Research On Techniques Of Mesh Deformation

Mesh deformation is the kernel part of the digital geometry processing which more and more researchers at home and abroad are focusing on recently. Mesh deformation has wide applications in many areas such as reverse engineering, numerical simulations, rapid innovative design and computer animation, etc. Based on the intensive survey and comprehensive analyses of various approaches to the mesh deformation, several deformation algorithms have been designed, implemented and verified in this dissertation which mainly aims at the weakness of the existing deformation techniques. The theories of computer graphics, computer-aided geometric design, discrete differential geometry, digital signal processing and computational geometry are all incorporated into our algorithms. Main contributions of the dissertation include:(1) A novel free-form deformation based on least-square mesh based is proposed in the dissertation. In order to preserve the geometry details of the original mesh, the least-square mesh of the original mesh is used to encode the displacement betweent the two meshes. The algorithm consists of the following main steps: First mean-value coordinates is used to control the least-square mesh instead of the original one; Second displacement vectors are encoded and decoded in the local frame of the vertice of the least-square mesh and drive the original mesh to deform accordingly. From the user's point of view, the control and speed of the algorithm is the same as they do in the traditional free-form deformation. However, the deformation result of our algorithm is better than the traditional ones especially in preservation of mesh's geometry details.(2) Local detail preserved mesh deformation based on mean-value skeleton subspace is introduced in the dissertation. The mean-value skeleton is used to control the mesh deformation, and the differential coordinates and skeleton subspace model are also incorporated in order to preserve the skeleton and geometry details of the original mesh. The algorithm consists of the following main steps: First the skeleton subspace deformation (SSD) model is used to control the skeleton's transformation; Second the deformation energy function with differential coordinates and mean-value skeleton coordinates is constructed; Finally the mesh deformation occurs through the optimization of the energy function linearly. Because the optimization of the energy function is computed in real-time, the operation taken by user is the same as the traditional SSD. While the result of the deformation of our method is better than the traditional ones in skeleton and geometry details (mean curvatures) preservation。(3) A novel mesh deformation transfer based on mean-value skeleton is introduced in the dissertation. Deformation transfer adds a general-purpose reuse mechanism to the animation pipeline by transferring any deformation of a source mesh onto a different target mesh. The target mesh establishes a corresponding relationship with the source mesh automatically through the mean-value skeleton, instead of the traditional corresponding markers specification by user. The mean-value skeleton and differential domain techniques are incorporated into the target mesh deformation, and the main computation is a solution of a linear energy constraint problem, so it produces the local geometry detail preserved target meshes efficiently. The algorithm produces vision plausible deformation transfer in real-time, and it's well suited for new animators.(4) A differential domain mesh deformation technique based active contour model is introduced in the dissertation. The key point of the algorithm is the skeleton and volume constraint are simulated by the active contour model. Then the active contour model is combined with the differential domain deformation and the deformation is computed through a linear least-square minimization. The purpose of the algorithm is to convert the nolinear skeleton and volume constraint into the linear ones. It trades off the computation time and the accurate preservation of the original mesh's characteristics.