Edge-unfolding nested prismatoids

IF 0.4 4区计算机科学 Q4 MATHEMATICS

Computational Geometry-Theory and Applications Pub Date : 2023-06-28 DOI:10.1016/j.comgeo.2023.102033

Manuel Radons

引用次数: 2

Abstract

A 3-prismatoid is the convex hull of two convex polygons A and B which lie in parallel planes $H_{A}, H_{B} \subset R^{3}$ . Let $\tilde{A}$ be the orthogonal projection of A onto $H_{B}$ . A 3-prismatoid is called nested if $\tilde{A}$ is properly contained in B, or vice versa. We show that every nested 3-prismatoid has an edge-unfolding to a non-overlapping polygon in the plane.

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边展开嵌套棱柱体

3-棱柱体是位于平行平面HA、HB⊂R3中的两个凸多边形A和B的凸包。设A~是A在HB上的正交投影。如果A~正确地包含在B中，则3棱柱体被称为嵌套，反之亦然。我们证明了每个嵌套的3-棱柱体都有一条边展开为平面中的非重叠多边形。

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.