Local Conditions for Triangulating Submanifolds of Euclidean Space

Authors

Jean Daniel Boissonnat, Université Côte d'Azur
Ramsay Dyer, Université Côte d'Azur
Arijit Ghosh, Indian Statistical Institute, Kolkata
Andre Lieutier, Dassault Systemes
Mathijs Wintraecken, Institute of Science and Technology Austria (ISTA)

Article Type

Research Article

Publication Title

Discrete and Computational Geometry

Abstract

We consider the following setting: suppose that we are given a manifold M in Rd with positive reach. Moreover assume that we have an embedded simplical complex A without boundary, whose vertex set lies on the manifold, is sufficiently dense and such that all simplices in A have sufficient quality. We prove that if, locally, interiors of the projection of the simplices onto the tangent space do not intersect, then A is a triangulation of the manifold, that is, they are homeomorphic.

First Page

666

Last Page

686

DOI

10.1007/s00454-020-00233-9

Publication Date

9-1-2021

Comments

Open Access, Hybrid Gold, Green

Recommended Citation

Boissonnat, Jean Daniel; Dyer, Ramsay; Ghosh, Arijit; Lieutier, Andre; and Wintraecken, Mathijs, "Local Conditions for Triangulating Submanifolds of Euclidean Space" (2021). Journal Articles. 1835.
https://digitalcommons.isical.ac.in/journal-articles/1835