Quartic splines on Powell-Sabin triangulations

The paper deals with the construction of bivariate quartic splines on Powell-Sabin triangulations. In particular, it provides a spline space that is C2 everywhere except across some edges of the refined triangulation. The splines that belong to this space can be described uniquely with interpolation values and derivatives of order at most two. Moreover, they can be represented in a locally supported basis that forms a convex partition of unity. As an application of this result, quasi-interpolants that reproduce polynomials of degree four are derived.