Shape Deformation Based on Tetrahedral Control Mesh

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.