Work

The most uniform distribution of points on the sphere

Year: 2024

Type: article

Abstract: How to distribute a set of points uniformly on a spherical surface is a longstanding problem that still lacks a definite answer. In this work, we introduce a physical measure of uniformity based on the distribution of distances between points, as an alternative to commonly adopted measures based on interaction potentials. We then use this new measure of uniformity to characterize several algorithms available in the literature. We also study the effect of optimizing the position of the points through the minimization of different interaction potentials via a gradient descent procedure. In this way, we can classify different algorithms and interaction potentials to find the one that generates the most uniform distribution of points on the sphere.

Source: PLoS ONE

DOI: 10.1371/journal.pone.0313863

Authors: Luca Maria Del Bono, Flavio Nicoletti, Federico Ricci-Tersenghi

Institutions: Sapienza University of Rome, Istituto di Nanotecnologia, Istituto Nazionale di Fisica Nucleare, Sezione di Roma I

Language: English

Topic: Mathematical Approximation and Integration

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,290

Funders: European Commission, NextGenerationEU