Bullet Collision Detection & Physics Library
btTransformUtil.h
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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:
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11 2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
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13 */
14 
15 #ifndef BT_TRANSFORM_UTIL_H
16 #define BT_TRANSFORM_UTIL_H
17 
18 #include "btTransform.h"
19 #define ANGULAR_MOTION_THRESHOLD btScalar(0.5) * SIMD_HALF_PI
20 
21 SIMD_FORCE_INLINE btVector3 btAabbSupport(const btVector3& halfExtents, const btVector3& supportDir)
22 {
23  return btVector3(supportDir.x() < btScalar(0.0) ? -halfExtents.x() : halfExtents.x(),
24  supportDir.y() < btScalar(0.0) ? -halfExtents.y() : halfExtents.y(),
25  supportDir.z() < btScalar(0.0) ? -halfExtents.z() : halfExtents.z());
26 }
27 
30 {
31 public:
32  static void integrateTransform(const btTransform& curTrans, const btVector3& linvel, const btVector3& angvel, btScalar timeStep, btTransform& predictedTransform)
33  {
34  predictedTransform.setOrigin(curTrans.getOrigin() + linvel * timeStep);
35  // #define QUATERNION_DERIVATIVE
36 #ifdef QUATERNION_DERIVATIVE
37  btQuaternion predictedOrn = curTrans.getRotation();
38  predictedOrn += (angvel * predictedOrn) * (timeStep * btScalar(0.5));
39  predictedOrn.safeNormalize();
40 #else
41  //Exponential map
42  //google for "Practical Parameterization of Rotations Using the Exponential Map", F. Sebastian Grassia
43 
44  btVector3 axis;
45  btScalar fAngle2 = angvel.length2();
46  btScalar fAngle = 0;
47  if (fAngle2 > SIMD_EPSILON)
48  {
49  fAngle = btSqrt(fAngle2);
50  }
51 
52  //limit the angular motion
53  if (fAngle * timeStep > ANGULAR_MOTION_THRESHOLD)
54  {
55  fAngle = ANGULAR_MOTION_THRESHOLD / timeStep;
56  }
57 
58  if (fAngle < btScalar(0.001))
59  {
60  // use Taylor's expansions of sync function
61  axis = angvel * (btScalar(0.5) * timeStep - (timeStep * timeStep * timeStep) * (btScalar(0.020833333333)) * fAngle * fAngle);
62  }
63  else
64  {
65  // sync(fAngle) = sin(c*fAngle)/t
66  axis = angvel * (btSin(btScalar(0.5) * fAngle * timeStep) / fAngle);
67  }
68  btQuaternion dorn(axis.x(), axis.y(), axis.z(), btCos(fAngle * timeStep * btScalar(0.5)));
69  btQuaternion orn0 = curTrans.getRotation();
70 
71  btQuaternion predictedOrn = dorn * orn0;
72  predictedOrn.safeNormalize();
73 #endif
74  if (predictedOrn.length2() > SIMD_EPSILON)
75  {
76  predictedTransform.setRotation(predictedOrn);
77  }
78  else
79  {
80  predictedTransform.setBasis(curTrans.getBasis());
81  }
82  }
83 
84  static void calculateVelocityQuaternion(const btVector3& pos0, const btVector3& pos1, const btQuaternion& orn0, const btQuaternion& orn1, btScalar timeStep, btVector3& linVel, btVector3& angVel)
85  {
86  linVel = (pos1 - pos0) / timeStep;
87  btVector3 axis;
88  btScalar angle;
89  if (orn0 != orn1)
90  {
91  calculateDiffAxisAngleQuaternion(orn0, orn1, axis, angle);
92  angVel = axis * angle / timeStep;
93  }
94  else
95  {
96  angVel.setValue(0, 0, 0);
97  }
98  }
99 
100  static void calculateDiffAxisAngleQuaternion(const btQuaternion& orn0, const btQuaternion& orn1a, btVector3& axis, btScalar& angle)
101  {
102  btQuaternion orn1 = orn0.nearest(orn1a);
103  btQuaternion dorn = orn1 * orn0.inverse();
104  angle = dorn.getAngle();
105  axis = btVector3(dorn.x(), dorn.y(), dorn.z());
106  axis[3] = btScalar(0.);
107  //check for axis length
108  btScalar len = axis.length2();
109  if (len < SIMD_EPSILON * SIMD_EPSILON)
110  axis = btVector3(btScalar(1.), btScalar(0.), btScalar(0.));
111  else
112  axis /= btSqrt(len);
113  }
114 
115  static void calculateVelocity(const btTransform& transform0, const btTransform& transform1, btScalar timeStep, btVector3& linVel, btVector3& angVel)
116  {
117  linVel = (transform1.getOrigin() - transform0.getOrigin()) / timeStep;
118  btVector3 axis;
119  btScalar angle;
120  calculateDiffAxisAngle(transform0, transform1, axis, angle);
121  angVel = axis * angle / timeStep;
122  }
123 
124  static void calculateDiffAxisAngle(const btTransform& transform0, const btTransform& transform1, btVector3& axis, btScalar& angle)
125  {
126  btMatrix3x3 dmat = transform1.getBasis() * transform0.getBasis().inverse();
127  btQuaternion dorn;
128  dmat.getRotation(dorn);
129 
131  dorn.normalize();
132 
133  angle = dorn.getAngle();
134  axis = btVector3(dorn.x(), dorn.y(), dorn.z());
135  axis[3] = btScalar(0.);
136  //check for axis length
137  btScalar len = axis.length2();
138  if (len < SIMD_EPSILON * SIMD_EPSILON)
139  axis = btVector3(btScalar(1.), btScalar(0.), btScalar(0.));
140  else
141  axis /= btSqrt(len);
142  }
143 };
144 
148 {
153 
155 
159 
160 public:
161  btConvexSeparatingDistanceUtil(btScalar boundingRadiusA, btScalar boundingRadiusB)
162  : m_boundingRadiusA(boundingRadiusA),
163  m_boundingRadiusB(boundingRadiusB),
165  {
166  }
167 
169  {
170  return m_separatingDistance;
171  }
172 
173  void updateSeparatingDistance(const btTransform& transA, const btTransform& transB)
174  {
175  const btVector3& toPosA = transA.getOrigin();
176  const btVector3& toPosB = transB.getOrigin();
177  btQuaternion toOrnA = transA.getRotation();
178  btQuaternion toOrnB = transB.getRotation();
179 
180  if (m_separatingDistance > 0.f)
181  {
182  btVector3 linVelA, angVelA, linVelB, angVelB;
183  btTransformUtil::calculateVelocityQuaternion(m_posA, toPosA, m_ornA, toOrnA, btScalar(1.), linVelA, angVelA);
184  btTransformUtil::calculateVelocityQuaternion(m_posB, toPosB, m_ornB, toOrnB, btScalar(1.), linVelB, angVelB);
185  btScalar maxAngularProjectedVelocity = angVelA.length() * m_boundingRadiusA + angVelB.length() * m_boundingRadiusB;
186  btVector3 relLinVel = (linVelB - linVelA);
187  btScalar relLinVelocLength = relLinVel.dot(m_separatingNormal);
188  if (relLinVelocLength < 0.f)
189  {
190  relLinVelocLength = 0.f;
191  }
192 
193  btScalar projectedMotion = maxAngularProjectedVelocity + relLinVelocLength;
194  m_separatingDistance -= projectedMotion;
195  }
196 
197  m_posA = toPosA;
198  m_posB = toPosB;
199  m_ornA = toOrnA;
200  m_ornB = toOrnB;
201  }
202 
203  void initSeparatingDistance(const btVector3& separatingVector, btScalar separatingDistance, const btTransform& transA, const btTransform& transB)
204  {
205  m_separatingDistance = separatingDistance;
206 
207  if (m_separatingDistance > 0.f)
208  {
209  m_separatingNormal = separatingVector;
210 
211  const btVector3& toPosA = transA.getOrigin();
212  const btVector3& toPosB = transB.getOrigin();
213  btQuaternion toOrnA = transA.getRotation();
214  btQuaternion toOrnB = transB.getRotation();
215  m_posA = toPosA;
216  m_posB = toPosB;
217  m_ornA = toOrnA;
218  m_ornB = toOrnB;
219  }
220  }
221 };
222 
223 #endif //BT_TRANSFORM_UTIL_H
void setOrigin(const btVector3 &origin)
Set the translational element.
Definition: btTransform.h:146
const btScalar & x() const
Return the x value.
Definition: btQuadWord.h:113
#define SIMD_EPSILON
Definition: btScalar.h:523
void setValue(const btScalar &_x, const btScalar &_y, const btScalar &_z)
Definition: btVector3.h:640
btScalar btSin(btScalar x)
Definition: btScalar.h:479
btScalar length2() const
Return the length of the vector squared.
Definition: btVector3.h:251
void setBasis(const btMatrix3x3 &basis)
Set the rotational element by btMatrix3x3.
Definition: btTransform.h:154
btQuaternion & safeNormalize()
Definition: btQuaternion.h:374
btConvexSeparatingDistanceUtil(btScalar boundingRadiusA, btScalar boundingRadiusB)
btScalar btSqrt(btScalar y)
Definition: btScalar.h:446
btQuaternion getRotation() const
Return a quaternion representing the rotation.
Definition: btTransform.h:118
static void calculateDiffAxisAngle(const btTransform &transform0, const btTransform &transform1, btVector3 &axis, btScalar &angle)
#define SIMD_FORCE_INLINE
Definition: btScalar.h:83
static void calculateDiffAxisAngleQuaternion(const btQuaternion &orn0, const btQuaternion &orn1a, btVector3 &axis, btScalar &angle)
#define ANGULAR_MOTION_THRESHOLD
btVector3 btAabbSupport(const btVector3 &halfExtents, const btVector3 &supportDir)
static void calculateVelocityQuaternion(const btVector3 &pos0, const btVector3 &pos1, const btQuaternion &orn0, const btQuaternion &orn1, btScalar timeStep, btVector3 &linVel, btVector3 &angVel)
btQuaternion inverse() const
Return the inverse of this quaternion.
Definition: btQuaternion.h:497
btVector3 & getOrigin()
Return the origin vector translation.
Definition: btTransform.h:113
void updateSeparatingDistance(const btTransform &transA, const btTransform &transB)
const btScalar & x() const
Return the x value.
Definition: btVector3.h:575
btQuaternion & normalize()
Normalize the quaternion Such that x^2 + y^2 + z^2 +w^2 = 1.
Definition: btQuaternion.h:385
btScalar dot(const btVector3 &v) const
Return the dot product.
Definition: btVector3.h:229
The btConvexSeparatingDistanceUtil can help speed up convex collision detection by conservatively upd...
void setRotation(const btQuaternion &q)
Set the rotational element by btQuaternion.
Definition: btTransform.h:160
const btScalar & y() const
Return the y value.
Definition: btVector3.h:577
const btScalar & z() const
Return the z value.
Definition: btVector3.h:579
btMatrix3x3 & getBasis()
Return the basis matrix for the rotation.
Definition: btTransform.h:108
const btScalar & z() const
Return the z value.
Definition: btQuadWord.h:117
btVector3 can be used to represent 3D points and vectors.
Definition: btVector3.h:80
static void integrateTransform(const btTransform &curTrans, const btVector3 &linvel, const btVector3 &angvel, btScalar timeStep, btTransform &predictedTransform)
btScalar getAngle() const
Return the angle [0, 2Pi] of rotation represented by this quaternion.
Definition: btQuaternion.h:468
The btTransform class supports rigid transforms with only translation and rotation and no scaling/she...
Definition: btTransform.h:28
btQuaternion nearest(const btQuaternion &qd) const
Definition: btQuaternion.h:563
btScalar length2() const
Return the length squared of the quaternion.
Definition: btQuaternion.h:364
The btMatrix3x3 class implements a 3x3 rotation matrix, to perform linear algebra in combination with...
Definition: btMatrix3x3.h:46
const btScalar & y() const
Return the y value.
Definition: btQuadWord.h:115
The btQuaternion implements quaternion to perform linear algebra rotations in combination with btMatr...
Definition: btQuaternion.h:49
btMatrix3x3 inverse() const
Return the inverse of the matrix.
Definition: btMatrix3x3.h:1070
Utils related to temporal transforms.
static void calculateVelocity(const btTransform &transform0, const btTransform &transform1, btScalar timeStep, btVector3 &linVel, btVector3 &angVel)
void initSeparatingDistance(const btVector3 &separatingVector, btScalar separatingDistance, const btTransform &transA, const btTransform &transB)
void getRotation(btQuaternion &q) const
Get the matrix represented as a quaternion.
Definition: btMatrix3x3.h:397
float btScalar
The btScalar type abstracts floating point numbers, to easily switch between double and single floati...
Definition: btScalar.h:294
btScalar btCos(btScalar x)
Definition: btScalar.h:478
btScalar length() const
Return the length of the vector.
Definition: btVector3.h:257