extern/bullet/LinearMath/SimdTransformUtil.h

   1 /*
   2 Copyright (c) 2003-2006 Gino van den Bergen / Erwin Coumans  http://continuousphysics.com/Bullet/
   3
   4 This software is provided 'as-is', without any express or implied warranty.
   5 In no event will the authors be held liable for any damages arising from the use of this software.
   6 Permission is granted to anyone to use this software for any purpose,
   7 including commercial applications, and to alter it and redistribute it freely,
   8 subject to the following restrictions:
   9
  10 1. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required.
  11 2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
  12 3. This notice may not be removed or altered from any source distribution.
  13 */
  14
  15
  16 #ifndef SIMD_TRANSFORM_UTIL_H
  17 #define SIMD_TRANSFORM_UTIL_H
  18
  19 #include "SimdTransform.h"
  20 #define ANGULAR_MOTION_TRESHOLD 0.5f*SIMD_HALF_PI
  21
  22
  23
  24 #define SIMDSQRT12 SimdScalar(0.7071067811865475244008443621048490)
  25
  26 #define SimdRecipSqrt(x) ((float)(1.0f/SimdSqrt(float(x))))             /* reciprocal square root */
  27
  28
  29 inline void SimdPlaneSpace1 (const SimdVector3& n, SimdVector3& p, SimdVector3& q)
  30 {
  31   if (SimdFabs(n[2]) > SIMDSQRT12) {
  32     // choose p in y-z plane
  33     SimdScalar a = n[1]*n[1] + n[2]*n[2];
  34     SimdScalar k = SimdRecipSqrt (a);
  35     p[0] = 0;
  36     p[1] = -n[2]*k;
  37     p[2] = n[1]*k;
  38     // set q = n x p
  39     q[0] = a*k;
  40     q[1] = -n[0]*p[2];
  41     q[2] = n[0]*p[1];
  42   }
  43   else {
  44     // choose p in x-y plane
  45     SimdScalar a = n[0]*n[0] + n[1]*n[1];
  46     SimdScalar k = SimdRecipSqrt (a);
  47     p[0] = -n[1]*k;
  48     p[1] = n[0]*k;
  49     p[2] = 0;
  50     // set q = n x p
  51     q[0] = -n[2]*p[1];
  52     q[1] = n[2]*p[0];
  53     q[2] = a*k;
  54   }
  55 }
  56
  57
  58
  59 /// Utils related to temporal transforms
  60 class SimdTransformUtil
  61 {
  62
  63 public:
  64
  65         static void IntegrateTransform(const SimdTransform& curTrans,const SimdVector3& linvel,const SimdVector3& angvel,SimdScalar timeStep,SimdTransform& predictedTransform)
  66         {
  67                 predictedTransform.setOrigin(curTrans.getOrigin() + linvel * timeStep);
  68 //      #define QUATERNION_DERIVATIVE
  69         #ifdef QUATERNION_DERIVATIVE
  70                 SimdQuaternion orn = curTrans.getRotation();
  71                 orn += (angvel * orn) * (timeStep * 0.5f);
  72                 orn.normalize();
  73         #else
  74                 //exponential map
  75                 SimdVector3 axis;
  76                 SimdScalar      fAngle = angvel.length();
  77                 //limit the angular motion
  78                 if (fAngle*timeStep > ANGULAR_MOTION_TRESHOLD)
  79                 {
  80                         fAngle = ANGULAR_MOTION_TRESHOLD / timeStep;
  81                 }
  82
  83                 if ( fAngle < 0.001f )
  84                 {
  85                         // use Taylor's expansions of sync function
  86                         axis   = angvel*( 0.5f*timeStep-(timeStep*timeStep*timeStep)*(0.020833333333f)*fAngle*fAngle );
  87                 }
  88                 else
  89                 {
  90                         // sync(fAngle) = sin(c*fAngle)/t
  91                         axis   = angvel*( SimdSin(0.5f*fAngle*timeStep)/fAngle );
  92                 }
  93                 SimdQuaternion dorn (axis.x(),axis.y(),axis.z(),SimdCos( fAngle*timeStep*0.5f ));
  94                 SimdQuaternion orn0 = curTrans.getRotation();
  95
  96                 SimdQuaternion predictedOrn = dorn * orn0;
  97         #endif
  98                 predictedTransform.setRotation(predictedOrn);
  99         }
 100
 101         static void     CalculateVelocity(const SimdTransform& transform0,const SimdTransform& transform1,SimdScalar timeStep,SimdVector3& linVel,SimdVector3& angVel)
 102         {
 103                 linVel = (transform1.getOrigin() - transform0.getOrigin()) / timeStep;
 104 #ifdef USE_QUATERNION_DIFF
 105                 SimdQuaternion orn0 = transform0.getRotation();
 106                 SimdQuaternion orn1a = transform1.getRotation();
 107                 SimdQuaternion orn1 = orn0.farthest(orn1a);
 108                 SimdQuaternion dorn = orn1 * orn0.inverse();
 109 #else
 110                 SimdMatrix3x3 dmat = transform1.getBasis() * transform0.getBasis().inverse();
 111                 SimdQuaternion dorn;
 112                 dmat.getRotation(dorn);
 113 #endif//USE_QUATERNION_DIFF
 114
 115                 SimdVector3 axis;
 116                 SimdScalar  angle;
 117                 angle = dorn.getAngle();
 118                 axis = SimdVector3(dorn.x(),dorn.y(),dorn.z());
 119                 axis[3] = 0.f;
 120                 //check for axis length
 121                 SimdScalar len = axis.length2();
 122                 if (len < SIMD_EPSILON*SIMD_EPSILON)
 123                         axis = SimdVector3(1.f,0.f,0.f);
 124                 else
 125                         axis /= SimdSqrt(len);
 126
 127
 128                 angVel = axis * angle / timeStep;
 129
 130         }
 131
 132
 133 };
 134
 135 #endif //SIMD_TRANSFORM_UTIL_H
 136