 cu->tb = MEM_callocN(MAXTEXTBOX * sizeof(TextBox), "textbox");
 199                 cu->tb[0].w = cu->tb[0].h = 0.0;
 200         }
 201
 202         return cu;
 203 }
 204
 205 Curve *BKE_curve_copy(Curve *cu)
 206 {
 207         Curve *cun;
 208         int a;
 209
 210         cun = BKE_libblock_copy(&cu->id);
 211         BLI_listbase_clear(&cun->nurb);
 212         BKE_nurbList_duplicate(&(cun->nurb), &(cu->nurb));
 213
 214         cun->mat = MEM_dupallocN(cu->mat);
 215         for (a = 0; a < cun->totcol; a++) {
 216                 id_us_plus((ID *)cun->mat[a]);
 217         }
 218
 219         cun->str = MEM_dupallocN(cu->str);
 220         cun->strinfo = MEM_dupallocN(cu->strinfo);
 221         cun->tb = MEM_dupallocN(cu->tb);
 222         cun->bb = MEM_dupallocN(cu->bb);
 223
 224         cun->key = BKE_key_copy(cu->key);
 225         if (cun->key) cun->key->from = (ID *)cun;
 226
 227         cun->editnurb = NULL;
 228         cun->editfont = NULL;
 229
 230 #if 0   // XXX old animation system
 231         /* single user ipo too */
 232         if (cun->ipo) cun->ipo = copy_ipo(cun->ipo);
 233 #endif // XXX old animation system
 234
 235         id_us_plus((ID *)cun->vfont);
 236         id_us_plus((ID *)cun->vfontb);
 237         id_us_plus((ID *)cun->vfonti);
 238         id_us_plus((ID *)cun->vfontbi);
 239
 240         return cun;
 241 }
 242
 243 static void extern_local_curve(Curve *cu)
 244 {
 245         id_lib_extern((ID *)cu->vfont);
 246         id_lib_extern((ID *)cu->vfontb);
 247         id_lib_extern((ID *)cu->vfonti);
 248         id_lib_extern((ID *)cu->vfontbi);
 249
 250         if (cu->mat) {
 251                 extern_local_matarar(cu->mat, cu->totcol);
 252         }
 253 }
 254
 255 void BKE_curve_make_local(Curve *cu)
 256 {
 257         Main *bmain = G.main;
 258         Object *ob;
 259         int is_local = FALSE, is_lib = FALSE;
 260
 261         /* - when there are only lib users: don't do
 262          * - when there are only local users: set flag
 263          * - mixed: do a copy
 264          */
 265
 266         if (cu->id.lib == NULL)
 267                 return;
 268
 269         if (cu->id.us == 1) {
 270                 id_clear_lib_data(bmain, &cu->id);
 271                 extern_local_curve(cu);
 272                 return;
 273         }
 274
 275         for (ob = bmain->object.first; ob && ELEM(0, is_lib, is_local); ob = ob->id.next) {
 276                 if (ob->data == cu) {
 277                         if (ob->id.lib) is_lib = TRUE;
 278                         else is_local = TRUE;
 279                 }
 280         }
 281
 282         if (is_local && is_lib == FALSE) {
 283                 id_clear_lib_data(bmain, &cu->id);
 284                 extern_local_curve(cu);
 285         }
 286         else if (is_local && is_lib) {
 287                 Curve *cu_new = BKE_curve_copy(cu);
 288                 cu_new->id.us = 0;
 289
 290                 BKE_id_lib_local_paths(bmain, cu->id.lib, &cu_new->id);
 291
 292                 for (ob = bmain->object.first; ob; ob = ob->id.next) {
 293                         if (ob->data == cu) {
 294                                 if (ob->id.lib == NULL) {
 295                                         ob->data = cu_new;
 296                                         cu_new->id.us++;
 297                                         cu->id.us--;
 298                                 }
 299                         }
 300                 }
 301         }
 302 }
 303
 304 /* Get list of nurbs from editnurbs structure */
 305 ListBase *BKE_curve_editNurbs_get(Curve *cu)
 306 {
 307         if (cu->editnurb) {
 308                 return &cu->editnurb->nurbs;
 309         }
 310
 311         return NULL;
 312 }
 313
 314 short BKE_curve_type_get(Curve *cu)
 315 {
 316         Nurb *nu;
 317         int type = cu->type;
 318
 319         if (cu->vfont) {
 320                 return OB_FONT;
 321         }
 322
 323         if (!cu->type) {
 324                 type = OB_CURVE;
 325
 326                 for (nu = cu->nurb.first; nu; nu = nu->next) {
 327                         if (nu->pntsv > 1) {
 328                                 type = OB_SURF;
 329                         }
 330                 }
 331         }
 332
 333         return type;
 334 }
 335
 336 void BKE_curve_curve_dimension_update(Curve *cu)
 337 {
 338         ListBase *nurbs = BKE_curve_nurbs_get(cu);
 339         Nurb *nu = nurbs->first;
 340
 341         if (cu->flag & CU_3D) {
 342                 for (; nu; nu = nu->next) {
 343                         nu->flag &= ~CU_2D;
 344                 }
 345         }
 346         else {
 347                 for (; nu; nu = nu->next) {
 348                         nu->flag |= CU_2D;
 349                         BKE_nurb_test2D(nu);
 350
 351                         /* since the handles are moved they need to be auto-located again */
 352                         if (nu->type == CU_BEZIER)
 353                                 BKE_nurb_handles_calc(nu);
 354                 }
 355         }
 356 }
 357
 358 void BKE_curve_type_test(Object *ob)
 359 {
 360         ob->type = BKE_curve_type_get(ob->data);
 361
 362         if (ob->type == OB_CURVE)
 363                 BKE_curve_curve_dimension_update((Curve *)ob->data);
 364 }
 365
 366 void BKE_curve_boundbox_calc(Curve *cu, float r_loc[3], float r_size[3])
 367 {
 368         BoundBox *bb;
 369         float min[3], max[3];
 370         float mloc[3], msize[3];
 371
 372         if (cu->bb == NULL) cu->bb = MEM_callocN(sizeof(BoundBox), "boundbox");
 373         bb = cu->bb;
 374
 375         if (!r_loc) r_loc = mloc;
 376         if (!r_size) r_size = msize;
 377
 378         INIT_MINMAX(min, max);
 379         if (!BKE_curve_minmax(cu, true, min, max)) {
 380                 min[0] = min[1] = min[2] = -1.0f;
 381                 max[0] = max[1] = max[2] = 1.0f;
 382         }
 383
 384         mid_v3_v3v3(r_loc, min, max);
 385
 386         r_size[0] = (max[0] - min[0]) / 2.0f;
 387         r_size[1] = (max[1] - min[1]) / 2.0f;
 388         r_size[2] = (max[2] - min[2]) / 2.0f;
 389
 390         BKE_boundbox_init_from_minmax(bb, min, max);
 391
 392         bb->flag &= ~BOUNDBOX_DIRTY;
 393 }
 394
 395 BoundBox *BKE_curve_boundbox_get(Object *ob)
 396 {
 397         Curve *cu = ob->data;
 398
 399         if (ob->bb)
 400                 return ob->bb;
 401
 402         if (cu->bb == NULL || (cu->bb->flag & BOUNDBOX_DIRTY)) {
 403                 BKE_curve_texspace_calc(cu);
 404         }
 405
 406         return cu->bb;
 407 }
 408
 409 void BKE_curve_texspace_calc(Curve *cu)
 410 {
 411         float loc[3], size[3];
 412         int a;
 413
 414         BKE_curve_boundbox_calc(cu, loc, size);
 415
 416         if (cu->texflag & CU_AUTOSPACE) {
 417                 for (a = 0; a < 3; a++) {
 418                         if (size[a] == 0.0f) size[a] = 1.0f;
 419                         else if (size[a] > 0.0f && size[a] < 0.00001f) size[a] = 0.00001f;
 420                         else if (size[a] < 0.0f && size[a] > -0.00001f) size[a] = -0.00001f;
 421                 }
 422
 423                 copy_v3_v3(cu->loc, loc);
 424                 copy_v3_v3(cu->size, size);
 425                 zero_v3(cu->rot);
 426         }
 427 }
 428
 429 void BKE_curve_texspace_get(Curve *cu, float r_loc[3], float r_rot[3], float r_size[3])
 430 {
 431         if (cu->bb == NULL || (cu->bb->flag & BOUNDBOX_DIRTY)) {
 432                 BKE_curve_texspace_calc(cu);
 433         }
 434
 435         if (r_loc) copy_v3_v3(r_loc,  cu->loc);
 436         if (r_rot) copy_v3_v3(r_rot,  cu->rot);
 437         if (r_size) copy_v3_v3(r_size, cu->size);
 438 }
 439
 440 int BKE_nurbList_index_get_co(ListBase *nurb, const int index, float r_co[3])
 441 {
 442         Nurb *nu;
 443         int tot = 0;
 444
 445         for (nu = nurb->first; nu; nu = nu->next) {
 446                 int tot_nu;
 447                 if (nu->type == CU_BEZIER) {
 448                         tot_nu = nu->pntsu;
 449                         if (index - tot < tot_nu) {
 450                                 copy_v3_v3(r_co, nu->bezt[index - tot].vec[1]);
 451                                 return TRUE;
 452                         }
 453                 }
 454                 else {
 455                         tot_nu = nu->pntsu * nu->pntsv;
 456                         if (index - tot < tot_nu) {
 457                                 copy_v3_v3(r_co, nu->bp[index - tot].vec);
 458                                 return TRUE;
 459                         }
 460                 }
 461                 tot += tot_nu;
 462         }
 463
 464         return FALSE;
 465 }
 466
 467 int BKE_nurbList_verts_count(ListBase *nurb)
 468 {
 469         Nurb *nu;
 470         int tot = 0;
 471
 472         nu = nurb->first;
 473         while (nu) {
 474                 if (nu->bezt)
 475                         tot += 3 * nu->pntsu;
 476                 else if (nu->bp)
 477                         tot += nu->pntsu * nu->pntsv;
 478
 479                 nu = nu->next;
 480         }
 481         return tot;
 482 }
 483
 484 int BKE_nurbList_verts_count_without_handles(ListBase *nurb)
 485 {
 486         Nurb *nu;
 487         int tot = 0;
 488
 489         nu = nurb->first;
 490         while (nu) {
 491                 if (nu->bezt)
 492                         tot += nu->pntsu;
 493                 else if (nu->bp)
 494                         tot += nu->pntsu * nu->pntsv;
 495
 496                 nu = nu->next;
 497         }
 498         return tot;
 499 }
 500
 501 /* **************** NURBS ROUTINES ******************** */
 502
 503 void BKE_nurb_free(Nurb *nu)
 504 {
 505
 506         if (nu == NULL) return;
 507
 508         if (nu->bezt)
 509                 MEM_freeN(nu->bezt);
 510         nu->bezt = NULL;
 511         if (nu->bp)
 512                 MEM_freeN(nu->bp);
 513         nu->bp = NULL;
 514         if (nu->knotsu)
 515                 MEM_freeN(nu->knotsu);
 516         nu->knotsu = NULL;
 517         if (nu->knotsv)
 518                 MEM_freeN(nu->knotsv);
 519         nu->knotsv = NULL;
 520         /* if (nu->trim.first) freeNurblist(&(nu->trim)); */
 521
 522         MEM_freeN(nu);
 523
 524 }
 525
 526
 527 void BKE_nurbList_free(ListBase *lb)
 528 {
 529         Nurb *nu, *next;
 530
 531         if (lb == NULL) return;
 532
 533         nu = lb->first;
 534         while (nu) {
 535                 next = nu->next;
 536                 BKE_nurb_free(nu);
 537                 nu = next;
 538         }
 539         BLI_listbase_clear(lb);
 540 }
 541
 542 Nurb *BKE_nurb_duplicate(Nurb *nu)
 543 {
 544         Nurb *newnu;
 545         int len;
 546
 547         newnu = (Nurb *)MEM_mallocN(sizeof(Nurb), "duplicateNurb");
 548         if (newnu == NULL) return NULL;
 549         memcpy(newnu, nu, sizeof(Nurb));
 550
 551         if (nu->bezt) {
 552                 newnu->bezt =
 553                     (BezTriple *)MEM_mallocN((nu->pntsu) * sizeof(BezTriple), "duplicateNurb2");
 554                 memcpy(newnu->bezt, nu->bezt, nu->pntsu * sizeof(BezTriple));
 555         }
 556         else {
 557                 len = nu->pntsu * nu->pntsv;
 558                 newnu->bp =
 559                     (BPoint *)MEM_mallocN((len) * sizeof(BPoint), "duplicateNurb3");
 560                 memcpy(newnu->bp, nu->bp, len * sizeof(BPoint));
 561
 562                 newnu->knotsu = newnu->knotsv = NULL;
 563
 564                 if (nu->knotsu) {
 565                         len = KNOTSU(nu);
 566                         if (len) {
 567                                 newnu->knotsu = MEM_mallocN(len * sizeof(float), "duplicateNurb4");
 568                                 memcpy(newnu->knotsu, nu->knotsu, sizeof(float) * len);
 569                         }
 570                 }
 571                 if (nu->pntsv > 1 && nu->knotsv) {
 572                         len = KNOTSV(nu);
 573                         if (len) {
 574                                 newnu->knotsv = MEM_mallocN(len * sizeof(float), "duplicateNurb5");
 575                                 memcpy(newnu->knotsv, nu->knotsv, sizeof(float) * len);
 576                         }
 577                 }
 578         }
 579         return newnu;
 580 }
 581
 582 /* copy the nurb but allow for different number of points (to be copied after this) */
 583 Nurb *BKE_nurb_copy(Nurb *src, int pntsu, int pntsv)
 584 {
 585         Nurb *newnu = (Nurb *)MEM_mallocN(sizeof(Nurb), "copyNurb");
 586         memcpy(newnu, src, sizeof(Nurb));
 587
 588         if (pntsu == 1) SWAP(int, pntsu, pntsv);
 589         newnu->pntsu = pntsu;
 590         newnu->pntsv = pntsv;
 591
 592         if (src->bezt) {
 593                 newnu->bezt = (BezTriple *)MEM_mallocN(pntsu * pntsv * sizeof(BezTriple), "copyNurb2");
 594         }
 595         else {
 596                 newnu->bp = (BPoint *)MEM_mallocN(pntsu * pntsv * sizeof(BPoint), "copyNurb3");
 597         }
 598
 599         return newnu;
 600 }
 601
 602 void BKE_nurbList_duplicate(ListBase *lb1, ListBase *lb2)
 603 {
 604         Nurb *nu, *nun;
 605
 606         BKE_nurbList_free(lb1);
 607
 608         nu = lb2->first;
 609         while (nu) {
 610                 nun = BKE_nurb_duplicate(nu);
 611                 BLI_addtail(lb1, nun);
 612
 613                 nu = nu->next;
 614         }
 615 }
 616
 617 void BKE_nurb_test2D(Nurb *nu)
 618 {
 619         BezTriple *bezt;
 620         BPoint *bp;
 621         int a;
 622
 623         if ((nu->flag & CU_2D) == 0)
 624                 return;
 625
 626         if (nu->type == CU_BEZIER) {
 627                 a = nu->pntsu;
 628                 bezt = nu->bezt;
 629                 while (a--) {
 630                         bezt->vec[0][2] = 0.0;
 631                         bezt->vec[1][2] = 0.0;
 632                         bezt->vec[2][2] = 0.0;
 633                         bezt++;
 634                 }
 635         }
 636         else {
 637                 a = nu->pntsu * nu->pntsv;
 638                 bp = nu->bp;
 639                 while (a--) {
 640                         bp->vec[2] = 0.0;
 641                         bp++;
 642                 }
 643         }
 644 }
 645
 646 /* if use_radius is truth, minmax will take points' radius into account,
 647  * which will make boundbox closer to bevelled curve.
 648  */
 649 void BKE_nurb_minmax(Nurb *nu, bool use_radius, float min[3], float max[3])
 650 {
 651         BezTriple *bezt;
 652         BPoint *bp;
 653         int a;
 654         float point[3];
 655
 656         if (nu->type == CU_BEZIER) {
 657                 a = nu->pntsu;
 658                 bezt = nu->bezt;
 659                 while (a--) {
 660                         if (use_radius) {
 661                                 float radius_vector[3];
 662                                 radius_vector[0] = radius_vector[1] = radius_vector[2] = bezt->radius;
 663
 664                                 add_v3_v3v3(point, bezt->vec[1], radius_vector);
 665                                 minmax_v3v3_v3(min, max, point);
 666
 667                                 sub_v3_v3v3(point, bezt->vec[1], radius_vector);
 668                                 minmax_v3v3_v3(min, max, point);
 669                         }
 670                         else {
 671                                 minmax_v3v3_v3(min, max, bezt->vec[1]);
 672                         }
 673                         minmax_v3v3_v3(min, max, bezt->vec[0]);
 674                         minmax_v3v3_v3(min, max, bezt->vec[2]);
 675                         bezt++;
 676                 }
 677         }
 678         else {
 679                 a = nu->pntsu * nu->pntsv;
 680                 bp = nu->bp;
 681                 while (a--) {
 682                         if (nu->pntsv == 1 && use_radius) {
 683                                 float radius_vector[3];
 684                                 radius_vector[0] = radius_vector[1] = radius_vector[2] = bp->radius;
 685
 686                                 add_v3_v3v3(point, bp->vec, radius_vector);
 687                                 minmax_v3v3_v3(min, max, point);
 688
 689                                 sub_v3_v3v3(point, bp->vec, radius_vector);
 690                                 minmax_v3v3_v3(min, max, point);
 691                         }
 692                         else {
 693                                 /* Surfaces doesn't use bevel, so no need to take radius into account. */
 694                                 minmax_v3v3_v3(min, max, bp->vec);
 695                         }
 696                         bp++;
 697                 }
 698         }
 699 }
 700
 701 /* be sure to call makeknots after this */
 702 void BKE_nurb_points_add(Nurb *nu, int number)
 703 {
 704         BPoint *tmp = nu->bp;
 705         int i;
 706         nu->bp = (BPoint *)MEM_mallocN((nu->pntsu + number) * sizeof(BPoint), "rna_Curve_spline_points_add");
 707
 708         if (tmp) {
 709                 memmove(nu->bp, tmp, nu->pntsu * sizeof(BPoint));
 710                 MEM_freeN(tmp);
 711         }
 712
 713         memset(nu->bp + nu->pntsu, 0, number * sizeof(BPoint));
 714
 715         for (i = 0, tmp = nu->bp + nu->pntsu; i < number; i++, tmp++) {
 716                 tmp->radius = 1.0f;
 717         }
 718
 719         nu->pntsu += number;
 720 }
 721
 722 void BKE_nurb_bezierPoints_add(Nurb *nu, int number)
 723 {
 724         BezTriple *tmp = nu->bezt;
 725         int i;
 726         nu->bezt = (BezTriple *)MEM_mallocN((nu->pntsu + number) * sizeof(BezTriple), "rna_Curve_spline_points_add");
 727
 728         if (tmp) {
 729                 memmove(nu->bezt, tmp, nu->pntsu * sizeof(BezTriple));
 730                 MEM_freeN(tmp);
 731         }
 732
 733         memset(nu->bezt + nu->pntsu, 0, number * sizeof(BezTriple));
 734
 735         for (i = 0, tmp = nu->bezt + nu->pntsu; i < number; i++, tmp++) {
 736                 tmp->radius = 1.0f;
 737         }
 738
 739         nu->pntsu += number;
 740 }
 741
 742
 743 BezTriple *BKE_nurb_bezt_get_next(Nurb *nu, BezTriple *bezt)
 744 {
 745         BezTriple *bezt_next;
 746
 747         BLI_assert(ARRAY_HAS_ITEM(bezt, nu->bezt, nu->pntsu));
 748
 749         if (bezt == &nu->bezt[nu->pntsu - 1]) {
 750                 if (nu->flagu & CU_NURB_CYCLIC) {
 751                         bezt_next = nu->bezt;
 752                 }
 753                 else {
 754                         bezt_next = NULL;
 755                 }
 756         }
 757         else {
 758                 bezt_next = bezt + 1;
 759         }
 760
 761         return bezt_next;
 762 }
 763
 764 BPoint *BKE_nurb_bpoint_get_next(Nurb *nu, BPoint *bp)
 765 {
 766         BPoint *bp_next;
 767
 768         BLI_assert(ARRAY_HAS_ITEM(bp, nu->bp, nu->pntsu));
 769
 770         if (bp == &nu->bp[nu->pntsu - 1]) {
 771                 if (nu->flagu & CU_NURB_CYCLIC) {
 772                         bp_next = nu->bp;
 773                 }
 774                 else {
 775                         bp_next = NULL;
 776                 }
 777         }
 778         else {
 779                 bp_next = bp + 1;
 780         }
 781
 782         return bp_next;
 783 }
 784
 785 BezTriple *BKE_nurb_bezt_get_prev(Nurb *nu, BezTriple *bezt)
 786 {
 787         BezTriple *bezt_prev;
 788
 789         BLI_assert(ARRAY_HAS_ITEM(bezt, nu->bezt, nu->pntsu));
 790
 791         if (bezt == nu->bezt) {
 792                 if (nu->flagu & CU_NURB_CYCLIC) {
 793                         bezt_prev = &nu->bezt[nu->pntsu - 1];
 794                 }
 795                 else {
 796                         bezt_prev = NULL;
 797                 }
 798         }
 799         else {
 800                 bezt_prev = bezt - 1;
 801         }
 802
 803         return bezt_prev;
 804 }
 805
 806 BPoint *BKE_nurb_bpoint_get_prev(Nurb *nu, BPoint *bp)
 807 {
 808         BPoint *bp_prev;
 809
 810         BLI_assert(ARRAY_HAS_ITEM(bp, nu->bp, nu->pntsu));
 811
 812         if (bp == nu->bp) {
 813                 if (nu->flagu & CU_NURB_CYCLIC) {
 814                         bp_prev = &nu->bp[nu->pntsu - 1];
 815                 }
 816                 else {
 817                         bp_prev = NULL;
 818                 }
 819         }
 820         else {
 821                 bp_prev = bp - 1;
 822         }
 823
 824         return bp_prev;
 825 }
 826
 827 void BKE_nurb_bezt_calc_normal(struct Nurb *UNUSED(nu), struct BezTriple *bezt, float r_normal[3])
 828 {
 829         /* calculate the axis matrix from the spline */
 830         float dir_prev[3], dir_next[3];
 831
 832         sub_v3_v3v3(dir_prev, bezt->vec[0], bezt->vec[1]);
 833         sub_v3_v3v3(dir_next, bezt->vec[1], bezt->vec[2]);
 834
 835         normalize_v3(dir_prev);
 836         normalize_v3(dir_next);
 837
 838         add_v3_v3v3(r_normal, dir_prev, dir_next);
 839         normalize_v3(r_normal);
 840 }
 841
 842 void BKE_nurb_bezt_calc_plane(struct Nurb *nu, struct BezTriple *bezt, float r_plane[3])
 843 {
 844         float dir_prev[3], dir_next[3];
 845
 846         sub_v3_v3v3(dir_prev, bezt->vec[0], bezt->vec[1]);
 847         sub_v3_v3v3(dir_next, bezt->vec[1], bezt->vec[2]);
 848
 849         normalize_v3(dir_prev);
 850         normalize_v3(dir_next);
 851
 852         cross_v3_v3v3(r_plane, dir_prev, dir_next);
 853         if (normalize_v3(r_plane) < FLT_EPSILON) {
 854                 BezTriple *bezt_prev = BKE_nurb_bezt_get_prev(nu, bezt);
 855                 BezTriple *bezt_next = BKE_nurb_bezt_get_next(nu, bezt);
 856
 857                 if (bezt_prev) {
 858                         sub_v3_v3v3(dir_prev, bezt_prev->vec[1], bezt->vec[1]);
 859                         normalize_v3(dir_prev);
 860                 }
 861                 if (bezt_next) {
 862                         sub_v3_v3v3(dir_next, bezt->vec[1], bezt_next->vec[1]);
 863                         normalize_v3(dir_next);
 864                 }
 865                 cross_v3_v3v3(r_plane, dir_prev, dir_next);
 866         }
 867
 868         /* matches with bones more closely */
 869         {
 870                 float dir_mid[3], tvec[3];
 871                 add_v3_v3v3(dir_mid, dir_prev, dir_next);
 872                 cross_v3_v3v3(tvec, r_plane, dir_mid);
 873                 copy_v3_v3(r_plane, tvec);
 874         }
 875
 876         normalize_v3(r_plane);
 877 }
 878
 879 /* ~~~~~~~~~~~~~~~~~~~~Non Uniform Rational B Spline calculations ~~~~~~~~~~~ */
 880
 881
 882 static void calcknots(float *knots, const int pnts, const short order, const short flag)
 883 {
 884         /* knots: number of pnts NOT corrected for cyclic */
 885         const int pnts_order = pnts + order;
 886         float k;
 887         int a;
 888
 889         switch (flag & (CU_NURB_ENDPOINT | CU_NURB_BEZIER)) {
 890                 case CU_NURB_ENDPOINT:
 891                         k = 0.0;
 892                         for (a = 1; a <= pnts_order; a++) {
 893                                 knots[a - 1] = k;
 894                                 if (a >= order && a <= pnts)
 895                                         k += 1.0f;
 896                         }
 897                         break;
 898                 case CU_NURB_BEZIER:
 899                         /* Warning, the order MUST be 2 or 4,
 900                          * if this is not enforced, the displist will be corrupt */
 901                         if (order == 4) {
 902                                 k = 0.34;
 903                                 for (a = 0; a < pnts_order; a++) {
 904                                         knots[a] = floorf(k);
 905                                         k += (1.0f / 3.0f);
 906                                 }
 907                         }
 908                         else if (order == 3) {
 909                                 k = 0.6f;
 910                                 for (a = 0; a < pnts_order; a++) {
 911                                         if (a >= order && a <= pnts)
 912                                                 k += 0.5f;
 913                                         knots[a] = floorf(k);
 914                                 }
 915                         }
 916                         else {
 917                                 printf("bez nurb curve order is not 3 or 4, should never happen\n");
 918                         }
 919                         break;
 920                 default:
 921                         for (a = 0; a < pnts_order; a++) {
 922                                 knots[a] = (float)a;
 923                         }
 924                         break;
 925         }
 926 }
 927
 928 static void makecyclicknots(float *knots, int pnts, short order)
 929 /* pnts, order: number of pnts NOT corrected for cyclic */
 930 {
 931         int a, b, order2, c;
 932
 933         if (knots == NULL)
 934                 return;
 935
 936         order2 = order - 1;
 937
 938         /* do first long rows (order -1), remove identical knots at endpoints */
 939         if (order > 2) {
 940                 b = pnts + order2;
 941                 for (a = 1; a < order2; a++) {
 942                         if (knots[b] != knots[b - a])
 943                                 break;
 944                 }
 945                 if (a == order2)
 946                         knots[pnts + order - 2] += 1.0f;
 947         }
 948
 949         b = order;
 950         c = pnts + order + order2;
 951         for (a = pnts + order2; a < c; a++) {
 952                 knots[a] = knots[a - 1] + (knots[b] - knots[b - 1]);
 953                 b--;
 954         }
 955 }
 956
 957
 958
 959 static void makeknots(Nurb *nu, short uv)
 960 {
 961         if (nu->type == CU_NURBS) {
 962                 if (uv == 1) {
 963                         if (nu->knotsu)
 964                                 MEM_freeN(nu->knotsu);
 965                         if (BKE_nurb_check_valid_u(nu)) {
 966                                 nu->knotsu = MEM_callocN(4 + sizeof(float) * KNOTSU(nu), "makeknots");
 967                                 if (nu->flagu & CU_NURB_CYCLIC) {
 968                                         calcknots(nu->knotsu, nu->pntsu, nu->orderu, 0);  /* cyclic should be uniform */
 969                                         makecyclicknots(nu->knotsu, nu->pntsu, nu->orderu);
 970                                 }
 971                                 else {
 972                                         calcknots(nu->knotsu, nu->pntsu, nu->orderu, nu->flagu);
 973                                 }
 974                         }
 975                         else
 976                                 nu->knotsu = NULL;
 977                 }
 978                 else if (uv == 2) {
 979                         if (nu->knotsv)
 980                                 MEM_freeN(nu->knotsv);
 981                         if (BKE_nurb_check_valid_v(nu)) {
 982                                 nu->knotsv = MEM_callocN(4 + sizeof(float) * KNOTSV(nu), "makeknots");
 983                                 if (nu->flagv & CU_NURB_CYCLIC) {
 984                                         calcknots(nu->knotsv, nu->pntsv, nu->orderv, 0);  /* cyclic should be uniform */
 985                                         makecyclicknots(nu->knotsv, nu->pntsv, nu->orderv);
 986                                 }
 987                                 else {
 988                                         calcknots(nu->knotsv, nu->pntsv, nu->orderv, nu->flagv);
 989                                 }
 990                         }
 991                         else {
 992                                 nu->knotsv = NULL;
 993                         }
 994                 }
 995         }
 996 }
 997
 998 void BKE_nurb_knot_calc_u(Nurb *nu)
 999 {
1000         makeknots(nu, 1);
1001 }
1002
1003 void BKE_nurb_knot_calc_v(Nurb *nu)
1004 {
1005         makeknots(nu, 2);
1006 }
1007
1008 static void basisNurb(float t, short order, int pnts, float *knots, float *basis, int *start, int *end)
1009 {
1010         float d, e;
1011         int i, i1 = 0, i2 = 0, j, orderpluspnts, opp2, o2;
1012
1013         orderpluspnts = order + pnts;
1014         opp2 = orderpluspnts - 1;
1015
1016         /* this is for float inaccuracy */
1017         if (t < knots[0])
1018                 t = knots[0];
1019         else if (t > knots[opp2])
1020                 t = knots[opp2];
1021
1022         /* this part is order '1' */
1023         o2 = order + 1;
1024         for (i = 0; i < opp2; i++) {
1025                 if (knots[i] != knots[i + 1] && t >= knots[i] && t <= knots[i + 1]) {
1026                         basis[i] = 1.0;
1027                         i1 = i - o2;
1028                         if (i1 < 0) i1 = 0;
1029                         i2 = i;
1030                         i++;
1031                         while (i < opp2) {
1032                                 basis[i] = 0.0;
1033                                 i++;
1034                         }
1035                         break;
1036                 }
1037                 else
1038                         basis[i] = 0.0;
1039         }
1040         basis[i] = 0.0;
1041
1042         /* this is order 2, 3, ... */
1043         for (j = 2; j <= order; j++) {
1044
1045                 if (i2 + j >= orderpluspnts) i2 = opp2 - j;
1046
1047                 for (i = i1; i <= i2; i++) {
1048                         if (basis[i] != 0.0f)
1049                                 d = ((t - knots[i]) * basis[i]) / (knots[i + j - 1] - knots[i]);
1050                         else
1051                                 d = 0.0f;
1052
1053                         if (basis[i + 1] != 0.0f)
1054                                 e = ((knots[i + j] - t) * basis[i + 1]) / (knots[i + j] - knots[i + 1]);
1055                         else
1056                                 e = 0.0;
1057
1058                         basis[i] = d + e;
1059                 }
1060         }
1061
1062         *start = 1000;
1063         *end = 0;
1064
1065         for (i = i1; i <= i2; i++) {
1066                 if (basis[i] > 0.0f) {
1067                         *end = i;
1068                         if (*start == 1000) *start = i;
1069                 }
1070         }
1071 }
1072
1073
1074 void BKE_nurb_makeFaces(Nurb *nu, float *coord_array, int rowstride, int resolu, int resolv)
1075 /* coord_array  has to be (3 * 4 * resolu * resolv) in size, and zero-ed */
1076 {
1077         BPoint *bp;
1078         float *basisu, *basis, *basisv, *sum, *fp, *in;
1079         float u, v, ustart, uend, ustep, vstart, vend, vstep, sumdiv;
1080         int i, j, iofs, jofs, cycl, len, curu, curv;
1081         int istart, iend, jsta, jen, *jstart, *jend, ratcomp;
1082
1083         int totu = nu->pntsu * resolu, totv = nu->pntsv * resolv;
1084
1085         if (nu->knotsu == NULL || nu->knotsv == NULL)
1086                 return;
1087         if (nu->orderu > nu->pntsu)
1088                 return;
1089         if (nu->orderv > nu->pntsv)
1090                 return;
1091         if (coord_array == NULL)
1092                 return;
1093
1094         /* allocate and initialize */
1095         len = totu * totv;
1096         if (len == 0)
1097                 return;
1098
1099         sum = (float *)MEM_callocN(sizeof(float) * len, "makeNurbfaces1");
1100
1101         len = totu * totv;
1102         if (len == 0) {
1103                 MEM_freeN(sum);
1104                 return;
1105         }
1106
1107         bp = nu->bp;
1108         i = nu->pntsu * nu->pntsv;
1109         ratcomp = 0;
1110         while (i--) {
1111                 if (bp->vec[3] != 1.0f) {
1112                         ratcomp = 1;
1113                         break;
1114                 }
1115                 bp++;
1116         }
1117
1118         fp = nu->knotsu;
1119         ustart = fp[nu->orderu - 1];
1120         if (nu->flagu & CU_NURB_CYCLIC)
1121                 uend = fp[nu->pntsu + nu->orderu - 1];
1122         else
1123                 uend = fp[nu->pntsu];
1124         ustep = (uend - ustart) / ((nu->flagu & CU_NURB_CYCLIC) ? totu : totu - 1);
1125
1126         basisu = (float *)MEM_mallocN(sizeof(float) * KNOTSU(nu), "makeNurbfaces3");
1127
1128         fp = nu->knotsv;
1129         vstart = fp[nu->orderv - 1];
1130
1131         if (nu->flagv & CU_NURB_CYCLIC)
1132                 vend = fp[nu->pntsv + nu->orderv - 1];
1133         else
1134                 vend = fp[nu->pntsv];
1135         vstep = (vend - vstart) / ((nu->flagv & CU_NURB_CYCLIC) ? totv : totv - 1);
1136
1137         len = KNOTSV(nu);
1138         basisv = (float *)MEM_mallocN(sizeof(float) * len * totv, "makeNurbfaces3");
1139         jstart = (int *)MEM_mallocN(sizeof(float) * totv, "makeNurbfaces4");
1140         jend = (int *)MEM_mallocN(sizeof(float) * totv, "makeNurbfaces5");
1141
1142         /* precalculation of basisv and jstart, jend */
1143         if (nu->flagv & CU_NURB_CYCLIC)
1144                 cycl = nu->orderv - 1;
1145         else cycl = 0;
1146         v = vstart;
1147         basis = basisv;
1148         curv = totv;
1149         while (curv--) {
1150                 basisNurb(v, nu->orderv, nu->pntsv + cycl, nu->knotsv, basis, jstart + curv, jend + curv);
1151                 basis += KNOTSV(nu);
1152                 v += vstep;
1153         }
1154
1155         if (nu->flagu & CU_NURB_CYCLIC)
1156                 cycl = nu->orderu - 1;
1157         else
1158                 cycl = 0;
1159         in = coord_array;
1160         u = ustart;
1161         curu = totu;
1162         while (curu--) {
1163                 basisNurb(u, nu->orderu, nu->pntsu + cycl, nu->knotsu, basisu, &istart, &iend);
1164
1165                 basis = basisv;
1166                 curv = totv;
1167                 while (curv--) {
1168                         jsta = jstart[curv];
1169                         jen = jend[curv];
1170
1171                         /* calculate sum */
1172                         sumdiv = 0.0;
1173                         fp = sum;
1174
1175                         for (j = jsta; j <= jen; j++) {
1176
1177                                 if (j >= nu->pntsv)
1178                                         jofs = (j - nu->pntsv);
1179                                 else
1180                                         jofs = j;
1181                                 bp = nu->bp + nu->pntsu * jofs + istart - 1;
1182
1183                                 for (i = istart; i <= iend; i++, fp++) {
1184                                         if (i >= nu->pntsu) {
1185                                                 iofs = i - nu->pntsu;
1186                                                 bp = nu->bp + nu->pntsu * jofs + iofs;
1187                                         }
1188                                         else
1189                                                 bp++;
1190
1191                                         if (ratcomp) {
1192                                                 *fp = basisu[i] * basis[j] * bp->vec[3];
1193                                                 sumdiv += *fp;
1194                                         }
1195                                         else
1196                                                 *fp = basisu[i] * basis[j];
1197                                 }
1198                         }
1199
1200                         if (ratcomp) {
1201                                 fp = sum;
1202                                 for (j = jsta; j <= jen; j++) {
1203                                         for (i = istart; i <= iend; i++, fp++) {
1204                                                 *fp /= sumdiv;
1205                                         }
1206                                 }
1207                         }
1208
1209                         /* one! (1.0) real point now */
1210                         fp = sum;
1211                         for (j = jsta; j <= jen; j++) {
1212
1213                                 if (j >= nu->pntsv)
1214                                         jofs = (j - nu->pntsv);
1215                                 else
1216                                         jofs = j;
1217                                 bp = nu->bp + nu->pntsu * jofs + istart - 1;
1218
1219                                 for (i = istart; i <= iend; i++, fp++) {
1220                                         if (i >= nu->pntsu) {
1221                                                 iofs = i - nu->pntsu;
1222                                                 bp = nu->bp + nu->pntsu * jofs + iofs;
1223                                         }
1224                                         else
1225                                                 bp++;
1226
1227                                         if (*fp != 0.0f) {
1228                                                 madd_v3_v3fl(in, bp->vec, *fp);
1229                                         }
1230                                 }
1231                         }
1232
1233                         in += 3;
1234                         basis += KNOTSV(nu);
1235                 }
1236                 u += ustep;
1237                 if (rowstride != 0)
1238                         in = (float *) (((unsigned char *) in) + (rowstride - 3 * totv * sizeof(*in)));
1239         }
1240
1241         /* free */
1242         MEM_freeN(sum);
1243         MEM_freeN(basisu);
1244         MEM_freeN(basisv);
1245         MEM_freeN(jstart);
1246         MEM_freeN(jend);
1247 }
1248
1249 /**
1250  * \param coord_array Has to be 3 * 4 * pntsu * resolu in size and zero-ed
1251  * \param tilt_array   set when non-NULL
1252  * \param radius_array set when non-NULL
1253  */
1254 void BKE_nurb_makeCurve(Nurb *nu, float *coord_array, float *tilt_array, float *radius_array, float *weight_array,
1255                         int resolu, int stride)
1256 {
1257         BPoint *bp;
1258         float u, ustart, uend, ustep, sumdiv;
1259         float *basisu, *sum, *fp;
1260         float *coord_fp = coord_array, *tilt_fp = tilt_array, *radius_fp = radius_array, *weight_fp = weight_array;
1261         int i, len, istart, iend, cycl;
1262
1263         if (nu->knotsu == NULL)
1264                 return;
1265         if (nu->orderu > nu->pntsu)
1266                 return;
1267         if (coord_array == NULL)
1268                 return;
1269
1270         /* allocate and initialize */
1271         len = nu->pntsu;
1272         if (len == 0)
1273                 return;
1274         sum = (float *)MEM_callocN(sizeof(float) * len, "makeNurbcurve1");
1275
1276         resolu = (resolu * SEGMENTSU(nu));
1277
1278         if (resolu == 0) {
1279                 MEM_freeN(sum);
1280                 return;
1281         }
1282
1283         fp = nu->knotsu;
1284         ustart = fp[nu->orderu - 1];
1285         if (nu->flagu & CU_NURB_CYCLIC)
1286                 uend = fp[nu->pntsu + nu->orderu - 1];
1287         else
1288                 uend = fp[nu->pntsu];
1289         ustep = (uend - ustart) / (resolu - ((nu->flagu & CU_NURB_CYCLIC) ? 0 : 1));
1290
1291         basisu = (float *)MEM_mallocN(sizeof(float) * KNOTSU(nu), "makeNurbcurve3");
1292
1293         if (nu->flagu & CU_NURB_CYCLIC)
1294                 cycl = nu->orderu - 1;
1295         else
1296                 cycl = 0;
1297
1298         u = ustart;
1299         while (resolu--) {
1300                 basisNurb(u, nu->orderu, nu->pntsu + cycl, nu->knotsu, basisu, &istart, &iend);
1301
1302                 /* calc sum */
1303                 sumdiv = 0.0;
1304                 fp = sum;
1305                 bp = nu->bp + istart - 1;
1306                 for (i = istart; i <= iend; i++, fp++) {
1307                         if (i >= nu->pntsu)
1308                                 bp = nu->bp + (i - nu->pntsu);
1309                         else
1310                                 bp++;
1311
1312                         *fp = basisu[i] * bp->vec[3];
1313                         sumdiv += *fp;
1314                 }
1315                 if ((sumdiv != 0.0f) && (sumdiv < 0.999f || sumdiv > 1.001f)) {
1316                         /* is normalizing needed? */
1317                         fp = sum;
1318                         for (i = istart; i <= iend; i++, fp++) {
1319                                 *fp /= sumdiv;
1320                         }
1321                 }
1322
1323                 /* one! (1.0) real point */
1324                 fp = sum;
1325                 bp = nu->bp + istart - 1;
1326                 for (i = istart; i <= iend; i++, fp++) {
1327                         if (i >= nu->pntsu)
1328                                 bp = nu->bp + (i - nu->pntsu);
1329                         else
1330                                 bp++;
1331
1332                         if (*fp != 0.0f) {
1333                                 madd_v3_v3fl(coord_fp, bp->vec, *fp);
1334
1335                                 if (tilt_fp)
1336                                         (*tilt_fp) += (*fp) * bp->alfa;
1337
1338                                 if (radius_fp)
1339                                         (*radius_fp) += (*fp) * bp->radius;
1340
1341                                 if (weight_fp)
1342                                         (*weight_fp) += (*fp) * bp->weight;
1343                         }
1344                 }
1345
1346                 coord_fp = (float *)(((char *)coord_fp) + stride);
1347
1348                 if (tilt_fp)
1349                         tilt_fp = (float *)(((char *)tilt_fp) + stride);
1350                 if (radius_fp)
1351                         radius_fp = (float *)(((char *)radius_fp) + stride);
1352                 if (weight_fp)
1353                         weight_fp = (float *)(((char *)weight_fp) + stride);
1354
1355                 u += ustep;
1356         }
1357
1358         /* free */
1359         MEM_freeN(sum);
1360         MEM_freeN(basisu);
1361 }
1362
1363 /* forward differencing method for bezier curve */
1364 void BKE_curve_forward_diff_bezier(float q0, float q1, float q2, float q3, float *p, int it, int stride)
1365 {
1366         float rt0, rt1, rt2, rt3, f;
1367         int a;
1368
1369         f = (float)it;
1370         rt0 = q0;
1371         rt1 = 3.0f * (q1 - q0) / f;
1372         f *= f;
1373         rt2 = 3.0f * (q0 - 2.0f * q1 + q2) / f;
1374         f *= it;
1375         rt3 = (q3 - q0 + 3.0f * (q1 - q2)) / f;
1376
1377         q0 = rt0;
1378         q1 = rt1 + rt2 + rt3;
1379         q2 = 2 * rt2 + 6 * rt3;
1380         q3 = 6 * rt3;
1381
1382         for (a = 0; a <= it; a++) {
1383                 *p = q0;
1384                 p = (float *)(((char *)p) + stride);
1385                 q0 += q1;
1386                 q1 += q2;
1387                 q2 += q3;
1388         }
1389 }
1390
1391 static void forward_diff_bezier_cotangent(const float p0[3], const float p1[3], const float p2[3], const float p3[3],
1392                                           float p[3], int it, int stride)
1393 {
1394         /* note that these are not perpendicular to the curve
1395          * they need to be rotated for this,
1396          *
1397          * This could also be optimized like BKE_curve_forward_diff_bezier */
1398         int a;
1399         for (a = 0; a <= it; a++) {
1400                 float t = (float)a / (float)it;
1401
1402                 int i;
1403                 for (i = 0; i < 3; i++) {
1404                         p[i] = (-6.0f  * t +  6.0f) * p0[i] +
1405                                ( 18.0f * t - 12.0f) * p1[i] +
1406                                (-18.0f * t +  6.0f) * p2[i] +
1407                                ( 6.0f  * t)         * p3[i];
1408                 }
1409                 normalize_v3(p);
1410                 p = (float *)(((char *)p) + stride);
1411         }
1412 }
1413
1414 /* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ */
1415
1416 float *BKE_curve_surf_make_orco(Object *ob)
1417 {
1418         /* Note: this function is used in convertblender only atm, so
1419          * suppose nonzero curve's render resolution should always be used */
1420         Curve *cu = ob->data;
1421         Nurb *nu;
1422         int a, b, tot = 0;
1423         int sizeu, sizev;
1424         int resolu, resolv;
1425         float *fp, *coord_array;
1426
1427         /* first calculate the size of the datablock */
1428         nu = cu->nurb.first;
1429         while (nu) {
1430                 /* as we want to avoid the seam in a cyclic nurbs
1431                  * texture wrapping, reserve extra orco data space to save these extra needed
1432                  * vertex based UV coordinates for the meridian vertices.
1433                  * Vertices on the 0/2pi boundary are not duplicated inside the displist but later in
1434                  * the renderface/vert construction.
1435                  *
1436                  * See also convertblender.c: init_render_surf()
1437                  */
1438
1439                 resolu = cu->resolu_ren ? cu->resolu_ren : nu->resolu;
1440                 resolv = cu->resolv_ren ? cu->resolv_ren : nu->resolv;
1441
1442                 sizeu = nu->pntsu * resolu;
1443                 sizev = nu->pntsv * resolv;
1444                 if (nu->flagu & CU_NURB_CYCLIC) sizeu++;
1445                 if (nu->flagv & CU_NURB_CYCLIC) sizev++;
1446                 if (nu->pntsv > 1) tot += sizeu * sizev;
1447
1448                 nu = nu->next;
1449         }
1450         /* makeNurbfaces wants zeros */
1451         fp = coord_array = MEM_callocN(3 * sizeof(float) * tot, "make_orco");
1452
1453         nu = cu->nurb.first;
1454         while (nu) {
1455                 resolu = cu->resolu_ren ? cu->resolu_ren : nu->resolu;
1456                 resolv = cu->resolv_ren ? cu->resolv_ren : nu->resolv;
1457
1458                 if (nu->pntsv > 1) {
1459                         sizeu = nu->pntsu * resolu;
1460                         sizev = nu->pntsv * resolv;
1461
1462                         if (nu->flagu & CU_NURB_CYCLIC)
1463                                 sizeu++;
1464                         if (nu->flagv & CU_NURB_CYCLIC)
1465                                 sizev++;
1466
1467                         if (cu->flag & CU_UV_ORCO) {
1468                                 for (b = 0; b < sizeu; b++) {
1469                                         for (a = 0; a < sizev; a++) {
1470
1471                                                 if (sizev < 2)
1472                                                         fp[0] = 0.0f;
1473                                                 else
1474                                                         fp[0] = -1.0f + 2.0f * ((float)a) / (sizev - 1);
1475
1476                                                 if (sizeu < 2)
1477                                                         fp[1] = 0.0f;
1478                                                 else
1479                                                         fp[1] = -1.0f + 2.0f * ((float)b) / (sizeu - 1);
1480
1481                                                 fp[2] = 0.0;
1482
1483                                                 fp += 3;
1484                                         }
1485                                 }
1486                         }
1487                         else {
1488                                 int size = (nu->pntsu * resolu) * (nu->pntsv * resolv) * 3 * sizeof(float);
1489                                 float *_tdata = MEM_callocN(size, "temp data");
1490                                 float *tdata = _tdata;
1491
1492                                 BKE_nurb_makeFaces(nu, tdata, 0, resolu, resolv);
1493
1494                                 for (b = 0; b < sizeu; b++) {
1495                                         int use_b = b;
1496                                         if (b == sizeu - 1 && (nu->flagu & CU_NURB_CYCLIC))
1497                                                 use_b = FALSE;
1498
1499                                         for (a = 0; a < sizev; a++) {
1500                                                 int use_a = a;
1501                                                 if (a == sizev - 1 && (nu->flagv & CU_NURB_CYCLIC))
1502                                                         use_a = FALSE;
1503
1504                                                 tdata = _tdata + 3 * (use_b * (nu->pntsv * resolv) + use_a);
1505
1506                                                 fp[0] = (tdata[0] - cu->loc[0]) / cu->size[0];
1507                                                 fp[1] = (tdata[1] - cu->loc[1]) / cu->size[1];
1508                                                 fp[2] = (tdata[2] - cu->loc[2]) / cu->size[2];
1509                                                 fp += 3;
1510                                         }
1511                                 }
1512
1513                                 MEM_freeN(_tdata);
1514                         }
1515                 }
1516                 nu = nu->next;
1517         }
1518
1519         return coord_array;
1520 }
1521
1522
1523 /* NOTE: This routine is tied to the order of vertex
1524  * built by displist and as passed to the renderer.
1525  */
1526 float *BKE_curve_make_orco(Scene *scene, Object *ob, int *r_numVerts)
1527 {
1528         Curve *cu = ob->data;
1529         DispList *dl;
1530         int u, v, numVerts;
1531         float *fp, *coord_array;
1532         ListBase disp = {NULL, NULL};
1533
1534         BKE_displist_make_curveTypes_forOrco(scene, ob, &disp);
1535
1536         numVerts = 0;
1537         for (dl = disp.first; dl; dl = dl->next) {
1538                 if (dl->type == DL_INDEX3) {
1539                         numVerts += dl->nr;
1540                 }
1541                 else if (dl->type == DL_SURF) {
1542                         /* convertblender.c uses the Surface code for creating renderfaces when cyclic U only
1543                          * (closed circle beveling)
1544                          */
1545                         if (dl->flag & DL_CYCL_U) {
1546                                 if (dl->flag & DL_CYCL_V)
1547                                         numVerts += (dl->parts + 1) * (dl->nr + 1);
1548                                 else
1549                                         numVerts += dl->parts * (dl->nr + 1);
1550                         }
1551                         else if (dl->flag & DL_CYCL_V) {
1552                                 numVerts += (dl->parts + 1) * dl->nr;
1553                         }
1554                         else
1555                                 numVerts += dl->parts * dl->nr;
1556                 }
1557         }
1558
1559         if (r_numVerts)
1560                 *r_numVerts = numVerts;
1561
1562         fp = coord_array = MEM_mallocN(3 * sizeof(float) * numVerts, "cu_orco");
1563         for (dl = disp.first; dl; dl = dl->next) {
1564                 if (dl->type == DL_INDEX3) {
1565                         for (u = 0; u < dl->nr; u++, fp += 3) {
1566                                 if (cu->flag & CU_UV_ORCO) {
1567                                         fp[0] = 2.0f * u / (dl->nr - 1) - 1.0f;
1568                                         fp[1] = 0.0;
1569                                         fp[2] = 0.0;
1570                                 }
1571                                 else {
1572                                         copy_v3_v3(fp, &dl->verts[u * 3]);
1573
1574                                         fp[0] = (fp[0] - cu->loc[0]) / cu->size[0];
1575                                         fp[1] = (fp[1] - cu->loc[1]) / cu->size[1];
1576                                         fp[2] = (fp[2] - cu->loc[2]) / cu->size[2];
1577                                 }
1578                         }
1579                 }
1580                 else if (dl->type == DL_SURF) {
1581                         int sizeu = dl->nr, sizev = dl->parts;
1582
1583                         /* exception as handled in convertblender.c too */
1584                         if (dl->flag & DL_CYCL_U) {
1585                                 sizeu++;
1586                                 if (dl->flag & DL_CYCL_V)
1587                                         sizev++;
1588                         }
1589                         else  if (dl->flag & DL_CYCL_V) {
1590                                 sizev++;
1591                         }
1592
1593                         for (u = 0; u < sizev; u++) {
1594                                 for (v = 0; v < sizeu; v++, fp += 3) {
1595                                         if (cu->flag & CU_UV_ORCO) {
1596                                                 fp[0] = 2.0f * u / (sizev - 1) - 1.0f;
1597                                                 fp[1] = 2.0f * v / (sizeu - 1) - 1.0f;
1598                                                 fp[2] = 0.0;
1599                                         }
1600                                         else {
1601                                                 float *vert;
1602                                                 int realv = v % dl->nr;
1603                                                 int realu = u % dl->parts;
1604
1605                                                 vert = dl->verts + 3 * (dl->nr * realu + realv);
1606                                                 copy_v3_v3(fp, vert);
1607
1608                                                 fp[0] = (fp[0] - cu->loc[0]) / cu->size[0];
1609                                                 fp[1] = (fp[1] - cu->loc[1]) / cu->size[1];
1610                                                 fp[2] = (fp[2] - cu->loc[2]) / cu->size[2];
1611                                         }
1612                                 }
1613                         }
1614                 }
1615         }
1616
1617         BKE_displist_free(&disp);
1618
1619         return coord_array;
1620 }
1621
1622
1623 /* ***************** BEVEL ****************** */
1624
1625 void BKE_curve_bevel_make(Scene *scene, Object *ob, ListBase *disp,
1626                           const bool for_render, const bool use_render_resolution)
1627 {
1628         DispList *dl, *dlnew;
1629         Curve *bevcu, *cu;
1630         float *fp, facx, facy, angle, dangle;
1631         int nr, a;
1632
1633         cu = ob->data;
1634         BLI_listbase_clear(disp);
1635
1636         /* if a font object is being edited, then do nothing */
1637 // XXX  if ( ob == obedit && ob->type == OB_FONT ) return;
1638
1639         if (cu->bevobj) {
1640                 if (cu->bevobj->type != OB_CURVE)
1641                         return;
1642
1643                 bevcu = cu->bevobj->data;
1644                 if (bevcu->ext1 == 0.0f && bevcu->ext2 == 0.0f) {
1645                         ListBase bevdisp = {NULL, NULL};
1646                         facx = cu->bevobj->size[0];
1647                         facy = cu->bevobj->size[1];
1648
1649                         if (for_render) {
1650                                 BKE_displist_make_curveTypes_forRender(scene, cu->bevobj, &bevdisp, NULL, false, use_render_resolution);
1651                                 dl = bevdisp.first;
1652                         }
1653                         else if (cu->bevobj->curve_cache) {
1654                                 dl = cu->bevobj->curve_cache->disp.first;
1655                         }
1656                         else {
1657                                 BLI_assert(cu->bevobj->curve_cache != NULL);
1658                                 dl = NULL;
1659                         }
1660
1661                         while (dl) {
1662                                 if (ELEM(dl->type, DL_POLY, DL_SEGM)) {
1663                                         dlnew = MEM_mallocN(sizeof(DispList), "makebevelcurve1");
1664                                         *dlnew = *dl;
1665                                         dlnew->verts = MEM_mallocN(3 * sizeof(float) * dl->parts * dl->nr, "makebevelcurve1");
1666                                         memcpy(dlnew->verts, dl->verts, 3 * sizeof(float) * dl->parts * dl->nr);
1667
1668                                         if (dlnew->type == DL_SEGM)
1669                                                 dlnew->flag |= (DL_FRONT_CURVE | DL_BACK_CURVE);
1670
1671                                         BLI_addtail(disp, dlnew);
1672                                         fp = dlnew->verts;
1673                                         nr = dlnew->parts * dlnew->nr;
1674                                         while (nr--) {
1675                                                 fp[2] = fp[1] * facy;
1676                                                 fp[1] = -fp[0] * facx;
1677                                                 fp[0] = 0.0;
1678                                                 fp += 3;
1679                                         }
1680                                 }
1681                                 dl = dl->next;
1682                         }
1683
1684                         BKE_displist_free(&bevdisp);
1685                 }
1686         }
1687         else if (cu->ext1 == 0.0f && cu->ext2 == 0.0f) {
1688                 /* pass */
1689         }
1690         else if (cu->ext2 == 0.0f) {
1691                 dl = MEM_callocN(sizeof(DispList), "makebevelcurve2");
1692                 dl->verts = MEM_mallocN(2 * 3 * sizeof(float), "makebevelcurve2");
1693                 BLI_addtail(disp, dl);
1694                 dl->type = DL_SEGM;
1695                 dl->parts = 1;
1696                 dl->flag = DL_FRONT_CURVE | DL_BACK_CURVE;
1697                 dl->nr = 2;
1698
1699                 fp = dl->verts;
1700                 fp[0] = fp[1] = 0.0;
1701                 fp[2] = -cu->ext1;
1702                 fp[3] = fp[4] = 0.0;
1703                 fp[5] = cu->ext1;
1704         }
1705         else if ( (cu->flag & (CU_FRONT | CU_BACK)) == 0 && cu->ext1 == 0.0f) { // we make a full round bevel in that case
1706                 nr = 4 + 2 * cu->bevresol;
1707
1708                 dl = MEM_callocN(sizeof(DispList), "makebevelcurve p1");
1709                 dl->verts = MEM_mallocN(nr * 3 * sizeof(float), "makebevelcurve p1");
1710                 BLI_addtail(disp, dl);
1711                 dl->type = DL_POLY;
1712                 dl->parts = 1;
1713                 dl->flag = DL_BACK_CURVE;
1714                 dl->nr = nr;
1715
1716                 /* a circle */
1717                 fp = dl->verts;
1718                 dangle = (2.0f * (float)M_PI / (nr));
1719                 angle = -(nr - 1) * dangle;
1720
1721                 for (a = 0; a < nr; a++) {
1722                         fp[0] = 0.0;
1723                         fp[1] = (cosf(angle) * (cu->ext2));
1724                         fp[2] = (sinf(angle) * (cu->ext2)) - cu->ext1;
1725                         angle += dangle;
1726                         fp += 3;
1727                 }
1728         }
1729         else {
1730                 short dnr;
1731
1732                 /* bevel now in three parts, for proper vertex normals */
1733                 /* part 1, back */
1734
1735                 if ((cu->flag & CU_BACK) || !(cu->flag & CU_FRONT)) {
1736                         dnr = nr = 2 + cu->bevresol;
1737                         if ( (cu->flag & (CU_FRONT | CU_BACK)) == 0)
1738                                 nr = 3 + 2 * cu->bevresol;
1739
1740                         dl = MEM_callocN(sizeof(DispList), "makebevelcurve p1");
1741                         dl->verts = MEM_mallocN(nr * 3 * sizeof(float), "makebevelcurve p1");
1742                         BLI_addtail(disp, dl);
1743                         dl->type = DL_SEGM;
1744                         dl->parts = 1;
1745                         dl->flag = DL_BACK_CURVE;
1746                         dl->nr = nr;
1747
1748                         /* half a circle */
1749                         fp = dl->verts;
1750                         dangle = (0.5 * M_PI / (dnr - 1));
1751                         angle = -(nr - 1) * dangle;
1752
1753                         for (a = 0; a < nr; a++) {
1754                                 fp[0] = 0.0;
1755                                 fp[1] = (float)(cosf(angle) * (cu->ext2));
1756                                 fp[2] = (float)(sinf(angle) * (cu->ext2)) - cu->ext1;
1757                                 angle += dangle;
1758                                 fp += 3;
1759                         }
1760                 }
1761
1762                 /* part 2, sidefaces */
1763                 if (cu->ext1 != 0.0f) {
1764                         nr = 2;
1765
1766                         dl = MEM_callocN(sizeof(DispList), "makebevelcurve p2");
1767                         dl->verts = MEM_callocN(nr * 3 * sizeof(float), "makebevelcurve p2");
1768                         BLI_addtail(disp, dl);
1769                         dl->type = DL_SEGM;
1770                         dl->parts = 1;
1771                         dl->nr = nr;
1772
1773                         fp = dl->verts;
1774                         fp[1] = cu->ext2;
1775                         fp[2] = -cu->ext1;
1776                         fp[4] = cu->ext2;
1777                         fp[5] = cu->ext1;
1778
1779                         if ( (cu->flag & (CU_FRONT | CU_BACK)) == 0) {
1780                                 dl = MEM_dupallocN(dl);
1781                                 dl->verts = MEM_dupallocN(dl->verts);
1782                                 BLI_addtail(disp, dl);
1783
1784                                 fp = dl->verts;
1785                                 fp[1] = -fp[1];
1786                                 fp[2] = -fp[2];
1787                                 fp[4] = -fp[4];
1788                                 fp[5] = -fp[5];
1789                         }
1790                 }
1791
1792                 /* part 3, front */
1793                 if ((cu->flag & CU_FRONT) || !(cu->flag & CU_BACK)) {
1794                         dnr = nr = 2 + cu->bevresol;
1795                         if ( (cu->flag & (CU_FRONT | CU_BACK)) == 0)
1796                                 nr = 3 + 2 * cu->bevresol;
1797
1798                         dl = MEM_callocN(sizeof(DispList), "makebevelcurve p3");
1799                         dl->verts = MEM_mallocN(nr * 3 * sizeof(float), "makebevelcurve p3");
1800                         BLI_addtail(disp, dl);
1801                         dl->type = DL_SEGM;
1802                         dl->flag = DL_FRONT_CURVE;
1803                         dl->parts = 1;
1804                         dl->nr = nr;
1805
1806                         /* half a circle */
1807                         fp = dl->verts;
1808                         angle = 0.0;
1809                         dangle = (0.5 * M_PI / (dnr - 1));
1810
1811                         for (a = 0; a < nr; a++) {
1812                                 fp[0] = 0.0;
1813                                 fp[1] = (float)(cosf(angle) * (cu->ext2));
1814                                 fp[2] = (float)(sinf(angle) * (cu->ext2)) + cu->ext1;
1815                                 angle += dangle;
1816                                 fp += 3;
1817                         }
1818                 }
1819         }
1820 }
1821
1822 static int cu_isectLL(const float v1[3], const float v2[3], const float v3[3], const float v4[3],
1823                       short cox, short coy,
1824                       float *lambda, float *mu, float vec[3])
1825 {
1826         /* return:
1827          * -1: collinear
1828          *  0: no intersection of segments
1829          *  1: exact intersection of segments
1830          *  2: cross-intersection of segments
1831          */
1832         float deler;
1833
1834         deler = (v1[cox] - v2[cox]) * (v3[coy] - v4[coy]) - (v3[cox] - v4[cox]) * (v1[coy] - v2[coy]);
1835         if (deler == 0.0f)
1836                 return -1;
1837
1838         *lambda = (v1[coy] - v3[coy]) * (v3[cox] - v4[cox]) - (v1[cox] - v3[cox]) * (v3[coy] - v4[coy]);
1839         *lambda = -(*lambda / deler);
1840
1841         deler = v3[coy] - v4[coy];
1842         if (deler == 0) {
1843                 deler = v3[cox] - v4[cox];
1844                 *mu = -(*lambda * (v2[cox] - v1[cox]) + v1[cox] - v3[cox]) / deler;
1845         }
1846         else {
1847                 *mu = -(*lambda * (v2[coy] - v1[coy]) + v1[coy] - v3[coy]) / deler;
1848         }
1849         vec[cox] = *lambda * (v2[cox] - v1[cox]) + v1[cox];
1850         vec[coy] = *lambda * (v2[coy] - v1[coy]) + v1[coy];
1851
1852         if (*lambda >= 0.0f && *lambda <= 1.0f && *mu >= 0.0f && *mu <= 1.0f) {
1853                 if (*lambda == 0.0f || *lambda == 1.0f || *mu == 0.0f || *mu == 1.0f)
1854                         return 1;
1855                 return 2;
1856         }
1857         return 0;
1858 }
1859
1860
1861 static bool bevelinside(BevList *bl1, BevList *bl2)
1862 {
1863         /* is bl2 INSIDE bl1 ? with left-right method and "lambda's" */
1864         /* returns '1' if correct hole  */
1865         BevPoint *bevp, *prevbevp;
1866         float min, max, vec[3], hvec1[3], hvec2[3], lab, mu;
1867         int nr, links = 0, rechts = 0, mode;
1868
1869         /* take first vertex of possible hole */
1870
1871         bevp = (BevPoint *)(bl2 + 1);
1872         hvec1[0] = bevp->vec[0];
1873         hvec1[1] = bevp->vec[1];
1874         hvec1[2] = 0.0;
1875         copy_v3_v3(hvec2, hvec1);
1876         hvec2[0] += 1000;
1877
1878         /* test it with all edges of potential surounding poly */
1879         /* count number of transitions left-right  */
1880
1881         bevp = (BevPoint *)(bl1 + 1);
1882         nr = bl1->nr;
1883         prevbevp = bevp + (nr - 1);
1884
1885         while (nr--) {
1886                 min = prevbevp->vec[1];
1887                 max = bevp->vec[1];
1888                 if (max < min) {
1889                         min = max;
1890                         max = prevbevp->vec[1];
1891                 }
1892                 if (min != max) {
1893                         if (min <= hvec1[1] && max >= hvec1[1]) {
1894                                 /* there's a transition, calc intersection point */
1895                                 mode = cu_isectLL(prevbevp->vec, bevp->vec, hvec1, hvec2, 0, 1, &lab, &mu, vec);
1896                                 /* if lab==0.0 or lab==1.0 then the edge intersects exactly a transition
1897                                  * only allow for one situation: we choose lab= 1.0
1898                                  */
1899                                 if (mode >= 0 && lab != 0.0f) {
1900                                         if (vec[0] < hvec1[0]) links++;
1901                                         else rechts++;
1902                                 }
1903                         }
1904                 }
1905                 prevbevp = bevp;
1906                 bevp++;
1907         }
1908
1909         return (links & 1) && (rechts & 1);
1910 }
1911
1912
1913 struct BevelSort {
1914         BevList *bl;
1915         float left;
1916         int dir;
1917 };
1918
1919 static int vergxcobev(const void *a1, const void *a2)
1920 {
1921         const struct BevelSort *x1 = a1, *x2 = a2;
1922
1923         if (x1->left > x2->left)
1924                 return 1;
1925         else if (x1->left < x2->left)
1926                 return -1;
1927         return 0;
1928 }
1929
1930 /* this function cannot be replaced with atan2, but why? */
1931
1932 static void calc_bevel_sin_cos(float x1, float y1, float x2, float y2, float *sina, float *cosa)
1933 {
1934         float t01, t02, x3, y3;
1935
1936         t01 = sqrtf(x1 * x1 + y1 * y1);
1937         t02 = sqrtf(x2 * x2 + y2 * y2);
1938         if (t01 == 0.0f)
1939                 t01 = 1.0f;
1940         if (t02 == 0.0f)
1941                 t02 = 1.0f;
1942
1943         x1 /= t01;
1944         y1 /= t01;
1945         x2 /= t02;
1946         y2 /= t02;
1947
1948         t02 = x1 * x2 + y1 * y2;
1949         if (fabsf(t02) >= 1.0f)
1950                 t02 = 0.5 * M_PI;
1951         else
1952                 t02 = (saacos(t02)) / 2.0f;
1953
1954         t02 = sinf(t02);
1955         if (t02 == 0.0f)
1956                 t02 = 1.0f;
1957
1958         x3 = x1 - x2;
1959         y3 = y1 - y2;
1960         if (x3 == 0 && y3 == 0) {
1961                 x3 = y1;
1962                 y3 = -x1;
1963         }
1964         else {
1965                 t01 = sqrtf(x3 * x3 + y3 * y3);
1966                 x3 /= t01;
1967                 y3 /= t01;
1968         }
1969
1970         *sina = -y3 / t02;
1971         *cosa = x3 / t02;
1972
1973 }
1974
1975 static void alfa_bezpart(BezTriple *prevbezt, BezTriple *bezt, Nurb *nu, float *tilt_array, float *radius_array,
1976                          float *weight_array, int resolu, int stride)
1977 {
1978         BezTriple *pprev, *next, *last;
1979         float fac, dfac, t[4];
1980         int a;
1981
1982         if (tilt_array == NULL && radius_array == NULL)
1983                 return;
1984
1985         last = nu->bezt + (nu->pntsu - 1);
1986
1987         /* returns a point */
1988         if (prevbezt == nu->bezt) {
1989                 if (nu->flagu & CU_NURB_CYCLIC)
1990                         pprev = last;
1991                 else
1992                         pprev = prevbezt;
1993         }
1994         else
1995                 pprev = prevbezt - 1;
1996
1997         /* next point */
1998         if (bezt == last) {
1999                 if (nu->flagu & CU_NURB_CYCLIC)
2000                         next = nu->bezt;
2001                 else
2002                         next = bezt;
2003         }
2004         else
2005                 next = bezt + 1;
2006
2007         fac = 0.0;
2008         dfac = 1.0f / (float)resolu;
2009
2010         for (a = 0; a < resolu; a++, fac += dfac) {
2011                 if (tilt_array) {
2012                         if (nu->tilt_interp == KEY_CU_EASE) { /* May as well support for tilt also 2.47 ease interp */
2013                                 *tilt_array = prevbezt->alfa +
2014                                         (bezt->alfa - prevbezt->alfa) * (3.0f * fac * fac - 2.0f * fac * fac * fac);
2015                         }
2016                         else {
2017                                 key_curve_position_weights(fac, t, nu->tilt_interp);
2018                                 *tilt_array = t[0] * pprev->alfa + t[1] * prevbezt->alfa + t[2] * bezt->alfa + t[3] * next->alfa;
2019                         }
2020
2021                         tilt_array = (float *)(((char *)tilt_array) + stride);
2022                 }
2023
2024                 if (radius_array) {
2025                         if (nu->radius_interp == KEY_CU_EASE) {
2026                                 /* Support 2.47 ease interp
2027                                  * Note! - this only takes the 2 points into account,
2028                                  * giving much more localized results to changes in radius, sometimes you want that */
2029                                 *radius_array = prevbezt->radius +
2030                                         (bezt->radius - prevbezt->radius) * (3.0f * fac * fac - 2.0f * fac * fac * fac);
2031                         }
2032                         else {
2033
2034                                 /* reuse interpolation from tilt if we can */
2035                                 if (tilt_array == NULL || nu->tilt_interp != nu->radius_interp) {
2036                                         key_curve_position_weights(fac, t, nu->radius_interp);
2037                                 }
2038                                 *radius_array = t[0] * pprev->radius + t[1] * prevbezt->radius +
2039                                         t[2] * bezt->radius + t[3] * next->radius;
2040                         }
2041
2042                         radius_array = (float *)(((char *)radius_array) + stride);
2043                 }
2044
2045                 if (weight_array) {
2046                         /* basic interpolation for now, could copy tilt interp too  */
2047                         *weight_array = prevbezt->weight +
2048                                 (bezt->weight - prevbezt->weight) * (3.0f * fac * fac - 2.0f * fac * fac * fac);
2049
2050                         weight_array = (float *)(((char *)weight_array) + stride);
2051                 }
2052         }
2053 }
2054
2055 /* make_bevel_list_3D_* funcs, at a minimum these must
2056  * fill in the bezp->quat and bezp->dir values */
2057
2058 /* utility for make_bevel_list_3D_* funcs */
2059 static void bevel_list_calc_bisect(BevList *bl)
2060 {
2061         BevPoint *bevp2, *bevp1, *bevp0;
2062         int nr;
2063         bool is_cyclic = bl->poly != -1;
2064
2065         if (is_cyclic) {
2066                 bevp2 = (BevPoint *)(bl + 1);
2067                 bevp1 = bevp2 + (bl->nr - 1);
2068                 bevp0 = bevp1 - 1;
2069                 nr = bl->nr;
2070         }
2071         else {
2072                 /* If spline is not cyclic, direction of first and
2073                  * last bevel points matches direction of CV handle.
2074                  *
2075                  * This is getting calculated earlier when we know
2076                  * CV's handles and here we might simply skip evaluation
2077                  * of direction for this guys.
2078                  */
2079
2080                 bevp0 = (BevPoint *)(bl + 1);
2081                 bevp1 = bevp0 + 1;
2082                 bevp2 = bevp1 + 1;
2083
2084                 nr = bl->nr - 2;
2085         }
2086
2087         while (nr--) {
2088                 /* totally simple */
2089                 bisect_v3_v3v3v3(bevp1->dir, bevp0->vec, bevp1->vec, bevp2->vec);
2090
2091                 bevp0 = bevp1;
2092                 bevp1 = bevp2;
2093                 bevp2++;
2094         }
2095 }
2096 static void bevel_list_flip_tangents(BevList *bl)
2097 {
2098         BevPoint *bevp2, *bevp1, *bevp0;
2099         int nr;
2100
2101         bevp2 = (BevPoint *)(bl + 1);
2102         bevp1 = bevp2 + (bl->nr - 1);
2103         bevp0 = bevp1 - 1;
2104
2105         nr = bl->nr;
2106         while (nr--) {
2107                 if (angle_normalized_v3v3(bevp0->tan, bevp1->tan) > DEG2RADF(90.0f))
2108                         negate_v3(bevp1->tan);
2109
2110                 bevp0 = bevp1;
2111                 bevp1 = bevp2;
2112                 bevp2++;
2113         }
2114 }
2115 /* apply user tilt */
2116 static void bevel_list_apply_tilt(BevList *bl)
2117 {
2118         BevPoint *bevp2, *bevp1;
2119         int nr;
2120         float q[4];
2121
2122         bevp2 = (BevPoint *)(bl + 1);
2123         bevp1 = bevp2 + (bl->nr - 1);
2124
2125         nr = bl->nr;
2126         while (nr--) {
2127                 axis_angle_to_quat(q, bevp1->dir, bevp1->alfa);
2128                 mul_qt_qtqt(bevp1->quat, q, bevp1->quat);
2129                 normalize_qt(bevp1->quat);
2130
2131                 bevp1 = bevp2;
2132                 bevp2++;
2133         }
2134 }
2135 /* smooth quats, this function should be optimized, it can get slow with many iterations. */
2136 static void bevel_list_smooth(BevList *bl, int smooth_iter)
2137 {
2138         BevPoint *bevp2, *bevp1, *bevp0;
2139         int nr;
2140
2141         float q[4];
2142         float bevp0_quat[4];
2143         int a;
2144
2145         for (a = 0; a < smooth_iter; a++) {
2146                 bevp2 = (BevPoint *)(bl + 1);
2147                 bevp1 = bevp2 + (bl->nr - 1);
2148                 bevp0 = bevp1 - 1;
2149
2150                 nr = bl->nr;
2151
2152                 if (bl->poly == -1) { /* check its not cyclic */
2153                         /* skip the first point */
2154                         /* bevp0 = bevp1; */
2155                         bevp1 = bevp2;
2156                         bevp2++;
2157                         nr--;
2158
2159                         bevp0 = bevp1;
2160                         bevp1 = bevp2;
2161                         bevp2++;
2162                         nr--;
2163                 }
2164
2165                 copy_qt_qt(bevp0_quat, bevp0->quat);
2166
2167                 while (nr--) {
2168                         /* interpolate quats */
2169                         float zaxis[3] = {0, 0, 1}, cross[3], q2[4];
2170                         interp_qt_qtqt(q, bevp0_quat, bevp2->quat, 0.5);
2171                         normalize_qt(q);
2172
2173                         mul_qt_v3(q, zaxis);
2174                         cross_v3_v3v3(cross, zaxis, bevp1->dir);
2175                         axis_angle_to_quat(q2, cross, angle_normalized_v3v3(zaxis, bevp1->dir));
2176                         normalize_qt(q2);
2177
2178                         copy_qt_qt(bevp0_quat, bevp1->quat);
2179                         mul_qt_qtqt(q, q2, q);
2180                         interp_qt_qtqt(bevp1->quat, bevp1->quat, q, 0.5);
2181                         normalize_qt(bevp1->quat);
2182
2183                         /* bevp0 = bevp1; */ /* UNUSED */
2184                         bevp1 = bevp2;
2185                         bevp2++;
2186                 }
2187         }
2188 }
2189
2190 static void make_bevel_list_3D_zup(BevList *bl)
2191 {
2192         BevPoint *bevp = (BevPoint *)(bl + 1);
2193         int nr = bl->nr;
2194
2195         bevel_list_calc_bisect(bl);
2196
2197         while (nr--) {
2198                 vec_to_quat(bevp->quat, bevp->dir, 5, 1);
2199                 bevp++;
2200         }
2201 }
2202
2203 static void minimum_twist_between_two_points(BevPoint *current_point, BevPoint *previous_point)
2204 {
2205         float angle = angle_normalized_v3v3(previous_point->dir, current_point->dir);
2206         float q[4];
2207
2208         if (angle > 0.0f) { /* otherwise we can keep as is */
2209                 float cross_tmp[3];
2210                 cross_v3_v3v3(cross_tmp, previous_point->dir, current_point->dir);
2211                 axis_angle_to_quat(q, cross_tmp, angle);
2212                 mul_qt_qtqt(current_point->quat, q, previous_point->quat);
2213         }
2214         else {
2215                 copy_qt_qt(current_point->quat, previous_point->quat);
2216         }
2217 }
2218
2219 static void make_bevel_list_3D_minimum_twist(BevList *bl)
2220 {
2221         BevPoint *bevp2, *bevp1, *bevp0; /* standard for all make_bevel_list_3D_* funcs */
2222         int nr;
2223         float q[4];
2224
2225         bevel_list_calc_bisect(bl);
2226
2227         bevp2 = (BevPoint *)(bl + 1);
2228         bevp1 = bevp2 + (bl->nr - 1);
2229         bevp0 = bevp1 - 1;
2230
2231         nr = bl->nr;
2232         while (nr--) {
2233
2234                 if (nr + 4 > bl->nr) { /* first time and second time, otherwise first point adjusts last */
2235                         vec_to_quat(bevp1->quat, bevp1->dir, 5, 1);
2236                 }
2237                 else {
2238                         minimum_twist_between_two_points(bevp1, bevp0);
2239                 }
2240
2241                 bevp0 = bevp1;
2242                 bevp1 = bevp2;
2243                 bevp2++;
2244         }
2245
2246         if (bl->poly != -1) { /* check for cyclic */
2247
2248                 /* Need to correct for the start/end points not matching
2249                  * do this by calculating the tilt angle difference, then apply
2250                  * the rotation gradually over the entire curve
2251                  *
2252                  * note that the split is between last and second last, rather than first/last as youd expect.
2253                  *
2254                  * real order is like this
2255                  * 0,1,2,3,4 --> 1,2,3,4,0
2256                  *
2257                  * this is why we compare last with second last
2258                  * */
2259                 float vec_1[3] = {0, 1, 0}, vec_2[3] = {0, 1, 0}, angle, ang_fac, cross_tmp[3];
2260
2261                 BevPoint *bevp_first;
2262                 BevPoint *bevp_last;
2263
2264
2265                 bevp_first = (BevPoint *)(bl + 1);
2266                 bevp_first += bl->nr - 1;
2267                 bevp_last = bevp_first;
2268                 bevp_last--;
2269
2270                 /* quats and vec's are normalized, should not need to re-normalize */
2271                 mul_qt_v3(bevp_first->quat, vec_1);
2272                 mul_qt_v3(bevp_last->quat, vec_2);
2273                 normalize_v3(vec_1);
2274                 normalize_v3(vec_2);
2275
2276                 /* align the vector, can avoid this and it looks 98% OK but
2277                  * better to align the angle quat roll's before comparing */
2278                 {
2279                         cross_v3_v3v3(cross_tmp, bevp_last->dir, bevp_first->dir);
2280                         angle = angle_normalized_v3v3(bevp_first->dir, bevp_last->dir);
2281                         axis_angle_to_quat(q, cross_tmp, angle);
2282                         mul_qt_v3(q, vec_2);
2283                 }
2284
2285                 angle = angle_normalized_v3v3(vec_1, vec_2);
2286
2287                 /* flip rotation if needs be */
2288                 cross_v3_v3v3(cross_tmp, vec_1, vec_2);
2289                 normalize_v3(cross_tmp);
2290                 if (angle_normalized_v3v3(bevp_first->dir, cross_tmp) < DEG2RADF(90.0f))
2291                         angle = -angle;
2292
2293                 bevp2 = (BevPoint *)(bl + 1);
2294                 bevp1 = bevp2 + (bl->nr - 1);
2295                 bevp0 = bevp1 - 1;
2296
2297                 nr = bl->nr;
2298                 while (nr--) {
2299                         ang_fac = angle * (1.0f - ((float)nr / bl->nr)); /* also works */
2300
2301                         axis_angle_to_quat(q, bevp1->dir, ang_fac);
2302                         mul_qt_qtqt(bevp1->quat, q, bevp1->quat);
2303
2304                         bevp0 = bevp1;
2305                         bevp1 = bevp2;
2306                         bevp2++;
2307                 }
2308         }
2309         else {
2310                 /* Need to correct quat for the first/last point,
2311                  * this is so because previously it was only calculated
2312                  * using it's own direction, which might not correspond
2313                  * the twist of neighbor point.
2314                  */
2315                 bevp1 = (BevPoint *)(bl + 1);
2316                 bevp0 = bevp1 + 1;
2317                 minimum_twist_between_two_points(bevp1, bevp0);
2318
2319                 bevp2 = (BevPoint *)(bl + 1);
2320                 bevp1 = bevp2 + (bl->nr - 1);
2321                 bevp0 = bevp1 - 1;
2322                 minimum_twist_between_two_points(bevp1, bevp0);
2323         }
2324 }
2325
2326 static void make_bevel_list_3D_tangent(BevList *bl)
2327 {
2328         BevPoint *bevp2, *bevp1, *bevp0; /* standard for all make_bevel_list_3D_* funcs */
2329         int nr;
2330
2331         float bevp0_tan[3];
2332
2333         bevel_list_calc_bisect(bl);
2334         bevel_list_flip_tangents(bl);
2335
2336         /* correct the tangents */
2337         bevp2 = (BevPoint *)(bl + 1);
2338         bevp1 = bevp2 + (bl->nr - 1);
2339         bevp0 = bevp1 - 1;
2340
2341         nr = bl->nr;
2342         while (nr--) {
2343                 float cross_tmp[3];
2344                 cross_v3_v3v3(cross_tmp, bevp1->tan, bevp1->dir);
2345                 cross_v3_v3v3(bevp1->tan, cross_tmp, bevp1->dir);
2346                 normalize_v3(bevp1->tan);
2347
2348                 bevp0 = bevp1;
2349                 bevp1 = bevp2;
2350                 bevp2++;
2351         }
2352
2353
2354         /* now for the real twist calc */
2355         bevp2 = (BevPoint *)(bl + 1);
2356         bevp1 = bevp2 + (bl->nr - 1);
2357         bevp0 = bevp1 - 1;
2358
2359         copy_v3_v3(bevp0_tan, bevp0->tan);
2360
2361         nr = bl->nr;
2362         while (nr--) {
2363                 /* make perpendicular, modify tan in place, is ok */
2364                 float cross_tmp[3];
2365                 float zero[3] = {0, 0, 0};
2366
2367                 cross_v3_v3v3(cross_tmp, bevp1->tan, bevp1->dir);
2368                 normalize_v3(cross_tmp);
2369                 tri_to_quat(bevp1->quat, zero, cross_tmp, bevp1->tan); /* XXX - could be faster */
2370
2371                 /* bevp0 = bevp1; */ /* UNUSED */
2372                 bevp1 = bevp2;
2373                 bevp2++;
2374         }
2375 }
2376
2377 static void make_bevel_list_3D(BevList *bl, int smooth_iter, int twist_mode)
2378 {
2379         switch (twist_mode) {
2380                 case CU_TWIST_TANGENT:
2381                         make_bevel_list_3D_tangent(bl);
2382                         break;
2383                 case CU_TWIST_MINIMUM:
2384                         make_bevel_list_3D_minimum_twist(bl);
2385                         break;
2386                 default: /* CU_TWIST_Z_UP default, pre 2.49c */
2387                         make_bevel_list_3D_zup(bl);
2388                         break;
2389         }
2390
2391         if (smooth_iter)
2392                 bevel_list_smooth(bl, smooth_iter);
2393
2394         bevel_list_apply_tilt(bl);
2395 }
2396
2397 /* only for 2 points */
2398 static void make_bevel_list_segment_3D(BevList *bl)
2399 {
2400         float q[4];
2401
2402         BevPoint *bevp2 = (BevPoint *)(bl + 1);
2403         BevPoint *bevp1 = bevp2 + 1;
2404
2405         /* simple quat/dir */
2406         sub_v3_v3v3(bevp1->dir, bevp1->vec, bevp2->vec);
2407         normalize_v3(bevp1->dir);
2408
2409         vec_to_quat(bevp1->quat, bevp1->dir, 5, 1);
2410
2411         axis_angle_to_quat(q, bevp1->dir, bevp1->alfa);
2412         mul_qt_qtqt(bevp1->quat, q, bevp1->quat);
2413         normalize_qt(bevp1->quat);
2414         copy_v3_v3(bevp2->dir, bevp1->dir);
2415         copy_qt_qt(bevp2->quat, bevp1->quat);
2416 }
2417
2418 /* only for 2 points */
2419 static void make_bevel_list_segment_2D(BevList *bl)
2420 {
2421         BevPoint *bevp2 = (BevPoint *)(bl + 1);
2422         BevPoint *bevp1 = bevp2 + 1;
2423
2424         const float x1 = bevp1->vec[0] - bevp2->vec[0];
2425         const float y1 = bevp1->vec[1] - bevp2->vec[1];
2426
2427         calc_bevel_sin_cos(x1, y1, -x1, -y1, &(bevp1->sina), &(bevp1->cosa));
2428         bevp2->sina = bevp1->sina;
2429         bevp2->cosa = bevp1->cosa;
2430
2431         /* fill in dir & quat */
2432         make_bevel_list_segment_3D(bl);
2433 }
2434
2435 static void make_bevel_list_2D(BevList *bl)
2436 {
2437         /* note: bevp->dir and bevp->quat are not needed for beveling but are
2438          * used when making a path from a 2D curve, therefor they need to be set - Campbell */
2439
2440         BevPoint *bevp0, *bevp1, *bevp2;
2441         int nr;
2442
2443         if (bl->poly != -1) {
2444                 bevp2 = (BevPoint *)(bl + 1);
2445                 bevp1 = bevp2 + (bl->nr - 1);
2446                 bevp0 = bevp1 - 1;
2447                 nr = bl->nr;
2448         }
2449         else {
2450                 bevp0 = (BevPoint *)(bl + 1);
2451                 bevp1 = bevp0 + 1;
2452                 bevp2 = bevp1 + 1;
2453
2454                 nr = bl->nr - 2;
2455         }
2456
2457         while (nr--) {
2458                 const float x1 = bevp1->vec[0] - bevp0->vec[0];
2459                 const float x2 = bevp1->vec[0] - bevp2->vec[0];
2460                 const float y1 = bevp1->vec[1] - bevp0->vec[1];
2461                 const float y2 = bevp1->vec[1] - bevp2->vec[1];
2462
2463                 calc_bevel_sin_cos(x1, y1, x2, y2, &(bevp1->sina), &(bevp1->cosa));
2464
2465                 /* from: make_bevel_list_3D_zup, could call but avoid a second loop.
2466                  * no need for tricky tilt calculation as with 3D curves */
2467                 bisect_v3_v3v3v3(bevp1->dir, bevp0->vec, bevp1->vec, bevp2->vec);
2468                 vec_to_quat(bevp1->quat, bevp1->dir, 5, 1);
2469                 /* done with inline make_bevel_list_3D_zup */
2470
2471                 bevp0 = bevp1;
2472                 bevp1 = bevp2;
2473                 bevp2++;
2474         }
2475
2476         /* correct non-cyclic cases */
2477         if (bl->poly == -1) {
2478                 BevPoint *bevp;
2479                 float angle;
2480
2481                 /* first */
2482                 bevp = (BevPoint *)(bl + 1);
2483                 angle = atan2(bevp->dir[0], bevp->dir[1]) - M_PI / 2.0;
2484                 bevp->sina = sinf(angle);
2485                 bevp->cosa = cosf(angle);
2486                 vec_to_quat(bevp->quat, bevp->dir, 5, 1);
2487
2488                 /* last */
2489                 bevp = (BevPoint *)(bl + 1);
2490                 bevp += (bl->nr - 1);
2491                 angle = atan2(bevp->dir[0], bevp->dir[1]) - M_PI / 2.0;
2492                 bevp->sina = sinf(angle);
2493                 bevp->cosa = cosf(angle);
2494                 vec_to_quat(bevp->quat, bevp->dir, 5, 1);
2495         }
2496 }
2497
2498 static void bevlist_firstlast_direction_calc_from_bpoint(Nurb *nu, BevList *bl)
2499 {
2500         if (nu->pntsu > 1) {
2501                 BPoint *first_bp = nu->bp, *last_bp = nu->bp + (nu->pntsu - 1);
2502                 BevPoint *first_bevp, *last_bevp;
2503
2504                 first_bevp = (BevPoint *)(bl + 1);
2505                 last_bevp = first_bevp + (bl->nr - 1);
2506
2507                 sub_v3_v3v3(first_bevp->dir, (first_bp + 1)->vec, first_bp->vec);
2508                 normalize_v3(first_bevp->dir);
2509
2510                 sub_v3_v3v3(last_bevp->dir, last_bp->vec, (last_bp - 1)->vec);
2511                 normalize_v3(last_bevp->dir);
2512         }
2513 }
2514
2515 void BKE_curve_bevelList_make(Object *ob, ListBase *nurbs, bool for_render)
2516 {
2517         /*
2518          * - convert all curves to polys, with indication of resol and flags for double-vertices
2519          * - possibly; do a smart vertice removal (in case Nurb)
2520          * - separate in individual blicks with BoundBox
2521          * - AutoHole detection
2522          */
2523         Curve *cu;
2524         Nurb *nu;
2525         BezTriple *bezt, *prevbezt;
2526         BPoint *bp;
2527         BevList *bl, *blnew, *blnext;
2528         BevPoint *bevp, *bevp2, *bevp1 = NULL, *bevp0;
2529         float min, inp;
2530         struct BevelSort *sortdata, *sd, *sd1;
2531         int a, b, nr, poly, resolu = 0, len = 0;
2532         int do_tilt, do_radius, do_weight;
2533         bool is_editmode = false;
2534         ListBase *bev;
2535
2536         /* this function needs an object, because of tflag and upflag */
2537         cu = ob->data;
2538
2539         bev = &ob->curve_cache->bev;
2540
2541         /* do we need to calculate the radius for each point? */
2542         /* do_radius = (cu->bevobj || cu->taperobj || (cu->flag & CU_FRONT) || (cu->flag & CU_BACK)) ? 0 : 1; */
2543
2544         /* STEP 1: MAKE POLYS  */
2545
2546         BLI_freelistN(&(ob->curve_cache->bev));
2547         nu = nurbs->first;
2548         if (cu->editnurb && ob->type != OB_FONT) {
2549                 is_editmode = 1;
2550         }
2551
2552         for (; nu; nu = nu->next) {
2553
2554                 if (nu->hide && is_editmode)
2555                         continue;
2556
2557                 /* check if we will calculate tilt data */
2558                 do_tilt = CU_DO_TILT(cu, nu);
2559                 do_radius = CU_DO_RADIUS(cu, nu); /* normal display uses the radius, better just to calculate them */
2560                 do_weight = TRUE;
2561
2562                 /* check we are a single point? also check we are not a surface and that the orderu is sane,
2563                  * enforced in the UI but can go wrong possibly */
2564                 if (!BKE_nurb_check_valid_u(nu)) {
2565                         bl = MEM_callocN(sizeof(BevList) + 1 * sizeof(BevPoint), "makeBevelList1");
2566                         BLI_addtail(bev, bl);
2567                         bl->nr = 0;
2568                         bl->charidx = nu->charidx;
2569                 }
2570                 else {
2571                         if (for_render && cu->resolu_ren != 0)
2572                                 resolu = cu->resolu_ren;
2573                         else
2574                                 resolu = nu->resolu;
2575
2576                         if (nu->type == CU_POLY) {
2577                                 len = nu->pntsu;
2578                                 bl = MEM_callocN(sizeof(BevList) + len * sizeof(BevPoint), "makeBevelList2");
2579                                 BLI_addtail(bev, bl);
2580
2581                                 bl->poly = (nu->flagu & CU_NURB_CYCLIC) ? 0 : -1;
2582                                 bl->nr = len;
2583                                 bl->dupe_nr = 0;
2584                                 bl->charidx = nu->charidx;
2585                                 bevp = (BevPoint *)(bl + 1);
2586                                 bp = nu->bp;
2587
2588                                 while (len--) {
2589                                         copy_v3_v3(bevp->vec, bp->vec);
2590                                         bevp->alfa = bp->alfa;
2591                                         bevp->radius = bp->radius;
2592                                         bevp->weight = bp->weight;
2593                                         bevp->split_tag = TRUE;
2594                                         bevp++;
2595                                         bp++;
2596                                 }
2597
2598                                 if ((nu->flagu & CU_NURB_CYCLIC) == 0) {
2599                                         bevlist_firstlast_direction_calc_from_bpoint(nu, bl);
2600                                 }
2601                         }
2602                         else if (nu->type == CU_BEZIER) {
2603                                 /* in case last point is not cyclic */
2604                                 len = resolu * (nu->pntsu + (nu->flagu & CU_NURB_CYCLIC) - 1) + 1;
2605                                 bl = MEM_callocN(sizeof(BevList) + len * sizeof(BevPoint), "makeBevelBPoints");
2606                                 BLI_addtail(bev, bl);
2607
2608                                 bl->poly = (nu->flagu & CU_NURB_CYCLIC) ? 0 : -1;
2609                                 bl->charidx = nu->charidx;
2610                                 bevp = (BevPoint *)(bl + 1);
2611
2612                                 a = nu->pntsu - 1;
2613                                 bezt = nu->bezt;
2614                                 if (nu->flagu & CU_NURB_CYCLIC) {
2615                                         a++;
2616                                         prevbezt = nu->bezt + (nu->pntsu - 1);
2617                                 }
2618                                 else {
2619                                         prevbezt = bezt;
2620                                         bezt++;
2621                                 }
2622
2623                                 sub_v3_v3v3(bevp->dir, prevbezt->vec[2], prevbezt->vec[1]);
2624                                 normalize_v3(bevp->dir);
2625
2626                                 while (a--) {
2627                                         if (prevbezt->h2 == HD_VECT && bezt->h1 == HD_VECT) {
2628
2629                                                 copy_v3_v3(bevp->vec, prevbezt->vec[1]);
2630                                                 bevp->alfa = prevbezt->alfa;
2631                                                 bevp->radius = prevbezt->radius;
2632                                                 bevp->weight = prevbezt->weight;
2633                                                 bevp->split_tag = TRUE;
2634                                                 bevp->dupe_tag = FALSE;
2635                                                 bevp++;
2636                                                 bl->nr++;
2637                                                 bl->dupe_nr = 1;
2638                                         }
2639                                         else {
2640                                                 /* always do all three, to prevent data hanging around */
2641                                                 int j;
2642
2643                                                 /* BevPoint must stay aligned to 4 so sizeof(BevPoint)/sizeof(float) works */
2644                                                 for (j = 0; j < 3; j++) {
2645                                                         BKE_curve_forward_diff_bezier(prevbezt->vec[1][j],  prevbezt->vec[2][j],
2646                                                                                       bezt->vec[0][j],      bezt->vec[1][j],
2647                                                                                       &(bevp->vec[j]), resolu, sizeof(BevPoint));
2648                                                 }
2649
2650                                                 /* if both arrays are NULL do nothiong */
2651                                                 alfa_bezpart(prevbezt, bezt, nu,
2652                                                              do_tilt    ? &bevp->alfa : NULL,
2653                                                              do_radius  ? &bevp->radius : NULL,
2654                                                              do_weight  ? &bevp->weight : NULL,
2655                                                              resolu, sizeof(BevPoint));
2656
2657
2658                                                 if (cu->twist_mode == CU_TWIST_TANGENT) {
2659                                                         forward_diff_bezier_cotangent(prevbezt->vec[1], prevbezt->vec[2],
2660                                                                                       bezt->vec[0],     bezt->vec[1],
2661                                                                                       bevp->tan, resolu, sizeof(BevPoint));
2662                                                 }
2663
2664                                                 /* indicate with handlecodes double points */
2665                                                 if (prevbezt->h1 == prevbezt->h2) {
2666                                                         if (prevbezt->h1 == 0 || prevbezt->h1 == HD_VECT)
2667                                                                 bevp->split_tag = TRUE;
2668                                                 }
2669                                                 else {
2670                                                         if (prevbezt->h1 == 0 || prevbezt->h1 == HD_VECT)
2671                                                                 bevp->split_tag = TRUE;
2672                                                         else if (prevbezt->h2 == 0 || prevbezt->h2 == HD_VECT)
2673                                                                 bevp->split_tag = TRUE;
2674                                                 }
2675                                                 bl->nr += resolu;
2676                                                 bevp += resolu;
2677                                         }
2678                                         prevbezt = bezt;
2679                                         bezt++;
2680                                 }
2681
2682                                 if ((nu->flagu & CU_NURB_CYCLIC) == 0) {      /* not cyclic: endpoint */
2683                                         copy_v3_v3(bevp->vec, prevbezt->vec[1]);
2684                                         bevp->alfa = prevbezt->alfa;
2685                                         bevp->radius = prevbezt->radius;
2686                                         bevp->weight = prevbezt->weight;
2687
2688                                         sub_v3_v3v3(bevp->dir, prevbezt->vec[1], prevbezt->vec[0]);
2689                                         normalize_v3(bevp->dir);
2690
2691                                         bl->nr++;
2692                                 }
2693                         }
2694                         else if (nu->type == CU_NURBS) {
2695                                 if (nu->pntsv == 1) {
2696                                         len = (resolu * SEGMENTSU(nu));
2697
2698                                         bl = MEM_callocN(sizeof(BevList) + len * sizeof(BevPoint), "makeBevelList3");
2699                                         BLI_addtail(bev, bl);
2700                                         bl->nr = len;
2701                                         bl->dupe_nr = 0;
2702                                         bl->poly = (nu->flagu & CU_NURB_CYCLIC) ? 0 : -1;
2703                                         bl->charidx = nu->charidx;
2704                                         bevp = (BevPoint *)(bl + 1);
2705
2706                                         BKE_nurb_makeCurve(nu, &bevp->vec[0],
2707                                                            do_tilt      ? &bevp->alfa : NULL,
2708                                                            do_radius    ? &bevp->radius : NULL,
2709                                                            do_weight    ? &bevp->weight : NULL,
2710                                                            resolu, sizeof(BevPoint));
2711
2712                                         if ((nu->flagu & CU_NURB_CYCLIC) == 0) {
2713                                                 bevlist_firstlast_direction_calc_from_bpoint(nu, bl);
2714                                         }
2715                                 }
2716                         }
2717                 }
2718         }
2719
2720         /* STEP 2: DOUBLE POINTS AND AUTOMATIC RESOLUTION, REDUCE DATABLOCKS */
2721         bl = bev->first;
2722         while (bl) {
2723                 if (bl->nr) { /* null bevel items come from single points */
2724                         bool is_cyclic = bl->poly != -1;
2725                         nr = bl->nr;
2726                         if (is_cyclic) {
2727                                 bevp1 = (BevPoint *)(bl + 1);
2728                                 bevp0 = bevp1 + (nr - 1);
2729                         }
2730                         else {
2731                                 bevp0 = (BevPoint *)(bl + 1);
2732                                 bevp1 = bevp0 + 1;
2733                         }
2734                         nr--;
2735                         while (nr--) {
2736                                 if (fabsf(bevp0->vec[0] - bevp1->vec[0]) < 0.00001f) {
2737                                         if (fabsf(bevp0->vec[1] - bevp1->vec[1]) < 0.00001f) {
2738                                                 if (fabsf(bevp0->vec[2] - bevp1->vec[2]) < 0.00001f) {
2739                                                         bevp0->dupe_tag = TRUE;
2740                                                         bl->dupe_nr++;
2741                                                 }
2742                                         }
2743                                 }
2744                                 bevp0 = bevp1;
2745                                 bevp1++;
2746                         }
2747                 }
2748                 bl = bl->next;
2749         }
2750         bl = bev->first;
2751         while (bl) {
2752                 blnext = bl->next;
2753                 if (bl->nr && bl->dupe_nr) {
2754                         nr = bl->nr - bl->dupe_nr + 1;  /* +1 because vectorbezier sets flag too */
2755                         blnew = MEM_mallocN(sizeof(BevList) + nr * sizeof(BevPoint), "makeBevelList4");
2756                         memcpy(blnew, bl, sizeof(BevList));
2757                         blnew->nr = 0;
2758                         BLI_remlink(bev, bl);
2759                         BLI_insertlinkbefore(bev, blnext, blnew);    /* to make sure bevlijst is tuned with nurblist */
2760                         bevp0 = (BevPoint *)(bl + 1);
2761                         bevp1 = (BevPoint *)(blnew + 1);
2762                         nr = bl->nr;
2763                         while (nr--) {
2764                                 if (bevp0->dupe_tag == 0) {
2765                                         memcpy(bevp1, bevp0, sizeof(BevPoint));
2766                                         bevp1++;
2767                                         blnew->nr++;
2768                                 }
2769                                 bevp0++;
2770                         }
2771                         MEM_freeN(bl);
2772                         blnew->dupe_nr = 0;
2773                 }
2774                 bl = blnext;
2775         }
2776
2777         /* STEP 3: POLYS COUNT AND AUTOHOLE */
2778         bl = bev->first;
2779         poly = 0;
2780         while (bl) {
2781                 if (bl->nr && bl->poly >= 0) {
2782                         poly++;
2783                         bl->poly = poly;
2784                         bl->hole = 0;
2785                 }
2786                 bl = bl->next;
2787         }
2788
2789         /* find extreme left points, also test (turning) direction */
2790         if (poly > 0) {
2791                 sd = sortdata = MEM_mallocN(sizeof(struct BevelSort) * poly, "makeBevelList5");
2792                 bl = bev->first;
2793                 while (bl) {
2794                         if (bl->poly > 0) {
2795
2796                                 min = 300000.0;
2797                                 bevp = (BevPoint *)(bl + 1);
2798                                 nr = bl->nr;
2799                                 while (nr--) {
2800                                         if (min > bevp->vec[0]) {
2801                                                 min = bevp->vec[0];
2802                                                 bevp1 = bevp;
2803                                         }
2804                                         bevp++;
2805                                 }
2806                                 sd->bl = bl;
2807                                 sd->left = min;
2808
2809                                 bevp = (BevPoint *)(bl + 1);
2810                                 if (bevp1 == bevp)
2811                                         bevp0 = bevp + (bl->nr - 1);
2812                                 else
2813                                         bevp0 = bevp1 - 1;
2814                                 bevp = bevp + (bl->nr - 1);
2815                                 if (bevp1 == bevp)
2816                                         bevp2 = (BevPoint *)(bl + 1);
2817                                 else
2818                                         bevp2 = bevp1 + 1;
2819
2820                                 inp = ((bevp1->vec[0] - bevp0->vec[0]) * (bevp0->vec[1] - bevp2->vec[1]) +
2821                                        (bevp0->vec[1] - bevp1->vec[1]) * (bevp0->vec[0] - bevp2->vec[0]));
2822
2823                                 if (inp > 0.0f)
2824                                         sd->dir = 1;
2825                                 else
2826                                         sd->dir = 0;
2827
2828                                 sd++;
2829                         }
2830
2831                         bl = bl->next;
2832                 }
2833                 qsort(sortdata, poly, sizeof(struct BevelSort), vergxcobev);
2834
2835                 sd = sortdata + 1;
2836                 for (a = 1; a < poly; a++, sd++) {
2837                         bl = sd->bl;     /* is bl a hole? */
2838                         sd1 = sortdata + (a - 1);
2839                         for (b = a - 1; b >= 0; b--, sd1--) { /* all polys to the left */
2840                                 if (sd1->bl->charidx == bl->charidx) { /* for text, only check matching char */
2841                                         if (bevelinside(sd1->bl, bl)) {
2842                                                 bl->hole = 1 - sd1->bl->hole;
2843                                                 break;
2844                                         }
2845                                 }
2846                         }
2847                 }
2848
2849                 /* turning direction */
2850                 if ((cu->flag & CU_3D) == 0) {
2851                         sd = sortdata;
2852                         for (a = 0; a < poly; a++, sd++) {
2853                                 if (sd->bl->hole == sd->dir) {
2854                                         bl = sd->bl;
2855                                         bevp1 = (BevPoint *)(bl + 1);
2856                                         bevp2 = bevp1 + (bl->nr - 1);
2857                                         nr = bl->nr / 2;
2858                                         while (nr--) {
2859                                                 SWAP(BevPoint, *bevp1, *bevp2);
2860                                                 bevp1++;
2861                                                 bevp2--;
2862                                         }
2863                                 }
2864                         }
2865                 }
2866                 MEM_freeN(sortdata);
2867         }
2868
2869         /* STEP 4: 2D-COSINES or 3D ORIENTATION */
2870         if ((cu->flag & CU_3D) == 0) {
2871                 /* 2D Curves */
2872                 for (bl = bev->first; bl; bl = bl->next) {
2873                         if (bl->nr < 2) {
2874                                 /* do nothing */
2875                         }
2876                         else if (bl->nr == 2) {   /* 2 pnt, treat separate */
2877                                 make_bevel_list_segment_2D(bl);
2878                         }
2879                         else {
2880                                 make_bevel_list_2D(bl);
2881                         }
2882                 }
2883         }
2884         else {
2885                 /* 3D Curves */
2886                 for (bl = bev->first; bl; bl = bl->next) {
2887                         if (bl->nr < 2) {
2888                                 /* do nothing */
2889                         }
2890                         else if (bl->nr == 2) {   /* 2 pnt, treat separate */
2891                                 make_bevel_list_segment_3D(bl);
2892                         }
2893                         else {
2894                                 make_bevel_list_3D(bl, (int)(resolu * cu->twist_smooth), cu->twist_mode);
2895                         }
2896                 }
2897         }
2898 }
2899
2900 /* ****************** HANDLES ************** */
2901
2902 static void calchandleNurb_intern(BezTriple *bezt, BezTriple *prev, BezTriple *next,
2903                                   bool is_fcurve, bool skip_align)
2904 {
2905         /* defines to avoid confusion */
2906 #define p2_h1 (p2 - 3)
2907 #define p2_h2 (p2 + 3)
2908
2909         float *p1, *p2, *p3, pt[3];
2910         float dvec_a[3], dvec_b[3];
2911         float len, len_a, len_b;
2912         const float eps = 1e-5;
2913
2914         if (bezt->h1 == 0 && bezt->h2 == 0) {
2915                 return;
2916         }
2917
2918         p2 = bezt->vec[1];
2919
2920         if (prev == NULL) {
2921                 p3 = next->vec[1];
2922                 pt[0] = 2.0f * p2[0] - p3[0];
2923                 pt[1] = 2.0f * p2[1] - p3[1];
2924                 pt[2] = 2.0f * p2[2] - p3[2];
2925                 p1 = pt;
2926         }
2927         else {
2928                 p1 = prev->vec[1];
2929         }
2930
2931         if (next == NULL) {
2932                 pt[0] = 2.0f * p2[0] - p1[0];
2933                 pt[1] = 2.0f * p2[1] - p1[1];
2934                 pt[2] = 2.0f * p2[2] - p1[2];
2935                 p3 = pt;
2936         }
2937         else {
2938                 p3 = next->vec[1];
2939         }
2940
2941         sub_v3_v3v3(dvec_a, p2, p1);
2942         sub_v3_v3v3(dvec_b, p3, p2);
2943
2944         if (is_fcurve) {
2945                 len_a = dvec_a[0];
2946                 len_b = dvec_b[0];
2947         }
2948         else {
2949                 len_a = len_v3(dvec_a);
2950                 len_b = len_v3(dvec_b);
2951         }
2952
2953         if (len_a == 0.0f) len_a = 1.0f;
2954         if (len_b == 0.0f) len_b = 1.0f;
2955
2956
2957         if (ELEM(bezt->h1, HD_AUTO, HD_AUTO_ANIM) || ELEM(bezt->h2, HD_AUTO, HD_AUTO_ANIM)) {    /* auto */
2958                 float tvec[3];
2959                 tvec[0] = dvec_b[0] / len_b + dvec_a[0] / len_a;
2960                 tvec[1] = dvec_b[1] / len_b + dvec_a[1] / len_a;
2961                 tvec[2] = dvec_b[2] / len_b + dvec_a[2] / len_a;
2962
2963                 if (is_fcurve) {
2964                         len = tvec[0];
2965                 }
2966                 else {
2967                         len = len_v3(tvec);
2968                 }
2969                 len *=  2.5614f;
2970
2971                 if (len != 0.0f) {
2972                         /* only for fcurves */
2973                         bool leftviolate = false, rightviolate = false;
2974
2975                         if (len_a > 5.0f * len_b)
2976                                 len_a = 5.0f * len_b;
2977                         if (len_b > 5.0f * len_a)
2978                                 len_b = 5.0f * len_a;
2979
2980                         if (ELEM(bezt->h1, HD_AUTO, HD_AUTO_ANIM)) {
2981                                 len_a /= len;
2982                                 madd_v3_v3v3fl(p2_h1, p2, tvec, -len_a);
2983
2984                                 if ((bezt->h1 == HD_AUTO_ANIM) && next && prev) { /* keep horizontal if extrema */
2985                                         float ydiff1 = prev->vec[1][1] - bezt->vec[1][1];
2986                                         float ydiff2 = next->vec[1][1] - bezt->vec[1][1];
2987                                         if ((ydiff1 <= 0.0f && ydiff2 <= 0.0f) || (ydiff1 >= 0.0f && ydiff2 >= 0.0f)) {
2988                                                 bezt->vec[0][1] = bezt->vec[1][1];
2989                                         }
2990                                         else { /* handles should not be beyond y coord of two others */
2991                                                 if (ydiff1 <= 0.0f) {
2992                                                         if (prev->vec[1][1] > bezt->vec[0][1]) {
2993                                                                 bezt->vec[0][1] = prev->vec[1][1];
2994                                                                 leftviolate = 1;
2995                                                         }
2996                                                 }
2997                                                 else {
2998                                                         if (prev->vec[1][1] < bezt->vec[0][1]) {
2999                                                                 bezt->vec[0][1] = prev->vec[1][1];
3000                                                                 leftviolate = 1;
3001                                                         }
3002                                                 }
3003                                         }
3004                                 }
3005                         }
3006                         if (ELEM(bezt->h2, HD_AUTO, HD_AUTO_ANIM)) {
3007                                 len_b /= len;
3008                                 madd_v3_v3v3fl(p2_h2, p2, tvec,  len_b);
3009
3010                                 if ((bezt->h2 == HD_AUTO_ANIM) && next && prev) { /* keep horizontal if extrema */
3011                                         float ydiff1 = prev->vec[1][1] - bezt->vec[1][1];
3012                                         float ydiff2 = next->vec[1][1] - bezt->vec[1][1];
3013                                         if ( (ydiff1 <= 0.0f && ydiff2 <= 0.0f) || (ydiff1 >= 0.0f && ydiff2 >= 0.0f) ) {
3014                                                 bezt->vec[2][1] = bezt->vec[1][1];
3015                                         }
3016                                         else { /* andles should not be beyond y coord of two others */
3017                                                 if (ydiff1 <= 0.0f) {
3018                                                         if (next->vec[1][1] < bezt->vec[2][1]) {
3019                                                                 bezt->vec[2][1] = next->vec[1][1];
3020                                                                 rightviolate = 1;
3021                                                         }
3022                                                 }
3023                                                 else {
3024                                                         if (next->vec[1][1] > bezt->vec[2][1]) {
3025                                                                 bezt->vec[2][1] = next->vec[1][1];
3026                                                                 rightviolate = 1;
3027                                                         }
3028                                                 }
3029                                         }
3030                                 }
3031                         }
3032                         if (leftviolate || rightviolate) { /* align left handle */
3033                                 BLI_assert(is_fcurve);
3034 #if 0
3035                                 if (is_fcurve)
3036 #endif
3037                                 {
3038                                         /* simple 2d calculation */
3039                                         float h1_x = p2_h1[0] - p2[0];
3040                                         float h2_x = p2[0] - p2_h2[0];
3041
3042                                         if (leftviolate) {
3043                                                 p2_h2[1] = p2[1] + ((p2[1] - p2_h1[1]) / h1_x) * h2_x;
3044                                         }
3045                                         else {
3046                                                 p2_h1[1] = p2[1] + ((p2[1] - p2_h2[1]) / h2_x) * h1_x;
3047                                         }
3048                                 }
3049 #if 0
3050                                 else {
3051                                         float h1[3], h2[3];
3052                                         float dot;
3053
3054                                         sub_v3_v3v3(h1, p2_h1, p2);
3055                                         sub_v3_v3v3(h2, p2, p2_h2);
3056
3057                                         len_a = normalize_v3(h1);
3058                                         len_b = normalize_v3(h2);
3059
3060                                         dot = dot_v3v3(h1, h2);
3061
3062                                         if (leftviolate) {
3063                                                 mul_v3_fl(h1, dot * len_b);
3064