Point sets on the sphere $\mathbb{S}^2$ with small spherical cap discrepancy
Numerical Analysis
2014-02-17 v1
Abstract
In this paper we study the geometric discrepancy of explicit constructions of uniformly distributed points on the two-dimensional unit sphere. We show that the spherical cap discrepancy of random point sets, of spherical digital nets and of spherical Fibonacci lattices converges with order . Such point sets are therefore useful for numerical integration and other computational simulations. The proof uses an area-preserving Lambert map. A detailed analysis of the level curves and sets of the pre-images of spherical caps under this map is given.
Cite
@article{arxiv.1109.3265,
title = {Point sets on the sphere $\mathbb{S}^2$ with small spherical cap discrepancy},
author = {Christoph Aistleitner and Johann Brauchart and Josef Dick},
journal= {arXiv preprint arXiv:1109.3265},
year = {2014}
}