void mrpt::math::slerp(
const CPose3DQuat & q0,
const CPose3DQuat & q1,
const double t,
CPose3DQuat & q)
{
// The quaternion part (this will raise exception on t not in [0,1])
mrpt::math::slerp(q0.quat(), q1.quat(),t, q.quat());
// XYZ:
q.x( (1-t)*q0.x()+t*q1.x() );
q.y( (1-t)*q0.y()+t*q1.y() );
q.z( (1-t)*q0.z()+t*q1.z() );
}
/*---------------------------------------------------------------
jacobiansPoseComposition
---------------------------------------------------------------*/
void CPose3DQuatPDF::jacobiansPoseComposition(
const CPose3DQuat &x,
const CPose3DQuat &u,
CMatrixDouble77 &df_dx,
CMatrixDouble77 &df_du,
CPose3DQuat *out_x_oplus_u
)
{
// For the derivation of the formulas, see the tech. report cited in the header file.
const double qr = x.quat().r();
const double qx = x.quat().x(); const double qx2 = square(qx);
const double qy = x.quat().y(); const double qy2 = square(qy);
const double qz = x.quat().z(); const double qz2 = square(qz);
const double ax = u.x();
const double ay = u.y();
const double az = u.z();
const double q2r = u.quat().r();
const double q2x = u.quat().x();
const double q2y = u.quat().y();
const double q2z = u.quat().z();
CPose3DQuat x_plus_u = x + u; // needed for the normalization Jacobian:
CMatrixDouble44 norm_jacob(UNINITIALIZED_MATRIX);
x_plus_u.quat().normalizationJacobian(norm_jacob);
CMatrixDouble44 norm_jacob_x(UNINITIALIZED_MATRIX);
x.quat().normalizationJacobian(norm_jacob_x);
// df_dx ===================================================
df_dx.zeros();
// first part 3x7: df_{qr} / dp
df_dx.set_unsafe(0,0, 1);
df_dx.set_unsafe(1,1, 1);
df_dx.set_unsafe(2,2, 1);
MRPT_ALIGN16 const double vals2[3*4] = {
2*(-qz*ay +qy*az ),
2*(qy*ay + qz*az ),
2*(-2*qy*ax + qx*ay +qr*az ),
2*(-2*qz*ax - qr*ay +qx*az ),
2*(qz*ax - qx*az ),
2*(qy*ax - 2*qx*ay -qr*az ),
2*(qx*ax +qz*az ),
2*(qr*ax - 2*qz*ay +qy*az ),
2*(-qy*ax + qx*ay ),
2*( qz*ax + qr*ay - 2*qx*az ),
2*(-qr*ax + qz*ay - 2*qy*az ),
2*( qx*ax + qy*ay )
};
// df_dx(0:3,3:7) = vals2 * NORM_JACOB
df_dx.block(0,3, 3,4).noalias() = (CMatrixFixedNumeric<double,3,4>(vals2) * norm_jacob_x).eval();
// second part:
{
MRPT_ALIGN16 const double aux44_data[4*4] = {
q2r,-q2x,-q2y,-q2z,
q2x, q2r, q2z,-q2y,
q2y,-q2z, q2r, q2x,
q2z, q2y,-q2x, q2r };
df_dx.block(3,3, 4,4).noalias() = (norm_jacob * CMatrixFixedNumeric<double,4,4>(aux44_data)).eval();
}
// df_du ===================================================
df_du.zeros();
// first part 3x3: df_{qr} / da
df_du.set_unsafe(0,0, 1-2*(qy2+qz2) );
df_du.set_unsafe(0,1, 2*(qx*qy - qr*qz ) );
df_du.set_unsafe(0,2, 2*(qr*qy + qx*qz ) );
df_du.set_unsafe(1,0, 2*(qr*qz + qx*qy ) );
df_du.set_unsafe(1,1, 1 - 2*( qx2+qz2) );
df_du.set_unsafe(1,2, 2*(qy*qz - qr*qx ) );
df_du.set_unsafe(2,0, 2*(qx*qz - qr*qy ) );
df_du.set_unsafe(2,1, 2*(qr*qx + qy*qz ) );
df_du.set_unsafe(2,2, 1-2*(qx2+qy2) );
// Second part:
{
MRPT_ALIGN16 const double aux44_data[4*4] = {
qr,-qx,-qy,-qz,
qx, qr,-qz, qy,
qy, qz, qr,-qx,
qz,-qy, qx, qr };
df_du.block(3,3, 4,4).noalias() = (norm_jacob * CMatrixFixedNumeric<double,4,4>(aux44_data)).eval();
}
if (out_x_oplus_u)
*out_x_oplus_u = x_plus_u;
}
bool mrpt::poses::operator==(const CPose3DQuat& p1, const CPose3DQuat& p2)
{
return p1.quat() == p2.quat() && p1.x() == p2.x() && p1.y() == p2.y() &&
p1.z() == p2.z();
}
