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Symmetry set : ウィキペディア英語版
Symmetry set

In geometry, the symmetry set is a method for representing the local symmetries of a curve, and can be used as a method for representing the shape of objects by finding the topological skeleton. The medial axis, a subset of the symmetry set is a set of curves which roughly run along the middle of an object.
==The symmetry set in 2 dimensions==
Let I \subseteq \mathbb be an open interval, and \gamma : I \to \mathbb^2 be a parametrisation of a smooth plane curve.
The symmetry set of \gamma (I) \subset \mathbb^2 is defined to be the closure of the set of centres of circles tangent to the curve at at least two distinct points (bitangent circles).
The symmetry set will have endpoints corresponding to vertices of the curve. Such points will lie at cusp of the evolute. At such points the curve will have 4-point contact with the circle.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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