//void dMatrix::PolarDecomposition (dMatrix& orthogonal, dMatrix& symetric) const
void dMatrix::PolarDecomposition (dMatrix & transformMatrix, dVector & scale, dMatrix & stretchAxis, const dMatrix & initialStretchAxis) const
{
// a polar decomposition decompose matrix A = O * S
// where S = sqrt (transpose (L) * L)
// calculate transpose (L) * L
dMatrix LL ((*this) * Transpose());
// check is this si a pure uniformScale * rotation * translation
dFloat det2 = (LL[0][0] + LL[1][1] + LL[2][2]) * (1.0f / 3.0f);
dFloat invdet2 = 1.0f / det2;
dMatrix pureRotation (LL);
pureRotation[0] = pureRotation[0].Scale (invdet2);
pureRotation[1] = pureRotation[1].Scale (invdet2);
pureRotation[2] = pureRotation[2].Scale (invdet2);
//dFloat soureSign = ((*this)[0] * (*this)[1]) % (*this)[2];
dFloat sign = ((((*this)[0] * (*this)[1]) % (*this)[2]) > 0.0f) ? 1.0f : -1.0f;
dFloat det = (pureRotation[0] * pureRotation[1]) % pureRotation[2];
if (dAbs (det - 1.0f) < 1.e-5f)
{
// this is a pure scale * rotation * translation
det = sign * dSqrt (det2);
scale[0] = det;
scale[1] = det;
scale[2] = det;
scale[3] = 1.0f;
det = 1.0f / det;
transformMatrix.m_front = m_front.Scale (det);
transformMatrix.m_up = m_up.Scale (det);
transformMatrix.m_right = m_right.Scale (det);
transformMatrix[0][3] = 0.0f;
transformMatrix[1][3] = 0.0f;
transformMatrix[2][3] = 0.0f;
transformMatrix.m_posit = m_posit;
stretchAxis = dGetIdentityMatrix();
}
else
{
stretchAxis = LL.JacobiDiagonalization (scale, initialStretchAxis);
// I need to deal with buy 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 * dSqrt (scale[0]);
scale[1] = sign * dSqrt (scale[1]);
scale[2] = sign * dSqrt (scale[2]);
scale[3] = 1.0f;
dMatrix scaledAxis;
scaledAxis[0] = stretchAxis[0].Scale (1.0f / scale[0]);
scaledAxis[1] = stretchAxis[1].Scale (1.0f / scale[1]);
scaledAxis[2] = stretchAxis[2].Scale (1.0f / scale[2]);
scaledAxis[3] = stretchAxis[3];
dMatrix symetricInv (stretchAxis.Transpose() * scaledAxis);
transformMatrix = symetricInv * (*this);
transformMatrix.m_posit = m_posit;
}
}
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;
}
