Minimal enclosing discs, circumcircles, and circumcenters in normed planes. II.
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.
scientific article; zbMATH DE number 6036559
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