Embedded Delaunay triangulations for point clouds of surfaces in $\mathbb {R}^3$
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- by Franco Vargas Pallete
- Proc. Amer. Math. Soc. 148 (2020), 5457-5467
- DOI: https://doi.org/10.1090/proc/15175
- Published electronically: September 4, 2020
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Abstract:
In the following article we discuss Delaunay triangulations for a point cloud on an embedded surface in $\mathbb {R}^3$. We give sufficient conditions on the point cloud to show that the diagonal switch algorithm finds an embedded Delaunay triangulation.References
- Ramsay Dyer, Self-delaunay meshes for surfaces, 2010, Thesis.
- Xianfeng David Gu, Feng Luo, Jian Sun, and Tianqi Wu, A discrete uniformization theorem for polyhedral surfaces, J. Differential Geom. 109 (2018), no. 2, 223–256. MR 3807319, DOI 10.4310/jdg/1527040872
- Xianfeng David Gu, Feng Luo, Jian Sun, and Tianqi Wu, A discrete uniformization theorem for polyhedral surfaces, J. Differential Geom. 109 (2018), no. 2, 223–256. MR 3807319, DOI 10.4310/jdg/1527040872
- P. Koehl and J. Hass, Automatic alignment of genus-zero surfaces, IEEE Trans. Pattern Anal. Mach. Intell. 36 (2014), 466–478.
- Feng Luo, Combinatorial Yamabe flow on surfaces, Commun. Contemp. Math. 6 (2004), no. 5, 765–780. MR 2100762, DOI 10.1142/S0219199704001501
- Howard Masur and John Smillie, Hausdorff dimension of sets of nonergodic measured foliations, Ann. of Math. (2) 134 (1991), no. 3, 455–543. MR 1135877, DOI 10.2307/2944356
- Robert J. Renka, Two simple methods for improving a triangle mesh surface, Computer Graphics Forum 35 (2016), no. 6, 46–58.
- Igor Rivin, Euclidean structures on simplicial surfaces and hyperbolic volume, Ann. of Math. (2) 139 (1994), no. 3, 553–580. MR 1283870, DOI 10.2307/2118572
Bibliographic Information
- Franco Vargas Pallete
- Affiliation: School of Mathematics, Institute for Advanced Study, 114 MOS, 1 Einstein Drive, Princeton, New Jersey 08540
- Address at time of publication: Department of Mathematics, Yale University, New Haven, Connecticut 06520
- MR Author ID: 1346657
- ORCID: 0000-0003-4180-1018
- Email: franco.vargaspallete@yale.edu
- Received by editor(s): July 24, 2019
- Received by editor(s) in revised form: February 17, 2020, and May 12, 2020
- Published electronically: September 4, 2020
- Additional Notes: This research was partially supported by NSF grant DMS-1406301 and by the Minerva Research Foundation
- Communicated by: Ken Bromberg
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 5457-5467
- MSC (2010): Primary 57Q15, 52C99
- DOI: https://doi.org/10.1090/proc/15175
- MathSciNet review: 4163856