Optimization Of Parametric Curve And Surface Based On The Estimation Of Distribution Algorithm

Reverse Engineering is an important content in the research of computer aided geometricdesign, and has been widely used in many fields. As efficient in data fitting, parametric curvesand surfaces are usually applied to the reverse engineering. With the development of society,as to many practical problems, people have more requirements for the fairness of a product’sshape. Nevertheless, the measured data points are noisy due to the measurement errors and theimpact of the physical object, and the parametric curves and surfaces that are generated by themeasured data points are often found to have poor fairness. so it is necessary to do fairingoperations on the parametric curves and surfaces obtained by the measured data points.Consequently, fairing parametric curves and surfaces are becoming one of the most importantcontent in the field of computer aided geometric design.Facing present problems existing in the optimization algorithms to the parametric curvesand surfaces, and in order to obtain fairing parametric curves and surfaces, we optimize theparametric curves and surfaces by combining the estimation of distribution algorithms withthe least square method in this paper. The major research contents are as follows:1. Do research on the theoretical knowledge associated with genetic algorithm and theestimation of distribution algorithms. The research includes the basic idea of the geneticalgorithm and the estimation of distribution algorithms, and also includes the connections anddifferences between the two.That is the basis for the following optimization study of theparametric curves and surfaces.2. Do research on the optimization methods for parametric B-spline curve. FairingB-spline curve is the important base and premise of B-spline surface’s fairness. This paperapplies the estimation of distribution algorithms to the optimization of parametric B-splinecurve. Feature points obtaining is a necessary step in data fitting by a parametric B-splinecurve. It decides whether the result is accurate or not. This paper uses the centroid balancesampling method to obtain the feature points. Then the B-spline curve is generated based onthe feature points. In general, the distribution of the knots and control points has a directlyeffect on the shape of the B-spline curve, and the B-spline curve that is generated by the existing methods which calculate the knots and control points respectively is not idealistic. Inorder to make the B-spline curve have better precision and obtain a better contour of theobject, this paper regards the knots and control points of the B-spline curve as variables, andthey are optimized by the estimation of distribution algorithms.3. Do research on the optimization methods for parametric B-spline surface. FairingB-spline surface is regarded as one major precondition for reconstruction of surfaces. In orderto obtain ideal surfaces, this paper applies the estimation of distribution algorithms in theoptimization of parametric B-spline surface. First of all, the data points are gained based onthe existing contours. Then B-spline surface is generated based on data points, at the sametime, the estimation of distribution algorithm is used to optimize the knots of the B-splinesurface.The experiment results show that the combination of the estimation of distributionalgorithms and the least square method can obtain more precise approximate contours ofobjects.