Optimization of the number of control points for curve fitting using b-splines

Carlos Eduardo Fanti¹; João Carlos Mendes Carvalho¹

¹ University Federal of Uberlândia

doi:10.20906/CPS/COB-2015-0430

Resumo

In surface reconstruction from a point-cloud, which are usually disorganized, usually cross-sections of the object are used with a points reduction method to reduce the computational cost. After the reduction of the number of points that defines the cross-section of the object, an approximation method is used to obtain the curve, which represents the cross-section shape. When B-Splines curves are used to obtain cross-sections, the control points are calculated from the set of known points, but there is no rule on how many is the number of control points that should be used. In this sense, the objective of this paper is to present an analysis of the number of control points used in curve fitting using B-Spline to obtain a low fitting error and a low time execution of the algorithm. The analysis is performed by the multi-objective optimization method. The objectives evaluated in this method seek to minimize: the least square error, the number of control points and the algorithm resolution time. The objectives are related by a weighted function, whose results are assembled for obtaining the Pareto's curve. The minimum of this curve define the optimum number of control points that allows a good curve fitting, combined with a good performance of the algorithm.

Palavras-chave: B-Spline; Curve fitting; Surface reconstruction; Optimization; Pareto's curve; Multi-objective