论文标题
计算双曲线表面的dirichlet域
Computing a Dirichlet domain for a hyperbolic surface
论文作者
论文摘要
本文的目的是展示和分析一种算法，该算法采用了给定的可定向双曲线表面并输出明确的Dirichlet域。输入是带有侧配对的基本多边形。虽然以拓扑考虑为基础，但该算法是表面几何形状的关键使用。我们介绍了反映几何和拓扑之间这种相互作用的数据结构，并表明该算法以多项式时间和表面属而在多项式时间内完成。
The goal of this paper is to exhibit and analyze an algorithm that takes a given closed orientable hyperbolic surface and outputs an explicit Dirichlet domain. The input is a fundamental polygon with side pairings. While grounded in topological considerations, the algorithm makes key use of the geometry of the surface. We introduce data structures that reflect this interplay between geometry and topology and show that the algorithm finishes in polynomial time, in terms of the initial perimeter and the genus of the surface.
