`scipy.spatial.transform._rigid_transform:RigidTransform.inv`

source: /scipy/spatial/transform/_rigid_transform.py:1680

Signature

def inv(self) → RigidTransform

Summary

Invert this transform.

Extended Summary

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.

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([[-0.45431,  0.67276, -0.58394,  0.68235],
       [-0.23272,  0.54311,  0.80677,  0.05382],
       [ 0.85991,  0.50242, -0.09017,  0.22036],
       [ 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.]])

Aliases

scipy.spatial.transform.RigidTransform.inv