Mesh Deformation Technology Based On Differential Coordinates

Mesh deformation has become an important element of mesh editing on three-dimension models, which is the process of three-dimension geometric models'transforming from one action sequence to another. The technology of mesh deformation has become one of the key research topics in computer graphics in recent years, and many results have been widely used in varied fields, such as animation, film, advertisement and visualization in scientific computing. It means that the three-dimension virtual world has been integrated into the daily lives of people. The algorithms of mesh deformation can be divided into two categories. One is based on interpretation and reconstruction, which is highly maneuverable and easy to actualize but inefficient and prone to bring distortion. The other is based on energy minimization, which belongs to the way of indirect deforming is fast and receives better results but is uncontrollable, and has narrow scope in practice. The development trend for mesh deformation in recent years is to make an integrated method with the advantages of several ways. This thesis focuses on the method of differential coordinates, which is the most popular technology in energy minimization. Our research includes three aspects.First, we present a method for automatic generation of control points based on mesh simplification. Mesh deformation with differential coordinates has an advantage of detail preserving and can make the results smooth and natural, but users have to choose a series of control points as constraints before deforming, and then manipulate these points to perform the deformation. Hence, it is a necessary issue to reduce the workload for selecting control points. This method, by triangle mesh simplification through edge collapse, tries to make the simplified model maintain the features of the original shape, and to make the vertices become the control points of mesh deformation finally. Our algorithms reduce the difficulty of selecting control points and relieve the preliminary workload in mesh deformation.Second, we study and implement a kind of deformation technology which combines differential coordinates with skeleton subspace. Deformation with differential coordinates is suitable for non-rigid transform because of its own characteristics, and has a small range of deforming. On the other hand, the skeleton deformation may be artificial in some cases. In this paper we present a method that combines differential coordinates with skeleton technology in order to integrate both the advantages. The examples show that this method achieves desired results with practical significance.Third, we provide a method of deformation for preserving the details, which is based on mesh subdivision. Because deformation with differential coordinate is not rotation-invariant, some high curvature vertices are not sensitive enough, and these vertices'normal may be distorted after deformation. By importing the ideas of Loop subdivision and multiresolution, the paper proposes an improved method, which records the information of high frequency by constructing local coordinates, and then restores the features of surface after reconstructing the points. From the illustrations, we can find that the algorithm can obtain satisfied results without some defects in differential coordinates.All the algorithms in this thesis are actualized under Windows XP operation system and VS2005 with C++ and OpenGL.