Extending neural networks for B-spline surface reconstruction

Recently, a new extension of the standard neural networks, the so-called functional networks, has been described [5]. This approach has been successfully applied to the reconstruction of a surface from a given set of 3D data points assumed to lie on unknown Bezier [17] and B-spline tensor-product surfaces [18]. In both cases the sets of data were fitted using Bezier surfaces. However, in general, the Bezier scheme is no longer used for practical applications. In this paper, the use of B-spline surfaces (by far, the most common family of surfaces in surface modeling and industry) for the surface reconstruction problem is proposed instead. The performance of this method is discussed by means of several illustrative examples. A careful analysis of the errors makes it possible to determine the number of B-spline surface fitting control points that best fit the data points. This analysis also includes the use of two sets of data (the training and the testing data) to check for overfitting, which does not occur here.