Applying functional networks to fit data points from B-spline surfaces

A powerful extension of neural networks, the so-called functional network, was recently introduced. This kind of network is more versatile than neural networks and so can be successfully applied to several problems in computer-aided geometric design (CAGD). As an illustration, the simplest functional network representing tensor product surfaces is obtained. Then, functional network formalism is advantageously used to fit given sets of data from B-spline surfaces through a Bezier surface. The proposed method also determines the degree and coefficients (control points) of the approximating surface that fits the given data better. This new approach is very general and can also be applied to any other interesting family of approximating basis functions in CAGD.