scipy.spatial.transform.RigidTransform.

from_exp_coords

classmethod RigidTransform.from_exp_coords(cls, exp_coords)

Initialize from exponential coordinates of transform.

This implements the exponential map that converts 6-dimensional real vectors to SE(3).

An exponential coordinate vector consists of 6 elements [rx, ry, rz, vx, vy, vz]. The first 3 encode rotation (and form a rotation vector used in Rotation.from_rotvec) and the last 3 encode translation (and form a translation vector for pure translations). The exponential mapping can be expressed as matrix exponential T = exp(tau), where T is a 4x4 matrix representing a rigid transform and tau is a 4x4 matrix formed from the elements of an exponential coordinate vector:

tau = [  0 -rz  ry vx]
      [ rz   0 -rx vy]
      [-ry  rx   0 vz]
      [  0   0   0  1]

Parameters:

exp_coordsarray_like, shape (N, 6) or (6,)

A single exponential coordinate vector or a stack of exponential coordinate vectors. The expected order of components is [rx, ry, rz, vx, vy, vz]. The first 3 components encode rotation and the last 3 encode translation.

Returns:

transformRigidTransform instance

A single transform or a stack of transforms.

Examples

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

Creating from a single 6d vector of exponential coordinates:

>>> tf = Tf.from_exp_coords([
...     -2.01041204, -0.52983629, 0.65773501,
...     0.10386614, 0.05855009, 0.54959179])
>>> tf.as_matrix()
array([[0.76406621, 0.10504613, -0.63652819, -0.10209961],
       [0.59956454, -0.47987325, 0.64050295, 0.40158789],
       [-0.2381705, -0.87102639, -0.42963687, 0.19637636],
       [0., 0., 0., 1.]])
>>> tf.single
True

A vector of zeros represents the identity transform:

>>> tf = Tf.from_exp_coords(np.zeros(6))
>>> tf.as_matrix()
array([[1., 0., 0., 0.],
       [0., 1., 0., 0.],
       [0., 0., 1., 0.],
       [0., 0., 0., 1.]])

The last three numbers encode translation. If the first three numbers are zero, the last three components can be interpreted as the translation:

>>> tf_trans = Tf.from_exp_coords([0, 0, 0, 4.3, -2, 3.4])
>>> tf_trans.translation
array([4.3, -2., 3.4])

The first three numbers encode rotation as a rotation vector:

>>> tf_rot = Tf.from_exp_coords([0.5, 0.3, 0.1, 0, 0, 0])
>>> tf_rot.rotation.as_rotvec()
array([0.5, 0.3, 0.1])

Combining translation and rotation preserves the rotation vector, but changes the last three components as they encode translation and rotation:

>>> (tf_trans * tf_rot).as_exp_coords()
array([0.5, 0.3, 0.1, 3.64305882, -1.25879559, 4.46109265])

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