Fast centroidal deformation for large mesh models

We present an algorithm that allows fast non-linear deformation editing on high-quality meshes. The proposed Fast Centroidal Deformation (FCD) method is based on a multi-resolution framework, where a centroidal deformation graph is built over the mesh in order to allow fast non-linear optimization at a coarse scale. The resulting deformation is then propagated to the initial dense mesh by exploiting the relationship between the constructed deformation graph and the input mesh through a mapping function that unifies local rotations and global translations without the need of solving a system composed by a number of linear equations of the same magnitude of the number of vertices of the mesh. A number of flexible user constraints can be imposed in the deformation through a handle-based metaphor where the user can redefine the position and orientation of single control points or entire portions of the input model. The proposed method addresses the obstacle of non-linear deformation on meshes composed by millions of vertices and is compared with the reference deformation techniques, showing significant improvements in terms of computational efficiency without renouncing to the quality of the results given by non-linear methods.