Minimal enclosing discs, circumcircles, and circumcenters in normed planes. II.
type: Item
instance of: scholarly article
title: Minimal enclosing discs, circumcircles, and circumcenters in normed planes. II.
zbMATH Open document ID: 1251.65016
author: Javier Alonso
author: Horst Martini
author: Margarita Spirova
published in: Computational Geometry
publication date: 2012-05-18T00:00:00Z
reviewed by: Jason Hanson
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 51B20
zbMATH DE Number: 6036559
zbMATH Keywords: circumcenters
zbMATH Keywords: intersection of norm circles
zbMATH Keywords: minimal enclosing balls
zbMATH Keywords: Minkowski geometry
zbMATH Keywords: normed plane
zbMATH Keywords: computational geometry
MaRDI profile type: Publication
full work available at URL: j.comgeo.2012.02.003
OpenAlex ID: W4206223441
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DOI: 10.1016/J.COMGEO.2012.02.003
review text: For part I see [the authors, ibid. 45, No. 5--6, 258--274 (2012; Zbl 1245.65022)].NEWLINENEWLINE Suppose that all distances in the plane are measured using a (possibly non-Euclidean) norm. A \textit{minimal enclosing disc} for a triangle \(T\) is a disc of smallest radius that contains the vertices of \(T\). Unlike the Euclidean case, such discs are not unique. The authors completely determine the set of all possible centers of the minimal enclosing discs of \(T\). In particular, this set is either a single point or a line segment, although the locations of the endpoints depend on the type of triangle: acute, obtuse, or right -- which may be defined in terms of the norm.NEWLINENEWLINEWhile the article is the second of two related articles, it may be read independently of the first. The article is intended for a general audience versed in computational geometry.
description: scientific article; zbMATH DE number 6036559