Study On Shape Modifing Of Catmull-Clark Subdivision Surfaces

Recently, the subdivision methods have become an important research item in international Computer Graphics. Especially , the Catmull-Clark subdivision surfaces had achieved great success in computer animation and geometric modeling. But there are still many difficulties, to extend Catmull-Clark subdivision surfaces to engineering application. The problems include Catmull-Clark subdivision surfaces can't precisely represent standard conicoid except paraboloid, and it can't modify the shape of limited surfaces when the original control mesh be given.This thesis studied the shape modifying of Catmull-Clark subdivision surfaces, and gave two solutions.Firstly, the article presents a new algorithm to design adjustable Catmull-Clark subdivision surfaces using a controlling parameter t(0≤t≤1). This new algorithm is easy to use, and can modify the surface shape in a bigger scope . And when adjusting parameter t, a family of subdivision surfaces can be constructed. The algorithm is explained in detail. When parameter t unequal to zero the limited surfaces are proved at least C1 continuous except at extraordinary points. Moreover, we can use this subdivision algorithm as pretreatment for Catmull-Clark subdivision.Secondly, an adjustable Catmull-Clark subdivision algorithm based on C-B-splines is proposed. Instead of the shape parameter a in C-B-splines, cosa, that is Ck here, is used for the C-B-splines, and the definition interval of Ck is extended to [-1, )for the construction of Catmull-Clark subdivision surfaces. If Ck is at [-1, 1), it is a common Catmull-Clark surface of C-B-splines, and it can't reach the area between the standard Catmull-Clark surface and the original control mesh. However, as the Ck increased to over 1, the surfaces can be located at this area too. This algorithm inherited the nearly all the properties that the C-B-splines and the Catmull-Clark subdivision surfaces have, such as representing the cylinders, and constructing the surface with arbitrary topologic structure meshes etc.Finally, a software system is designed with Visual C++ 6.0 and OpenGL in order to realize the two schemes. Through plentiful practical example, the two schemes in this article are proved to be right and feasible.