Hyperbolic Voronoi Diagram

机译：双曲Voronoi图

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Voronoi diagrams are among the most extensively studied objects in computational geometry with useful applications in different areas of science. To understand impacts of non-Euclidean geometry on computational geometry, this paper investigates the Voronoi diagram in hyperbolic space specially the one in the Poincare hyperbolic disk, which is a 2-dimensional manifold with negative curvature. We first prove some lemma in Poincare hyperbolic disk and then give an incremental algorithm to construct Voronoi diagram.

机译：Voronoi图是计算几何学中研究最广泛的对象之一，在不同的科学领域中都有有用的应用。为了理解非欧几里德几何对计算几何的影响，本文研究了双曲空间中的Voronoi图，特别是Poincare双曲圆盘中的Voronoi图，它是具有负曲率的二维流形。我们首先证明Poincare双曲圆盘上的一些引理，然后给出一种增量算法构造Voronoi图。

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来源
《International Conference on Computational Science and Its Applications(ICCSA 2006) pt.5; 20060508-11; Glasgow(GB)》|2006年|P.735-742|共8页
会议地点 Glasgow(GB)
作者
Zahra Nilforoushan; Ali Mohades;
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作者单位

Faculty of Math. and Computer Sc., AmirKabir University of Tech., 424 Hafez Ave. Tehran, Iran;

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会议组织
原文格式 PDF
正文语种 eng
中图分类计算技术、计算机技术;
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Hyperbolic Voronoi Diagram

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