Bézier curve and surface fitting of 3D point clouds through genetic algorithms, functional networks and least-squares approximation

Authors:
Akemi Gálvez;Andrés Iglesias;Angel Cobo;Jaime Puig-Pey;Jesús Espinola
Affiliations:
Department of Applied Mathematics and Computational Sciences, University of Cantabria, Santander, Spain;Department of Applied Mathematics and Computational Sciences, University of Cantabria, Santander, Spain;Department of Applied Mathematics and Computational Sciences, University of Cantabria, Santander, Spain;Department of Applied Mathematics and Computational Sciences, University of Cantabria, Santander, Spain;Faculty of Sciences, National University Santiago Antúnez de Mayolo, Perú
Venue:
ICCSA'07 Proceedings of the 2007 international conference on Computational science and Its applications - Volume Part II
Year:
2007

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Abstract

This work concerns the problem of curve and surface fitting. In particular, we focus on the case of 3D point clouds fitted with Bézier 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 Bézier curve and surface fitting. To illustrate the performance of those methods, some examples of their application on 3D point clouds are given.