Minimal enclosing discs, circumcircles, and circumcenters in normed planes (Part II)

被引：15

作者：

Alonso, Javier ^{[2
]}

Martini, Horst ^{[1
]}

Spirova, Margarita ^{[1
]}

机构：

[1] TU Chemnitz, Fak Math, D-09107 Chemnitz, Germany

[2] Univ Extremadura, Dept Matemat, Badajoz 06006, Spain

来源：

COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS | 2012年 / 45卷 / 07期

关键词：

Circumcenters; Intersection of norm circles; Minimal enclosing balls; Minkowski geometry; Normed plane; GEOMETRY;

D O I：

10.1016/j.comgeo.2012.02.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 [应用数学];

摘要：

Until now there are almost no results on the precise geometric location of minimal enclosing balls of simplices in finite-dimensional real Banach spaces. We give a complete solution of the two-dimensional version of this problem, namely to locate minimal enclosing discs of triangles in arbitrary normed planes. It turns out that this solution is based on the classification of all possible shapes that the intersection of two norm circles can have, and on a new classification of triangles in normed planes via their angles. We also mention that our results are closely related to basic notions like coresets, Jung constants, the monotonicity lemma, and d-segments. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：350 / 369

页数：20

共 31 条

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[2]

Minimal enclosing discs, circumcircles, and circumcenters in normed planes (Part I) [J].