As-rigid-as-possible mesh deformation based on tetrahedral cells
四面体胞的尽可能刚性网格变形算法

In this paper, we introduce a novel approach to as-rigid-as-possible mesh deformation based on tetrahedral cells. The most distinctive feature of this approach is that users can modify the original mesh by selecting a couple of vertices on the mesh. First, sets of tetrahedral cells are produced, which fit well to the mesh surface, through sparse voxelization. Preserving the rigidity of local transformations of the mesh surface and these tetrahedra during deformation is achieved by minimizing the corresponding energy formulation that prevents unnatural artifacts both on the surface and in the interior of the model. Meanwhile, in order to avoid the possible collapse emerged under large-scale deformation, we present a simple adaptive tetrahedron decomposition method, which brings more local deformation freedom to the interior of the mesh to eliminate the implausible deformation effects based on these dramatic volume changes in the local area. In addition, a few tetrahedra are generated by this method, and then more tetrahedral cells would be densely involved into the deformation process if necessary, there by resulting in highly efficient and robust results. In our experiments, we show that the volume and the surface details of the whole mesh can be approximately preserved and the local degeneration inside the mesh under the large-scale deformation could be efficiently avoided.