The Bases of the Non-Uniform Cubic Spline Space S_(3)^(1,2)(Δ_(mn)^((2))

In this paper,the dimension of the nonuniform bivariate spline space S_(3)^(1,2)(Δ_(mn)^((2))is discussed based on the theory of multivariate spline space.Moreover,by means of the Conformality of Smoothing Cofactor Method,the basis ofS_(3)^(1,2)(Δ_(mn)^((2))composed of two sets of splines are worked out in the form of the values at ten domain points in each triangular cell,both of which possess distinct local supports.Furthermore,the explicit coefficients in terms of B-net are obtained for the two sets of splines respectively.