On the convexity of Bézier nets of quadratic Powell–Sabin splines on 12-fold refined triangulations

In this paper, we give a geometrical characterization of the convexity of Bézier nets of some piecewise quadratic Powell–Sabin surfaces. This condition also guarantees the convexity of the underlying surfaces. We first study the local problem for the Powell–Sabin finite element decomposed into 12 triangles (the PS2 finite element). Then, we extend our results to surfaces obtained by assembling these finite elements.