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Affinely invariant symmetry sets

100%

Giblin P.

Banach Center Publications

2008

tom 82

nr 1

71-84

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.

The centre symmetry set

63%

Giblin P., Holtom P.

Banach Center Publications

1999

tom 50

nr 1

91-105

A centrally symmetric plane curve has a point called it's centre of symmetry. We define (following Janeczko) a set which measures the central symmetry of an arbitrary strictly convex plane curve, or surface in $R^3$. We investigate some of it's properties, and begin the study of non-convex cases.

Ograniczanie wyników

2 Banach Center Publications

2 Giblin P.

1 Holtom P.

1 2008

1 1999

Wyniki wyszukiwania

Affinely invariant symmetry sets

The centre symmetry set