Local Criteria for Triangulating General Manifolds

Authors

Jean Daniel Boissonnat, Centre Inria Sophia Antipolis - Méditerranée
Ramsay Dyer, Centre Inria Sophia Antipolis - Méditerranée
Arijit Ghosh, Indian Statistical Institute, Kolkata
Mathijs Wintraecken, Institute of Science and Technology Austria (ISTA)

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

Recommended Citation

Boissonnat, Jean Daniel; Dyer, Ramsay; Ghosh, Arijit; and Wintraecken, Mathijs, "Local Criteria for Triangulating General Manifolds" (2023). Journal Articles. 4015.
https://digitalcommons.isical.ac.in/journal-articles/4015