Research On Critical Technology Of Subdivision Surface Appling To CAM

Free-form surface has been widely used in varied areas along with the development of CAD/CAM technology. Subdivision surface behaves best in modeling complex free-form surface among existing methods, for it not only preserves several advantages of traditional NURBS, especially the properties of local controllability and affine invariance, but also has some special advantages such as arbitrary topology and compatibility which parameter surfaces don't have. As a result, subdivision surface has become one of the hot topics in international CAD/CG areas in recent years.At present, subdivision surface has been applied to many areas, such as animation, games, multiresolution and medical image process, but little research has been carried on applying to engineering. The relevant research focuses on reconstruction of subdivision surfaces. As to applying to CAM, much more problems need to be solved, such as offsetting and intersecting. This thesis mostly researches the critical technologies of subdivision surfaces applying to CAM, including the following points:1. The history of subdivision surface is briefly introduced, and the base theory is also addressed. In order to choose an appropriate scheme for CAM application, an overview of typical subdivision schemes is investigated and the properties of these schemes are summarized.2. An adaptive subdivision scheme based on vertex flatness is presented. By adaptive subdivision, dada increasing with exponential rate is avoided, and the efficiency of data transmission and process is well improved.3. Two algorithms to generate the offset of Loop subdivision surface are discussed. The first one directly finds the control polygon mesh of the offset surface from original control mesh, and then using subdivision rules to generating limited surface. The second one is using control mesh which is very approximating the subdivision surface to replace the limited surface and offset it. Qualitative analysis of the average error of the two methods is done, and the maximal error of the two methods is quantificationally analysed. At last, the cost of the two methods is evaluated respectively. After full consideration of the above three factors, the second method proves to have better quality and higher efficiency.4. Key problems of offset surface such as feature preserving and intersection detecting are well processed. Strategy of treating sharp features and smooth features separately is put forward. In the process of keeping sharp features, uniform offset is realized by defining normals of crease vertex and corner vertex. As to intersection during offset, two instances that allowing and not allowing intersection are considered, and invalid loop is removed.5. An improved Z-Buffer algorithm of generating NC cutter path for Loop subdivision surface is proposed. This method considers not only the finish cut but also the rough cut. Precision and efficiency is controlled by the grid interval of Z-map.6. Some examples are maded by Visual C++, and combined with OpenGL to verify the validity of the algorithm in this thesis.