Local criteria for triangulating general manifolds

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Journal Article | Published | English

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Author
Boissonnat, Jean-Daniel; Dyer, Ramsay; Ghosh, Arijit; Wintraecken, MathijsISTA
Department
Abstract
We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex A, and a map H from the underlying space of A to M, our criteria are presented in local coordinate charts for M, and ensure that H is a homeomorphism. These criteria do not require a differentiable structure, or even an explicit metric on M. No Delaunay property of A is assumed. The result provides a triangulation guarantee for algorithms that construct a simplicial complex by working in local coordinate patches. Because the criteria are easily verified in such a setting, they are expected to be of general use.
Publishing Year
Date Published
2023-01-01
Journal Title
Discrete & Computational Geometry
Volume
69
Page
156-191
ISSN
eISSN
IST-REx-ID

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