Generalization of the potential method for blending three surfaces

Abstract The potential method is one of the methods of generating a blending surface along the intersection curves of implicit surfaces. The paper describes a generalized method, for three surfaces, of yielding the formulae for the convex and nonconvex combinations, each of which retains the locality of the blending regions, and has the ability to control the ranges of the edge blends along the original sharp edges. This is analogous to variable-radius rolling-ball blends. To obtain the satisfactory blending functions, the polarity and special pencils of quadrics are applied. After these derivations, it is pointed out that the other quadratic blends for three surfaces correspond to the special cases of the described method. Further, the projective potential method is presented for a convex combination of the three surfaces.