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A local refinement algorithm for the longest-edge trisection of triangle meshes

Author

Listed:
  • Plaza, Ángel
  • Falcón, Sergio
  • Suárez, José P.
  • Abad, Pilar

Abstract

In this paper we present a local refinement algorithm based on the longest-edge trisection of triangles. Local trisection patterns are used to generate a conforming triangulation, depending on the number of non-conforming nodes per edge presented. We describe the algorithm and provide a study of the efficiency (cost analysis) of the triangulation refinement problem. The algorithm presented, and its associated triangle partition, afford a valid strategy to refine triangular meshes. Some numerical studies are analysed together with examples of applications in the field of mesh refinement.

Suggested Citation

  • Plaza, Ángel & Falcón, Sergio & Suárez, José P. & Abad, Pilar, 2012. "A local refinement algorithm for the longest-edge trisection of triangle meshes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(12), pages 2971-2981.
    • Handle: RePEc:eee:matcom:v:82:y:2012:i:12:p:2971-2981
    DOI: 10.1016/j.matcom.2011.07.003
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    References listed on IDEAS

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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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    Cited by:

    1. Perdomo, Francisco & Plaza, Ángel & Quevedo, Eduardo & Suárez, José P., 2014. "A mathematical proof of how fast the diameters of a triangle mesh tend to zero after repeated trisection," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 106(C), pages 95-108.

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    1. Perdomo, Francisco & Plaza, Ángel & Quevedo, Eduardo & Suárez, José P., 2014. "A mathematical proof of how fast the diameters of a triangle mesh tend to zero after repeated trisection," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 106(C), pages 95-108.

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