Affinely invariant symmetry sets

Volume 82 / 2008

Peter Giblin Banach Center Publications 82 (2008), 71-84 MSC: 53A04, 53A15, 58K05. DOI: 10.4064/bc82-0-5


The classical medial axis and symmetry set of a smooth simple plane curve $M$, depending as they do on circles bitangent to $M$, are invariant under euclidean transformations. This article surveys the various ways in which the construction has been adapted to be invariant under affine transformations. They include affine distance and area constructions, and also the `centre symmetry set' which generalizes central symmetry. A connexion is also made with the tricentre set of a convex plane curve, which is the set of points which are the centres of three chords.


  • Peter GiblinDepartment of Mathematical Sciences
    The University of Liverpool
    Liverpool L69 7ZL, U.K.

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