Optimizing the Parameters of Data Points in Curve and Surface Fitting

The key point in smooth and fairing fitting of curves and surfaces is to search the optimal parameters of data points,and then construct an optimal fitting equation according to the least square method and get control points based on the equation.As existing techniques for choosing parameters do not embody the geometric characteristic of the optimal parameters,the fitting is either imprecise or of great cost.In order to improve fitting precision and computing speed,we offers an algorithm on optimizing the parameters of data points.By using the orthogonal projection of data points to corresponding curve or surface,and making a search for the neighborhood of the parametric coordinate computation is speed up and the parameters can be ceaselessly corrected with the iterative process of the curves and the surfaces,so that the resulting parameters will possess distinct geometrical meaning,and the optimal fitting effect can be obtained.Comparing with the algorithms of Hoschek,Carlos and Piegl in some examples,it is validated that this method can cut down iteration times about 10%~90%,reduce time consumption around 20%~70%,or improve precision nearly 40%.