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 R2, 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 redu...
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| Veröffentlicht in: | Applied mathematics and computation Jg. 481; S. 128931 |
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| Sprache: | Englisch |
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15.11.2024
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| ISSN: | 0096-3003, 1873-5649 |
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| Abstract | This paper is devoted to an octagonal cut algorithm and a hexadecagonal cut algorithm for finding the convex hull of n points in R2, 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 bleast-bmost-boundedly in some rectangle can be determined with the complexity O(n). 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. |
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| AbstractList | This paper is devoted to an octagonal cut algorithm and a hexadecagonal cut algorithm for finding the convex hull of n points in R2, 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 bleast-bmost-boundedly in some rectangle can be determined with the complexity O(n). 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. |
| ArticleNumber | 128931 |
| Author | Hoang, Nam-Dũng Linh, Nguyen Kieu Phu, Hoang Xuan |
| Author_xml | – sequence: 1 givenname: Nam-Dũng orcidid: 0000-0001-7752-824X surname: Hoang fullname: Hoang, Nam-Dũng email: hoangnamdung@hus.edu.vn organization: Faculty of Mathematics, Mechanics and Informatics, VNU University of Science, Vietnam National University, 334 Nguyen Trai, Hanoi, Viet Nam – sequence: 2 givenname: Nguyen Kieu surname: Linh fullname: Linh, Nguyen Kieu email: linhnk@ptit.edu.vn organization: Posts and Telecommunications Institute of Technology, Km10, Nguyen Trai, Ha Dong, Hanoi, Viet Nam – sequence: 3 givenname: Hoang Xuan surname: Phu fullname: Phu, Hoang Xuan email: hxphu@math.ac.vn organization: Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Road, Hanoi, Viet Nam |
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| Cites_doi | 10.1007/BF02237955 10.1145/359423.359430 10.1145/235815.235821 10.1016/0020-0190(73)90020-3 10.1137/0215021 10.1080/01630569508816643 10.1016/0020-0190(87)90207-9 10.1007/BF02712873 10.1080/02331934.2011.623163 10.1016/S0022-0000(05)80056-X 10.1007/s10013-014-0067-1 10.1016/0020-0190(78)90003-0 10.1016/j.cad.2015.07.013 10.1016/j.cam.2019.06.014 10.1016/0020-0190(84)90084-X 10.1007/BF02523195 10.1007/s11075-020-00873-1 10.1080/02331930802434732 10.1080/02331939208843821 10.1080/02331938708843244 10.1016/0020-0190(78)90021-2 10.1080/02331938708843217 10.1080/01630569108816423 10.1016/0020-0190(72)90045-2 10.1080/02331938708843234 10.1016/0020-0190(79)90072-3 10.1080/01630569708816755 10.1145/321556.321564 10.1145/355759.355766 |
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| Keywords | Linear time algorithm 68Q25 Convex hull Orienting curves 52B55 65Y20 65D18 Quickhull algorithm |
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| SubjectTerms | Convex hull Linear time algorithm Orienting curves Quickhull algorithm |
| Title | Octagonal and hexadecagonal cut algorithms for finding the convex hull of finite sets with linear time complexity |
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