Generating $N$-point spherical configurations with low mesh ratios using spherical area coordinates

TL;DR

This paper introduces a method to generate large, well-distributed $N$-point configurations on spheres with low mesh ratios by extending icosahedral grids using planar barycentric and spherical area coordinates.

Contribution

It extends Caspar-Klug icosahedral point-grids to non-icosahedral nets using planar barycentric coordinates interpreted as spherical area coordinates.

Findings

Generated point sets with lower mesh ratios than previous methods for N<10^6

Method is iterative and parameterized by integer pairs

Applicable to large-scale spherical point configurations

Abstract

This short contribution presents a method for generating $N$-point spherical configurations with low mesh ratios. The method extends Caspar-Klug icosahedral point-grids to non-icosahedral nets through the use of planar barycentric coordinates, which are subsequently interpreted as spherical area coordinates for spherical point sets. The proposed procedure may be applied iteratively and is parameterised by a sequence of integer pairs. For well-chosen input parameters, the proposed method is able to generate point sets with mesh ratios that are lower than previously reported for $N<10^6$.