bullet/LinearMath/btTransformUtil.h

/*
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