Some Data Fitting Methods Based On Bivariate B-Spline

Multivariate splines are applied widely in approximation theory, computer aided geometric design and finite element method. In this thesis, we study some important spline spaces defined on special triangulations. We focus on uniform type-2 triangulation. Moreover, we consider the application of those splines in scattered data fitting and interpolation.In chapter 1, we introduce some basic results of multivariate splines briefly.In chapter 2, a special crosscut partition, or a four-directional mesh is introduced which is used widely because of its simple construction and good symmetry. In this thesis, we mainly use bivariate splines on type-2 triangulation to fit scattered data.In chapter 3, a new scattered data interpolation method is discussed which is called blending function method based on non-tensor product B splines. The numerical experiments show the practical utility and effectiveness of our method.In chapter 4, a least squares method to fit scattered data is presented by using a spline space S21(Δmn(2)). An error bound is derived.