Article ID Journal Published Year Pages File Type
414723 Computational Geometry 2012 20 Pages PDF
Abstract

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.

Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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