The geometric dilation of three points

Q4 Mathematics

International Journal of Computational Geometry & Applications Pub Date : 2019-01-01 DOI:10.20382/jocg.v10i1a18

Annette Ebbers-Baumann, R. Klein, Christian Knauer, G. Rote

引用次数: 0

Abstract

Given three points in the plane, we construct the plane geometric network of smallest geometric dilation that connects them. The geometric dilation of a plane network is defined as the maximum dilation (distance along the network divided by Euclidean distance) between any two points on its edges. We show that the optimum network is either a line segment, a Steiner tree, or a curve consisting of two straight edges and a segment of a logarithmic spiral.

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三点的几何膨胀

给定平面上的三个点，我们构造了连接它们的最小几何膨胀平面几何网络。平面网络的几何扩张被定义为其边缘任意两点之间的最大扩张(沿网络的距离除以欧几里得距离)。我们证明了最优网络要么是线段，要么是斯坦纳树，要么是由两条直边和对数螺旋段组成的曲线。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Computational Geometry & Applications 数学-计算机：理论方法

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The International Journal of Computational Geometry & Applications (IJCGA) is a quarterly journal devoted to the field of computational geometry within the framework of design and analysis of algorithms. Emphasis is placed on the computational aspects of geometric problems that arise in various fields of science and engineering including computer-aided geometry design (CAGD), computer graphics, constructive solid geometry (CSG), operations research, pattern recognition, robotics, solid modelling, VLSI routing/layout, and others. Research contributions ranging from theoretical results in algorithm design — sequential or parallel, probabilistic or randomized algorithms — to applications in the above-mentioned areas are welcome. Research findings or experiences in the implementations of geometric algorithms, such as numerical stability, and papers with a geometric flavour related to algorithms or the application areas of computational geometry are also welcome.