scipy.spatial.transform.RigidTransform.

as_components#

RigidTransform.as_components(self)#

Return the translation and rotation components of the transform, where the rotation is applied first, followed by the translation.

4x4 rigid transformation matrices are of the form:

[R | t] [0 | 1]

Where R is a 3x3 orthonormal rotation matrix and t is a 3x1 translation vector [tx, ty, tz]. This function returns the rotation corresponding to this rotation matrix r = Rotation.from_matrix(R) and the translation vector t.

Take a transform tf and a vector v. When applying the transform to the vector, the result is the same as if the transform was applied to the vector in the following way: tf.apply(v) == translation + rotation.apply(v)

Returns:

translationnumpy.ndarray, shape (N, 3) or (3,): The translation of the transform.
rotationRotation instance: The rotation of the transform.

Examples

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

Recover the rotation and translation from a transform:

>>> t = np.array([2, 3, 4])
>>> r = R.from_matrix([[0, 0, 1],
...                    [1, 0, 0],
...                    [0, 1, 0]])
>>> tf = Tf.from_components(t, r)
>>> tf_t, tf_r = tf.as_components()
>>> tf_t
array([2., 3., 4.])
>>> tf_r.as_matrix()
array([[0., 0., 1.],
       [1., 0., 0.],
       [0., 1., 0.]])

The transform applied to a vector is equivalent to the rotation applied to the vector followed by the translation:

>>> r.apply([1, 0, 0])
array([0., 1., 0.])
>>> t + r.apply([1, 0, 0])
array([2., 4., 4.])
>>> tf.apply([1, 0, 0])
array([2., 4., 4.])