Geometric dilation of closed planar curves:: New lower bounds

被引：8

作者：

Ebbers-Baumann, Annette ^{[1
]}

Gruene, Ansgar ^{[1
]}

Klein, Rolf ^{[1
]}

机构：

[1] Univ Bonn, Dept Comp Sci 1, D-53117 Bonn, Germany

来源：

COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS | 2007年 / 37卷 / 03期

关键词：

computational geometry; convex geometry; convex curves; dilation; detour; lower bound; halving pair; halving pair transformation;

D O I：

10.1016/j.comgeo.2004.12.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given two points on a closed planar curve, C, we can divide the length of a shortest connecting path in C by their Euclidean distance. The supremum of these ratios, taken over all pairs of points on the curve, is called the geometric dilation of C. We provide lower bounds for the dilation of closed curves in terms of their geometric properties, and prove that the circle is the only closed curve achieving a dilation of pi/2, which is the smallest dilation possible. Our main tool is a new geometric transformation technique based on the perimeter halving pairs of C. (C) 2006 Elsevier B.V. All rights reserved.

引用

页码：188 / 208

页数：21

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