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

source: build-install/usr/lib/python3.14/site-packages/scipy/spatial/transform/_rigid_transform.py:1453

Signature

def __mul__(self, other: RigidTransform | Rotation) → RigidTransform

Summary

Compose this transform with the other.

Extended Summary

If p and q are two transforms, then the composition of 'q followed by p' is equivalent to p * q. In terms of transformation matrices, the composition can be expressed as p.as_matrix() @ q.as_matrix().

In terms of translations and rotations, the composition when applied to a vector v is equivalent to p.translation + p.rotation.apply(q.translation) + (p.rotation * q.rotation).apply(v).

This function supports composition of multiple transforms at a time using broadcasting rules. The resulting shape for two RigidTransform instances p and q is np.broadcast_shapes(p.shape, q.shape).

If other is a Rotation, it is automatically promoted to a RigidTransform with zero translation.

Parameters

other : `RigidTransform` or `Rotation` instance: Transform(s) or rotation(s) to be composed with this one. The shapes must be broadcastable.

Returns

: `RigidTransform` instance: The composed transform.

Examples

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

✓

Compose two transforms:

tf1 = Tf.from_translation([1, 0, 0])
tf2 = Tf.from_translation([0, 1, 0])
tf = tf1 * tf2
tf.translation
tf.single

✓

True

When applied to a vector, the composition of two transforms is applied in right-to-left order.

t1, r1 = [1, 2, 3], R.from_euler('z', 60, degrees=True)
t2, r2 = [0, 1, 0], R.from_euler('x', 30, degrees=True)
tf1 = Tf.from_components(t1, r1)
tf2 = Tf.from_components(t2, r2)
tf = tf1 * tf2

✓

tf.apply([1, 0, 0])
tf1.apply(tf2.apply([1, 0, 0]))

✗

array([0.63397, 3.36603, 3.     ])

When at least one of the transforms is not single, the result is a stack of transforms.

tf1 = Tf.from_translation([1, 0, 0])
tf2 = Tf.from_translation([[0, 2, 0], [0, 0, 3]])
tf = tf1 * tf2
tf.translation
tf.single
len(tf)

✓

Broadcasting rules apply when composing multiple transforms at a time.

tf1 = Tf.from_translation(np.ones((5, 1, 3)))  # Shape (5, 1, 3)
tf2 = Tf.from_translation(np.ones((1, 4, 3)))  # Shape (1, 4, 3)
tf = tf1 * tf2  # Shape (5, 4, 3)
tf.translation.shape

✓

(5, 4, 3)

Aliases

scipy.spatial.transform.RigidTransform.__mul__