Reeve, Graham, and Tari, Farid (2017) Minkowski symmetry sets of plane curves. Proceedings of the Edinburgh Mathematical Society, 60 (2). pp. 461480. ISSN 00130915

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Abstract
We study in this paper the Minkowski Symmetry Set (MSS) of a closed smooth curve gamma in the Minkowski plane. We answer the following question which is analogous to one concerning curves in Euclidean plane that was treated in [7]: given a point p on gamma, does there exist a bitangent pseudocircle that is tangent to gamma at both p and at some other point q on gamma? The answer is yes, but as pseudocircles with nonzero radii have two branches (connected components) it is possible to refine the above question to the following one: given a point p on gamma does there exist a branch of a pseudocircle that is tangent to gamma at both p and at some other point q on gamma? This question is motivated by the quest in [12] to define the Minkowski Blum medial axis, a counterpart of the Blum medial axis of curves in the Euclidean plane ([3]).
Item Type:  Article 

Additional Information and Comments:  Reeve, G., & Tari, F. (2017). Minkowski Symmetry Sets of Plane Curves. Proceedings of the Edinburgh Mathematical Society, 60(2), 461480. Copyright held by Cambridge University Press. https://www.cambridge.org/core/journals/proceedingsoftheedinburghmathematicalsociety/article/minkowskisymmetrysetsofplanecurves/543EF1AC6C74B2691B3853CC0AEC6BCE 
Keywords:  Minkowski plane, symmetry sets, evolutes, caustics, singularities. 
Faculty / Department:  Faculty of Science > Mathematics and Computer Science 
Depositing User:  Graham Reeve 
Date Deposited:  07 Sep 2017 11:34 
Last Modified:  07 Sep 2017 11:34 
URI:  http://hira.hope.ac.uk/id/eprint/2132 
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