Partitions of unity and barycentric algebras
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910044303392768 |
|---|---|
| author | Zamojska-Dzienio, Anna |
| author_facet | Zamojska-Dzienio, Anna |
| contents | Barycentric coordinates provide solutions to the problem of expressing an element of a compact convex set as a convex combination of a finite number of extreme points of the set. They have been studied widely within the geometric literature, typically in response to the demands of interpolation, numerical analysis and computer graphics. In this note we bring an algebraic perspective to the problem, based on barycentric algebras. We focus on the discussion of relations between different subclasses of partitions of unity, one arising in the context of barycentric coordinates, based on the tautological map introduced by Guessab. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00937 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partitions of unity and barycentric algebras Zamojska-Dzienio, Anna Metric Geometry Rings and Algebras 51M20, 52A01, 52B99 Barycentric coordinates provide solutions to the problem of expressing an element of a compact convex set as a convex combination of a finite number of extreme points of the set. They have been studied widely within the geometric literature, typically in response to the demands of interpolation, numerical analysis and computer graphics. In this note we bring an algebraic perspective to the problem, based on barycentric algebras. We focus on the discussion of relations between different subclasses of partitions of unity, one arising in the context of barycentric coordinates, based on the tautological map introduced by Guessab. |
| title | Partitions of unity and barycentric algebras |
| topic | Metric Geometry Rings and Algebras 51M20, 52A01, 52B99 |
| url | https://arxiv.org/abs/2501.00937 |