规范平面上球壳和球交的算法

Q4 Mathematics International Journal of Computational Geometry & Applications Pub Date : 2015-05-21 DOI:10.20382/jocg.v6i1a4

Pedro Martín, H. Martini

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引用次数: 2

摘要

推广Hershberger和Suri在欧几里得平面上的结果，证明了赋范平面上n个点集合的球壳和球交可以在O(n \log n)$时间内构造。此外，我们还证实了任意赋范平面的带约束圆的二中心问题可以在$O(n^2)$时间内得到解决。本文还对球壳在规范平面上的几何结构提出了一些看法。

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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Algorithms for ball hulls and ball intersections in normed planes

Extending results of Hershberger and Suri for the Euclidean plane, we show that ball hulls and ball intersections of sets of $n$ points in normed planes can be constructed in $O(n \log n)$ time. In addition, we confirm that the 2-center problem with constrained circles for arbitrary normed planes can be solved in $O(n^2)$ time. Some ideas about the geometric structure of the ball hull in a normed plane are also presented.

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来源期刊

International Journal of Computational Geometry & Applications 数学-计算机：理论方法

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The International Journal of Computational Geometry & Applications (IJCGA) is a quarterly journal devoted to the field of computational geometry within the framework of design and analysis of algorithms. Emphasis is placed on the computational aspects of geometric problems that arise in various fields of science and engineering including computer-aided geometry design (CAGD), computer graphics, constructive solid geometry (CSG), operations research, pattern recognition, robotics, solid modelling, VLSI routing/layout, and others. Research contributions ranging from theoretical results in algorithm design — sequential or parallel, probabilistic or randomized algorithms — to applications in the above-mentioned areas are welcome. Research findings or experiences in the implementations of geometric algorithms, such as numerical stability, and papers with a geometric flavour related to algorithms or the application areas of computational geometry are also welcome.

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