Generating blending surfaces with an iterative solution to fourth order PDE

Abstract

In this paper, we develop an efficient method for surface blending. It is based on our previously proposed fourth order partial differential equation (PDE) with three vector-valued shape parameters. In order to solve this PDE efficiently, we have previously developed a closed form resolution method. However, a closed form solution only exists in a small number of situations, and therefore the application of a closed form solution based method is limited. By transforming the original PDE into an algebra equation, we can achieve an approximate closed form solution. The examples given in this paper indicate that the developed method can generate blending surfaces almost as accurately and quickly as the closed form solution. In addition, it can deal with any combinations of the shape parameters and greatly facilitate the computer programming of various surface blending tasks.