A new B-spline representation for cubic splines over Powell-Sabin triangulations

We consider a C1 cubic spline space defined over a triangulation with Powell-Sabin refinement. The space has some local C2 super-smoothness and can be seen as a close extension of the classical cubic Clough-Tocher spline space. In addition, we construct a suitable normalized B-spline representation for this spline space. The basis functions have a local support, they are nonnegative, and they form a partition of unity. We also show how to compute the Bézier control net of such a spline in a stable way.