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Title: Proving the non-degeneracy of the longest-edge trisection by a space of triangular shapes with hyperbolic metric
Authors: Perdomo, Francisco 
Plaza, Ángel 
UNESCO Clasification: 120603 Análisis de errores
Keywords: Finite element method
Mesh quality
Triangle subdivision
Issue Date: 2013
Project: Particiones Triangulares y Algoritmos de Refinamiento. 
Journal: Applied Mathematics and Computation 
Abstract: From an initial triangle, three triangles are obtained joining the two equally spaced points of the longest-edge with the opposite vertex. This construction is the base of the longest-edge trisection method. Let Δ be an arbitrary triangle with minimum angle α. Let Δ′ be any triangle generated in the iterated application of the longest-edge trisection. Let α′ be the minimum angle of Δ′. Thus α′≥α/c with c=π/3arctan3/11 is proved in this paper. A region of the complex half-plane, endowed with the Poincare hyperbolic metric, is used as the space of triangular shapes. The metric properties of the piecewise-smooth complex dynamic defined by the longest-edge trisection are studied. This allows us to obtain the value c.
ISSN: 0096-3003
DOI: 10.1016/j.amc.2013.06.075
Source: Applied Mathematics and Computation [ISSN 0096-3003], v. 221, p. 424-432
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