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The Shortest-Edge Duplication of Triangles

Author

Listed:
  • Miguel Ángel Padrón

    (IUMA Information and Communications System, University of Las Palmas de Gran Canaria, 35017 Canary Islands, Spain
    These authors contributed equally to this work.)

  • Francisco Perdomo

    (IUMA Information and Communications System, University of Las Palmas de Gran Canaria, 35017 Canary Islands, Spain
    These authors contributed equally to this work.)

  • Ángel Plaza

    (IUMA Information and Communications System, University of Las Palmas de Gran Canaria, 35017 Canary Islands, Spain
    These authors contributed equally to this work.)

  • José Pablo Suárez

    (IUMA Information and Communications System, University of Las Palmas de Gran Canaria, 35017 Canary Islands, Spain
    These authors contributed equally to this work.)

Abstract

We introduce a new triangle transformation, the shortest-edge (SE) duplication, as a natural way of mesh derefinement suitable to those meshes obtained by iterative application of longest-edge bisection refinement. Metric properties of the SE duplication of a triangle in the region of normalised triangles endowed with the Poincare hyperbolic metric are studied. The self-improvement of this transformation is easily proven, as well as the minimum angle condition. We give a lower bound for the maximum of the smallest angles of the triangles produced by the iterative SE duplication α = π 6 . This bound does not depend on the shape of the initial triangle.

Suggested Citation

  • Miguel Ángel Padrón & Francisco Perdomo & Ángel Plaza & José Pablo Suárez, 2022. "The Shortest-Edge Duplication of Triangles," Mathematics, MDPI, vol. 10(19), pages 1-13, October.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3643-:d:934053
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