Research On Mesh Surface Modeling

Recently, following the rapid development of 3D data acquisition techniques, it is convenient to obtain 3D models with fine details. For the simplicity and suitability of the polygon meshes, they have become the most appropriate representation of those models. However, the piecewise linear characteristic of mesh surface causes millions of polygons to represent the complex geometry details, which will result in more difficulties for the subsequenct processing.This dissertation is concerned with the above promising issues, and some novel techniques of mesh modeling are extensively investigated. These techniques are, the forward transformation problem from discrete mesh to continuous surface, that is, the subdivision method of mesh model; mesh editing; and the inverse fitting problem from the mesh surface to the parametric surface, that is, surface reconstruction.Detailed speaking, the main contributions of our work contain three issues as follows.Firstly, combined with the latest development of C-B-Spline, a new type of parametric surface is proposed, namely forth-order and cubic direction C-Box-Spline, which is defined on the triangular mesh. Its analytical formulation is derived and its geometric properties are also discussed. Moreover, we investigate the discrete representation of C-Box-Spline, a semi-stationary loop subdivision scheme. We point out that the subdivision procedure is convergent, and the subdivision surface has the property of tangent plane continuity. In addition, we extend the method to the anisotropic version and the one capable of representing sharp features.Secondly, to address the key issue of mesh modeling, a novel mesh spectrum editing method is proposed in this thesis, which integrates the techniques of free-form deformation and geometry signal processing. We take the deformation of proxy as geometry signal, and impose its spectrum upon the geometry model to be deformed. The resultant signal is inversely transformed into the space domain, and then the edited mesh could be obtained. The proposed method has advantages of easy manipulation and facilitative preserving for the smoothness of resultant models. As an essential step, an adaptive sampling scheme, which is...