Research On Local Fitting Method Based On NURBS Curve

With the rapid development of industry and technology,non-uniform rational B-spline(NURBS)as the core technology of computer-aided geometric design and computer aided manufacturing,with its unique ability to accurately represent and design the curves and the surfaces,has successively become a mathematical standard and method defined by the international and domestic major standards organizations that describe the geometric shape of industrial products,and were widely used in industrial design and modeling areas.The fitting problem was of great significance in the representation and construction of curved surface modeling,at present,the research about matching technology and fitting theory of Bézier and B-spline methods are relatively mature,but lack of theoretical algorithms and concrete examples that applying the NURBS method to fit the curves and surfaces.This thesis is based on the analysis of the important theoretical system of NURBS curves,taking the most representative of cubic NURBS curves in industrial research and design as the research object,starting from the interpolation and approximation in two ways of curve fitting,through careful and meticulous reasoning,calculation and simulation experiments and then achieved the following main research results:From the theoretical improvement of the convenient Bézier as the starting point,by using the rational Bézier method to construct the adjacent curve segment.By means of rational Bézier splicing technique,each adjacent rational Bézier curve segment is connected,and the node deletion algorithm is called to eliminate the heavy node and finally form the local interpolation NURBS curve.On the basis of the least squares approximation method of the non-rational B-spline curves,we take the research ideas from special to general.By means of analogy in the homogeneous coordinate space for weighted data points to do the least squares approximation means,calling the standard perfect least squares algorithm,and using the partial derivative to zero to solve the linear equations,and a least squares approximation algorithm is proposed for the NURBS curves with the attached weight and the vector constraint.Then we analyse and compare the situation and the evolution process under different constraints.The approximation accuracy error is reduced by successive iterations,and the range of tuning factor and the conditions of approximation cut-off are given according to the approximation error.Simulation is carried out through computer programming,which verifies the validity of the proposed algorithm.The experimental results show that the fitting curve generated by the approximation algorithm has excellent efficiency and smoothness,and the efficiency of industrial design has been significantly improved.The work of this thesis was summarized and reviewed at last,and pointed out the direction of future research work on the local fitting of NURBS curves and surfaces.