Reconstruction of implicit curves and surfaces via RBF interpolation

Representation of curves and surfaces is a basic topic in computer graphic and computer aided design (CAD). In this paper we focus on theoretical and practical issues in using radial basis functions (RBF) for reconstructing implicit curves and surfaces from point clouds. We study the conditioning of the problem and give some insight on how the problem parameters and the results have to be taken in order to achieve meaningful solutions and avoid artifacts. Moreover, a strategy for decreasing the conditioning of the problem is suggested and a general framework for preconditioning and solving the problem, even for large datasets, is also provided.