Surface Fitting Of Scattered Data With B-Spline Method

Surface fitting of scattered data is always an important part of function approxi-mation theory, and it applied widely in many fields. B-spline method is an important method in CAGD. Some B-spline methods for surface fitting of scattered data are discussed in this dissertation.Chapter 1 introduces univariate B-spline, tensor B-spline and quadratic spline space S₂¹ (â–³_mm²)Chapter 2 introduces multilevel B-spline surface fitting method based on scattered data. It summarizes the achievement that Forsey, Seungyong Lee etc. did. The chapter discusses uniform bi-cubic B-spline approximation and multilevel B-spline approximation which discuss the Oslo algorithm for B-spline refinement mostly and deduces the optimized multilevel approximation algorithm.Chapter 3 describes a type of hierarchy non-tensor B-spline approximation method. The algorithm exploits quadratic bivariate B-spline basis over uniform type-2 triangu-lationâ–³_mn² to reconstruct a non-tensor-product B-spline surface. Then the multilevel approximation algorithm is proposed to deduce a series of linear equation system. Numerical examples are presented and the results show the algorithm is fast and produce fair results.Chapter 4 discusses least squares approximation method of B-spline over scattered data. It discusses surface fitting with tensor B-spline, quadratic bivariate B-spline overâ–³_mn² and B-spline over Powell-Sabine triangulation.Chapter 5 summarizes the whole dissertation and gives some expectation for future research.