论文标题
双曲线表面的最小Delaunay三角剖分
Minimal Delaunay triangulations of hyperbolic surfaces
论文作者
论文摘要
由于最近关于双曲线表面的Delaunay三角剖分的工作，我们考虑了此类三角剖分的顶点数量最少。首先，我们将表明，$ g $的每个双曲线表面都有一个简单的Delaunay三角剖分，并带有$ o（g）$顶点，其中边缘由距离路径给出。然后，我们将构建一类双曲线表面，该界限的顺序是最佳的。最后，为了给出一个一般的下限，我们将证明$ω（\ sqrt {g}）$下限对于$ g $的拓扑表面的简单三角剖分的数量也很紧，对于高压表面也很紧。
Motivated by recent work on Delaunay triangulations of hyperbolic surfaces, we consider the minimal number of vertices of such triangulations. First, we will show that every hyperbolic surface of genus $g$ has a simplicial Delaunay triangulation with $O(g)$ vertices, where edges are given by distance paths. Then, we will construct a class of hyperbolic surfaces for which the order of this bound is optimal. Finally, to give a general lower bound, we will show that the $Ω(\sqrt{g})$ lower bound for the number of vertices of a simplicial triangulation of a topological surface of genus $g$ is tight for hyperbolic surfaces as well.
