Article

A linear bound on the complexity of the delaunay triangulation of points on polyhedral surfaces

Authors:

Dominique Attali,

Jean-Daniel BoissonnatAuthors Info & Claims

SMA '02: Proceedings of the seventh ACM symposium on Solid modeling and applications

Pages 139 - 146

https://doi.org/10.1145/566282.566304

Published: 17 June 2002 Publication History

Abstract

Delaunay triangulations and Voronoi diagrams have found numerous applications in surface modeling, surface mesh generation, deformable surface modeling and surface reconstruction. Many algorithms in these applications begin by constructing the three-dimensional Delaunay triangulation of a finite set of points scattered over a surface. Their running-time therefore depends on the complexity of the Delaunay triangulation of such point sets. Although the complexity of the Delaunay triangulation of points may be quadratic in the worst-case, we show in this paper that it is only linear when the points are distributed on a fixed number of well-sampled facets (e.g. the facets of a polyhedron). Our bound is deterministic and the constants are explicitly given.

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Cited By

Chaine RGandoin PRoudet C(2009)Reconstruction Algorithms as a Suitable Basis for Mesh Connectivity CompressionIEEE Transactions on Automation Science and Engineering10.1109/TASE.2009.20213366:3(443-453)Online publication date: Jul-2009
https://doi.org/10.1109/TASE.2009.2021336
Toumpaniaris PSkalkidis IGiakoumaki AKoutsouris D(2009)Volume estimation of non-geometric shape cavity using an array of normal distributed distance sensors on a spherical mount, applicable in the right ventricle2009 9th International Conference on Information Technology and Applications in Biomedicine10.1109/ITAB.2009.5394405(1-4)Online publication date: Nov-2009
https://doi.org/10.1109/ITAB.2009.5394405
Navarra A(2008)3-Dimensional minimum energy broadcasting problemAd Hoc Networks10.1016/j.adhoc.2007.06.0036:5(734-743)Online publication date: 1-Jul-2008
https://dl.acm.org/doi/10.1016/j.adhoc.2007.06.003
Show More Cited By

Index Terms

A linear bound on the complexity of the delaunay triangulation of points on polyhedral surfaces
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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Published In

cover image ACM Conferences

SMA '02: Proceedings of the seventh ACM symposium on Solid modeling and applications

June 2002

424 pages

ISBN:1581135068

DOI:10.1145/566282

Conference Chairs:
Hans-Peter Seidel
Max-Planck-Institut für Informatik, Saarbrücken, Germany
,
Vadim Shapiro
University of Wisconsin, Madison, U.S.A.
,
Program Chairs:
Kunwoo Lee
Seoul National University, Seoul, Korea
,
Nick Patrikalakis
Massachsetts Institute of Technology, Cambridge, U.S.A.

Copyright © 2002 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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New York, NY, United States

Publication History

Published: 17 June 2002

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SM02: ACM Symposium on Solid Modeling and Applications 2002

June 17 - 21, 2002

Saarbrücken, Germany

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SMA '02 Paper Acceptance Rate 43 of 93 submissions, 46%;

Overall Acceptance Rate 86 of 173 submissions, 50%

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Cited By

Chaine RGandoin PRoudet C(2009)Reconstruction Algorithms as a Suitable Basis for Mesh Connectivity CompressionIEEE Transactions on Automation Science and Engineering10.1109/TASE.2009.20213366:3(443-453)Online publication date: Jul-2009
https://doi.org/10.1109/TASE.2009.2021336
Toumpaniaris PSkalkidis IGiakoumaki AKoutsouris D(2009)Volume estimation of non-geometric shape cavity using an array of normal distributed distance sensors on a spherical mount, applicable in the right ventricle2009 9th International Conference on Information Technology and Applications in Biomedicine10.1109/ITAB.2009.5394405(1-4)Online publication date: Nov-2009
https://doi.org/10.1109/ITAB.2009.5394405
Navarra A(2008)3-Dimensional minimum energy broadcasting problemAd Hoc Networks10.1016/j.adhoc.2007.06.0036:5(734-743)Online publication date: 1-Jul-2008
https://dl.acm.org/doi/10.1016/j.adhoc.2007.06.003
Leymarie FKimia B(2007)The Medial Scaffold of 3D Unorganized Point CloudsIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2007.4429:2(313-330)Online publication date: 1-Feb-2007
https://dl.acm.org/doi/10.1109/TPAMI.2007.44
Navarra A(2006)3-D minimum energy broadcastingProceedings of the 13th international conference on Structural Information and Communication Complexity10.1007/11780823_19(240-252)Online publication date: 2-Jul-2006
https://dl.acm.org/doi/10.1007/11780823_19
Erickson J(2005)Dense Point Sets Have Sparse Delaunay Triangulations or "... But Not Too Nasty"Discrete & Computational Geometry10.5555/3115459.311569133:1(83-115)Online publication date: 1-Jan-2005
https://dl.acm.org/doi/10.5555/3115459.3115691
Chazal FSoufflet R(2004)Stability and Finiteness Properties of Medial Axis and SkeletonJournal of Dynamical and Control Systems10.1023/B:JODS.0000024119.38784.ff10:2(149-170)Online publication date: 1-Apr-2004
https://dl.acm.org/doi/10.1023/B%3AJODS.0000024119.38784.ff
Chaine RKobbelt LSchröder PHoppe H(2003)A geometric convection approach of 3-D reconstructionProceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing10.5555/882370.882400(218-229)Online publication date: 23-Jun-2003
https://dl.acm.org/doi/10.5555/882370.882400
Boissonnat JKaravelas M(2003)On the combinatorial complexity of euclidean Voronoi cells and convex hulls of d-dimensional spheresProceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms10.5555/644108.644159(305-312)Online publication date: 12-Jan-2003
https://dl.acm.org/doi/10.5555/644108.644159
Foskey MLin MManocha DTurkiyyah GBrunet PElber GShapiro V(2003)Efficient computation of a simplified medial axisProceedings of the eighth ACM symposium on Solid modeling and applications10.1145/781606.781623(96-107)Online publication date: 16-Jun-2003
https://dl.acm.org/doi/10.1145/781606.781623
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