Research On Modeling And NC Processing Technology For Loop Subdivision Surfaces With Feature Keeping

Subdivision scheme is a new discrete modeling technology. Subdivision surface can express modeling surface through control mesh and subdivision rules. This technology not only preserves several advantages of traditional NURBS surface, especially the properties of localness and affine-invariance, but also has some special advantages such as adaptability to arbitrary topology and multiresolution property to data compression and simplifition which NURBS surfaces don't have. These lead subdivision surface into one of the most powerful geometric modeling tools. However, without global analytic representation, the research about subdivision surface is difficult.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)The classification of subdivision schemes is introduced, with comparing the subdivision rules, quality and contractibility of limited surface based on several common schemes, the principle to choose subdivision schemes in practice is presented, and for further research, the geometric theory of Loop subdivision scheme is introduced together with some impotant conclusions in exact computation.(2)Though subdivision surfaces have good smoothness, some non-smooth effects are required in engineering surface modeling. Combined with Loop subdivision scheme, an algorithm to modify subdivision rules is presented and implemented for generating the sharp features. Firstly, edges and vertises that need special treat should be tagged as sharp edges and vertises, and then different rules are applied to calcurate the results. Meanwhile, an improved tree data structure suitable for subdivision is developed, our algorithm are implemented via this data structure. The technique of OpenGL is utilized to accomplish some basic operations, such as rotation, zoom, pan and so on. Finally a system based on our algorithm is developed.(3)There are commonnesses and individualities between subdivision surface and NURBS surface, based on the research of the algorithm of NC tool path generation for NURBS surface, a cross-section method is put forward to obtain the NC tool path of the refinement surface. Firstly, a series of parallel plane intersect with subdivision model to get cutter contact trajectory, then NC tool path is obtained by offset cutter contact trajectory along the the normal vector of triangle. Lastly, the NC tool path of the refined model is verified with the MasterCAM software. The research is valuable for the improvement of the subdivision scheme commonly used in CAD/CAM system.