The shock scaffold by Frederic

The Symmetry Set ( ) is the closure of the locus of centers of spheres tangent to smooth surface patches in two or more loci; such bitangent spheres are called “contact spheres.” The Medial Axis ( ) is the subset of the for which all such spheres are maximal, i.e., such that no other contact spheres are contained in them.2 A classification of points was introduced by Giblin and Kimia [6, 7], which we now summarize. Let denote a circle (in 2D) or a sphere (in 3D) osculating a boundary element at distinct points, each with degree of contact, Figure 1: denotes regular tangency; denotes a sphere of curvature for a surface patch; denotes a sphere of curvature at a ridge point; denotes a sphere of curvature at a turning point of a ridge, etc. [8, Ch.6]. Only odd orders of contact (i.e., ) can contribute to a type of shock, that is, as being the center of a maximal sphere. Then, a classification based on the number and order of contact [6] leads to five principal types of shock points: !