Well-centered planar triangulation - An iterative approach

Evan Vanderzee, Anil N. Hirani, Damrong Guoy, Edgar Ramos

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

Abstract

We present an iterative algorithm to transform a given planar triangle mesh into a well-centered one by moving the interior vertices while keeping the connectivity fixed. A well-centered planar triangulation is one in which all angles are acute. Our approach is based on minimizing a certain energy that we propose. Well-centered meshes have the advantage of having nice orthogonal dual meshes (the dual Voronoi diagram). This may be useful in scientific computing, for example, in discrete exterior calculus, in covolume method, and in space-time meshing. For some connectivities with no well-centered configurations, we present preprocessing steps that increase the possibility of finding a well-centered configuration. We show the results of applying our energy minimization approach to small and large meshes, with and without holes and gradations. Results are generally good, but in certain cases the method might result in inverted elements.

Original languageEnglish (US)
Title of host publicationProceedings of the 16th International Meshing Roundtable, IMR 2007
Pages121-138
Number of pages18
DOIs
StatePublished - Dec 1 2008
Event16th International Meshing Roundtable, IMR 2007 - Seattle, WA, United States
Duration: Oct 14 2007Oct 17 2007

Publication series

NameProceedings of the 16th International Meshing Roundtable, IMR 2007

Other

Other16th International Meshing Roundtable, IMR 2007
CountryUnited States
CitySeattle, WA
Period10/14/0710/17/07

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Modeling and Simulation

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    Vanderzee, E., Hirani, A. N., Guoy, D., & Ramos, E. (2008). Well-centered planar triangulation - An iterative approach. In Proceedings of the 16th International Meshing Roundtable, IMR 2007 (pp. 121-138). (Proceedings of the 16th International Meshing Roundtable, IMR 2007). https://doi.org/10.1007/978-3-540-75103-8_7