论文标题
使用Hausdorff距离和Voronoi图的抽象变形
Abstract morphing using the Hausdorff distance and Voronoi diagrams
论文作者
论文摘要
本文介绍了两个新的抽象形态，分别是两个$ 2 $维的形状。中间形状逐渐将Hausdorff距离降低到目标形状，并将Hausdorff距离提高到初始形状。形态在概念上很简单，并且适用于具有多个组件和/或孔的形状。我们证明了一些与连续性，遏制和区域有关的基本属性。然后，我们提供了一个实验分析，其中包括两个新的形态和最近引入的抽象变体，它也基于Hausdorff距离（Van Kreveld等人之间的形状，使用Hausdorff距离。计算几何100：101817，2022）。我们显示了整个变体的区域和周边发育的结果，以及组件和孔的数量。视觉比较表明，其中一种新形态似乎最有吸引力。
This paper introduces two new abstract morphs for two $2$-dimensional shapes. The intermediate shapes gradually reduce the Hausdorff distance to the goal shape and increase the Hausdorff distance to the initial shape. The morphs are conceptually simple and apply to shapes with multiple components and/or holes. We prove some basic properties relating to continuity, containment, and area. Then we give an experimental analysis that includes the two new morphs and a recently introduced abstract morph that is also based on the Hausdorff distance (Van Kreveld et al. Between shapes, using the Hausdorff distance. Computational Geometry 100:101817, 2022). We show results on the area and perimeter development throughout the morph, and also the number of components and holes. A visual comparison shows that one of the new morphs appears most attractive.
