论文标题
在形状之间，使用Hausdorff距离
Between Shapes, Using the Hausdorff Distance
论文作者
论文摘要
给定两个形状$ a $ a $和$ b $，带有hausdorff距离$ 1 $的飞机，是否有hausdorff距离$ 1/2 $的形状$ s $ for $ a $ a $和$ b $？答案始终是肯定的，取决于$ a $和/或$ b $，$ s $的凸度，可以是凸，连接或断开连接的。我们表明，对于任何插值变量$ a $α$，可以在$ 0 $ 0 $和$ 1 $之间提供插值之间的插值形状，并证明所产生的变体相对于$α$具有有限的变化率。最后，我们探讨了Hausdorff中部对两个以上输入集的概念的概括。我们展示了如何近似或计算这种中间形状，以及与Hausdorff中间的连接性相关的属性，并使用两个输入集延伸。我们还在中间组和输入之间的豪斯多夫距离上给出了界限。
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 that our result can be generalised to give an interpolated shape between $A$ and $B$ for any interpolation variable $α$ between $0$ and $1$, and prove that the resulting morph has a bounded rate of change with respect to $α$. Finally, we explore a generalization of the concept of a Hausdorff middle to more than two input sets. We show how to approximate or compute this middle shape, and that the properties relating to the connectedness of the Hausdorff middle extend from the case with two input sets. We also give bounds on the Hausdorff distance between the middle set and the input.
