The critical point and related symmetry measures of a planar convex set

The critical point and related invariant points of a planar convex set are computed using an exhaustive search strategy based on a formulation due to Neumann. Algorithms to compute the critical point based on the Minkowski formulation and Euclidean duality is also presented. The functionals associated with the critical points are illustrated, and computational experience lends support to a conjecture due to Neumann in regard to the lower bound of a perimeter functional. Related symmetry measures based on cut areas and chords are also examined.