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Quality mesh generation in three dimensions

Authors:

Scott A. Mitchell,

Stephen A. VavasisAuthors Info & Claims

SCG '92: Proceedings of the eighth annual symposium on Computational geometry

Pages 212 - 221

https://doi.org/10.1145/142675.142720

Published: 01 July 1992 Publication History

Abstract

We show how to triangulate a three dimensional polyhedral region with holes. Our triangulation is optimal in the following two senses. First, our triangulation achieves the best possible aspect ratio up to a constant. Second, for any other triangulation of the same region into m triangles with bounded aspect ratio, our triangulation has size n = O(m). Such a triangulation is desired as an initial mesh for a finite element mesh refinement algorithm. Previous three dimensional triangulation schemes either worked only on a restricted class of input, or did not guarantee well-shaped tetrahedra, or were not able to bound the output size. We build on some of the ideas presented in previous work by Bern, Eppstein, and Gilbert, who have shown how to triangulate a two dimensional polyhedral region with holes, with similar quality and optimality bounds.

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Cited By

Pietroni NCampen MSheffer ACherchi GBommes DGao XScateni RLedoux FRemacle JLivesu M(2022)Hex-Mesh Generation and Processing: A SurveyACM Transactions on Graphics10.1145/355492042:2(1-44)Online publication date: 18-Oct-2022
https://dl.acm.org/doi/10.1145/3554920
Pietroni NCampen MSheffer ACherchi GBommes DGao XScateni RLedoux FRemacle JLivesu MJung S(2022)A Course on Hex-Mesh Generation and ProcessingSIGGRAPH Asia 2022 Courses10.1145/3550495.3558207(1-78)Online publication date: 6-Dec-2022
https://dl.acm.org/doi/10.1145/3550495.3558207
Pitzalis LLivesu MCherchi GGobbetti EScateni R(2021)Generalized adaptive refinement for grid-based hexahedral meshingACM Transactions on Graphics10.1145/3478513.348050840:6(1-13)Online publication date: 10-Dec-2021
https://dl.acm.org/doi/10.1145/3478513.3480508
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Index Terms

Quality mesh generation in three dimensions
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations in finite fields
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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Published In

cover image ACM Conferences

SCG '92: Proceedings of the eighth annual symposium on Computational geometry

July 1992

384 pages

ISBN:0897915178

DOI:10.1145/142675

Chairman:
David Avis

Copyright © 1992 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 01 July 1992

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SOCG92

Sponsor:

SOCG92: 8th Annual Symposium on Computational Geometry 1992

June 10 - 12, 1992

Berlin, Germany

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Overall Acceptance Rate 625 of 1,685 submissions, 37%

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Cited By

Pietroni NCampen MSheffer ACherchi GBommes DGao XScateni RLedoux FRemacle JLivesu M(2022)Hex-Mesh Generation and Processing: A SurveyACM Transactions on Graphics10.1145/355492042:2(1-44)Online publication date: 18-Oct-2022
https://dl.acm.org/doi/10.1145/3554920
Pietroni NCampen MSheffer ACherchi GBommes DGao XScateni RLedoux FRemacle JLivesu MJung S(2022)A Course on Hex-Mesh Generation and ProcessingSIGGRAPH Asia 2022 Courses10.1145/3550495.3558207(1-78)Online publication date: 6-Dec-2022
https://dl.acm.org/doi/10.1145/3550495.3558207
Pitzalis LLivesu MCherchi GGobbetti EScateni R(2021)Generalized adaptive refinement for grid-based hexahedral meshingACM Transactions on Graphics10.1145/3478513.348050840:6(1-13)Online publication date: 10-Dec-2021
https://dl.acm.org/doi/10.1145/3478513.3480508
Taramón JMorgan JShi CHasenclever J(2019)Generation of unstructured meshes in 2-D, 3-D, and spherical geometries with embedded high-resolution sub-regionsComputers & Geosciences10.1016/j.cageo.2019.104324133(104324)Online publication date: Dec-2019
https://doi.org/10.1016/j.cageo.2019.104324
Kyng RPeng RSchwieterman RZhang PDiakonikolas IKempe DHenzinger M(2018)Incomplete nested dissectionProceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3188745.3188960(404-417)Online publication date: 20-Jun-2018
https://dl.acm.org/doi/10.1145/3188745.3188960
Ni SZhong ZHuang JWang WGuo X(2018)Field‐Aligned and Lattice‐Guided Tetrahedral MeshingComputer Graphics Forum10.1111/cgf.1349937:5(161-172)Online publication date: 8-Aug-2018
https://doi.org/10.1111/cgf.13499
Rangarajan RKabaria HLew A(2018)An algorithm for triangulating smooth three‐dimensional domains immersed in universal meshesInternational Journal for Numerical Methods in Engineering10.1002/nme.5949117:1(84-117)Online publication date: 30-Sep-2018
https://doi.org/10.1002/nme.5949
Zakasovskaya ETarasov VGlushchenko A(2017)Information security issues in the distributed information measurement system2017 International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM)10.1109/ICIEAM.2017.8076372(1-5)Online publication date: May-2017
https://doi.org/10.1109/ICIEAM.2017.8076372
Teng S(2016)Scalable Algorithms for Data and Network AnalysisFoundations and Trends® in Theoretical Computer Science10.1561/040000005112:1–2(1-274)Online publication date: 1-May-2016
https://dl.acm.org/doi/10.1561/0400000051
Cheng SDey TShewchuk J(2016)Meshing piecewise smooth complexesDelaunay Mesh Generation10.1201/b12987-17(349-384)Online publication date: 19-Apr-2016
https://doi.org/10.1201/b12987-17
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