快捷外壳线:多边形的受顶点限制的外部简化

IF 0.4 4区 计算机科学 Q4 MATHEMATICS
Annika Bonerath , Jan-Henrik Haunert , Joseph S.B. Mitchell , Benjamin Niedermann
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引用次数: 0

摘要

设P是一个多边形,C是一组快捷方式,其中每个快捷方式是连接P的两个顶点的有向直线段。P的快捷方式外壳是另一个包围P的多边形,其定向边界由来自C的元素组成。我们要求P和输出快捷方式外壳为弱简单多边形,我们将其定义为简单多边形的推广。快捷外壳线在制图中得到了应用,其中一个常见的任务是计算区域特征的简化表示。我们瞄准的是一个面积小、周长小的捷径船体。我们的优化目标是最小化这两个标准的凸组合。如果捷径外壳上不允许有洞,则该问题可以通过计算最短路径来直接求解。对于快捷外壳可能包含孔的更具挑战性的情况,我们提出了一种多项式时间算法,该算法基于计算输入多边形外部的约束加权三角测量。我们将这个问题作为研究进一步变体的起点,例如,限制边缘或弯曲的数量。我们证明了快捷外壳可以用于多边形的模式化。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Shortcut hulls: Vertex-restricted outer simplifications of polygons

Let P be a polygon and C a set of shortcuts, where each shortcut is a directed straight-line segment connecting two vertices of P. A shortcut hull of P is another polygon that encloses P and whose oriented boundary is composed of elements from C. We require P and the output shortcut hull to be weakly simple polygons, which we define as a generalization of simple polygons. Shortcut hulls find their application in cartography, where a common task is to compute simplified representations of area features. We aim at a shortcut hull that has a small area and a small perimeter. Our optimization objective is to minimize a convex combination of these two criteria. If no holes in the shortcut hull are allowed, the problem admits a straight-forward solution via computation of shortest paths. For the more challenging case in which the shortcut hull may contain holes, we present a polynomial-time algorithm that is based on computing a constrained, weighted triangulation of the input polygon's exterior. We use this problem as a starting point for investigating further variants, e.g., restricting the number of edges or bends. We demonstrate that shortcut hulls can be used for the schematization of polygons.

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来源期刊
CiteScore
1.60
自引率
16.70%
发文量
43
审稿时长
>12 weeks
期刊介绍: Computational Geometry is a forum for research in theoretical and applied aspects of computational geometry. The journal publishes fundamental research in all areas of the subject, as well as disseminating information on the applications, techniques, and use of computational geometry. Computational Geometry publishes articles on the design and analysis of geometric algorithms. All aspects of computational geometry are covered, including the numerical, graph theoretical and combinatorial aspects. Also welcomed are computational geometry solutions to fundamental problems arising in computer graphics, pattern recognition, robotics, image processing, CAD-CAM, VLSI design and geographical information systems. Computational Geometry features a special section containing open problems and concise reports on implementations of computational geometry tools.
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