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/* Copyright (c) <2003-2011> <Julio Jerez, Newton Game Dynamics>
*
* 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.
*/
#include "dgStdafx.h"
#include "dgVector.h"
#include "dgMatrix.h"
#include "dgQuaternion.h"
dgQuaternion::dgQuaternion(const dgMatrix &matrix) {
enum QUAT_INDEX {
X_INDEX = 0, Y_INDEX = 1, Z_INDEX = 2
};
static QUAT_INDEX QIndex[] =
{ Y_INDEX, Z_INDEX, X_INDEX };
dgFloat32 *ptr;
dgFloat32 trace;
QUAT_INDEX i;
QUAT_INDEX j;
QUAT_INDEX k;
trace = matrix[0][0] + matrix[1][1] + matrix[2][2];
if (trace > dgFloat32(0.0f)) {
trace = dgSqrt(trace + dgFloat32(1.0f));
m_q0 = dgFloat32(0.5f) * trace;
trace = dgFloat32(0.5f) / trace;
m_q1 = (matrix[1][2] - matrix[2][1]) * trace;
m_q2 = (matrix[2][0] - matrix[0][2]) * trace;
m_q3 = (matrix[0][1] - matrix[1][0]) * trace;
} else {
i = X_INDEX;
if (matrix[Y_INDEX][Y_INDEX] > matrix[X_INDEX][X_INDEX]) {
i = Y_INDEX;
}
if (matrix[Z_INDEX][Z_INDEX] > matrix[i][i]) {
i = Z_INDEX;
}
j = QIndex[i];
k = QIndex[j];
trace = dgFloat32(1.0f) + matrix[i][i] - matrix[j][j] - matrix[k][k];
trace = dgSqrt(trace);
ptr = &m_q1;
ptr[i] = dgFloat32(0.5f) * trace;
trace = dgFloat32(0.5f) / trace;
m_q0 = (matrix[j][k] - matrix[k][j]) * trace;
ptr[j] = (matrix[i][j] + matrix[j][i]) * trace;
ptr[k] = (matrix[i][k] + matrix[k][i]) * trace;
}
#ifdef _DEBUG
dgMatrix tmp(*this, matrix.m_posit);
dgMatrix unitMatrix(tmp * matrix.Inverse());
for (dgInt32 di = 0; di < 4; di++) {
dgFloat32 err = dgAbsf(unitMatrix[di][di] - dgFloat32(1.0f));
NEWTON_ASSERT(err < dgFloat32(1.0e-2f));
}
dgFloat32 err = dgAbsf(DotProduct(*this) - dgFloat32(1.0f));
NEWTON_ASSERT(err < dgFloat32(dgEPSILON * 100.0f));
#endif
}
dgQuaternion::dgQuaternion(const dgVector &unitAxis, dgFloat32 Angle) {
dgFloat32 sinAng;
Angle *= dgFloat32(0.5f);
m_q0 = dgCos(Angle);
sinAng = dgSin(Angle);
#ifdef _DEBUG
if (dgAbsf(Angle) > dgFloat32(dgEPSILON / 10.0f)) {
NEWTON_ASSERT(
dgAbsf(dgFloat32(1.0f) - unitAxis % unitAxis) < dgFloat32(dgEPSILON * 10.0f));
}
#endif
m_q1 = unitAxis.m_x * sinAng;
m_q2 = unitAxis.m_y * sinAng;
m_q3 = unitAxis.m_z * sinAng;
}
dgVector dgQuaternion::CalcAverageOmega(const dgQuaternion &QB,
dgFloat32 dt) const {
NEWTON_ASSERT(0);
return dgVector(0, 0, 0, 0);
/*
dgFloat32 dirMag;
dgFloat32 dirMag2;
dgFloat32 omegaMag;
dgFloat32 dirMagInv;
NEWTON_ASSERT (0);
dgQuaternion dq (Inverse() * QB);
// dgQuaternion dq (QB * Inverse());
dgVector omegaDir (dq.m_q1, dq.m_q2, dq.m_q3, dgFloat32 (0.0f));
dirMag2 = omegaDir % omegaDir;
if (dirMag2 < dgFloat32(dgFloat32 (1.0e-5f) * dgFloat32 (1.0e-5f))) {
return dgVector (dgFloat32(0.0f), dgFloat32(0.0f), dgFloat32(0.0f), dgFloat32(0.0f));
}
dirMagInv = dgRsqrt (dirMag2);
dirMag = dirMag2 * dirMagInv;
omegaMag = dgFloat32(2.0f) * dgAtan2 (dirMag, dq.m_q0) / dt;
return omegaDir.Scale (dirMagInv * omegaMag);
*/
}
dgQuaternion dgQuaternion::Slerp(const dgQuaternion &QB, dgFloat32 t) const {
NEWTON_ASSERT(0);
return dgQuaternion();
/*
dgFloat32 dot;
dgFloat32 ang;
dgFloat32 Sclp;
dgFloat32 Sclq;
dgFloat32 den;
dgFloat32 sinAng;
dgQuaternion Q;
dot = DotProduct (QB);
if ((dot + dgFloat32(1.0f)) > dgEPSILON) {
if (dot < (dgFloat32(1.0f) - dgEPSILON) ) {
ang = dgAcos (dot);
sinAng = dgSin (ang);
den = dgFloat32(1.0f) / sinAng;
Sclp = dgSin ((dgFloat32(1.0f) - t ) * ang) * den;
Sclq = dgSin (t * ang) * den;
} else {
Sclp = dgFloat32(1.0f) - t;
Sclq = t;
}
Q.m_q0 = m_q0 * Sclp + QB.m_q0 * Sclq;
Q.m_q1 = m_q1 * Sclp + QB.m_q1 * Sclq;
Q.m_q2 = m_q2 * Sclp + QB.m_q2 * Sclq;
Q.m_q3 = m_q3 * Sclp + QB.m_q3 * Sclq;
} else {
Q.m_q0 = m_q3;
Q.m_q1 = -m_q2;
Q.m_q2 = m_q1;
Q.m_q3 = m_q0;
Sclp = dgSin ((dgFloat32(1.0f) - t) * dgPI * dgFloat32 (0.5f));
Sclq = dgSin (t * dgPI * dgFloat32 (0.5f));
Q.m_q0 = m_q0 * Sclp + Q.m_q0 * Sclq;
Q.m_q1 = m_q1 * Sclp + Q.m_q1 * Sclq;
Q.m_q2 = m_q2 * Sclp + Q.m_q2 * Sclq;
Q.m_q3 = m_q3 * Sclp + Q.m_q3 * Sclq;
}
dot = Q.DotProduct (Q);
if ((dot) < dgFloat32(1.0f - dgEPSILON * 10.0f) ) {
//dot = dgFloat32(1.0f) / dgSqrt (dot);
dot = dgRsqrt (dot);
Q.m_q0 *= dot;
Q.m_q1 *= dot;
Q.m_q2 *= dot;
Q.m_q3 *= dot;
}
return Q;
*/
}
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