article

Dynamic Skin Triangulation

Authors:

H. Edelsbrunner,

J. SullivanAuthors Info & Claims

Discrete & Computational Geometry, Volume 25, Issue 4

Pages 525 - 568

https://doi.org/10.1007/s00454-001-0007-1

Published: 01 April 2001 Publication History

Abstract

This paper describes an algorithm for maintaining an approximating triangulation of a deforming surface in R ³ . The surface is the envelope of an infinite family of spheres defined and controlled by a finite collection of weighted points. The triangulation adapts dynamically to changing shape, curvature, and topology of the surface.

References

[1]

H. I. Aaronson, ed. Lectures on the Theory of Phase Transformation. American Institute of Mining, Metallurgical and Petroleum Engineer, New York, 1975.

[2]

P. S. Alexandrov. Combinatorial Topology. Dover, New York, 1956.

[3]

N. Amenta and M. Bern. Surface reconstruction by Voronoi filtering. Discrete Comput. Geom. 22 (1999), 481-504.

[4]

H.-L. Cheng, H. Edelsbrunner, and P. Fu. Shape space from deformation. In Proc. 6th Pacific Conf. Comput. Graphics Appl., Singapore, 1998, pp. 104-113.

[5]

T. E. Creighton. Proteins. Structures and Molecular Principles. Freeman, New York, 1984.

[6]

C. J. A. Delfinado and H. Edelsbrunner. An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere. Comput. Aided Geom. Design 12 (1995), 771-784.

Digital Library

[7]

H. Edelsbrunner. The union of balls and its dual shape. Discrete Comput. Geom. 13 (1995), 415-440.

Digital Library

[8]

H. Edelsbrunner. Deformable smooth surface design. Discrete Comput. Geom. 21 (1999), 87-115.

[9]

H. Edelsbrunner and E. P. Mücke. Three-dimensional alpha shapes. ACM Trans. Graph. 13 (1994), 43-72.

Digital Library

[10]

H. Edelsbrunner and N. R. Shah. Triangulating topological spaces. Internat. J. Comput. Geom. Appl. 7 (1997), 365-378.

[11]

M. A. Facello. Geometric techniques for molecular shape analysis. Ph.D. thesis, Report UIUCDCS-R-96- 1967, Dept. Comput. Sci., Univ. Illinois, Urbana, Illinois, 1996.

[12]

A. Gray. Modern Differential Geometry of Curves and Surfaces. CRC Press, Boca Raton, Florida, 1993.

[13]

L. Guibas and J. Stolfi. Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams. ACM Trans. Graph. 4 (1985), 74-123.

Digital Library

[14]

J. Milnor. Morse Theory. Princeton University Press, Princeton, New Jersey, 1963.

[15]

T. E. Morthland, P. E. Byrne, D. A. Tortorelli, and J. A. Dantzig. Optimal riser design for metal castings. Metall. Material Trans. 26B (1995), 871-885.

[16]

D. Pedoe. Geometry: a Comprehensive Course. Dover, New York, 1988.

[17]

N. Provatas, N. Goldenfeld, and J. A. Dantzig. Adaptive grid methods in solidification microstructure modeling. Phys. Rev. Lett. 80 (1998), 3308-3311.

Cited By

Cisneros Ramos AKilian MAikyn APottmann HMüller C(2024)Approximation by Meshes with Spherical FacesACM Transactions on Graphics10.1145/368794243:6(1-18)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687942
Kilian MCisneros AMüller CPottmann H(2023)Meshes with Spherical FacesACM Transactions on Graphics10.1145/361834542:6(1-19)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618345
Boissonnat JKachanovich SWintraecken M(2021)Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s MethodDiscrete & Computational Geometry10.1007/s00454-020-00250-866:1(386-434)Online publication date: 1-Jul-2021
https://dl.acm.org/doi/10.1007/s00454-020-00250-8
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Dynamic Skin Triangulation
1. Computing methodologies
  1. Computer graphics
2. Theory of computation
  1. Randomness, geometry and discrete structures

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Published In

cover image Discrete & Computational Geometry

Discrete & Computational Geometry Volume 25, Issue 4

April 2001

133 pages

ISSN:0179-5376

Issue’s Table of Contents

Copyright © Copyright © 2001 Springer-Verlag New York Inc.

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 April 2001

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Cited By

Cisneros Ramos AKilian MAikyn APottmann HMüller C(2024)Approximation by Meshes with Spherical FacesACM Transactions on Graphics10.1145/368794243:6(1-18)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687942
Kilian MCisneros AMüller CPottmann H(2023)Meshes with Spherical FacesACM Transactions on Graphics10.1145/361834542:6(1-19)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618345
Boissonnat JKachanovich SWintraecken M(2021)Triangulating Submanifolds: An Elementary and Quantified Version of Whitney’s MethodDiscrete & Computational Geometry10.1007/s00454-020-00250-866:1(386-434)Online publication date: 1-Jul-2021
https://dl.acm.org/doi/10.1007/s00454-020-00250-8
(2015)Simple and branched skins of systems of circles and convex shapesGraphical Models10.1016/j.gmod.2014.12.00178:C(1-9)Online publication date: 1-Mar-2015
https://dl.acm.org/doi/10.1016/j.gmod.2014.12.001
Yan KCheng H(2012)On Simplifying Deformation of Smooth Manifolds Defined by Large Weighted Point SetsRevised Selected Papers of the Thailand-Japan Joint Conference on Computational Geometry and Graphs - Volume 829610.1007/978-3-642-45281-9_15(150-161)Online publication date: 6-Dec-2012
https://dl.acm.org/doi/10.1007/978-3-642-45281-9_15
Wang BEdelsbrunner HMorozov D(2011)Computing elevation maxima by searching the gauss sphereACM Journal of Experimental Algorithmics10.1145/1963190.197037516(2.1-2.13)Online publication date: 27-Jul-2011
https://dl.acm.org/doi/10.1145/1963190.1970375
Jiao XColombi ANi XHart J(2010)Anisotropic mesh adaptation for evolving triangulated surfacesEngineering with Computers10.5555/3225288.322557926:4(363-376)Online publication date: 1-Aug-2010
https://dl.acm.org/doi/10.5555/3225288.3225579
Dey TRay T(2010)Polygonal surface remeshing with Delaunay refinementEngineering with Computers10.5555/3225282.322553726:3(289-301)Online publication date: 1-Jun-2010
https://dl.acm.org/doi/10.5555/3225282.3225537
Shi XKoehl PWyvill BMagnenat-Thalmann NWyvill B(2009)Adaptive surface meshes coarsening with guaranteed quality and topologyProceedings of the 2009 Computer Graphics International Conference10.1145/1629739.1629746(53-61)Online publication date: 26-May-2009
https://dl.acm.org/doi/10.1145/1629739.1629746
Cheng HShi X(2009)Quality mesh generation for molecular skin surfaces using restricted union of ballsComputational Geometry: Theory and Applications10.1016/j.comgeo.2008.10.00142:3(196-206)Online publication date: 1-Apr-2009
https://dl.acm.org/doi/10.1016/j.comgeo.2008.10.001
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