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There are simple and robust refinements (almost) as good as Delaunay

Author

Listed:
  • Márquez, Alberto
  • Moreno-González, Auxiliadora
  • Plaza, Ángel
  • Suárez, José P.

Abstract

A new edge-based partition for triangle meshes is presented, the Seven Triangle Quasi-Delaunay partition (7T-QD). The proposed partition joins together ideas of the Seven Triangle Longest-Edge partition (7T-LE), and the classical criteria for constructing Delaunay meshes. The new partition performs similarly compared to the Delaunay triangulation (7T-D) with the benefit of being more robust and with a cheaper cost in computation. It will be proved that in most of the cases the 7T-QD is equal to the 7T-D. In addition, numerical tests will show that the difference on the minimum angle obtained by the 7T-QD and by the 7T-D is negligible.

Suggested Citation

  • Márquez, Alberto & Moreno-González, Auxiliadora & Plaza, Ángel & Suárez, José P., 2014. "There are simple and robust refinements (almost) as good as Delaunay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 106(C), pages 84-94.
    • Handle: RePEc:eee:matcom:v:106:y:2014:i:c:p:84-94
    DOI: 10.1016/j.matcom.2012.06.001
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    References listed on IDEAS

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    1. Padrón, Miguel A. & Suárez, José P. & Plaza, Ángel, 2007. "Refinement based on longest-edge and self-similar four-triangle partitions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 75(5), pages 251-262.
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    1. Plaza, Ángel & Márquez, Alberto & Moreno-González, Auxiliadora & Suárez, José P., 2009. "Local refinement based on the 7-triangle longest-edge partition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2444-2457.

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