3D geometric modeling has numerous applications in the fileds of virtual reality, film and game production, and relic protection. The development in 3D scanning and computer technologies, along with the increasing requirement for the reality of the model, has made the measure based modeling become an important trend in computer graphics. This thesis centers on the issue of surface reconstruction from unorganized points and mesh simplification,which are the two main parts of 3D geometric modeling. The proposed algorithms of surface reconstruction can be divided into two kinds: interpolation and approxmation. The result of the former kind is more faithful to the original surface. Interpolation algorithms usually find the topological relations among the samples through Voronoi diagram and its dual Delaunay triangulation. Among these algorithms, Voronoi filtering can correctly reconstruct the surface from sufficiently dense samples. However, the algorithm is restricted in practical application because it takes too long time to run. In practice, the sampling density required for correct reconstruction is varied in different area: dense in detailed areas and sparse in featurelss ones. Based on this fact, we presented a fast algorithm for surface reconstruction from unorganized points. We non-uniformly sample the input point sets according to sampling condition, so that the amount of points used for reconstruction is greatly decreased and the speed of reconstruction is improved. The results show that the reconstructed surface is topologically correct and the important details are kept very well. The majority of mesh simplification algorithms are based on geometric elements decimation. In these algorithms, the local error not only discribs the approximation between the simplified model and the original model, but also supervises the simplification. The local error cannot globally discrib the details in the model. On the other hand, it is very complex to comput. Enlighten by the sampling condition of surface reconstruction, we introduce the local feature size into simplification and propose a new simplification criterion. In this method, we first compare the distance between a vertex and its neighbor, then delete the neighbor within the local scale and triangulate the hole caused by deletion. Because of the local feature size, the local scale can automatically adjust according to the local area with a gobal precision control. The results show that this method can decrease the amount of data effectively, as well as preserve the vision characters very well.
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