Efficient generation of random rotation matrices in four dimensions
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.
Cite
@article{arxiv.2302.06230,
title = {Efficient generation of random rotation matrices in four dimensions},
author = {Jakob Tómas Bullerjahn and Balázs Fábián and Gerhard Hummer},
journal= {arXiv preprint arXiv:2302.06230},
year = {2023}
}
Comments
9 pages, 2 figures, 1 table