weldx.transformations.WXRotation.from_mrp

WXRotation.from_mrp(type cls, mrp)

Initialize from 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 singuarity 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.

Parameters:

mrp (array_like, shape (N, 3) or (3,)) – A single vector or a stack of vectors, where mrp[i] gives the ith set of MRPs.

Returns:

rotation – Object containing the rotations represented by input MRPs.

Return type:

Rotation instance

References

[1]

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

Notes

New in version 1.6.0.

Examples

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

Initialize a single rotation:

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

Initialize multiple rotations in one object:

>>> r = R.from_mrp([
... [0, 0, 1],
... [1, 0, 0]])
>>> r.as_euler('xyz', degrees=True)
array([[0.        , 0.        , 180.      ],
       [180.0     , 0.        , 0.        ]])
>>> r.as_euler('xyz').shape
(2, 3)

It is also possible to have a stack of a single rotation:

>>> r = R.from_mrp([[0, 0, np.pi/2]])
>>> r.as_euler('xyz').shape
(1, 3)