skip to main content
10.1145/1998196.1998253acmconferencesArticle/Chapter ViewAbstractPublication PagessocgConference Proceedingsconference-collections
research-article

Edge flips and deforming surface meshes

Published: 13 June 2011 Publication History

Abstract

We study edge flips in a surface mesh and the maintenance of a deforming surface mesh. If the vertices are dense with respect to the local feature size and the triangles have angles at least a constant, we can flip edges in linear time such that all triangles have almost empty diametric balls. For a planar triangulation with a constant angle lower bound, we can flip it to the Delaunay triangulation in linear time. We combine edge flips and vertex nsertions and deletions in an algorithm to maintain a deforming surface mesh, specified only by a dense sample of n points that move with the surface. Under a reasonable motion model, we can enforce bounded aspect ratios and a small approximation error throughout the deformation. The update takes O(n) time at each time step. Our surface mesh maintenance algorithm also gives a good performance in experiments.

References

[1]
. Amenta and M. Bern.Surface reconstruction by Voronoi filtering. Discrete Comput. Geom., 22 (1999), 481--504.
[2]
. Amenta, S. Choi, T. K. Dey and N. Leekha. A simple algorithm for homeomorphic surface reconstruction. Int. J. Comput.Geom. Appl. 12 (2002), 125--141.
[3]
F. Aurenhammer and R. Klein.Voronoi diagrams.In J. Sack and G. Urrutia, editors, Handbook of Computational Geometry,201--290, Elsevier, 2000.
[4]
D. Baraff and A. Witkin.Large steps in cloth simulation.SIGGRAPH, 1998, 43--54.
[5]
G. Beer, I. Smith and C. Duenser. The Boundary Element Method with Programming,Springer, 2008.
[6]
J.-D. Boissonnat and F. Cazals.Natural coordinates of points on a surface. Comput. Geom. Theory and Appl., 19 (2001), 155--173.
[7]
T.M. Chan. Approximate nearest neighbor queries revisited. Discrete Comput. Geom., 20 (1998), 359--373.
[8]
.-W. Cheng and T. K. Dey. Maintaining Deforming Surface Meshes. Proc. 19th ACM-SIAM Sympos. Discrete Alg., 2008, 112--121.
[9]
.-W. Cheng and T. K. Dey. Delaunay Edge Flips in Dense Surface Triangulations. Proc. 24th Euro. Workshop Comput. Geom., 2008, 1--4.
[10]
. Delingette. Towards realistic soft tissue modeling in medical simulation. Proc. IEEE: Special issue on Surgery Simulation, 1998, 512--523.
[11]
. K. Dey. Curve and surface reconstruction : Algorithms with mathematical analysis. Cambridge University Press, New York, 2006.
[12]
R. Dyer, H. Zhang, and T. Möller. Gabriel meshes and Delaunay edge flips. Proc. Geom. Phys. Model. 2009.
[13]
D. Enright, R. Fedkiw, J. Ferziger, and I. Mitchell. A Hybrid Particle Level Set Method for Improved Interface Capturing. J. Comput. Phys., 183 (2002), 83--116.
[14]
. Funke and E.A. Ramos. Smooth-surface reconstruction in near-linear time. Proc. 13th ACM-SIAM Sympos. Discrete Alg., 2002,781--790.
[15]
O.S. Galaktionov, P.D. Anderson, G.W.M. Peters, and F.N. Van de Vosse. An adaptive front tracking technique for three-dimensional transientflows. Int. J. Numer. Meth. Fl.,32 (2000), 201--217.
[16]
J. Glimm, J.W. Grove, X.L. Li, and D.C. Tan.Robust computational algorithms for dynamic interface tracking in threedimensions. SIAM J. Sci. Comput., 21 (1999), 2240--2256.
[17]
W.S. Hall. The Boundary Element Method,Kluwer Academic Publishers, 1994.
[18]
R.E. Khayat.Three-dimensional boundary element analysis of drop deformation in confined flow for Newtonian and viscoelastic systems. Int. J. Numer. Meth. Fl.,34 (2000), 241--275.
[19]
R.K. Koch, M.H. Gross, F.R. Carls, D.F. von Büren, G. Fankhauser, and Y.I.H. Parish. Simulating facial surgery using finite element methods. SIGGRAPH, 1996, 421--428.
[20]
R.J. LeVeque. High-Resolution Conservative Algorithms for Advection in Incompressible Flow. SIAM J. Numer. Anal., 33 (1996), 627--665.
[21]
T. Liu, D. Shen, and C. Davatzikos.Deformable registration of cortical structures via hybrid volumetric and surface warping. NeuroImage, 22 (2004), 1790--1801.
[22]
G. Tryggvason, B. Bunner, A. Esmaeeli, D. Juric, N. Al-Rawahi, W. Tauber, J. Han, S. Nas, and Y.-J. Jan.A front-tracking method for the computations of multiphase flow. J. Comput. Phys. 169, 2 (2001), 708--759.
[23]
P. Volino and N. Magnenat-Thalmann.Comparing efficiency of integration methods for cloth simulation. Comput. Graphics Int., 2001, 265--272.

Cited By

View all

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences
SoCG '11: Proceedings of the twenty-seventh annual symposium on Computational geometry
June 2011
532 pages
ISBN:9781450306829
DOI:10.1145/1998196
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]

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 13 June 2011

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. deforming surface
  2. delaunay triangulation
  3. edge flip

Qualifiers

  • Research-article

Conference

SoCG '11
SoCG '11: Symposium on Computational Geometry
June 13 - 15, 2011
Paris, France

Acceptance Rates

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

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)6
  • Downloads (Last 6 weeks)0
Reflects downloads up to 22 Feb 2025

Other Metrics

Citations

Cited By

View all

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media