Automatic Polycubic Parameterization And Cross-parameterization

With the rapid development of 3D scanning technology, meshes have become a widespread and popular representation of models in computer graphics, and mesh processing techniques have received a lot of interest lately.A parameterization of a surface can be viewed as a one-to-one mapping from a suitable domain to the surface, which is fundamental in many areas dealing with meshes, such as texture mapping, remeshing, mesh editing and morphing.According to the parameter domain, all kinds of parameterization methods can be classified into planar parameterization, spherical parameterization, simplicial parameterization and the recently proposed polycubic parameterization. A polycube is a shape composed of axis-aligned unit cubes that are attached face to face. The special structure of polycube leads to a seamless texture mapping method.In this thesis, we present an automatic polycubic parameterization method and propose a cross-parameterization approach based on polycube. Our main work and contributions can be summarized as the following:1. Automatic polycubic parameterizationThe existing polycube-maps are constructed semi-automatically which need a lot of user intervention. We propose an automatic polycubic parameterization. First, the mesh is decomposed into a set of feature regions, each of which is then approximated by a simple polycube and splitted into several patches further. Each patch is corresponding to a rectangular sub-surface of the polycube which can be parameterized independently. Finally, a smoothing procedure between patches is performed to reduce the overall parametric distortion. At last, we obtain the polycubic parameterization efficiently.2. Cross-parameterization based on polycubeThe ability to bijectively map one mesh to another is useful for many applications. The models which need to be cross-parameterized usually have similar features and the parameterization must respect those. Since the polycubes resemble the shape of the models, directly mapping between the matchingrectangles of two polycubes can preserve the large features of the models. If the user specifies some feature vertices, the source mesh is parameterized firstly. Then for each rectangle containing feature vertices, the algorithm finds a triangulation of the rectangle of the source polycube and a matching triangulation of the corresponding patch of the target mesh. Then each patch of the target mesh is mapped to the corresponding rectangle or triangle sub-surface of the source polycube, and we obtain the feature preserving cross-parameterization. We can also build maps with singularities between models with different genus.Our methods work well for meshes with arbitrary genus. The cross-parameterization method can also be used to constrained texture mapping directly.