Implementation of Surface Interpolators for Compound Surfaces without C2-continuity

Abstract

Numerical Controls (NCs) are used to manufacture freeform surfaces such as B-Spline surfaces or Non-Uniform Rational B-Spline Surfaces by subtractive or additive manufacturing processes. Although parametric surfaces are common for these processes, it is in general not possible, to transfer parametric curves or surfaces to the NC. However, some authors examine this possibility. In this context, surface interpolation is the idea to transfer the mathematical surface description of the freeform surface to the NC. This opens the possibility to receive a faster and exacter process as well as better surface quality, compared to the standard process chain, where surface information is reduced to a minimum before it is transferred to the NC. Earlier work considers surface interpolation with the restriction, that the part to manufacture is composed out of a single surface, only. As surfaces of complex parts are merely composed of several surfaces, this paper extends the definition of surface interpolators to these so-called compound surfaces. Depending on the transition between two neighboring surfaces, different strategies have to be defined when the interpolation process reaches surface boundaries. In this paper, we focus on intersecting surfaces that do not intersect smoothly such that the computation of intersection points and smoothing of paths between two surfaces is considered.