形状之间,使用豪斯多夫距离

M. V. Kreveld, Tillmann Miltzow, Tim Ophelders, Willem Sonke, J. Vermeulen
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引用次数: 7

摘要

给定平面上的两个形状A和B,其豪斯多夫距离为1,是否存在一个形状S,其与A和B之间的豪斯多夫距离为1/2 ?答案总是肯定的,并且根据$A$和/或$B$的凸性,$S$可能是凸的、连通的或不连通的。我们将这一结果推广到豪斯多夫距离和中间形状,以及各种相关性质。我们还证明了这种中间形状的泛化意味着具有有界变化率的变形。最后,我们将Hausdorff中间的概念推广到两个以上的集合,并展示了如何近似或计算它。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Between Shapes, Using the Hausdorff Distance
Given two shapes $A$ and $B$ in the plane with Hausdorff distance $1$, is there a shape $S$ with Hausdorff distance $1/2$ to and from $A$ and $B$? The answer is always yes, and depending on convexity of $A$ and/or $B$, $S$ may be convex, connected, or disconnected. We show a generalization of this result on Hausdorff distances and middle shapes, and various related properties. We also show that a generalization of such middle shapes implies a morph with a bounded rate of change. Finally, we explore a generalization of the concept of a Hausdorff middle to more than two sets and show how to approximate or compute it.
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