Bézier Curve and Surface Fitting of 3D Point Clouds Through Genetic Algorithms, Functional Networks and Least-Squares Approximation

Abstract

This work concerns the problem of curve and surface fitting. In particular, we focus on the case of 3D point clouds fitted with Bezier curves and surfaces. Because these curves and surfaces are parametric, we are confronted with the problem of obtaining an appropriate parameterization of the data points. On the other hand, the addition of functional constraints introduces new elements that classical fitting methods do not account for. To tackle these issues, two Artificial Intelligence (AI) techniques are considered in this paper: (1) for the curve/surface parameterization, the use of genetic algorithms is proposed; (2) for the functional constraints problem, the functional networks scheme is applied. Both approaches are combined with the least-squares approximation method in order to yield suitable methods for Bezier curve and surface fitting. To illustrate the performance of those methods, some examples of their application on 3D point clouds are given.