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

Authors:
Javier Alonso;Horst Martini;Margarita Spirova
Affiliations:
Departamento de Matemáticas, Universidad de Extremadura, 06006 Badajoz, Spain;Fakultät für Mathematik, TU Chemnitz, D-09107 Chemnitz, Germany;Fakultät für Mathematik, TU Chemnitz, D-09107 Chemnitz, Germany
Venue:
Computational Geometry: Theory and Applications
Year:
2012

Citing 4
Cited 0

Convex distance functions in 3-space are different

SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Optimal core-sets for balls

Computational Geometry: Theory and Applications
Minimal enclosing discs, circumcircles, and circumcenters in normed planes (Part I)

Computational Geometry: Theory and Applications
The weighted euclidean 1-center problem

Operations Research Letters

Quantified Score

Hi-index	0.00

Visualization

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.