变形矩形对偶
Morphing Rectangular Duals
摘要：
平面图$G$的矩形对偶是$G$通过相邻不相交的轴对齐矩形的接触表示，使得（i）没有四个矩形共享一个点，并且（ii）所有矩形的并集是矩形。矩形对偶产生规则边缘标记（REL），其捕获矩形接触的方向。研究同一平面图的两个矩形顶点之间的变形问题。如果我们要求，在整个变形的任何时候，都有一个矩形对偶，那么只有当两个矩形对偶实现相同的REL时，变形才存在。因此，我们允许中间接触表示的非矩形多边形的恒定复杂性。给定一个$n$ -顶点平面图，我们展示了如何在$O(n^3)$时间内计算由$O(n^2)$线性变形步骤组成的分段线性变形。
英文摘要：
A rectangular dual of a plane graph $G$ is a contact representations of $G$ by interior-disjoint axis-aligned rectangles such that (i) no four rectangles share a point and (ii) the union of all rectangles is a rectangle. A rectangular dual gives rise to a regular edge labeling (REL), which captures the orientations of the rectangle contacts. We study the problem of morphing between two rectangular duals of the same plane graph. If we require that, at any time throughout the morph, there is a rectangular dual, then a morph exists only if the two rectangular duals realize the same REL. Therefore, we allow intermediate contact representations of non-rectangular polygons of constant complexity. Given an $n$-vertex plane graph, we show how to compute in $O(n^3)$ time a piecewise linear morph that consists of $O(n^2)$ linear morphing steps.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
