Research On Smoothing And B-Splines Surfaces Fitting Of Triangular Mesh Models

Triangular meshes acquisition from the existing physical object is more convenient with the development of coordinate measure system. But the triangular meshes reconstructed from measured data may contain unavoidable noise and many irregular triangles, so mesh fairing is needed before using them. At the same time, we need to transform triangular meshes to B-Splines surfaces, which are the general surfaces in Computer-aided designing field, in order to satisfy other consequent applications. Smoothing and B-Splines surfaces fitting of triangular meshes have been studied in this dissertation, the following are the mainly contains: In this paper, a new method for the calculation of mesh vertex normal vector is presented, these vertexes can be classified according to their normal vectors, and an adaptive mesh fairing algorithm based on vertices classification is put forward too. Besides eliminating noise and uniforming triangles, this smoothing method can effectively preserve features of the original meshes as well. The B-Splines surfaces fitting technique based on parameterization of triangular meshes is studied, and the mean value coordinate parameterization method is realized. Researching the parameter points sampling algorithm, realize uniform and non-uniform sampling algorithms respectively. Then with inverse mapping, new three-dimensional sampling points can be computed and cubic B-Splines surfaces are fitted. The B-Splines surfaces fitting algorithm with Multilevel B-Splines is also studied. And a modified fitting method about sparse meshes is put forward. An adaptive Multilevel B-Splines surfaces fitting method is realized, and it enhance performance greatly. Finally, a part distortion of mesh is realized with both Multilevel B-Splines surfaces fitting method and triangular parameterization.