Research On Technology Of Adaptive Subdivision Surface Based On Catmull-Clark Scheme

Subdivision scheme is a new discrete modeling technology which describes the modeling surface through controlling mesh and subdivision rules. It has many advantages such as localness and affine-invariance of traditional B-spline surface, adaptability to arbitrary topology which parameter surfaces not have, and becoming one of the most powerful geometric modeling tools. Subdivision scheme for surface is gradual subdivision which obtains final surface by discrete to discrete method, and the disadvantage of conventional method from discrete to continuous and then from continuous to discrete is avoided. Due to its simpleness and convenience to implement, the subdivision scheme has become a focus topic on computer aided geometric design and computer graphics recently. There are many subdivision schemes, such as Catmull-Clark subdivision, Doo-Sabin subdivision, Loop subdivision and etc. The Catmull-Clark subdivision scheme is generalized of B-spline surfaces, it can be blent with NURBS surfaces easily and be unified with the NC processing commendably. The paper focuses on the Catmull-Clark subdivision surfaces modeling techniques and the adaptive subdivision method is adapted to improve modeling abilities of subdivision surface from different viewpoints, and constructs more relations between subdivision surfaces and NURBS surfaces. The main contents are as follows:1. The Catmull-Clark subdivision scheme is emphasized, including its basic theories, development, research and rules of subdivision. The related research about adaptive subdivision is summarized and analyzed from the subdivision criterion, handling strategy of cracks and calculating of mesh vertexes.2. A new adaptive subdivision method based on Catmull-Clark for quadrilateral mesh is applying. The dihedral angle value is set as the threshold to evaluate the flatness of the mesh, and through the value to command the partial subdivision depths. This method can limit the number of the meshes and a method is also presented to avoid generating cracks by different subdivision depths. Through simulation, it proves that this method can reduce data quantity and increase computing speed.3. Adaptive subdivision method has an influence on the continuity of surface meshes, a modified adaptive subdivision scheme which based on Catmull-Clark scheme is discussed for quadrilateral mesh. The method uses the inscribed polygon replacing the control mesh of subdivision surface to approximate the surface. This method can avoid the possibility of over-tessellation problem as well as simplify the processing of crack check and eliminate.