The Orthogonal Decomposition Of Geometric Model Based On The V-system Over The Triangular Domain And Its Application

The V-system is a new class of complete orthogonal functions defined on L,[0,1] or over triangulated domain, and it has various applications in the field of signal processing and analysis. The V-system has particular capability to exactly represent and reconstruct the geometric models in CAGD by eliminating the famous and undesirable Gibbs phenomenon, no matter the model is continuous or discontinuities. Specially, the V-system over triangulated domain has an important application to the global spectrum analysis of the object group of3-dimensional complex geometric models. This dissertation focuses on the exact representation and efficient retrieval of the3-D geometric models based on the spectrum analysis of V-system and the triangular meshes of3-D models.The contribution of this dissertation is briefly described as follows.First, we presented the mathematical expression of the V-system over triangulated domain, and applied it to the orthogonal representation of3-D models. For the geometric models constructed by triangular meshes, they can be represented exactly by a finite number of the basis functions of the V-system over triangulated domain. Thus, the orthogonalde composition and reconstruction of geometric models can be performed between the spatial spectrum domains.Consequently,data compression,feature classification and model retrieval of the3-D geometric models can be achieved by spectrum analysis.Second, we explored the classification and retrieval of3-D model by using the V-system over triangulated domain. For the performance evaluation, a3-D model database with capacity of1250was created. The experimental results on the database demonstrate that our method outperforms the classical geometric moments and Silhouette FV.