A Weighted Delaunay Triangulation Framework for Merging Triangulations in a Connectivity Oblivious Fashion

Simplicial meshes are useful as discrete approximations of continuous spaces in numerical simulations. In some applications, however, meshes need to be modified over time. Mesh update operations are often expensive and brittle, making the simulations unstable. In this paper we propose a framework fo...

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Published in:Computer graphics forum Vol. 33; no. 6; pp. 18 - 30
Main Authors: Silva, Luis F., Scheidegger, Luiz F., Etiene, Tiago, Comba, João L. D., Nonato, Luis G., Silva, Cláudio T.
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.09.2014
Subjects:
Analysis
Computer graphics
Computer Graphics I.3.5 Computational Geometry and Object Modelling Geometric algorithms languages and systems
Connectivity
merging algorithms
Numerical analysis
regular triangulations
Simulation
Studies
triangulations
weighted Delaunay triangulations
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:Simplicial meshes are useful as discrete approximations of continuous spaces in numerical simulations. In some applications, however, meshes need to be modified over time. Mesh update operations are often expensive and brittle, making the simulations unstable. In this paper we propose a framework for updating simplicial meshes that undergo geometric and topological changes. Instead of explicitly maintaining connectivity information, we keep a collection of weights associated with mesh vertices, using a Weighted Delaunay Triangulation (WDT). These weights implicitly define mesh connectivity and allow direct merging of triangulations. We propose two formulations for computing the weights, and two techniques for merging triangulations, and finally illustrate our results with examples in two and three dimensions. Simplicial meshes are useful as discrete approximations of continuous spaces in numerical simulations. In some applications, however, meshes need to be modified over time. Mesh update operations are often expensive and brittle, making the simulations unstable. In this paper we propose a framework for updating simplicial meshes that undergo geometric and topological changes. Instead of explicitly maintaining connectivity information, we keep a collection of weights associated with mesh vertices, using a Weighted Delaunay Triangulation (WDT). These weights implicitly define mesh connectivity and allow direct merging of triangulations
Bibliography:National Science Foundation - No. CCF-08560; No. CCF-0702817; No. CNS-0751152; No. CNS-1153503; No. IIS-0844572; No. IIS-0904631; No. IIS-0906379; No. IIS-1153728
ark:/67375/WNG-9DVNXL26-H
istex:512BBBAE23C004ABF9FACF10EFAC0CFFD1FD15D5
Department of Energy, FAPESP, CNPq - No. 309483/2011-5; No. 131322/2008-7; No. 491034/2008-3
IBM Faculty Awards and NVIDIA Fellowships
ArticleID:CGF12274
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12274