Research On Some Problems Of Surface Subdivision

Subdivision method has become an important tool in computer graphics. It can express modeling surface through control mesh and subdivision rules. Because it preserves some advantages, such as arbitrary topology, compatibility and affine invariance, it has been widely used.However, to more widely extend application areas, many problems need to be solved. For example, how to create a new subdivision scheme, how to reduce the quantity of face and how to solve uniform interface of subdivision, and so on. The thesis investigates some effective modeling approaches for enhancing efficiency of the subdivision methods.A new ternary subdivision scheme is presented in this paper. Firstly as example for quadratic B-spline, ternary subdivision scheme of quadratic B-spline curve is obtained by analyzing the elements of ternary subdivision. Then binary loop subdivision is imported to ternary subdivision scheme, subdivision rule of ternary loop subdivision scheme is obtained by the research of the subdivision matrix. The experiment shows that ternary loop subdivision method is faster in the speed of convergence than binary loop subdivision, and can ensure the smooth of the subdivision surface. Last ternary Catmull-Clark subdivision scheme is obtained by extending the Catmull-Clark subdivision scheme.At the same time, for analysis of subdivision methods and testify of math theory, a new adaptive subdivision scheme is presented based on traditional loop subdivision scheme. The method divides the control mesh into many connected regions by region partition, and local subdivision scheme is adopted for roughness region. Simultaneously aiming at the boundary crack produced by region partition, a new scheme of processed crack is provided. The experiment shows that the method could reduce the capacity, and then increase the speed of model render.