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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
+