Modeling With C-B-Splines And The System Development For Its Subdivision Surfaces

According to the requirements of a national science fund (60073025), this thesis discusses the engineering applications of C-B-splines in the surface modeling and some other related techniques. As well as a surfaces modeling system based on C-B-splines and Catmull-Clark subdivision surfaces is developed for both real application and the testing of new similar subdivision algorithms. The major contributions of this thesis are: D The algorithms of interpolation and fitting with C-B-splines for discrete pointsare provided. The algorithm of artificial neural network is introduced to the approximate calculation of the offset curves for C-B-splines. For different applications, two neural network models of C-B-splines are provided, and their corresponding algorithms are simple in computation, and have high precision in approximation. A modeling scheme of revolution surfaces with C-B-splines for engineering is proposed. With this scheme, the modeling process is simple, the parameter for selection has a definite geometric meaning, and the resulting shape of revolution surfaces is adjustable. An adjustable Catmull-Clark subdivision algorithm is proposed. By changing the shape parameter in C-B-splines subdivision curves, the algorithm extends its adjustable scope. Using the above result, the thesis models the adjustable Catmull-Clark subdivision surfaces. The shape can be adjusted in a wide range. A practical system is developed for surfaces modeling based on C-B-splines and Catmull-Clark subdivision surfaces. The system adopts effective, real-time, interactive user-interface. With it, the resulting surfaces can be adjusted dynamically and the operation is easy. Meanwhile, equipped with data exchange interfaces, the system and the other CAD/CAM systems can exchange data through DXF each other. At last, after a lot of optimization, the data structure and program framework of the system is reasonable and flexible. It can be used notonly for practical applications, but also to debug and study for other subdivision surfaces algorithms.