Surface blending with curvature continuity

Abstract

In this paper, a simple, accurate and efficient method is presented for free-form surface blending with curvature continuity. The method is based on an approximate analytical solution to a sixth order partial differential equation (PDE) subjected to blending boundary constraints. The most accurate and fast solution to a PDE is the closed form solution, which however is either very difficult to come by or does not exist. Comparison studies show that our proposed method has similar accuracy and computational efficiency to those of the closed form solution. We also examine the effects of the vector-valued parameters on the shape of blending surfaces and apply our proposed method in various surface blending examples. The outcomes indicate that the proposed approach is able to solve not only simple surface blending problems, but also complex ones which otherwise could only be solved using expensive numerical methods. In addition, this method can be extended to satisfy up to curvature continuities along 3 or 4 boundaries of a 3- or 4-sided patch and serve as an effective tool for the generation and manipulation of complex surfaces.