Skinning rational B-spline curves to construct an interpolatory surface

Abstract

Skinning is a process by which a set of curves (called generator curves) is interpolated to form a surface. The standard skinning algorithm for polynomial B-spline curves is fairly straightforward and has the desirable property that the created surface is as smooth as the generator curves. Tiller has generalized this algorithm to rational B-spline curves in a way that preserves the simplicity of the algorithm but does not guarantee that the surface will be as smooth as the generator curves. In this paper, we explain how discontinuities can arise, derive the exact conditions under which the surface will be smooth, examine possible modifications to the skinning algorithm, and describe in detail the algorithm that we feel is best.