pytransform3d.transformations.concatenate_dual_quaternions

pytransform3d.transformations.concatenate_dual_quaternions(dq1, dq2, unit=True)

Concatenate dual quaternions.

We concatenate two dual quaternions by dual quaternion multiplication

\[(\boldsymbol{p}_1 + \epsilon \boldsymbol{q}_1) (\boldsymbol{p}_2 + \epsilon \boldsymbol{q}_2) = \boldsymbol{p}_1 \boldsymbol{p}_2 + \epsilon ( \boldsymbol{p}_1 \boldsymbol{q}_2 + \boldsymbol{q}_1 \boldsymbol{p}_2)\]

using Hamilton multiplication of quaternions.

Warning

Note that the order of arguments is different than the order in concat().

Parameters:

dq1array-like, shape (8,)

Dual quaternion to represent transform: (pw, px, py, pz, qw, qx, qy, qz)

dq2array-like, shape (8,)

Dual quaternion to represent transform: (pw, px, py, pz, qw, qx, qy, qz)

unitbool, optional (default: True)

Normalize the dual quaternion so that it is a unit dual quaternion. A unit dual quaternion has the properties \(p_w^2 + p_x^2 + p_y^2 + p_z^2 = 1\) and \(p_w q_w + p_x q_x + p_y q_y + p_z q_z = 0\).

Returns:

dq3array, shape (8,)

Product of the two dual quaternions: (pw, px, py, pz, qw, qx, qy, qz)

See also

pytransform3d.rotations.concatenate_quaternions

Quaternion multiplication.