Local refinement based on the 7-triangle longest-edge partition

Authors:
Ángel Plaza;Alberto Márquez;Auxiliadora Moreno-González;José P. Suárez
Affiliations:
Department of Mathematics, ULPGC, 35017-Las Palmas de Gran Canaria, Spain;Department of Mathematics, University of Seville, Spain;Department of Mathematics, University of Seville, Spain;Department of Cartography and Graphic Engineering, ULPGC, Spain
Venue:
Mathematics and Computers in Simulation
Year:
2009

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

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Abstract

The triangle longest-edge bisection constitutes an efficient scheme for refining a mesh by reducing the obtuse triangles, since the largest interior angles are subdivided. In this paper we specifically introduce a new local refinement for triangulations based on the longest-edge trisection, the 7-triangle longest-edge (7T-LE) local refinement algorithm. Each triangle to be refined is subdivided in seven sub-triangles by determining its longest edge. The conformity of the new mesh is assured by an automatic point insertion criterion using the oriented 1-skeleton graph of the triangulation and three partial division patterns.