Fillet and surface intersections defined by rolling balls (Q1195079)

The problem addressed here is to connect two surface patches by a third surface tangent to the two given ones along smooth curves. The authors use envelopes of spheres of constant radius as fillet surface. The problem is to compute the curve of centers of these spheres together with the curves of contact with the two given surfaces. The authors show explicitly how to obtain cubic spline approximations of the three curves for one segment. The segments will form \(C^ 1\) curves when appropriately patched together.