Bivariate Spline Spaces Over Special Triangulations And Interpolations

In this thesis, firstly, by using the Bernstein-Bézier method and the technique of minimal determining sets, a minimal determining set for bivariate quadratic spline space S₂¹((?)) over (?) is given, and the dimension of bivariate spline space S₂¹((?)) is determined. Secondly, for two sub-spaces of bivariate cubic spline spaces over nonuniform type-Ⅱtriangulations, which are bivariate cubic spline spaces with boundary conditions and with double periodic boundary conditions, by using the coloring method, the Bézier-net method and the technique of minimal determining set, Lagrange interpolation schemes by those spaces on nonuniform type-Ⅱtriangulations are constructed and their locally supported dual basis are given. At the end, their approximation errors are estimated, respectively.