Study On The Theory And Technology Of B-Spline Surface Reconstruction Based On Scattered Points

According to the particular characteristics of CAD modeling in reverse engineering and the practical demands from customers, the author made an elaborate and in-depth study on B-spline surface reconstruction in three aspects, including B-spline surface fairing, local B-spline surface designing and B-spline surface approximating based on complicated boundary constraints.Surface fairing is an inevitable operation on reconstructed B-spline surface in reverse engineering CAD modeling. Because of some random factors in data acquisition process or limitation on modeling methods, the quality of the constructed B-spline surfaces may not always satisfy the users' requirements. In order to solve this problem, three fairing methods, which can efficiently improve the surface quality, are systematically discussed and implemented in reverse engineering software, RE-SOFT. On the basis of analysis and comparison of their strengths and weaknesses, each method can find its applied occasion. With energy method, we can conveniently control the precision of the objective surface and add boundary constraints for preserving the model's global geometric continuity, but this method is very time-consuming. Stiffness adjustment is the easiest method to be implemented and the fairing result is always satisfying except that the acquired surface editing is awkward. Based on wavelets decomposition, the surface model's data size can be compressed efficiently and this method is running fast, however, the error and boundary constraints are difficult to be considered. In general, the quality of the reconstructed surface can be ameliorated greatly to meet practical application with appropriate fairing method above.Local B-spline surface designing strategy, a surface coincided technology, is proposed entirely originated from practical requirements in reverse engineering CAD modeling. After a series of operations on the surface model built from measured data points, the continuity along the common boundary or around the corner region of some adjacent surfaces may be destroyed. So as to deal with this problem, local B-spline surface designing method with complicated trimmed boundary constraints is advanced. For two neighboring surfaces, we first trim a belt along the common boundary and then bridge a B-spline surface between these two trimmed surfaces with a smooth blending. With respect to the comer area comprised of several adjoining surfaces, a rectangular region covering the comer area is obtained by trimming operations at first, and later a local B-spline for filling the rectangular region is completed through interpolation or approximation. Many application examples show that this local B-spline surface designing strategy cannot only guarantee the quality of the surface, but also preserve the global geometric continuity of the whole CAD model.Free form surface reconstruction is a key step in reverse engineering CAD modeling. On the basis of segmentation, an approach of B-spline surface reconstruction with complicated boundary constraints is addressed. The author has analyzed and compared several main cases of boundary constraints thoroughly, furthermore, mathematical modeling and error analysis of the most complex boundary constrains case has been lucubrated. With this approach, the surface model can approximate inner scattered points and interpolate boundary conditions while keeping the global Gl continuity. Actually, the study on the theory and technology of B-spline surface reconstruction with complicated boundary constraints is an essential and innovative point of this thesis.All the research work mentioned above is derived from background of reverse engineering CAD modeling and it has strong applied value. In practical application, the methods presented in this thesis are proved to be robust and satisfying.