Efficient generation of random rotation matrices in four dimensions

TL;DR

This paper introduces an efficient algorithm for generating unbiased random rotation matrices in four dimensions, enabling uniform sampling of the SO(4) group for applications in Monte Carlo methods, molecular dynamics, robotics, and computer vision.

Contribution

The authors present a novel, efficient algorithm for generating random 4D rotation matrices covering arbitrary angles, ensuring unbiased and uniform sampling of SO(4).

Findings

Matrices enable uniform sampling over SO(4).

Algorithm improves efficiency in 4D rotation sampling.

Applicable to molecular dynamics, robotics, and computer vision.

Abstract

Markov-chain Monte Carlo algorithms rely on trial moves that are either rejected or accepted based on certain criteria. Here, we provide an efficient algorithm to generate random rotation matrices in four dimensions (4D) covering an arbitrary pre-defined range of rotation angles. The matrices can be combined with Monte Carlo methods for the efficient sampling of the SO(4) group of 4D rotations. The matrices are unbiased and constructed such that repeated rotations result in uniform sampling over SO(4). 4D rotations can be used to optimize the mass partitioning for stable time integration in coarse-grained molecular dynamics simulations and should find further applications in the fields of robotics and computer vision.