Reconstruction of implicit curves and surfaces via RBF interpolation

Many problems in computer visualization, scientific computing, medical imag- ing, computer-aided design and manufacturing (CAD/CAM) require to recon- struct a graphic object starting from an unorganized 2D/3D point cloud, i.e. a set of scattered points in R^2 or R^3. Here, we – establish how the problem parameters and the results have to be taken in order to find meaningful solutions and avoid artifacts and similar drawbacks; – study the conditioning of the problem in terms of number of points, point cloud topology and standard deviation of several functions; – suggest a strategy for decreasing the condition number of the problem by means of a two stages selective reduction of the cloud points; – show a parallel code for preconditioning and solving the problem with very large data sets.