C2-smooth subdivision surface construction from cross-sections

Abstract

This paper presents an alternative to the approach proposed by Gabrielides et al. for the construction of a smooth surface to interpolate data points given on parallel cross sections. The method presented there focuses on handling the general case of planar cross sections consisting of disjoint smooth Jordan curves, referred to there as contours, whose number may vary from plane to plane. Their approach relies on a combination of modeling contexts and a variety of modeling techniques guaranteeing a G1 interpolation surface. Gabrielides et al. also provide a number of application domains where the solution of this interpolation problem is employed. They also detail a number of methods and tools that were used in the implementation of solutions of this problem. By comparison, the interpolation problem addressed in this paper concerns the interpolation of the given data points and not the cross sections carrying them. In this context, one does not fail to see the relationship between this interpolation problem and another problem known as lofting, which concerns the generation of a smooth surface interpolating a set of (parallel) curves. Historically, the term lofting is used in the old days when ship bodies used to be designed manually.