scipy.spatial.transform.Rotation.

as_mrp#

Rotation.as_mrp()[source]#

Represent as Modified Rodrigues Parameters (MRPs).

MRPs are a 3 dimensional vector co-directional to the axis of rotation and whose magnitude is equal to tan(theta / 4), where theta is the angle of rotation (in radians) [1].

MRPs have a singularity at 360 degrees which can be avoided by ensuring the angle of rotation does not exceed 180 degrees, i.e. switching the direction of the rotation when it is past 180 degrees. This function will always return MRPs corresponding to a rotation of less than or equal to 180 degrees.

Returns:

mrpsndarray, shape (3,) or (N, 3): Shape depends on shape of inputs used for initialization.

Notes

Added in version 1.6.0.

Array API Standard Support

as_mrp 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.

References

[1]

Shuster, M. D. “A Survey of Attitude Representations”, The Journal of Astronautical Sciences, Vol. 41, No.4, 1993, pp. 475-476

Examples

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

Represent a single rotation:

>>> r = R.from_rotvec([0, 0, np.pi])
>>> r.as_mrp()
array([0.        , 0.        , 1.         ])
>>> r.as_mrp().shape
(3,)

Represent a stack with a single rotation:

>>> r = R.from_euler('xyz', [[180, 0, 0]], degrees=True)
>>> r.as_mrp()
array([[1.       , 0.        , 0.         ]])
>>> r.as_mrp().shape
(1, 3)

Represent multiple rotations:

>>> r = R.from_rotvec([[np.pi/2, 0, 0], [0, 0, np.pi/2]])
>>> r.as_mrp()
array([[0.41421356, 0.        , 0.        ],
       [0.        , 0.        , 0.41421356]])
>>> r.as_mrp().shape
(2, 3)