Free-Form Surface Model Based On Subdivision Method

The modeling of subdivision surfaces is one of the advanced subjects in the science and technology fields, which is included in many subjects. From the metaphase and anaphase of 70th in the 20th century, with the developing of subdivision theories and the expanding of application fields, the modeling of subdivision surfaces has become an absolute subject system gradually. The old modeling of subdivision surfaces is improving and the new modeling of subdivision is emerging in endlessly. At the same time, it gets the new developing power and appears new life force by uniting the new mathematics theories, such as Wavelet transformation theory and Multiresolution analysis theory etc. It has become one of important methods in free form surface modeling after the NURBS method. Today, the modeling of subdivision surfaces has been applied successfully in many important fields of object modeling, reverse engineering of parts of an apparatus and article, movie animation and making of toy and so on.The biggest advantage of subdivision method is that it can generate smooth surface from arbitrary initial mesh. In general, these subdivision schemes can be categorized into two distinct classes: 1) approximating subdivision techniques and 2) interpolating subdivision techniques. Approximating subdivision techniques is a contractive method, and we can't control the surface effectively. But the effective control to the surface is the key in surface design and characteristic animation. By comparison, interpolating subdivision techniques remains initial mesh vertices changeless, but it is difficult for the fairing of the surface to be controlled. It is a challenging task to enhance subdivision method's life-force by using the adjusting capability of controllable vertices of the mesh.This paper introduces physical model to control the controllable vertices of approximating subdivision surface, and various subdivision surface can be obtained by adjusting the parameters in physical model. This method enhanced the flexibility of subdivision techniques. In the paper we use Loop subdivision scheme and Lagrange dynamic equation based on spring model.