Local Criteria for Triangulating General Manifolds

Article Type

Research Article

Publication Title

Discrete and Computational Geometry

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.

First Page

156

Last Page

191

DOI

https://10.1007/s00454-022-00431-7

Publication Date

1-1-2023

Comments

Open Access, Hybrid Gold

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