Some Research On The Generating And Manipulating Of PDE Transition Surface

Surface modeling is one of the uppermost content in Computer Aided Geometric Design and Computer Graphics. Its central is the representation, design, show and analysis of the surface in the computer environment. The PDE surface generation is a method for generating surface by regarding them as the solution to some partial differential equation. The method was initially proposed by M.I.J.Bloor and J.Wilson and has been enhanced and applied widely from then on.With the development of the computer science, it is necessary to seek an effective numerical method. In this paper, a numerical method to generate and manipulate transition surface between two surfaces by using partial differential equation is presented. The boundary element method is introduced to solve partial differential equation for solving surfaces blending problem in this paper. It is convenient to use the boundary element method in the application. Moreover, spline interpolation is made use of supplying unknown boundary condition, from which the surface can be manipulate effectively. The method presented in this paper has excellent succinctness, practicality and adapt to interactive design.This paper is organized as follows: In section 1, the course of surface modeling is retrospected and the basis theory and some typical methods of PDE surface is" introduced. In section 2. the boundary element method is introduced in brief. The content from section 3 to section 5 is the main part of the paper, in which the process of PDE surface generating by boundary element method is described and some typical numerical examples are shown. Furthermore, the way how to manipulate surface by designing their unknown boundary conditions is brought forth. Finally, in section 6, a summary for our work and a tentative idea is given.