Characterization of Extremal Antipodal Polygons

被引：3

作者：

Aichholzer, O. ^{[1
]}

Caraballo, L. E. ^{[2
]}

Diaz-Banez, J. M. ^{[2
]}

Fabila-Monroy, R. ^{[3
]}

Ochoa, C. ^{[4
]}

Nigsch, P. ^{[5
]}

机构：

[1] Graz Univ Technol, Inst Software Technol, A-8010 Graz, Austria

[2] Univ Seville, Dept Matemat Aplicada 2, Seville, Spain

[3] Inst Politecn Nacl, Ctr Invest & Estudios Avanzados, Dept Matemat, Mexico City, DF, Mexico

[4] Univ Chile, DCC, Santiago, Chile

[5] Graz Univ Technol, A-8010 Graz, Austria

来源：

GRAPHS AND COMBINATORICS | 2015年 / 31卷 / 02期

基金：

奥地利科学基金会;

关键词：

Antipodal points; Extremal area polygons; Discrete and computational geometry;

D O I：

10.1007/s00373-015-1548-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let be a set of points on a circle such that for each point also its antipodal (mirrored with respect to the circle center) point belongs to . A polygon of size is called antipodal if it consists of precisely one point of each antipodal pair of . We provide a complete characterization of antipodal polygons which maximize (minimize, respectively) the area among all antipodal polygons of . Based on this characterization, a simple linear time algorithm is presented for computing extremal antipodal polygons. Moreover, for the generalization of antipodal polygons to higher dimensions we show that a similar characterization does not exist.

引用

页码：321 / 333

页数：13

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