Differential geometry of G1 variable radius rolling ball blend surfaces Original Research Article

Variable radius rolling ball (VRRB) blend surfaces can be considered as envelopes of one parameter families of varying radius balls. These families are usually G1 continuous but often only piecewise curvature continuous. In this paper these (spherical) VRRB surfaces will be analyzed on the basis of the theory of envelopes and discriminant sets. The differential geometric invariants of the VRRB surface are determined and the progressive and regressive points on the VRRB surface are characterized. The concept of geodesic blend surface is introduced and analyzed which avoids local selfintersections if both surfaces locally enclose the variable radius balls.