scipy.spatial.transform.RigidTransform.

inv#

RigidTransform.inv()[source]#

Invert this transform.

Composition of a transform with its inverse results in an identity transform.

A rigid transform is a composition of a rotation and a translation, where the rotation is applied first, followed by the translation. So the inverse transform is equivalent to the inverse translation followed by the inverse rotation.

Returns:

RigidTransform instance: The inverse of this transform.

Notes

Array API Standard Support

inv has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	✅
PyTorch	✅	✅
JAX	✅	✅
Dask	⛔	n/a

See Support for the array API standard for more information.

Examples

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

A transform composed with its inverse results in an identity transform:

>>> rng = np.random.default_rng(seed=123)
>>> t = rng.random(3)
>>> r = R.random(rng=rng)
>>> tf = Tf.from_components(t, r)
>>> tf.as_matrix()
array([[-0.45431291,  0.67276178, -0.58394466,  0.68235186],
       [-0.23272031,  0.54310598,  0.80676958,  0.05382102],
       [ 0.85990758,  0.50242162, -0.09017473,  0.22035987],
       [ 0.        ,  0.        ,  0.        ,  1.        ]])

>>> (tf.inv() * tf).as_matrix()
array([[[1., 0., 0., 0.],
        [0., 1., 0., 0.],
        [0., 0., 1., 0.],
        [0., 0., 0., 1.]]])

The inverse rigid transform is the same as the inverse translation followed by the inverse rotation:

>>> t, r = tf.as_components()
>>> r_inv = r.inv()  # inverse rotation
>>> t_inv = -t  # inverse translation
>>> tf_r_inv = Tf.from_rotation(r_inv)
>>> tf_t_inv = Tf.from_translation(t_inv)
>>> np.allclose((tf_r_inv * tf_t_inv).as_matrix(),
...             tf.inv().as_matrix(),
...             atol=1e-12)
True
>>> (tf_r_inv * tf_t_inv * tf).as_matrix()
array([[[1., 0., 0., 0.],
        [0., 1., 0., 0.],
        [0., 0., 1., 0.],
        [0., 0., 0., 1.]]])