Set-Valued Analysis of Generalized Barycentric Coordinates and Their Geometric Properties
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909122981527552 |
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| author | Difonzo, Fabio V. |
| author_facet | Difonzo, Fabio V. |
| contents | Letting $P$ be a convex polytope in $\mathbb{R}^d$ with $n>d$ vertices, we study geometric and analytical properties of the set of generalized barycentric coordinates relative to any point $p\in P$. We prove that such sets are polytopes in $\mathbb{R}^n$ with at most $n-d-1$ vertices, and provide results about continuity and differentiability for the corresponding set-valued maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_00710 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Set-Valued Analysis of Generalized Barycentric Coordinates and Their Geometric Properties Difonzo, Fabio V. Metric Geometry Letting $P$ be a convex polytope in $\mathbb{R}^d$ with $n>d$ vertices, we study geometric and analytical properties of the set of generalized barycentric coordinates relative to any point $p\in P$. We prove that such sets are polytopes in $\mathbb{R}^n$ with at most $n-d-1$ vertices, and provide results about continuity and differentiability for the corresponding set-valued maps. |
| title | Set-Valued Analysis of Generalized Barycentric Coordinates and Their Geometric Properties |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2306.00710 |