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C2-Smooth Subdivision Surface Construction from Cross-Sections

This paper presents a framework for constructing C2 Catmull-Clark subdivision surfaces that interpolate data points on parallel cross sections, consisting of simple disjoined and non-nested contours, the number of which may vary from plane to plane. In comparison to recent approaches that address the same problem, the use of subdivision surfaces transforms the problem to a mesh generation process, which simplifies and unifies the approach. Furthermore, the existence of extraordinary points on the control mesh will limit the reduction to the continuity of the resulting surface to C1 in the worst case.