A bivariate C1C1 cubic super spline space on Powell–Sabin triangulation

A bivariate C1C1 cubic super spline is constructed on Powell–Sabin type-1 split with the additional smoothness at vertices in the original triangulation being C2C2, which permits the Hermite interpolation up to the second order partial derivatives exactly on all the vertices in the original triangulation. The locally supported dual basis and computational details using derivatives around each vertex are given.