pytransform3d.transformations.dual_quaternion_double

pytransform3d.transformations.dual_quaternion_double(dq)

Create another dual quaternion that represents the same transformation.

The unit dual quaternions \(\boldsymbol{\sigma} = \boldsymbol{p} + \epsilon \boldsymbol{q}\) and \(-\boldsymbol{\sigma}\) represent exactly the same transformation. The reason for this ambiguity is that the real quaternion \(\boldsymbol{p}\) represents the orientation component, the dual quaternion encodes the translation component as \(\boldsymbol{q} = 0.5 \boldsymbol{t} \boldsymbol{p}\), where \(\boldsymbol{t}\) is a quaternion with the translation in the vector component and the scalar 0, and rotation quaternions have the same ambiguity.

Parameters:

dqarray-like, shape (8,)

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

Returns:

dq_doublearray, shape (8,)

-dq