A weighted Delaunay triangulation framework for merging triangulations in a connectivity oblivious fashion

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

Research output: Contribution to journalArticlepeer-review

Abstract

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

Original languageEnglish (US)
Pages (from-to)18-30
Number of pages13
JournalComputer Graphics Forum
Volume33
Issue number6
DOIs
StatePublished - Sep 1 2014

Keywords

  • merging algorithms
  • regular triangulations
  • triangulations
  • weighted Delaunay triangulations

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design

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