Generate uniformly distributed rotations.

numint or None, optional

Number of random rotations to generate. If None (default), then a single rotation is generated.

random_state{None, int, numpy.random.Generator,

If seed is None (or np.random), the numpy.random.RandomState singleton is used. If seed is an int, a new RandomState instance is used, seeded with seed. If seed is already a Generator or RandomState instance then that instance is used.

random_rotationRotation instance

Contains a single rotation if num is None. Otherwise contains a stack of num rotations.


This function is optimized for efficiently sampling random rotation matrices in three dimensions. For generating random rotation matrices in higher dimensions, see scipy.stats.special_ortho_group.


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

Sample a single rotation:

>>> R.random().as_euler('zxy', degrees=True)
array([-110.5976185 ,   55.32758512,   76.3289269 ])  # random

Sample a stack of rotations:

>>> R.random(5).as_euler('zxy', degrees=True)
array([[-110.5976185 ,   55.32758512,   76.3289269 ],  # random
       [ -91.59132005,  -14.3629884 ,  -93.91933182],
       [  25.23835501,   45.02035145, -121.67867086],
       [ -51.51414184,  -15.29022692, -172.46870023],
       [ -81.63376847,  -27.39521579,    2.60408416]])