Bivariate Cubic Spline Space On Wang's Rerined Triangulation

Bivariate spline spaces have been widely applied in numerical approximation, surfacefitting, scattered data interpolation, finite element method, numerical solution of partial dif-ferential equations, computer aided geometric design and computer graphics.In this thesis, bivariate C~1 cubic spline spaces on Wang's refined triangulation are dis-cussed. By B-net techniques and minimal determining set, the dimension of bivariate splinespaces on Wang's refined triangulation is determined and a locally supported dual basis forthis space is given. Hermite interpolation schemes are constructed based on C~1 cubic splineson Wang's refined triangulations. The existence and the uniqueness of the interpolation arediscussed. The interpolant has local support and explicit representation. Moreover, localLagrange interpolation schemes are constructed for C1 cubic splines on Wang's refined trian-gulation and the interpolation points are chosen such that the fundamental splines have localsupports.