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Convergence of the R1+ tetrahedra family in iterative Longest Edge Bisection

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  • Padrón, Miguel A.
  • Trujillo-Pino, Agustín
  • Suárez, Jose Pablo

Abstract

We study the similarity classes appearing in the iterative Longest Edge Bisection (LEB), of an improved family of nearly equilateral tetrahedra. We focus here on the R1+ family as a generalization of the family mentioned by Adler in Adler (1983). We characterize the finite convergence of similarity classes using the Similarity Classes Longest Edge Bisection (SCLEB) algorithm. We prove that below the bound of 37 similarity classes, a number n≤37 classes are generated where n∈{4,8,9,13,21,37}. Using a tetrahedra sextuple representation and SCLEB, all the generated classes are clearly delimited, thereby improving the results by Adler and others.

Suggested Citation

  • Padrón, Miguel A. & Trujillo-Pino, Agustín & Suárez, Jose Pablo, 2025. "Convergence of the R1+ tetrahedra family in iterative Longest Edge Bisection," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 238(C), pages 555-567.
    • Handle: RePEc:eee:matcom:v:238:y:2025:i:c:p:555-567
    DOI: 10.1016/j.matcom.2025.06.023
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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.
    2. Jose P. Suárez & Agustín Trujillo & Tania Moreno, 2021. "Computing the Exact Number of Similarity Classes in the Longest Edge Bisection of Tetrahedra," Mathematics, MDPI, vol. 9(12), pages 1-13, June.
    3. Trujillo-Pino, Agustín & Suárez, Jose Pablo & Padrón, Miguel A., 2024. "Finite number of similarity classes in Longest Edge Bisection of nearly equilateral tetrahedra," Applied Mathematics and Computation, Elsevier, vol. 472(C).
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