Local Basis And Dimensions Of Bivariate Spline Spaces Over Some Special Triangulations

In this thesis, local basis and dimensions of bivariate spline spaces over some specialtriangulations are discussed. Firstly, representations of a locally supported dual basis for thebivariate C2 spline space S 52(?W) on Wang's refined triangulation ?W are given by using theHermite interpolation conditions. Secondly, by using the method of Bernstein-Be′zier netand the technique of minimal determining sets, a minimal determinining set for the bivariatespline space S 62(+?mn) over the generalized type II triangulation +?mn is given, and the dimensionof bivariate spline space S 62(+?mn) is determined. Finally, the generalized type I triangulation?m(1n) is defined, a minimal determinining set for bivariate quintic C2 spline space S52(?m(1n)) over?m(1n) is given and the dimension of S52(?m(1n)) is determined.