bullet3/LinearMath/SimdTransformUtil.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 SIMD_TRANSFORM_UTIL_H
#define SIMD_TRANSFORM_UTIL_H

#include "SimdTransform.h"
#define ANGULAR_MOTION_TRESHOLD 0.5f*SIMD_HALF_PI



#define SIMDSQRT12 SimdScalar(0.7071067811865475244008443621048490)

#define SimdRecipSqrt(x) ((float)(1.0f/SimdSqrt(float(x))))		/* reciprocal square root */

inline SimdVector3 SimdAabbSupport(const SimdVector3& halfExtents,const SimdVector3& supportDir)
{
	return SimdVector3(supportDir.x() < SimdScalar(0.0f) ? -halfExtents.x() : halfExtents.x(),
      supportDir.y() < SimdScalar(0.0f) ? -halfExtents.y() : halfExtents.y(),
      supportDir.z() < SimdScalar(0.0f) ? -halfExtents.z() : halfExtents.z()); 
}


inline void SimdPlaneSpace1 (const SimdVector3& n, SimdVector3& p, SimdVector3& q)
{
  if (SimdFabs(n[2]) > SIMDSQRT12) {
    // choose p in y-z plane
    SimdScalar a = n[1]*n[1] + n[2]*n[2];
    SimdScalar k = SimdRecipSqrt (a);
    p[0] = 0;
    p[1] = -n[2]*k;
    p[2] = n[1]*k;
    // set q = n x p
    q[0] = a*k;
    q[1] = -n[0]*p[2];
    q[2] = n[0]*p[1];
  }
  else {
    // choose p in x-y plane
    SimdScalar a = n[0]*n[0] + n[1]*n[1];
    SimdScalar k = SimdRecipSqrt (a);
    p[0] = -n[1]*k;
    p[1] = n[0]*k;
    p[2] = 0;
    // set q = n x p
    q[0] = -n[2]*p[1];
    q[1] = n[2]*p[0];
    q[2] = a*k;
  }
}



/// Utils related to temporal transforms
class SimdTransformUtil
{

public:

	static void IntegrateTransform(const SimdTransform& curTrans,const SimdVector3& linvel,const SimdVector3& angvel,SimdScalar timeStep,SimdTransform& predictedTransform)
	{
		predictedTransform.setOrigin(curTrans.getOrigin() + linvel * timeStep);
//	#define QUATERNION_DERIVATIVE
	#ifdef QUATERNION_DERIVATIVE
		SimdQuaternion orn = curTrans.getRotation();
		orn += (angvel * orn) * (timeStep * 0.5f);
		orn.normalize();
	#else
		//exponential map
		SimdVector3 axis;
		SimdScalar	fAngle = angvel.length(); 
		//limit the angular motion
		if (fAngle*timeStep > ANGULAR_MOTION_TRESHOLD)
		{
			fAngle = ANGULAR_MOTION_TRESHOLD / timeStep;
		}

		if ( fAngle < 0.001f )
		{
			// use Taylor's expansions of sync function
			axis   = angvel*( 0.5f*timeStep-(timeStep*timeStep*timeStep)*(0.020833333333f)*fAngle*fAngle );
		}
		else
		{
			// sync(fAngle) = sin(c*fAngle)/t
			axis   = angvel*( SimdSin(0.5f*fAngle*timeStep)/fAngle );
		}
		SimdQuaternion dorn (axis.x(),axis.y(),axis.z(),SimdCos( fAngle*timeStep*0.5f ));
		SimdQuaternion orn0 = curTrans.getRotation();

		SimdQuaternion predictedOrn = dorn * orn0;
	#endif
		predictedTransform.setRotation(predictedOrn);
	}

	static void	CalculateVelocity(const SimdTransform& transform0,const SimdTransform& transform1,SimdScalar timeStep,SimdVector3& linVel,SimdVector3& angVel)
	{
		linVel = (transform1.getOrigin() - transform0.getOrigin()) / timeStep;
#ifdef USE_QUATERNION_DIFF
		SimdQuaternion orn0 = transform0.getRotation();
		SimdQuaternion orn1a = transform1.getRotation();
		SimdQuaternion orn1 = orn0.farthest(orn1a);
		SimdQuaternion dorn = orn1 * orn0.inverse();
#else
		SimdMatrix3x3 dmat = transform1.getBasis() * transform0.getBasis().inverse();
		SimdQuaternion dorn;
		dmat.getRotation(dorn);
#endif//USE_QUATERNION_DIFF

		SimdVector3 axis;
		SimdScalar  angle;
		angle = dorn.getAngle();
		axis = SimdVector3(dorn.x(),dorn.y(),dorn.z());
		axis[3] = 0.f;
		//check for axis length
		SimdScalar len = axis.length2();
		if (len < SIMD_EPSILON*SIMD_EPSILON)
			axis = SimdVector3(1.f,0.f,0.f);
		else
			axis /= SimdSqrt(len);

		
		angVel = axis * angle / timeStep;

	}


};

#endif //SIMD_TRANSFORM_UTIL_H