WOLFRAM NOTEBOOK

WOLFRAM|DEMONSTRATIONS PROJECT

Sampling a Uniformly Random Rotation

number of sampled rotations

100

generate random

rotations

perturbations

axis rotation

axis deflection

The orientation of a sphere is an element of

SO(3)

and can be represented by three Euler angles. However, uniformly sampling three Euler angles does not result in a uniform sampling of

SO(3)

. To generate a uniformly distributed random rotation in

SO(3)

, first perform a random rotation about the

axis, then rotate the

axis to a random position on the sphere.

We can use this same method to generate uniformly distributed perturbations in

SO(3)

by scaling the

axis rotation and deflection by a number less than 1.

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.

I understand and wish to continue anyway »