Shape deformation via interior RBF

We present a new framework for real-time shape deformation with local shape preservation and volume control. Given a 3D object, in any form, one would like to manipulate the object using convenient handles, so that the resulting shape is a natural variation of the given object. It is also important that the deformation is controlled, thereby enabling localized changes that do not influence nearby branches. For example, given a horse model, a movement of one of its hooves should not affect the other hooves. Another goal is the minimization of local shape distortion throughout the object. The first ingredient of our method is the use of interior radial basis functions (IRBF), where the functions are radial with respect to interior distances within the object. The second important ingredient is the reduction of local distortions by minimizing the distortion of a set of spheres placed within the object. Our method achieves the goals of convenient shape manipulation and local influence property, and improves the latest state-of-the-art cage-based methods by replacing the cage with the more flexible IRBF centers. The latter enables extra flexibility and fully automated construction, as well as simpler formulation. We also suggest the IRBF interpolation method that can extend any surface mapping to the whole subspace in a shape-aware manner.