Multiple Weighted Geometric Iterative Method And Its Application

In computer aided geometric design and reverse engineering,it is an important task to construct a sequence of curves(surfaces)which meet the accuracy requirements to interpolate or approximate a given set of ordered points.In practice,a large-scale linear system of equations has to be solved for the computation of control points in reverse engineering.It is hard to popularize for its big computation amount.Many scholars have put forward different forms of interpolating and fitting methods.Progressive iterative approximation method(PIA,also known as geometric iterative method)is favored by most scholars for its good adaptability and convergent stability.One can continuously adjust and iterate a set of vectors,the final curve and surface will interpolates the original set of data points.The method not only greatly reduces the calculation,but also has obvious geometric meaning.In view of the above research.In order to interpolation type,Interaction design of curves/surfaces usually need local interpolation of data maintain the shape of the curves/surfaces simultaneously,but deal with detail features of parameter curves/surfaces,through the data points given different weights,to study the local data interpolation point set.In fitting type geometric iteration method,Deal with large size3 D data points has always been a hot issue.in the existing method of least square PIA method(LSPIA),in order to make the operation more simple and flexible,by adopting the idea of with different weights given a new type of surface fitting model geometry iteration method.Specifically:this paper presents two modified PIA methods :1.A modification of interpolation type of geometric iterative method,multiple weighted geometric iterative method has been proposed by adjusting each weight for different vectors,the method can deal with detail features flexibly and the iteration errors are relatively small.Finally,analyze its convergence and iteration effect;2.A modification of fitting type of geometric iterative method,a mutiple weighted least square PIA method has been presented,which can not only fitting large-scale data points effectively,but also control all the vertices flexibly.Different kinds of choices of control points and weights.In addition,the generalized B-splines basis function is adopted,which can make the iterative algorithm more flexible and can make the method more flexible to be applied in real applications.