The Dimension Of Bivariate C～2 Splines Spaces Over A Refined Triangulation

In this thesis, we consider a special refined triangulationΔ_w , which subdivides each triangle ofΔinto 7 subtriangles. Let S₆²(Δ-w)and S₇²(Δ_w) be the bivariate 2C spline spaces of degree six and degree seven overΔ_w , respectively. The smooth conditions of bivariate spline are presented firstly. By these conditions, dimensions of S₆²(Δ_w) and S₇²(Δ_w) are determined.