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
thetais the angle of rotation (in radians) .
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. This function will always return MRPs corresponding to a rotation of less than or equal to 180 degrees.
- mrpsndarray, shape (3,) or (N, 3)
Shape depends on shape of inputs used for initialization.
New in version 1.6.0.
Shuster, M. D. “A Survery of Attitude Representations”, The Journal of Astronautical Sciences, Vol. 41, No.4, 1993, pp. 475-476
>>> 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)