NURBS Surface Reconstruction Using Rational B-spline Neural Networks

Surface reconstruction is a very challenging step in Reverse Engineering. It generates a surface from point cloud acquired from a part surface. NURBS surfaces are commonly used for freeform surface reconstruction. There are several algorithms of NURBS surface reconstruction including: Least Squares Methods, simulated annealing, and particle swarm optimization. The major problem of these methods is that they require parameters and knots optimization which increases the complexity of the problem. The purpose of this paper is to introduce basis function neural networks which eliminates the need for parameters or knots optimization besides providing acceptable error. They are called Rational B-spline Neural Networks (RBNN). Also, they have the advantage of providing the control points and weights of approximated NURBS surface over regular function approximation networks. Training of the network is done using the back-propagation algorithm. Results showed that the RBNN have better approximation to NURBS with acceptable error provided that the number of control points and training rate are selected properly. Keywords—Freeform Surface, Reverse Engineering, Surface Reconstruction, NURBS, Neural Networks