Fitting Method Based On Radial Basis Function Of Scattered Data

The problems of constructing approximations based upon scattereddata are encountered in many areas of scientific applications. This fieldhas been researched for a long time and many methods have beendeveloped and formed. In this paper, the author improved and applied thenew method to examples. The results show that the improved algorithmworks better in computing complexity and the surface can be fitted better.The main work of this paper is listed as follow:(1) We construct a localized method for interpolation with radialbasis functions (global supported) based on the idea of multivariate spline.Moreover, we verify that this method is feasible through theoreticanalysis and numerical experiments. These methods perform almost asgood as the global supported radial basis functions interpolation methodsdo.(2) The algorithm that the author employed to fit scatted data usescompactly supported radial basic function which changes the coefficientmatrix into sparse matrix and combined with conjugate gradient methodto settle the equations. By this, the computation is simplified and the onlysolution.(3) This paper proposes a fitting method of curved surface which isbased on the radial basis functions used together with the B-spline surface.With the banding radical basis functions, we obtain ordered mesh pointsfrom 3-dimension scattered data, and then use tensor product B-splineinterpolate these ordered mesh points to get the approximating surface.This method is a good solution for the numerical instability of scattereddata interpolation and fitting.(4) The simplification of unorganized cloud data. Based on thecluster result of the unorganized cloud data, two simplification methods,based on the nearest distance and based on Moving Least-Squares (MLS),is the preparation for the surface fitting of unorganized cloud data.(5) The proposed method applies the RBFNN to the free surfacereconstruction from an unorganized cloud of points in which always involve noise. In this part, the author used the improved studyingalgorithm.(6) The author also analyzed the merits and weaknesses of variousfitting methods of RFB and discussed their applicable situation.