The Subdivision Research On Improved Algorithm Over Arbitrary Topological Meshes

The key idea of Subdivision Modeling is to process a series of subdivisions on the initial control vertexes or initial controls meshes, and generate the needed curve or surface after the subdivision. The biggest advantage of subdivision method is that it can generate smooth surface from arbitrary initial mesh. There are three types of algorithms for the meshes with arbitrary topology: approximation subdivision algorithm, interpolation subdivision algorithm and mixed subdivision algorithm. Most surface modeling methods use only approximation algorithm or interpolation algorithm solely. Approximating subdivision techniques is a contractive method, and we can't control the surface efectively. 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.The main focus of this paper is the further study of modeling technology in subdivision surface. Its main contents and contributions are as follows:1. Based on the analyses of subdivision schemes in common use, an improved winged-edge data structure suitable for subdivision is developed. The principle to choose subdivision schemes in practice is presented.2. Basic theories of subdivision surfaces are studied. Deriving method, matrix representation and eigen analysis of subdivision are presented. relationships between spline and subdivision, and convergence and continuity of subdivision are analyzed. Some of well-known stationary subdivision schemes are introduced and discussed.3. The shape of the subdivision surface and the final object model are determined by the initial control mesh given when improving arbitrary topological meshes to construct smooth meshes, it's unadjustable. So, control parameters and perturbation is presented during the mesh subdivision.Because of the parameter, the subdivision over arbitrary topological meshes is under control by changing the parameter. Kinds of subdivision surfaces can be created.The shape of the meshes can be locally adjusted using perturbation which is developed to modify the spatial positions Some examples of the subdivision surfaces given demonstrate the simpleness, flexibility and efficiency of the algorithm.