Continuity and Self-intersections of Variable Radius Rolling Ball Blend Surfaces

Variable radius rolling ball (VRRB) blend surfaces can be considered as envelopes of one parameter families of varying radius balls. As compared to circular blends Joseph Pegna called this type of surface a “spherical (tubular) blend” (Pegna, 1990). Here spherical VRRB surfaces are analyzed on the basis of the theory of envelopes (see e.g (Zalgaller, 1975)). Envelope surfaces are special cases of discriminant sets which have several useful properties, above all under certain natural conditions they are G’ continuous provided the defining equations are C1 (and piecewise C2) continuous as well. In addition to spherical blends, offset surfaces can be defined as envelopes. Voronoi surfaces can be considered as discriminant sets.