void dgCollisionScene::CalcAABB (const dgMatrix& matrix, dgVector& p0, dgVector& p1) const
{
dgVector origin (matrix.TransformVector(m_boxOrigin));
dgVector size (m_boxSize.m_x * dgAbsf(matrix[0][0]) + m_boxSize.m_y * dgAbsf(matrix[1][0]) + m_boxSize.m_z * dgAbsf(matrix[2][0]) + DG_MAX_COLLISION_PADDING,
m_boxSize.m_x * dgAbsf(matrix[0][1]) + m_boxSize.m_y * dgAbsf(matrix[1][1]) + m_boxSize.m_z * dgAbsf(matrix[2][1]) + DG_MAX_COLLISION_PADDING,
m_boxSize.m_x * dgAbsf(matrix[0][2]) + m_boxSize.m_y * dgAbsf(matrix[1][2]) + m_boxSize.m_z * dgAbsf(matrix[2][2]) + DG_MAX_COLLISION_PADDING,
dgFloat32 (0.0f));
p0 = origin - size;
p1 = origin + size;
#ifdef DG_DEBUG_AABB
dgInt32 i;
dgVector q0;
dgVector q1;
dgMatrix trans (matrix.Transpose());
for (i = 0; i < 3; i ++) {
q0[i] = matrix.m_posit[i] + matrix.RotateVector (BoxSupportMapping(trans[i].Scale (-1.0f)))[i];
q1[i] = matrix.m_posit[i] + matrix.RotateVector (BoxSupportMapping(trans[i]))[i];
}
dgVector err0 (p0 - q0);
dgVector err1 (p1 - q1);
dgFloat32 err;
err = GetMax (size.m_x, size.m_y, size.m_z) * 0.5f;
_ASSERTE ((err0 % err0) < err);
_ASSERTE ((err1 % err1) < err);
#endif
}
dgMatrix::dgMatrix (const dgMatrix& transformMatrix, const dgVector& scale, const dgMatrix& stretchAxis)
{
dgMatrix scaledAxis;
scaledAxis[0] = stretchAxis[0].Scale4 (scale[0]);
scaledAxis[1] = stretchAxis[1].Scale4 (scale[1]);
scaledAxis[2] = stretchAxis[2].Scale4 (scale[2]);
scaledAxis[3] = stretchAxis[3];
*this = stretchAxis.Transpose() * scaledAxis * transformMatrix;
}
void dgMatrix::PolarDecomposition (dgMatrix& transformMatrix, dgVector& scale, dgMatrix& stretchAxis, const dgMatrix* const initialStretchAxis) const
{
// a polar decomposition decompose matrix A = O * S
// where S = sqrt (transpose (L) * L)
/*
// calculate transpose (L) * L
dgMatrix LL ((*this) * Transpose());
// check is this is a pure uniformScale * rotation * translation
dgFloat32 det2 = (LL[0][0] + LL[1][1] + LL[2][2]) * dgFloat32 (1.0f / 3.0f);
dgFloat32 invdet2 = 1.0f / det2;
dgMatrix pureRotation (LL);
pureRotation[0] = pureRotation[0].Scale3 (invdet2);
pureRotation[1] = pureRotation[1].Scale3 (invdet2);
pureRotation[2] = pureRotation[2].Scale3 (invdet2);
dgFloat32 sign = ((((*this)[0] * (*this)[1]) % (*this)[2]) > 0.0f) ? 1.0f : -1.0f;
dgFloat32 det = (pureRotation[0] * pureRotation[1]) % pureRotation[2];
if (dgAbsf (det - dgFloat32 (1.0f)) < dgFloat32 (1.0e-5f)) {
// this is a pure scale * rotation * translation
det = sign * dgSqrt (det2);
scale[0] = det;
scale[1] = det;
scale[2] = det;
det = dgFloat32 (1.0f)/ det;
transformMatrix.m_front = m_front.Scale3 (det);
transformMatrix.m_up = m_up.Scale3 (det);
transformMatrix.m_right = m_right.Scale3 (det);
transformMatrix[0][3] = dgFloat32 (0.0f);
transformMatrix[1][3] = dgFloat32 (0.0f);
transformMatrix[2][3] = dgFloat32 (0.0f);
transformMatrix.m_posit = m_posit;
stretchAxis = dgGetIdentityMatrix();
} else {
stretchAxis = LL;
stretchAxis.EigenVectors (scale);
// I need to deal with by seeing of some of the Scale are duplicated
// do this later (maybe by a given rotation around the non uniform axis but I do not know if it will work)
// for now just us the matrix
scale[0] = sign * dgSqrt (scale[0]);
scale[1] = sign * dgSqrt (scale[1]);
scale[2] = sign * dgSqrt (scale[2]);
scale[3] = dgFloat32 (0.0f);
dgMatrix scaledAxis;
scaledAxis[0] = stretchAxis[0].Scale3 (dgFloat32 (1.0f) / scale[0]);
scaledAxis[1] = stretchAxis[1].Scale3 (dgFloat32 (1.0f) / scale[1]);
scaledAxis[2] = stretchAxis[2].Scale3 (dgFloat32 (1.0f) / scale[2]);
scaledAxis[3] = stretchAxis[3];
dgMatrix symetricInv (stretchAxis.Transpose() * scaledAxis);
transformMatrix = symetricInv * (*this);
transformMatrix.m_posit = m_posit;
}
*/
// test the f*****g factorization
dgMatrix xxxxx(dgRollMatrix(30.0f * 3.1416f / 180.0f));
xxxxx = dgYawMatrix(30.0f * 3.1416f / 180.0f) * xxxxx;
dgMatrix xxxxx1(dgGetIdentityMatrix());
xxxxx1[0][0] = 2.0f;
dgMatrix xxxxx2(xxxxx.Inverse() * xxxxx1 * xxxxx);
dgMatrix xxxxx3 (xxxxx2);
xxxxx2.EigenVectors(scale);
dgMatrix xxxxx4(xxxxx2.Inverse() * xxxxx1 * xxxxx2);
//dgFloat32 sign = ((((*this)[0] * (*this)[1]) % (*this)[2]) > 0.0f) ? 1.0f : -1.0f;
dgFloat32 sign = dgSign(((*this)[0] * (*this)[1]) % (*this)[2]);
stretchAxis = (*this) * Transpose();
stretchAxis.EigenVectors (scale);
// I need to deal with by seeing of some of the Scale are duplicated
// do this later (maybe by a given rotation around the non uniform axis but I do not know if it will work)
// for now just us the matrix
scale[0] = sign * dgSqrt (scale[0]);
scale[1] = sign * dgSqrt (scale[1]);
scale[2] = sign * dgSqrt (scale[2]);
scale[3] = dgFloat32 (0.0f);
dgMatrix scaledAxis;
scaledAxis[0] = stretchAxis[0].Scale3 (dgFloat32 (1.0f) / scale[0]);
scaledAxis[1] = stretchAxis[1].Scale3 (dgFloat32 (1.0f) / scale[1]);
scaledAxis[2] = stretchAxis[2].Scale3 (dgFloat32 (1.0f) / scale[2]);
scaledAxis[3] = stretchAxis[3];
dgMatrix symetricInv (stretchAxis.Transpose() * scaledAxis);
transformMatrix = symetricInv * (*this);
transformMatrix.m_posit = m_posit;
}