Technology Of Generating Features Of Adaptive Subdivision Surface Based On Catmull-Clark Scheme

Subdivision scheme is a new discrete modeling technology which models the surfaces through globally applying some certain rules to a given control mesh. Subdivision surfaces have a clear advantage over NURBS and Bezier tensor product patches, that are traditionally used in computer modeling and animation applications, because subdivision surfaces can describe arbitray complicated topology. In addition, subdivision surfaces do not have the continuity problems which parametric patches have when connecting multiple patches to produce piecewise smooth surfaces. Among all the subdivision schemes, Catmull-Clark subdivision scheme is generalization of bicubic uniform B-spline knot insertion scheme, and so it is easy to apply this scheme to the widely-used commercial modeling softwares. This paper focuses on the methods of generating sharp and semi-sharp features of subdivision surfaces, and also on the adaptive subdivision scheme which is finally applied to the modeling of features mentioned above. The paper is divided into the following aspects:1. Although subdivision surfaces have good smoothness, some non-smooth effects are required in engineering surface modeling. These effects are called sharp features in the paper. Two methods of generating sharp features based on Catmull-Clark subdivision scheme are described in this paper, one is based on modified subdivision schemes, the other is based on the reconstruction of mesh topology.2. Actually real-world features are never infinitely sharp, especially for mechanical parts whose sharp features are often changed into fillets. The features similar to these fillets are called semi-sharp features. This paper introduced a method of generating semi-sharp features, which is based on the sharp feature schemes. The general idea is to use infinitely sharp rules for a finite but arbitrary number of subdivision steps, followed by use of the smooth rules for subsequent subdivision steps. Intuitively this leads to surfaces that are sharp at coarse scales, but smooth at finer scales.3. This paper develops an dihedral-angle-based adaptive subdivision method, in order to solve the problems that arise when after a few subdivision steps, the amount of vertices increases sharply and leads to heavy computational load, but the smoothness of high-curvature areas and the areas consisting of features are far away from being satisfying. This method expanded the specified region of the mesh to its r-ring neighborhood such that when it was adaptively subdivided, it produced a smooth surface whose selected area was identical to when the entire mesh was refined. This technique also produced a surface with an increasing level of detail from coarse to fine areas of the surface.