Local criteria for triangulating general manifolds

Boissonnat, Jean-Daniel; Dyer, Ramsay; Ghosh, Arijit; Wintraecken, Mathijs

Local criteria for triangulating general manifolds

Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. 2023. Local criteria for triangulating general manifolds. Discrete & Computational Geometry. 69, 156–191.

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DOI

10.1007/s00454-022-00431-7

Journal Article | Published | English

Scopus indexed

Author

Boissonnat, Jean-Daniel; Dyer, Ramsay; Ghosh, Arijit; Wintraecken, Mathijs^ISTA

Corresponding author has ISTA affiliation

Department

Edelsbrunner Group

Grant

ISTplus - Postdoctoral Fellowships
Learning and triangulating manifolds via collapses

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.

Keywords

Computational Theory and Mathematics; Discrete Mathematics and Combinatorics; Geometry and Topology; Theoretical Computer Science

Publishing Year

2023

Date Published

2023-01-01

Journal Title

Discrete & Computational Geometry

Publisher

Springer Nature

Acknowledgement

This work has been funded by the European Research Council under the European Union’s ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding in Higher Dimensions). Arijit Ghosh is supported by Ramanujan Fellowship (No. SB/S2/RJN-064/2015). Part of this work was done when Arijit Ghosh was a Researcher at Max-Planck-Institute for Informatics, Germany, supported by the IndoGerman Max Planck Center for Computer Science (IMPECS). Mathijs Wintraecken also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411 and the Austrian Science Fund (FWF): M-3073. A part of the results described in this paper were presented at SoCG 2018 and in [3]. Open access funding provided by the Austrian Science Fund (FWF).

Volume

Page

156-191

ISSN

0179-5376

eISSN

1432-0444

IST-REx-ID

12287

Cite this

Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. Local criteria for triangulating general manifolds. Discrete & Computational Geometry. 2023;69:156-191. doi:10.1007/s00454-022-00431-7

Boissonnat, J.-D., Dyer, R., Ghosh, A., & Wintraecken, M. (2023). Local criteria for triangulating general manifolds. Discrete & Computational Geometry. Springer Nature. https://doi.org/10.1007/s00454-022-00431-7

Boissonnat, Jean-Daniel, Ramsay Dyer, Arijit Ghosh, and Mathijs Wintraecken. “Local Criteria for Triangulating General Manifolds.” Discrete & Computational Geometry. Springer Nature, 2023. https://doi.org/10.1007/s00454-022-00431-7.

J.-D. Boissonnat, R. Dyer, A. Ghosh, and M. Wintraecken, “Local criteria for triangulating general manifolds,” Discrete & Computational Geometry, vol. 69. Springer Nature, pp. 156–191, 2023.

Boissonnat J-D, Dyer R, Ghosh A, Wintraecken M. 2023. Local criteria for triangulating general manifolds. Discrete & Computational Geometry. 69, 156–191.

Boissonnat, Jean-Daniel, et al. “Local Criteria for Triangulating General Manifolds.” Discrete & Computational Geometry, vol. 69, Springer Nature, 2023, pp. 156–91, doi:10.1007/s00454-022-00431-7.

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