Uniformly sample rotations.

[wang-chen]

Problem to solve

• Sampling uniformly over the space of rotations is often needed for robotic planning.
• Thus possible interfaces can be rand_SO3, rand_SE3, rand_Sim3, rand_RxSO3.
• The Haar distribution may be useful for this purpose.

[sihengt]

Am implementing rand_SO3 based on the following resources:
https://github.com/scipy/scipy/blob/v1.8.1/scipy/stats/_multivariate.py#L3271-L3387
https://github.com/mdp-toolkit/mdp-toolkit/blob/300d288d75ac8495f7f4a0ef40cb71d4ff58a311/mdp/utils/routines.py#L178-L203

Algorithm is based on drawing a random variable from the Haar distribution, the only known uniform distribution on SO(n). It is described in the paper by Stewart, G.W., “The efficient generation of random orthogonal matrices with an application to condition estimators”.

[neanea04]

Hello, Please Look into this simple rotation sampling algorithm from cvpr 2022. https://marcalexa.github.io/superfibonacci/