Details

This Demonstration provides a fast way to generate observations from a uniform distribution on . It also provides a way to generate uniformly distributed perturbations about the axis, which may be useful for simulations and sampling-based planners.

Reference

[1] J. Arvo, "Fast Random Rotation Matrices," Graphics Gems III, 1991.

Arvo's code results in a rotation of about the world axis, leading to incorrect results when the code is used to sample a perturbation. This Demonstration removes that error by premultiplying Arvo's result by a rotation of about the world axis. This flips the signs of st and ct, which flips the sign of the first two columns of the rotation matrix. This Demonstration also centers the perturbations about zero instead of biasing the result.