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bundles / scipy latest / scipy / spatial / transform / _rotation / Rotation / as_quat

function

scipy.spatial.transform._rotation:Rotation.as_quat

source: /scipy/spatial/transform/_rotation.py :961

Signature

def   as_quat ( self ,  canonical : bool = False ,  * ,  scalar_first : bool = False )  →  Array

Summary

Represent as quaternions.

Extended Summary

Rotations in 3 dimensions can be represented using unit norm quaternions [1].

The 4 components of a quaternion are divided into a scalar part w and a vector part (x, y, z) and can be expressed from the angle theta and the axis n of a rotation as follows 

w = cos(theta / 2)
x = sin(theta / 2) * n_x
y = sin(theta / 2) * n_y
z = sin(theta / 2) * n_z

There are 2 conventions to order the components in a quaternion:

  • scalar-first order -- (w, x, y, z)

  • scalar-last order -- (x, y, z, w)

The choice is controlled by scalar_first argument. By default, it is False and the scalar-last order is used.

The mapping from quaternions to rotations is two-to-one, i.e. quaternions q and -q, where -q simply reverses the sign of each component, represent the same spatial rotation.

Parameters

canonical : `bool`, default False

Whether to map the redundant double cover of rotation space to a unique "canonical" single cover. If True, then the quaternion is chosen from {q, -q} such that the w term is positive. If the w term is 0, then the quaternion is chosen such that the first nonzero term of the x, y, and z terms is positive.

scalar_first : bool, optional

Whether the scalar component goes first or last. Default is False, i.e. the scalar-last order is used.

Returns

quat : `numpy.ndarray`, shape (..., 4)

Shape depends on shape of inputs used for initialization.

Notes

Array API Standard Support

as_quat 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 dev-arrayapi for more information.

Examples

from scipy.spatial.transform import Rotation as R
import numpy as np
✓
A rotation can be represented as a quaternion with either scalar-last (default) or scalar-first component order. This is shown for a single rotation: 
r = R.from_matrix(np.eye(3))
r.as_quat()
r.as_quat(scalar_first=True)
✓
The resulting shape of the quaternion is always the shape of the Rotation object with an added last dimension of size 4. E.g. when the `Rotation` object contains an N-dimensional array (N, M, K) of rotations, the result will be a 4-dimensional array: 
r = R.from_rotvec(np.ones((2, 3, 4, 3)))
r.as_quat().shape
✓
Quaternions can be mapped from a redundant double cover of the rotation space to a canonical representation with a positive w term. 
r = R.from_quat([0, 0, 0, -1])
✓
r.as_quat()
r.as_quat(canonical=True)
✗

Aliases

  • scipy.spatial.transform.Rotation.as_quat

Referenced by

This package