{"title":"以线性时间复杂度寻找有限集凸壳的八边形和十六边形切割算法","authors":"","doi":"10.1016/j.amc.2024.128931","DOIUrl":null,"url":null,"abstract":"<div><p>This paper is devoted to an octagonal cut algorithm and a hexadecagonal cut algorithm for finding the convex hull of <em>n</em> points in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, where some octagon and hexadecagon are used for discarding most of the given points interior to these polygons. In this way, the scope of the given problem can be reduced significantly. In particular, the convex hull of <em>n</em> points distributed <span><math><msub><mrow><mi>b</mi></mrow><mrow><mi>least</mi></mrow></msub></math></span>-<span><math><msub><mrow><mi>b</mi></mrow><mrow><mi>most</mi></mrow></msub></math></span>-boundedly in some rectangle can be determined with the complexity <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>. Computational experiments demonstrate that our algorithms outperform the Quickhull algorithm by a significant factor of up to 47 times when applied to the tested data sets. The speedup compared to the CGAL library is even more pronounced.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5000,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Octagonal and hexadecagonal cut algorithms for finding the convex hull of finite sets with linear time complexity\",\"authors\":\"\",\"doi\":\"10.1016/j.amc.2024.128931\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper is devoted to an octagonal cut algorithm and a hexadecagonal cut algorithm for finding the convex hull of <em>n</em> points in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, where some octagon and hexadecagon are used for discarding most of the given points interior to these polygons. In this way, the scope of the given problem can be reduced significantly. In particular, the convex hull of <em>n</em> points distributed <span><math><msub><mrow><mi>b</mi></mrow><mrow><mi>least</mi></mrow></msub></math></span>-<span><math><msub><mrow><mi>b</mi></mrow><mrow><mi>most</mi></mrow></msub></math></span>-boundedly in some rectangle can be determined with the complexity <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>. Computational experiments demonstrate that our algorithms outperform the Quickhull algorithm by a significant factor of up to 47 times when applied to the tested data sets. The speedup compared to the CGAL library is even more pronounced.</p></div>\",\"PeriodicalId\":55496,\"journal\":{\"name\":\"Applied Mathematics and Computation\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.5000,\"publicationDate\":\"2024-07-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics and Computation\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0096300324003928\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0096300324003928","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
本文主要介绍一种八边形切割算法和一种十六边形切割算法,用于寻找 R2 中 n 个点的凸壳,其中一些八边形和十六边形用于放弃这些多边形内部的大部分给定点。这样,给定问题的范围就可以大大缩小。特别是,可以用 O(n)的复杂度确定在某个矩形中几乎无边界地分布着 n 个点的凸壳。计算实验证明,当应用于测试数据集时,我们的算法比 Quickhull 算法快 47 倍。与 CGAL 库相比,我们的算法速度提升更为明显。
Octagonal and hexadecagonal cut algorithms for finding the convex hull of finite sets with linear time complexity
This paper is devoted to an octagonal cut algorithm and a hexadecagonal cut algorithm for finding the convex hull of n points in , where some octagon and hexadecagon are used for discarding most of the given points interior to these polygons. In this way, the scope of the given problem can be reduced significantly. In particular, the convex hull of n points distributed --boundedly in some rectangle can be determined with the complexity . Computational experiments demonstrate that our algorithms outperform the Quickhull algorithm by a significant factor of up to 47 times when applied to the tested data sets. The speedup compared to the CGAL library is even more pronounced.
期刊介绍:
Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results.
In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.