as_dual_quat#

RigidTransform.as_dual_quat(self, *, scalar_first=False)#

Return the dual quaternion representation of the transform.

Unit dual quaternions encode orientation in a real unit quaternion and translation in a dual quaternion. There is a double cover, i.e., the unit dual quaternions q and -q represent the same transform.

Parameters:

scalar_firstbool, optional

Whether the scalar component goes first or last in the two individual quaternions that represent the real and the dual part. Default is False, i.e. the scalar-last order is used.

Returns:

dual_quatnumpy.ndarray, shape (N, 8) or (8,)

A single unit dual quaternion vector or a stack of unit dual quaternion vectors. The real part is stored in the first four components and the dual part in the last four components.

Examples

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>>> from scipy.spatial.transform import RigidTransform as Tf
>>> import numpy as np

Get identity dual quaternion (we use scalar-last by default):

>>> Tf.identity().as_dual_quat()
array([0., 0., 0., 1., 0., 0., 0., 0.])

When we want to use the scalar-first convention, we use the argument:

>>> Tf.identity().as_dual_quat(scalar_first=True)
array([1., 0., 0., 0., 0., 0., 0., 0.])

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