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.
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