DIFFERENTIAL GEOMETRY OF G(1) VARIABLE RADIUS ROLLING BALL BLEND SURFACES

Variable radius rolling ball (VRRB) blend surfaces can be considered a s envelopes of one parameter families of varying radius balls. These f amilies are usually G(1) continuous but often only piecewise curvature continuous. Tn this paper these (spherical) VRRB surfaces will be ana lyzed on the basis of the theory of envelopes and discriminant sets. T he differential geometric invariants of the VRRB surface are determine d and the progressive and regressive points on the VRRB surface are ch aracterized. The concept of geodesic blend surface is introduced and a nalyzed which avoids local selfintersections if both surfaces locally enclose the variable radius balls. (C) 1998 Elsevier Science B.V.