Studies On Shape Editing Techniques Of 3D Geometric Models

With the development of the 3D scanning technology, the acquisition of point set surface and mesh models becomes easier and easier. Shape editing with these 3D models are now intensively involved in many applications, such as computer animation, computer game, film industry, and so on, which also makes shape editing as an important research topic in the field of computer graphics. Although many researches on mesh editing have been existed, e.g. detail-preserving gradient domain mesh deformation, multi-resolution mesh editing, in order to create some vivid models, the user has to learn 3D modeling skills and aesthetic knowledge. On the other hand, point set surface becomes another important representation of 3D models, due to its simple data structure and intrinsic power of expressing arbitrary complex shapes. However, the editing methods for point set surface are rare, especially for the case of easy for use and reusability.This thesis focused on the aforementioned problems. As to the mesh editing, a method of image driven shape deformation with styles was proposed. It used a 2D drawing or 2D picture to produce the 3D mesh deformation. The deformed 3D mesh has the similar styles with the original 2D image. Since novels used to use 2D sketch as interaction interface, and 2D picture can lead to vivid deformed results, this method can reduce the requirement of the 3D modeling experience and aesthetic knowledge. As to the point set surface editing, discussions on detail-preserving shape deformation for large scale point set surface, shape interpolation between key frames and deform transfer for point set surface were intensively involved, all of which are the most frequently used technologies in key-framed animation system. This thesis also presented some algorithms and their implementation for these aspects. The examples shown in this thesis proved the feasibility and effectiveness of these methods.The main research topics and contributions of this thesis include:·Proposed a method of detail-preserving deformation for large scale point set surface. This method inherits the advantages of free form deformation and gradient domain deformation. It can well preserve the local details of the point set surface and keep a high efficiency during deformation. Firstly, the proxy model of the point set surface was constructed based on the idea of OBBTree and the intersection test of the oriented bounding box. The deformation of the original point set surface was driven by the deformation of the proxy model and the local details preservation was implemented via constraining the affine transformation of each node of the proxy model to be rigid transformation. Since the interaction for the traditional free form deformation is performed on the proxy model, which was not so intuitive for the users, this method allows direct actions on the point set surface through a nearest-neighbor mapping technology.·Proposed the definition of vertex deformation gradient of point set surface. The closed form solution of which was also presented. Compared with the traditional deformation gradient which is defined on each triangle face of the mesh, the vertex deformation gradient is defined on each point of the point set surface directly and can be got from its k nearest points. From the view of quadratic energy optimization, we also presented the closed form solution of the vertex deformation gradient.·By applying the vertex deformation gradient into the problem of shape interpolation and deformation transfer for the point set surface, correspondence between the source point set surface and the target point set surface was well established. The reconstruction for the deformed point set surface can be also well solved. For the case of shape interpolation, the shrinkage problem was avoided by decomposing the vertex deformation gradient into rational part and scale part with polar decomposition and each part was interpolated individually. The vertex deformation gradient of the target point set surface during deformation transfer was interpolated with matrix exponential mapping, which avoids the non-commutative property of the spherical linear interpolation, namely, different order of interpolation will lead to different result. ·Proposed a method of image driven shape deformation with styles. This method represents the shape styles with four kinds of shape descriptions from different levels in the context of triangular mesh. Namely, the object contour, the context curves, local geometric details, perception-driven features. The transfer of each of these styles can be formulated as a quadratic energy optimization. The whole deformation of the 3D mesh was implemented as energy optimization via combining all these energy items together. The coefficient of each energy item in the total energy equation can be adjusted with users' intents, so that user can get different resulting styles and get more controls for the stylization of the 3D mesh.