Minkowski Symmetry Sets of Plane Curves
| Autor: | Farid Tari, Graham Reeve |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Plane curve
General Mathematics Plane symmetry Classification of electromagnetic fields 010102 general mathematics Minkowski's theorem Mathematical analysis 01 natural sciences Minkowski addition 010101 applied mathematics Combinatorics Minkowski plane TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY Minkowski space 0101 mathematics Symmetry set SINGULARIDADES ComputingMethodologies_COMPUTERGRAPHICS Mathematics |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| ISSN: | 1464-3839 0013-0915 |
| Popis: | We study the Minkowski symmetry set of a closed smooth curveγin the Minkowski plane. We answer the following question, which is analogous to one concerning curves in the Euclidean plane that was treated by Giblin and O’Shea (1990): given a pointponγ, does there exist a bi-tangent pseudo-circle that is tangent toγboth atpand at some other pointqonγ? The answer is yes, but as pseudo-circles with non-zero radii have two branches (connected components) it is possible to refine the above question to the following one: given a pointponγ, does there exist a branch of a pseudo-circle that is tangent toγboth atpand at some other pointqonγ? This question is motivated by the earlier quest of Reeve and Tari (2014) to define the Minkowski Blum medial axis, a counterpart of the Blum medial axis of curves in the Euclidean plane. |
| Databáze: | OpenAIRE |
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