B-spline Surface Fitting Based On Quasi-interpolation

The problem of surface fitting from scattered data is an important area in approximation theory.It is of great significance and extensive applications in many fields. B-spline method plays an important part in Computer Aided Geometry Design(CAGD). Some analysis and discussions on the method of B-spline surface fitting from scattered data are presented in this dissertation.The problem of surface fitting from scattered data is introduced in chapter 1,and also several important methods are presented.B-spline curves and surfaces and their main properties are described in chapter 2.A kind of saurface reconstruction method from scattered data is presented in chapter 3.It is based on multilevel B-spline approximation algorithm and quasi-interpolation.In chapter 4,a surface fitting method based on quasi-interpolation from scattered data is discussed.Using this method,non-tensor product B-spline surface is constructed with binary quadratic B-spine on uniform type-2 triangulation.Then multilevel Bspline approximation algorithm is used to circumvent the tradeoff between the shape smoothness and accuracy of the approximation.Experimental results demonstrate that this method is feasible and has good performance on surface fitting from scattered data.Finally a summary of this dissertation is given and several problems which await further discussion are proposed.