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https://accedacris.ulpgc.es/handle/10553/51605
Title: | Properties of triangulations obtained by the longest-edge bisection | Authors: | Perdomo, Francisco Plaza, Ángel |
UNESCO Clasification: | 120601 Construcción de algoritmos | Keywords: | Finite element method Longest-edge bisection Mesh refinement Mesh regularity Triangulation |
Issue Date: | 2014 | Project: | Particiones Triangulares y Algoritmos de Refinamiento. | Journal: | Central European Journal of Mathematics | Abstract: | The Longest-Edge (LE) bisection of a triangle is obtained by joining the midpoint of its longest edge with the opposite vertex. Here two properties of the longest-edge bisection scheme for triangles are proved. For any triangle, the number of distinct triangles (up to similarity) generated by longest-edge bisection is finite. In addition, if LE-bisection is iteratively applied to an initial triangle, then minimum angle of the resulting triangles is greater or equal than a half of the minimum angle of the initial angle. The novelty of the proofs is the use of an hyperbolic metric in a shape space for triangles. | URI: | https://accedacris.ulpgc.es/handle/10553/51605 | ISSN: | 1895-1074 | DOI: | 10.2478/s11533-014-0448-4 | Source: | Central European Journal of Mathematics [ISSN 1895-1074], v. 12 (12), p. 1796-1810 |
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