The most uniform distribution of points on the sphere.
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...
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2024-01-01
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| Series: | PLoS ONE |
| Online Access: | https://doi.org/10.1371/journal.pone.0313863 |
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| _version_ | 1841555533804339200 |
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| author | Luca Maria Del Bono Flavio Nicoletti Federico Ricci-Tersenghi |
| author_facet | Luca Maria Del Bono Flavio Nicoletti Federico Ricci-Tersenghi |
| author_sort | Luca Maria Del Bono |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c6806dccc47b4ac6b774784d45458c5a |
| institution | Kabale University |
| issn | 1932-6203 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj-art-c6806dccc47b4ac6b774784d45458c5a2025-01-08T05:32:25ZengPublic Library of Science (PLoS)PLoS ONE1932-62032024-01-011912e031386310.1371/journal.pone.0313863The most uniform distribution of points on the sphere.Luca Maria Del BonoFlavio NicolettiFederico Ricci-TersenghiHow 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.https://doi.org/10.1371/journal.pone.0313863 |
| spellingShingle | Luca Maria Del Bono Flavio Nicoletti Federico Ricci-Tersenghi The most uniform distribution of points on the sphere. PLoS ONE |
| title | The most uniform distribution of points on the sphere. |
| title_full | The most uniform distribution of points on the sphere. |
| title_fullStr | The most uniform distribution of points on the sphere. |
| title_full_unstemmed | The most uniform distribution of points on the sphere. |
| title_short | The most uniform distribution of points on the sphere. |
| title_sort | most uniform distribution of points on the sphere |
| url | https://doi.org/10.1371/journal.pone.0313863 |
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