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

[21] Minimal convex k-gons containing a given convex polygon
Zalgaller V.A.
Journal of Mathematical Sciences, 2001, 104 (4) : 1272 - 1275
[22] ON THE NUMBER OF DIGITAL CONVEX POLYGONS INSCRIBED INTO AN (M,M)-GRID
IVIC, A
KOPLOWITZ, J
ZUNIC, J
IEEE TRANSACTIONS ON INFORMATION THEORY, 1994, 40 (05) : 1681 - 1686
[23] Decomposing a simple polygon into pseudo-triangles and convex polygons
Gerdjikov, Stefan
Wolff, Alexander
COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 2008, 41 (1-2): : 21 - 30
[24] FINDING THE SMALLEST TRIANGLES CONTAINING A GIVEN CONVEX POLYGON
KLEE, V
LASKOWSKI, MC
JOURNAL OF ALGORITHMS, 1985, 6 (03) : 359 - 375
[25] CONVEX POLYGONS AND SEPARATION OF CONVEX
Rivera-Campo, Eduardo
Urrutia, Jorge
STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 2022, 59 (3-4) : 274 - 283
[26] Polygons inscribed in a closed curve and a three-dimensional convex body
Makeev V.V.
Journal of Mathematical Sciences, 2009, 161 (3) : 419 - 423
[27] A simple proof of Pach's Extremal Theorem for convex polygons
Toussaint, Godfried T.
PATTERN RECOGNITION LETTERS, 1982, 1 (02) : 85 - 86
[28] An algorithm to find maximum area polygons circumscribed about a convex polygon
Ausserhofer, Markus
Dann, Susanna
Langi, Zsolt
Toth, Geza
DISCRETE APPLIED MATHEMATICS, 2019, 255 : 98 - 108
[29] ON POLYGONS SIMILAR TO A GIVEN POLYGON
EVANS, C
SANDOR, H
AMERICAN MATHEMATICAL MONTHLY, 1965, 72 (05): : 556 - &
[30] Minimum convex partition of a polygon with holes by cuts in given directions
Lingas, A
Soltan, V
THEORY OF COMPUTING SYSTEMS, 1998, 31 (05) : 507 - 538

← 1 2 3 4 5 →