Mesh Editing With Hierarchical B-Splines

With the rapid development of 3D scanning technology, mesh processing has become one of the hottest topics in geometry modelling as well as computer graphics and its research results have been widely applied into a great deal of areas, such as mechanical manufacture, movie entertainment, game technology and so on.As the core technology of mesh processing, mesh editing aims at the effective construction of complex geometry models with intuitive and high-efficiency editing approach. In recent years, lots of mesh editing algorithms have been promoted, which can be mainly classified into two categories: the FFD based editing methods which embed the surface into 3D uniform lattice volume and surface differential properties based methods. FFD method provides intuitive editing mode and easy-to-control editing style, while its user interaction is not flexible. The differential properties based methods can bring outstanding deformation result, but it is difficult to be integrated into existing technologies duing to its special representation form.So it is great important to investigate on effective mesh editing method featured with intuitive interaction, easy-to-control editing style and unified data representation. Motivated by this, an unified multi-resolution geometry representation form is proposed in this thesis, which precisely denote the internal geometric properties of surface. After the decomposition of original surface, we can get the unified geometry representation form consisting of a smoothing base surface and a group of local variables defined on the base surface. Using hierarchical B-splines to represent the base surface, we construct a comprehensive and powerful mesh editing framework and implement most of mesh editing applications such as freeform deformation, geometric detail transfer and so on. During the pipeline of our framework, First Region Of Interest (ROI) is selected interactively on the mesh. Then the ROI is parameterized and re-sampled uniformly. The re-sampled points are fitted with hierarchical B-spline surfaces. The local coordinates of the vertices in the ROI corresponding to the hierarchical B-spline surfaces are computed(These local variables are translation and rotation invariant, which could be regarded as intrinsic geometric variables for the mesh and remained unchanged during editing). Based on this, the original mesh could be manipulated through editing the B-spline base surface and multi-resolution editing could be archived easily. Gen-eralizing DFFD method to the framework, the direct mesh manipulation could also be implemented effectively.Furthermore, the extractive local variables could be mapped to different meshes' base surfaces. The framework also can realize the geometric detail transfer. Experimental results demonstrate that our method provides intuitive and powerful operations for both global and local mesh editing. Since the hierarchical B-splines are widely applied, our method can be seamlessly integrated into current animation and modelling systems.