Approximation by GP splines on a four direction mesh.

On a four-directional uniform mesh of the plane, we define and study C-0 Gori-Pitolli (abbreviated as GP) quadratics and C-1 GP quartics generated by integer translates of GP box-splines generalizing respectively the classical C-1 quadratic box-spline and one of the C-2 quartic box-splines. More specifically, we study the approximation of a bivariate function f by some quasi-interpolants and interpolants with values in these generalized spline spaces