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

摘要

In this paper, we give a geometrical characterization of the convexity of Bezier 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.