Special multivariate quadratic spline space

In this paper, we present a special multivariate quadratic spline space S21,0(♦) over a refined quadrangulation. We get its dimension, and construct its basis splines. At the same time, we obtain the explicit representations of the basis splines by the smoothing cofactor-conformality method. The approximation properties of two constructed quasi-interpolation operators are discussed, some supporting numerical results are presented. We also compare our spline with some traditional splines in this paper. The results can be applied to many fields such as CAGD, function approximation, numerical analysis, finite element method, and so on.