Local conditions for triangulating submanifolds of Euclidean space

J.-D. Boissonnat, R. Dyer, A. Ghosh, A. Lieutier, M. Wintraecken, Discrete & Computational Geometry (2020).


Journal Article | Epub ahead of print | English

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Author
Boissonnat, Jean-Daniel; Dyer, Ramsay; Ghosh, Arijit; Lieutier, Andre; Wintraecken, MathijsIST Austria
Department
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.
Publishing Year
Date Published
2020-08-10
Journal Title
Discrete & Computational Geometry
Acknowledgement
Open access funding provided by the Institute of Science and Technology (IST Austria). Arijit Ghosh is supported by the Ramanujan Fellowship (No. SB/S2/RJN-064/2015), India. 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). The third author is supported by Ramanujan Fellowship (No. SB/S2/RJN-064/2015), India. The fifth author also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.
IST-REx-ID

Cite this

Boissonnat J-D, Dyer R, Ghosh A, Lieutier A, Wintraecken M. Local conditions for triangulating submanifolds of Euclidean space. Discrete & Computational Geometry. 2020. doi:10.1007/s00454-020-00233-9
Boissonnat, J.-D., Dyer, R., Ghosh, A., Lieutier, A., & Wintraecken, M. (2020). Local conditions for triangulating submanifolds of Euclidean space. Discrete & Computational Geometry. https://doi.org/10.1007/s00454-020-00233-9
Boissonnat, Jean-Daniel, Ramsay Dyer, Arijit Ghosh, Andre Lieutier, and Mathijs Wintraecken. “Local Conditions for Triangulating Submanifolds of Euclidean Space.” Discrete & Computational Geometry, 2020. https://doi.org/10.1007/s00454-020-00233-9.
J.-D. Boissonnat, R. Dyer, A. Ghosh, A. Lieutier, and M. Wintraecken, “Local conditions for triangulating submanifolds of Euclidean space,” Discrete & Computational Geometry, 2020.
Boissonnat J-D, Dyer R, Ghosh A, Lieutier A, Wintraecken M. 2020. Local conditions for triangulating submanifolds of Euclidean space. Discrete & Computational Geometry.
Boissonnat, Jean-Daniel, et al. “Local Conditions for Triangulating Submanifolds of Euclidean Space.” Discrete & Computational Geometry, Springer Nature, 2020, doi:10.1007/s00454-020-00233-9.
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