Bivariate Cubic Spline Spaces On Powell-Sabin Triangulations

In this thesis, we study bivariate cubic spline spaces and super spline spaces on Powell-Sabin triangulation. The thesis is organized as follows: In Chapter 1, we brie?y introducebivariate spline spaces, summarise some known results on the dimension of bivariate splinespaces. In Chapter 2, B-net techniques and determining set are introduced. Chapter 3 dealswith the dimension of bivariate spline spaces on Powell-Sabin triangulation and constructslocally supported dual basis for these two spaces. In Chapter 4, Lagrange interpolationschemes are constructed based on C1 cubic splines on Powell-Sabin refined triangulations.Finally, super spline space S 31 ,2( PS1) is studied, a locally supported dual basis, Hermiteinterpolation and computational details using derivatives around each vertex are given.