A Laplacian Based Approach for Free-Form Deformation of Sparse Low-degree IMplicit Surfaces

Sparse low-degree implicit (SLIM) surface is a recently developed non-conforming surface representation. In this paper, a method for free-form deformation of SLIM surfaces is presented. By employing a Laplacian based mesh deformation technique, a global deformation is realized as movements of the centers of the local function supports. A graph connectivity for defining the Laplacians is simply created using inclusion of other centers in the supports. By following the global deformation according to the movements of the centers, we update each local function and its support size via several times of local least square fittings by using the new positions of the neighboring centers. Since the additional computations for updating local functions are very computationally cheap, the proposed SLIM surface deformation achieves an interactive surface deformation similarly to Laplacian based mesh deformation techniques. Further, because a SLIM surface requires a smaller number of elements than a mesh for representing the same geometrical details, the computational effort for a global Laplacian based deformation is dramatically reduced