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-/*
-Copyright (c) 2003-2006 Gino van den Bergen / Erwin Coumans http://continuousphysics.com/Bullet/
-
-This software is provided 'as-is', without any express or implied warranty.
-In no event will the authors be held liable for any damages arising from the use of this software.
-Permission is granted to anyone to use this software for any purpose,
-including commercial applications, and to alter it and redistribute it freely,
-subject to the following restrictions:
-
-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.
-2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
-3. This notice may not be removed or altered from any source distribution.
-*/
-
-#ifndef BT_TRANSFORM_UTIL_H
-#define BT_TRANSFORM_UTIL_H
-
-#include "btTransform.h"
-#define ANGULAR_MOTION_THRESHOLD btScalar(0.5) * SIMD_HALF_PI
-
-SIMD_FORCE_INLINE btVector3 btAabbSupport(const btVector3& halfExtents, const btVector3& supportDir)
-{
- return btVector3(supportDir.x() < btScalar(0.0) ? -halfExtents.x() : halfExtents.x(),
- supportDir.y() < btScalar(0.0) ? -halfExtents.y() : halfExtents.y(),
- supportDir.z() < btScalar(0.0) ? -halfExtents.z() : halfExtents.z());
-}
-
-/// Utils related to temporal transforms
-class btTransformUtil
-{
-public:
- static void integrateTransform(const btTransform& curTrans, const btVector3& linvel, const btVector3& angvel, btScalar timeStep, btTransform& predictedTransform)
- {
- predictedTransform.setOrigin(curTrans.getOrigin() + linvel * timeStep);
- // #define QUATERNION_DERIVATIVE
-#ifdef QUATERNION_DERIVATIVE
- btQuaternion predictedOrn = curTrans.getRotation();
- predictedOrn += (angvel * predictedOrn) * (timeStep * btScalar(0.5));
- predictedOrn.safeNormalize();
-#else
- //Exponential map
- //google for "Practical Parameterization of Rotations Using the Exponential Map", F. Sebastian Grassia
-
- btVector3 axis;
- btScalar fAngle2 = angvel.length2();
- btScalar fAngle = 0;
- if (fAngle2 > SIMD_EPSILON)
- {
- fAngle = btSqrt(fAngle2);
- }
-
- //limit the angular motion
- if (fAngle * timeStep > ANGULAR_MOTION_THRESHOLD)
- {
- fAngle = ANGULAR_MOTION_THRESHOLD / timeStep;
- }
-
- if (fAngle < btScalar(0.001))
- {
- // use Taylor's expansions of sync function
- axis = angvel * (btScalar(0.5) * timeStep - (timeStep * timeStep * timeStep) * (btScalar(0.020833333333)) * fAngle * fAngle);
- }
- else
- {
- // sync(fAngle) = sin(c*fAngle)/t
- axis = angvel * (btSin(btScalar(0.5) * fAngle * timeStep) / fAngle);
- }
- btQuaternion dorn(axis.x(), axis.y(), axis.z(), btCos(fAngle * timeStep * btScalar(0.5)));
- btQuaternion orn0 = curTrans.getRotation();
-
- btQuaternion predictedOrn = dorn * orn0;
- predictedOrn.safeNormalize();
-#endif
- if (predictedOrn.length2() > SIMD_EPSILON)
- {
- predictedTransform.setRotation(predictedOrn);
- }
- else
- {
- predictedTransform.setBasis(curTrans.getBasis());
- }
- }
-
- static void calculateVelocityQuaternion(const btVector3& pos0, const btVector3& pos1, const btQuaternion& orn0, const btQuaternion& orn1, btScalar timeStep, btVector3& linVel, btVector3& angVel)
- {
- linVel = (pos1 - pos0) / timeStep;
- btVector3 axis;
- btScalar angle;
- if (orn0 != orn1)
- {
- calculateDiffAxisAngleQuaternion(orn0, orn1, axis, angle);
- angVel = axis * angle / timeStep;
- }
- else
- {
- angVel.setValue(0, 0, 0);
- }
- }
-
- static void calculateDiffAxisAngleQuaternion(const btQuaternion& orn0, const btQuaternion& orn1a, btVector3& axis, btScalar& angle)
- {
- btQuaternion orn1 = orn0.nearest(orn1a);
- btQuaternion dorn = orn1 * orn0.inverse();
- angle = dorn.getAngle();
- axis = btVector3(dorn.x(), dorn.y(), dorn.z());
- axis[3] = btScalar(0.);
- //check for axis length
- btScalar len = axis.length2();
- if (len < SIMD_EPSILON * SIMD_EPSILON)
- axis = btVector3(btScalar(1.), btScalar(0.), btScalar(0.));
- else
- axis /= btSqrt(len);
- }
-
- static void calculateVelocity(const btTransform& transform0, const btTransform& transform1, btScalar timeStep, btVector3& linVel, btVector3& angVel)
- {
- linVel = (transform1.getOrigin() - transform0.getOrigin()) / timeStep;
- btVector3 axis;
- btScalar angle;
- calculateDiffAxisAngle(transform0, transform1, axis, angle);
- angVel = axis * angle / timeStep;
- }
-
- static void calculateDiffAxisAngle(const btTransform& transform0, const btTransform& transform1, btVector3& axis, btScalar& angle)
- {
- btMatrix3x3 dmat = transform1.getBasis() * transform0.getBasis().inverse();
- btQuaternion dorn;
- dmat.getRotation(dorn);
-
- ///floating point inaccuracy can lead to w component > 1..., which breaks
- dorn.normalize();
-
- angle = dorn.getAngle();
- axis = btVector3(dorn.x(), dorn.y(), dorn.z());
- axis[3] = btScalar(0.);
- //check for axis length
- btScalar len = axis.length2();
- if (len < SIMD_EPSILON * SIMD_EPSILON)
- axis = btVector3(btScalar(1.), btScalar(0.), btScalar(0.));
- else
- axis /= btSqrt(len);
- }
-};
-
-///The btConvexSeparatingDistanceUtil can help speed up convex collision detection
-///by conservatively updating a cached separating distance/vector instead of re-calculating the closest distance
-class btConvexSeparatingDistanceUtil
-{
- btQuaternion m_ornA;
- btQuaternion m_ornB;
- btVector3 m_posA;
- btVector3 m_posB;
-
- btVector3 m_separatingNormal;
-
- btScalar m_boundingRadiusA;
- btScalar m_boundingRadiusB;
- btScalar m_separatingDistance;
-
-public:
- btConvexSeparatingDistanceUtil(btScalar boundingRadiusA, btScalar boundingRadiusB)
- : m_boundingRadiusA(boundingRadiusA),
- m_boundingRadiusB(boundingRadiusB),
- m_separatingDistance(0.f)
- {
- }
-
- btScalar getConservativeSeparatingDistance()
- {
- return m_separatingDistance;
- }
-
- void updateSeparatingDistance(const btTransform& transA, const btTransform& transB)
- {
- const btVector3& toPosA = transA.getOrigin();
- const btVector3& toPosB = transB.getOrigin();
- btQuaternion toOrnA = transA.getRotation();
- btQuaternion toOrnB = transB.getRotation();
-
- if (m_separatingDistance > 0.f)
- {
- btVector3 linVelA, angVelA, linVelB, angVelB;
- btTransformUtil::calculateVelocityQuaternion(m_posA, toPosA, m_ornA, toOrnA, btScalar(1.), linVelA, angVelA);
- btTransformUtil::calculateVelocityQuaternion(m_posB, toPosB, m_ornB, toOrnB, btScalar(1.), linVelB, angVelB);
- btScalar maxAngularProjectedVelocity = angVelA.length() * m_boundingRadiusA + angVelB.length() * m_boundingRadiusB;
- btVector3 relLinVel = (linVelB - linVelA);
- btScalar relLinVelocLength = relLinVel.dot(m_separatingNormal);
- if (relLinVelocLength < 0.f)
- {
- relLinVelocLength = 0.f;
- }
-
- btScalar projectedMotion = maxAngularProjectedVelocity + relLinVelocLength;
- m_separatingDistance -= projectedMotion;
- }
-
- m_posA = toPosA;
- m_posB = toPosB;
- m_ornA = toOrnA;
- m_ornB = toOrnB;
- }
-
- void initSeparatingDistance(const btVector3& separatingVector, btScalar separatingDistance, const btTransform& transA, const btTransform& transB)
- {
- m_separatingDistance = separatingDistance;
-
- if (m_separatingDistance > 0.f)
- {
- m_separatingNormal = separatingVector;
-
- const btVector3& toPosA = transA.getOrigin();
- const btVector3& toPosB = transB.getOrigin();
- btQuaternion toOrnA = transA.getRotation();
- btQuaternion toOrnB = transB.getRotation();
- m_posA = toPosA;
- m_posB = toPosB;
- m_ornA = toOrnA;
- m_ornB = toOrnB;
- }
- }
-};
-
-#endif //BT_TRANSFORM_UTIL_H