We consider a C 1 cubic spline space defined over a triangulation with Powell–Sabin refinement. The space has some local C 2 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. 
A new B-spline representation for cubic splines over Powell–Sabin triangulations