Extremal convex polygons inscribed in a given convex polygon

被引：0

作者：

Kodmon, Csenge Lili ^{[1
]}

Langi, Zsolt ^{[2
,3
]}

机构：

[1] Tech Univ Budapest, Dept Geometry, Egey Jozsef Utca 1, H-1111 Budapest, Hungary

[2] Tech Univ Budapest, MTA BME Morphodynam Res Grp, Egry Jozsef Utca 1, H-1111 Budapest, Hungary

[3] Tech Univ Budapest, Dept Geometry, Egry Jozsef Utca 1, H-1111 Budapest, Hungary

来源：

COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS | 2022年 / 102卷

关键词：

Convex polygon; Perimeter; Area; Billiard; Dual billiard; ALGORITHM; TRAJECTORIES;

D O I：

10.1016/j.comgeo.2021.101844

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A convex polygon Q is inscribed in a convex polygon P if every side of P contains at least one vertex of Q. We present algorithms for finding a minimum area and a minimum perimeter convex polygon inscribed in any given convex n-gon in O(n) and O(n(3)) time, respectively. We also investigate other variants of this problem. (c) 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

引用

页数：10

共 50 条

[31] Minimum Convex Partition of a Polygon with Holes by Cuts in Given Directions
A. Lingas
V. Soltan
Theory of Computing Systems, 1998, 31 : 507 - 538
[32] Minimum convex partition of a polygon with holes by cuts in given directions
Department of Computer Science, Lund University, S-22100 Lund, Sweden
不详
Theory Comput. Syst., 5 (507-538):
[33] Minimum convex partition of a polygon with holes by cuts in given directions
Lingas, A
Soltan, V
ALGORITHMS AND COMPUTATION, 1996, 1178 : 315 - 325
[34] An Efficient Algorithm for Touring a Sequence of given Convex Polygons in the Plane
Xu, Changan
Jiang, Bo
Wang, Lijuan
PROCEEDINGS OF 2017 6TH INTERNATIONAL CONFERENCE ON COMPUTER SCIENCE AND NETWORK TECHNOLOGY (ICCSNT 2017), 2017, : 74 - 78
[35] A Fast Algorithm for Touring the Disjoint Convex Polygons in the Given Order
Wang Lijuan
He Dandan
Hou Hongfeng
Jiang Bo
Ning Tao
PROCEEDINGS OF 2017 6TH INTERNATIONAL CONFERENCE ON COMPUTER SCIENCE AND NETWORK TECHNOLOGY (ICCSNT 2017), 2017, : 107 - 111
[36] PROBABILITY POLYGONS IN CONVEX POLYGONS
BUCHTA, C
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1984, 347 : 212 - 220
[37] DISSECTIONS OF POLYGONS INTO CONVEX POLYGONS
Zak, Andrzej
INTERNATIONAL JOURNAL OF COMPUTATIONAL GEOMETRY & APPLICATIONS, 2010, 20 (02) : 223 - 244
[38] Approximation of convex polygons by polygons
Koutschan, Christoph
Ponomarchuk, Anton
Schicho, Josef
2021 23RD INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND NUMERIC ALGORITHMS FOR SCIENTIFIC COMPUTING (SYNASC 2021), 2021, : 91 - 98
[39] Extremal problems on convex lattice polygons in sense of lp-metrics
Zunic, J
DISCRETE MATHEMATICS, 2002, 259 (1-3) : 237 - 250
[40] Extremal Problems for Convex Curves with a Given Self Chebyshev Radius
Balestro, Vitor
Martini, Horst
Nikonorov, Yurii
Nikonorova, Yulia
RESULTS IN MATHEMATICS, 2021, 76 (02)

← 1 2 3 4 5 →