Uma avaliação de sequências de inserção em algoritmos incrementais para a tesselação de Delaunay

Abstract

In this work, it is evaluated 8 insertion-point sequences in incremental algorithms to generate the Delaunay tessellation. Four of these sequences are considered for the first time: H-Indexing, spiral, red-black tree in-order and red-black-tree in level-order traversal. These sequences are compared with: point-insertion order given by cut-longest-edge kd-tree; with the order given by Hilbert space-filling curve; with Lebesgue space- filling curve and with the random point-insertion order. Using the GNU MPFR library, 6 dataset distributions were tested on unit square and 7 dataset distributions on the unit cube. The incremental algorithms with the 4 sequences that were proposed in this work are not competitive with the incremental algorithm using the point-insertion given by cut-longest-edge kd-tree. More specifically, the incremental algorithm using point-insertion sequence in the order given by the cut-longest-edge kd-tree, shows the lowest computational cost on mesh generation in tests carried out on 2D and on 3D.