There are many ways to generate a set of nodes on the sphere for use in a
variety of problems in numerical analysis. We present a survey of quickly
generated point sets on $S^2$, examine their equidistribution
properties, separation, covering, and mesh ratio constants and present a new
point set, equal area icosahedral points, with low mesh ratio. We analyze
numerically the leading order asymptotics for the Riesz and logarithmic
potential energy for these configurations with total points $N<50,000$ and
present some new conjectures.
Description
[1607.04590] A Comparison of Popular Point Configurations on $\mathbb{S}^2$
%0 Generic
%1 hardin2016comparison
%A Hardin, D. P.
%A Michaels, T. J.
%A Saff, E. B.
%D 2016
%K 2016 arxiv geometry paper point-cloud
%T A Comparison of Popular Point Configurations on $S^2$
%U http://arxiv.org/abs/1607.04590
%X There are many ways to generate a set of nodes on the sphere for use in a
variety of problems in numerical analysis. We present a survey of quickly
generated point sets on $S^2$, examine their equidistribution
properties, separation, covering, and mesh ratio constants and present a new
point set, equal area icosahedral points, with low mesh ratio. We analyze
numerically the leading order asymptotics for the Riesz and logarithmic
potential energy for these configurations with total points $N<50,000$ and
present some new conjectures.
@misc{hardin2016comparison,
abstract = {There are many ways to generate a set of nodes on the sphere for use in a
variety of problems in numerical analysis. We present a survey of quickly
generated point sets on $\mathbb{S}^2$, examine their equidistribution
properties, separation, covering, and mesh ratio constants and present a new
point set, equal area icosahedral points, with low mesh ratio. We analyze
numerically the leading order asymptotics for the Riesz and logarithmic
potential energy for these configurations with total points $N<50,000$ and
present some new conjectures.},
added-at = {2018-08-24T19:50:17.000+0200},
author = {Hardin, D. P. and Michaels, T. J. and Saff, E. B.},
biburl = {https://www.bibsonomy.org/bibtex/2cb8972e6e3608abc2c32772efe8b9723/analyst},
description = {[1607.04590] A Comparison of Popular Point Configurations on $\mathbb{S}^2$},
interhash = {de60c15cc958a18b2c002287deceda94},
intrahash = {cb8972e6e3608abc2c32772efe8b9723},
keywords = {2016 arxiv geometry paper point-cloud},
note = {cite arxiv:1607.04590Comment: 48 pages, 29 figures},
timestamp = {2018-08-24T19:50:17.000+0200},
title = {A Comparison of Popular Point Configurations on $\mathbb{S}^2$},
url = {http://arxiv.org/abs/1607.04590},
year = 2016
}