Symmetry Sets

The Symmetry Set of a shape is defined as the closure of the centres of circles tangent to the shape at at least two points.

symmetry set

Left: An egg shape (bold) with a series of circles probing it. The circles are tangent at the red dots. The centres are given by the blue dots. These dots form three curved branches of the Symmetry Set.
Right: The pre-Symmetry Set is given by the diagonal-symmetric diagram formed by the pairs of points along the shapes where the circles are tangent. Horizontally and vertically the points alonog the shape are given. Each point pair of a tangent circleo ccurs twice, as (x,y) and (y,x). For each Symmetry Set branch a curve in the pre-Symmetry Set is present.