Partial Differential Equations (pde) Surface Modeling And Interactive Surface Design Techniques

With the spreading application of CAD/CAM, people place more and higher acquirements on CAGD. The traditional NURBS based surface modeling can't satisfy the needs to construct the complicated surfaces and generate high quality shape. This is a major challenge facing system on CAGD and has given rise to a number of alternative approaches: the wavelets-based surface modeling, the PDE surface modeling, the energy-based surface modeling and so on.In order to investigate the potentials of PDE surface modeling technique, a systematic study is carried out in the dissertation.This paper proposes a more general fourth order partial differential equation with three vector shape functions. It covers all forms of existing fourth order PDE used for free form surface generating. It is capable of generating surfaces of much greater variety. As we replace the constant coefficient using arbitrary functions of u and v, which can be defined by users, this can offer users more flexibility for interactive shape design and achieve local control on PDE surfaces.In this paper, the application of the PDE method in generating blending surfaces and free-form surfaces is discussed. In the interactive shape design a global and local set of design tools that allow users to interactively modify the shape of PDE surface are offered. Using the finite element method, we make some research on the B-spline approximations of PDE surfaces. The PDE surface data obtained by this method can be transferred to the system based on NURBS.