Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
414723 | Computational Geometry | 2012 | 20 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Javier Alonso, Horst Martini, Margarita Spirova,