The Application Of Intelligent Optimization Algorithms In Genmetric Design

Data fitting is a very significant issue in the filed of geometric design.Owing to the difference of fitting precision,it can be classified into two categories: interpolation and approximation.In order to meet the special requirements of designers or consumers for the shape and the function of geometric modeling entity,it is essential to add various constraints at the same time of fitting such as,tangential conditions,normal conditions,curvatures,torsion conditions,special isoparametric lines,and so on.Fitting methods as well as its related problems also showed diversity,for example,solving equations directly,energy optimization,finite element analysis,geometric construction,iterative approximation,etc.As industrial standard of CAD&CAM,B-spline has its outstanding superiority in the expression of curves and surfaces,and often used as a means to deal with the problem of fitting.There are three essential elements in a B-spline fitting curves or surfaces: the knot vector,the parametrization of data points,and the control vertexes.Most of the traditional methods are based on the premise of the fixed knots and theparametrization of data points,it comes up to expectations hardly in fitting accuracy on condition that only taking the solution of the control vertexes into account.With the consideration of the knot vector and the parametrization of data points,the fitting problem will become a multi-variable,multi-dimension and highly nonlinear problem,which results in many troubles on solving.In recent years,a variety of intelligent optimization algorithms and their hybrid algorithms are used to solve the fitting problems of curves and surfaces increasingly.The fitting problem with constrains can be transformed into that without constraints using the penalty function method,and then it is possible to satisfy the constraints at the same time of fitting data points by means of optimizing the knot vector or the parameter values of data points with particle swarm optimization algorithm(PSO)or genetic algorithm(GA),the results show that the method has good reliability and validity authentically.Aiming at the calculating problems of parameter values of progressive iterative approximation(PIA)interpolation under an arbitrary knot vector,by using the intelligent optimization algorithm to find the optimal parameter values,the results show that the method has the effect of reducing the iterative interpolation distortion.The convergence rate of PIA iterative interpolation is slow,so the successive over relaxation(SOR)method is introduced to deal with the iterative interpolation problem,which greatly accelerates the iterative process.