Mos Surfaces: Medial Surface Transforms With Rational Domain Boundaries

We consider rational surface patches s(u,v) in the four-dimensional Minkowski space IR3,1, which describe parts of the medial surface (or medial axis) transform of spatial domains. The corresponding segments of the domain boundary are then obtained as the envelopes of the associated two-parameter family of spheres. If the Plucker coordinates of the line at infinity of the (two-dimensional) tangent plane of s satisfy a sum-of-squares condition, then the two envelope surfaces are shown to be rational surfaces. We characterize these Plucker coordinates and analyze the case, where the medial surface transform is contained in a hyperplane of the four-dimensional Minkowski space.