<title>Adaptive reconstruction of closed Bezier surfaces</title>

Abstract

This paper presents a technique for reconstructing smooth closed Bezier surfaces from coordinate measurements based on a Bernstein Basis Function (BBF) network. While various neural networks, such as the backpropagation network and radial basis function networks, have been effective in functional approximation and surface fitting these neural networks produce system dependent solutions that are not easily transferable to commercially available design software. The BBF network has an advantage over other networks by directly employing the same Bernstein polynomial basis functions that are used in describing Bezier surfaces. The BBF network is capable of implementing a close approximation to any continuous nonlinear mapping by forming a linear combination of nonlinear Bernstein polynomial basis functions. Changing the number of basis neurons in the network architecture is equivalent to modifying the degree of the Bernstein polynomials. Complex smooth surfaces can be reconstructed by using several simultaneously updated networks, each corresponding to a separate surface patch. A smooth transition between adjacent Bezier surface patches can be achieved by imposing additional positional C 0 and tangential C 1 continuity constraints on the weights during the adaptation process. Once adapted, the final weights of the networks correspond to the control points of the Bezier surface, and can therefore be used directly in commercial CAD software packages that utilize parametric modelers.