Rectilinear convex hull of points in 3D and applications

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-04 DOI:10.1007/s10898-024-01402-3

Pablo Pérez-Lantero, Carlos Seara, Jorge Urrutia

引用次数: 0

Abstract

Let P be a set of n points in \(\mathbb {R}^3\) in general position, and let RCH(P) be the rectilinear convex hull of P. In this paper we obtain an optimal \(O(n\log n)\) time and O(n) space algorithm to compute RCH(P). We also obtain an efficient \(O(n\log ^2 n)\) time and \(O(n\log n)\) space algorithm to compute and maintain the set of vertices of the rectilinear convex hull of P as we rotate \({\mathbb {R}}^3\) around the Z-axis. We study some combinatorial properties of the rectilinear convex hulls of point sets in \(\mathbb {R}^3\). Finally, as an application of the obtained results, we show an approximation algorithm to an optimization fitting problem in \(\mathbb {R}^3\).

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三维中点的直线凸壳及其应用

让 P 是在\(\mathbb {R}^3\)中处于一般位置的 n 个点的集合，让 RCH(P) 是 P 的直线凸壳。在本文中，我们得到了一个最优的 \(O(n\log n)\)时间和 \(O(n) 空间算法来计算 RCH(P)。我们还得到了一种高效的（O(n\log ^2 n)）时间和（O(n\log n)）空间算法，当我们绕Z轴旋转\({mathbb {R}}^3\) 时，可以计算并维护P的直角凸壳的顶点集。我们研究了 \(\mathbb {R}^3\) 中点集的直线凸壳的一些组合性质。最后，作为所得结果的一个应用，我们展示了一种在 \(\mathbb {R}^3\) 中优化拟合问题的近似算法。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.