pytransform3d.transformations.dq_q_conj

pytransform3d.transformations.dq_q_conj(dq, unit=True)

Quaternion conjugate of dual quaternion.

For unit dual quaternions that represent transformations, this function is equivalent to the inverse of the corresponding transformation matrix.

There are three different conjugates for dual quaternions. The one that we use here converts (pw, px, py, pz, qw, qx, qy, qz) to (pw, -px, -py, -pz, qw, -qx, -qy, -qz). It is the quaternion conjugate applied to each of the two quaternions.

Parameters:

dqarray-like, shape (8,)

Unit 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:

dq_q_conjugatearray, shape (8,)

Conjugate of dual quaternion: (pw, -px, -py, -pz, qw, -qx, -qy, -qz)

See also

dq_conj

Conjugate of a dual quaternion.