Connectivity oblivious merging of triangulations

Luis F. Silva, Luiz F. Scheidegger, Tiago Etiene, João L D Comba, Luis G. Nonato, Cláudio T. Silva

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Simplicial meshes are extremely 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, which tends to make the numerical simulations unstable. In this paper we propose an alternative technique for updating simplicial meshes that undergo geometric and topological changes. We exploit the property that a Weighted Delaunay Triangulation (WDT) can be used to implicitly define the connectivity of a mesh. Instead of explicitly maintaining connectivity information, we simply keep a collection of weights associated with each vertex. This approach allows for a simple way to merge triangulations, which we illustrate with examples in 2D and 3D.

Original languageEnglish (US)
Title of host publicationProceedings - 25th SIBGRAPI
Subtitle of host publicationConference on Graphics, Patterns and Images, SIBGRAPI 2012
Pages118-125
Number of pages8
DOIs
StatePublished - Dec 1 2012
Event25th Conference on Graphics, Patterns and Images, SIBGRAPI 2012 - Ouro Preto, Brazil
Duration: Aug 22 2012Aug 25 2012

Publication series

NameBrazilian Symposium of Computer Graphic and Image Processing
ISSN (Print)1530-1834

Other

Other25th Conference on Graphics, Patterns and Images, SIBGRAPI 2012
CountryBrazil
CityOuro Preto
Period8/22/128/25/12

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Keywords

  • Power diagram
  • Triangulations
  • Weighted Delaunay

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Signal Processing
  • Software

Cite this

Silva, L. F., Scheidegger, L. F., Etiene, T., Comba, J. L. D., Nonato, L. G., & Silva, C. T. (2012). Connectivity oblivious merging of triangulations. In Proceedings - 25th SIBGRAPI: Conference on Graphics, Patterns and Images, SIBGRAPI 2012 (pp. 118-125). [6382747] (Brazilian Symposium of Computer Graphic and Image Processing). https://doi.org/10.1109/SIBGRAPI.2012.25