Minkowski Symmetry Sets for 1-Parameter Families of Plane Curves

Reeve, Graham (2022) Minkowski Symmetry Sets for 1-Parameter Families of Plane Curves. Journal of Singularities, 25. pp. 361-376. ISSN 1949-2006

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Abstract

In this paper the generic bifurcations of the Minkowski symmetry set for 1-parameter families of plane curves are classified and the necessary and sufficient geometric criteria for each type are given. The Minkowski symmetry set is an analogue of the standard Euclidean symmetry set, and is defined to be the locus of centres of all of its bitangent pseudocircles. It is shown that the list of possible bifurcation types is different to that of the list of possible types for the Euclidean symmetry set.

Item Type:	Article
Keywords:	Medial Axis, Minkowski Plane, Minkowski Symmetry Set, Plane Curve, Singularity, Symmetry Set, transitions, 1-parameter family.
Faculty / Department:	Faculty of Human and Digital Sciences > Mathematics and Computer Science
Depositing User:	Graham Reeve
Date Deposited:	09 Sep 2022 08:48
Last Modified:	09 Sep 2022 08:48
URI:	https://hira.hope.ac.uk/id/eprint/3607

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