Minkowski symmetry sets of plane curves

Reeve, Graham, and Tari, Farid (2017) Minkowski symmetry sets of plane curves. Proceedings of the Edinburgh Mathematical Society, 60 (2). pp. 461-480. ISSN 0013-0915

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Official URL: https://doi.org/10.1017/S0013091516000055

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 bi-tangent pseudo-circle that is tangent to gamma at both p and at some other point q on gamma? 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 point p on gamma does there exist a branch of a pseudo-circle 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), 461-480. Copyright held by Cambridge University Press. https://www.cambridge.org/core/journals/proceedings-of-the-edinburgh-mathematical-society/article/minkowski-symmetry-sets-of-plane-curves/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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