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Triangulating a non-convex polytype

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L. PaliosAuthors Info & Claims

SCG '89: Proceedings of the fifth annual symposium on Computational geometry

Pages 393 - 400

https://doi.org/10.1145/73833.73876

Published: 05 June 1989 Publication History

Abstract

This paper is concerned with the problem of partitioning a three-dimensional polytope into a small number of elementary convex parts. The need for such decompositions arises in tool design, computer-aided manufacturing, finite-element methods, and robotics. Our main result is an algorithm for decomposing a polytope with n vertices and r reflex edges into Ο(n+r²) tetrahedra. This bound is asymptotically tight in the worst case. The algorithm is simple and practical. Its running time is Ο(nr + r² log r).

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Cited By

Timalsina AKnepley M(2024)Tetrahedralization of Hexahedral MeshSIAM International Meshing Roundtable 202310.1007/978-3-031-40594-5_11(239-251)Online publication date: 21-Mar-2024
https://doi.org/10.1007/978-3-031-40594-5_11
Rao Lei Liu Wenyu Guo Peng (2007)A coverage algorithm for three-dimensional large-scale sensor network2007 International Symposium on Intelligent Signal Processing and Communication Systems10.1109/ISPACS.2007.4445913(420-423)Online publication date: Dec-2007
https://doi.org/10.1109/ISPACS.2007.4445913
Bajaj CDey T(2005)Robust decompositions of polyhedraFoundations of Software Technology and Theoretical Computer Science10.1007/3-540-52048-1_49(267-279)Online publication date: 1-Jun-2005
https://doi.org/10.1007/3-540-52048-1_49
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Triangulating a non-convex polytype

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cover image ACM Conferences

SCG '89: Proceedings of the fifth annual symposium on Computational geometry

June 1989

401 pages

ISBN:0897913183

DOI:10.1145/73833

Chairman:
Kurt Mehlhorn

Copyright © 1989 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: 05 June 1989

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Cited By

Timalsina AKnepley M(2024)Tetrahedralization of Hexahedral MeshSIAM International Meshing Roundtable 202310.1007/978-3-031-40594-5_11(239-251)Online publication date: 21-Mar-2024
https://doi.org/10.1007/978-3-031-40594-5_11
Rao Lei Liu Wenyu Guo Peng (2007)A coverage algorithm for three-dimensional large-scale sensor network2007 International Symposium on Intelligent Signal Processing and Communication Systems10.1109/ISPACS.2007.4445913(420-423)Online publication date: Dec-2007
https://doi.org/10.1109/ISPACS.2007.4445913
Bajaj CDey T(2005)Robust decompositions of polyhedraFoundations of Software Technology and Theoretical Computer Science10.1007/3-540-52048-1_49(267-279)Online publication date: 1-Jun-2005
https://doi.org/10.1007/3-540-52048-1_49
Alexa M(2002)Recent Advances in Mesh MorphingComputer Graphics Forum10.1111/1467-8659.0057521:2(173-198)Online publication date: 9-Aug-2002
https://doi.org/10.1111/1467-8659.00575
Wu JWu G(1998)Element-partition-based methods for visualization of 3D unstructured grid dataJournal of Computer Science and Technology10.1007/BF0294850013:5(417-425)Online publication date: Oct-1998
https://doi.org/10.1007/BF02948500
Renze KOliver J(1996)Generalized Surface and Volume Decimation for Unstructured Tessellated DomainsProceedings of the 1996 Virtual Reality Annual International Symposium (VRAIS 96)10.5555/832290.836034Online publication date: 30-Mar-1996
https://dl.acm.org/doi/10.5555/832290.836034
Renze KOliver J(1996)Generalized surface and volume decimation for unstructured tessellated domainsProceedings of the IEEE 1996 Virtual Reality Annual International Symposium10.1109/VRAIS.1996.490518(111-121)Online publication date: 1996
https://doi.org/10.1109/VRAIS.1996.490518
Renze KOliver J(1996)Generalized Unstructured DecimationIEEE Computer Graphics and Applications10.1109/38.54406916:6(24-32)Online publication date: 1-Nov-1996
https://dl.acm.org/doi/10.1109/38.544069
Mitchell SVavasis SAvis D(1992)Quality mesh generation in three dimensionsProceedings of the eighth annual symposium on Computational geometry10.1145/142675.142720(212-221)Online publication date: 1-Jul-1992
https://dl.acm.org/doi/10.1145/142675.142720
Kolarov KRoth B(1992)Best estimates for the construction of robots in environments with obstaclesProceedings 1992 IEEE International Conference on Robotics and Automation10.1109/ROBOT.1992.220310(377-382)Online publication date: 1992
https://doi.org/10.1109/ROBOT.1992.220310
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