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“…Hence it has an accumulation point which corresponds to the fixed point z = 1 2 . This completes the argument of the paper [1] for the case n = 4.…”

confidence: 49%

“…Even though, the subsequent argument in [1] is correct for the case n > 4. But, the case n = 4 needs a closer look.…”

confidence: 99%

“…By considering a dynamical system of sequentially refined triangles in hyperbolic geometry, it was shown in Perdomo and Plaza (2013) that trisection guarantees high-quality refined meshes; whereas the n -section method for n ≥ 4 can produce degenerate triangles (Perdomo and Plaza, 2012). Other advanced refinement strategies are discussed in Brandts et al (2009), Choi et al (2003), and Korotov and Křížek (2001).…”

confidence: 99%

“…See in this sense [3,8,9] and references therein. While previous demonstrations employed ad hoc methods of Euclidean geometry, the methodology of the proofs given here is generalizable to other partition methods [17][18][19]. The proofs are not necessarily shorter, but they are structured in an systematic way.…”

confidence: 99%

“…One of methods used in the literature on triangular mesh refinement is to normalize triangles [10,17,22]. The method consists of applying several possible isometries and dilations to a triangle, in such way one side can be identify with the segment whose endpoints are (0 0) and (1 0 The LE-bisection of a triangle ∆ is obtained by joining the midpoint on the longest edge of the triangle to the opposite vertex.…”

confidence: 99%