Discrete NURBS-Surface Approximation using an Evolutionary Strategy

Abstract

This article presents a study about the application of Computational Intelligence (CI) methods to the problem of optimal discrete surface approximation. The class of CI methods comprises subsymbolic algorithms like neural networks, fuzzy logic systems and evolutionary algorithms. Non-Uniform Rational B-Splines (NURBS) are exible parametric functions which are commonly used in modern CAD/CAM systems. Here, a special CI method - the evolution strategy (ES) - will be used to approximate NURBS-surfaces to discrete 3D-point sets. The evolution strategy is a numeric optimization method that deals well with multi-modal optimization problems in real value vector spaces. The article focuses on the convergence behavior of ES regarding different parameterizations. The dependencies of the spline surface approximation algorithm on different surface structures are analyzed. The results are discussed from a mathematical and a practical point of view.