2019/08/06 by Dan Ismailescu, Joehyun Kim, Ismailescu, Dan +5 · 1 citation
Computer Science · Engineering · #Computational Geometry and Mesh Generation #Advanced Numerical Analysis Techniques #Digital Image Processing Techniques
paper · pdf · doi:10.48550/arxiv.1908.02749
The \it largest angle bisection procedure is the operation which partitions a given triangle, T, into two smaller triangles by constructing the angle bisector of the largest angle of T. Applying the procedure to each of these two triangles produces a partition of T into four smaller triangles. Continuing in this manner, after n iterations, the initial triangle is divided into 2n small triangles. We prove that as n approaches infinity, the diameters of all these 2n triangles tend to 0, the smallest angle of all these triangles is bounded away from 0, and that, with the exception of T being an isosceles right triangle, the number of dissimilar triangles is unbounded.