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

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 $N<10^6$.