A vertex-first parametric algorithm for polyhedron blending

This paper enhances the conventional parametric algorithms for polyhedron blending, by strategically inverting the edges-first approach to vertex-first, so that matching the vertex blending surface (using a triangular or tensor product Bézier surface, or an SS-patch) with the edge blending surfaces (generated by Hartmann method) becomes essentially easier. Based on a study of cross boundary derivatives (those of SS-patches are deduced herein), GgGg-continuity between all the above surfaces and the primary planar faces is achieved by a novel trick as a first step: assigning the vertex, some edge points and some face points to be the proper control points. This still leaves enough free parameters usable for changing the blending configuration. The new algorithm is illustrated with two practical examples involving miscellaneous vertices up to 6-edge convex–concave.