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arXiv · 2306.00710

Set-Valued Analysis of Generalized Barycentric Coordinates and Their Geometric Properties

Fabio V. Difonzo
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Abstract

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.

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Fabio V. Difonzo. 2023-05-05. Set-Valued Analysis of Generalized Barycentric Coordinates and Their Geometric Properties. https://arxiv.org/abs/2306.00710

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