void
MT_ExpMap::
compute_dRdVi(
const MT_Quaternion &dQdvi,
MT_Matrix3x3 & dRdvi
) const {
MT_Scalar prod[9];
/* This efficient formulation is arrived at by writing out the
* entire chain rule product dRdq * dqdv in terms of 'q' and
* noticing that all the entries are formed from sums of just
* nine products of 'q' and 'dqdv' */
prod[0] = -MT_Scalar(4)*m_q.x()*dQdvi.x();
prod[1] = -MT_Scalar(4)*m_q.y()*dQdvi.y();
prod[2] = -MT_Scalar(4)*m_q.z()*dQdvi.z();
prod[3] = MT_Scalar(2)*(m_q.y()*dQdvi.x() + m_q.x()*dQdvi.y());
prod[4] = MT_Scalar(2)*(m_q.w()*dQdvi.z() + m_q.z()*dQdvi.w());
prod[5] = MT_Scalar(2)*(m_q.z()*dQdvi.x() + m_q.x()*dQdvi.z());
prod[6] = MT_Scalar(2)*(m_q.w()*dQdvi.y() + m_q.y()*dQdvi.w());
prod[7] = MT_Scalar(2)*(m_q.z()*dQdvi.y() + m_q.y()*dQdvi.z());
prod[8] = MT_Scalar(2)*(m_q.w()*dQdvi.x() + m_q.x()*dQdvi.w());
/* first row, followed by second and third */
dRdvi[0][0] = prod[1] + prod[2];
dRdvi[0][1] = prod[3] - prod[4];
dRdvi[0][2] = prod[5] + prod[6];
dRdvi[1][0] = prod[3] + prod[4];
dRdvi[1][1] = prod[0] + prod[2];
dRdvi[1][2] = prod[7] - prod[8];
dRdvi[2][0] = prod[5] - prod[6];
dRdvi[2][1] = prod[7] + prod[8];
dRdvi[2][2] = prod[0] + prod[1];
}
