Free-Form Surface Using Polyharmonic Function and Polyharmonic Function with Area Distribution

Abstract

Free–form surface can be produced by Piosson′s equations and polyharmonic functions. This method is useful for a solid modelling, because scattered data can be used. In previous paper, the boundary integral equations are used, and values on the boundary must be given. In this paper, two–dimensional polyharmonic functions and polyharmonic functions with area distribution are used instead off the boundary integral equations. Morphing and Boolean operations can be easily obtained using this method. A smoothing method using a least–squares approximation can be also used. In order to investigate the effectiveness of this method, several examples are given.