基于四面体控制网格的模型变形算法

Shape Deformation Based on Tetrahedral Control Mesh

提出一种鲁棒的保体积保表面细节的模型变形算法.首先将输入模型嵌入到一个稀疏的四面体控制网格中,并且通过一种改进的重心坐标来建立两者的对应关系;然后通过用户的交互,对控制网格建立一个二次非线性能量函数对其进行变形,而输入模型的变形结果则可以通过插值来直接获得.由于能量函数的优化是在控制网格上进行的,从而大大提高了算法的效率.与此同时,提出一种新的能量——Laplacian能量,可以使四面体控制网格进行尽量刚性的变形,从而有效地防止了大尺度编辑过程中模型形状的退化现象.文中算法还具有通用性,可支持多种模型的表示方式,如三角网格模型、点模型等.实验结果表明,该算法可以有效地保持输入模型的几何细节、防止明显的体积变化,得到了令人满意的结果.

A robust shape deformation algorithm with the feature of both volume and surface detail preserving is presented. First, the input model is embedded into a coarse tetrahedral control mesh, and the modified barycentric coordinates are employed to establish their relationship. Then according to users editing, the control mesh is deformed by solving a quadric nonlinear energy minimization problem, and the deformation is passed to the embedded model by interpolation. As the optimization process is applied to the control mesh composed of sparse vertices, the efficiency is greatly improved. Meantime, we incorporate a new energy, called Laplacian energy, into the energy equation to make the tetrahedral control mesh deform as rigidly as possible, thus avoiding shape degenerations even under extreme editing. Our algorithm accommodates various shape representations, such as triangular meshes, point clouds etc. Experiments demonstrate that the Laplacian energy is very effective in preserving geometric details and preventing unreasonable volume changes.