High-Order Implicit Blending Surfaces of Low Degree

摘要

The applicability of the so-called potential method for blending implicitlydefined surfaces is extended. The extended method is able to produce blendings which are C to the power k-continuous, where k may be chosen arbitrarily large. The blendings consist of piecewise algebraic surfaces of low degree. Specifically, the degree is k+1 for so-called convex corners, and 2k for an important class of non-convex corners. The method is illustrated by a concrete example, where a C squared blending surface of degree 4 is constructed for a certain non-convex corner.