Angles of arc-polygons and Lombardi drawings of cacti

IF 0.4 4区计算机科学 Q4 MATHEMATICS

Computational Geometry-Theory and Applications Pub Date : 2023-06-01 DOI:10.1016/j.comgeo.2023.101982

David Eppstein, Daniel Frishberg, Martha C. Osegueda

引用次数: 2

Abstract

We characterize the triples of interior angles that are possible in non-self-crossing triangles with circular-arc sides, and we prove that a given cyclic sequence of angles can be realized by a non-self-crossing polygon with circular-arc sides whenever all angles are ≤π. As a consequence of these results, we prove that every cactus has a planar Lombardi drawing (a drawing with edges depicted as circular arcs, meeting at equal angles at each vertex) for its natural embedding in which every cycle of the cactus is a face of the drawing. However, there exist planar embeddings of cacti that do not have planar Lombardi drawings.

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弧多边形的角度与仙人掌的Lombardi绘画

我们刻画了在具有圆弧边的非自交三角形中可能存在的内角的三元组，并证明了当所有角度≤π时，给定的角的循环序列可以由具有圆弧面的非自交多边形实现。由于这些结果，我们证明了每个仙人掌都有一个平面的Lombardi图（一个边缘被描绘成圆弧的图，在每个顶点以相等的角度相交），用于其自然嵌入，其中仙人掌的每个循环都是图的一个面。然而，有一些仙人掌的平面嵌入物没有隆巴迪平面图。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational Geometry-Theory and Applications 数学-数学

CiteScore

1.60

自引率

16.70%

发文量

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.