Research On GCS-Based Surface Reconstruction And Mesh Optimization

At present, it is a hot research topic in Computer Graphics (CG) field to realize surface reconstruction and mesh optimization using a set of 3D scattered data points obtained by scanning object surface. The research findings have great practical value in many fields, such as machine building, virtual reality and so on.The traditional algorithms of surface reconstruction, including Zero-Set algorithm, a -shape algorithm, Voronoi algorithm, etc., have obtained good results. But, the errors are large between the actual surface and the reconstructed one by Zero-Set algorithm. And the memory space, required by the interpolation mesh surfaces by a -shape and Voronoi algorithms, is rather big. Furthermore, the speed of above algorithms drops quickly when amount of scattered data points increasing. The traditional algorithms of mesh optimization, such as Edge exchanging, Edge collapse and Edge splitting, etc., can only partially optimize a mesh with not very good result. So it is necessary to do further research about approaches of surface reconstruction and mesh optimization.The main works in this dissertation are as follows:1 , The method of fast surface reconstruction using Growing Cell Structure (GCS) is studied. When dealing with input data, GCS samples just one point a time. Its speed of processing is independent of amount of input data. And it is very effective to deal with the noisy data . So, it is well suited for surface reconstruction based on a set of scattered data points and has a good foreground of applications. During surface reconstruction, the method of linear combination is used to split nodes, and a simple method to calculate the area of Voronoi cells to assign a value to the signal counter of the new node. And the surface is further optimized by a method in the end.2, An algorithm of mesh optimization based on energy minimization is presented. For a set of 3D scattered data points and an initial triangular mesh, the energy minimization method is used for mesh optimization to make all vertex position approach the scattered data points.3, A new algorithm for integrated mesh optimization is proposed. For a set of3D scattered data points of an object surface and an initial triangular mesh, we use a mesh optimization algorithm based on Self-Organizing Mapping(SOM) to make all vertex position approach the scattered data points and make the distribution of vertices close to the probability distribution, of scattered data points. The vertices with very high valence are splitted in order to make the shape of mesh more smooth. 4n Some experiments have been done about surface reconstruction and mesh optimization, the results of which show that the methods presented in this dissertation are effective and rapid in surface reconstruction.