四面体胞的尽可能刚性网格变形算法

提出一种基于四面体胞的尽可能刚性三角形网格变形算法。用户通过操作网格上的若干顶点以得到所需的模型变形结果。首先，算法对网格模型内部进行稀疏四面体化，以产生一个贴合模型表面的四面体胞集。在模型变形过程中，算法通过最小化相应的变形能量函数，以保持网格模型表面局部区域的刚性以及每个四面体胞的刚性，从而有效避免模型表面及其内部的扭曲。同时，针对大尺度编辑可能造成的模型局部塌陷，提出一种简单的四面体胞自适应剖分方法，根据模型局部体积的剧烈变化，自动剖分对应的四面体胞以增加模型内部的局部变形自由度，进而消除不正确的变形效果。此外，自适应的四面体胞剖分允许算法在初始时只需对网格模型进行稀疏的四面体化，而在变形过程中根据需要进一步提高四面体胞的局部稠密度，因而保证了算法的鲁棒性及其效率。实验结果表明，该变形算法可以有效保持模型的表面细节以及模型的内部体积，并能够有效避免模型形状在大尺度变形时的局部退化。

As-rigid-as-possible mesh deformation based on tetrahedral cells

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.