On the convexity of Bézier nets of quadratic Powell-Sabin splines on 12-fold refined triangulations
Considering the partition of a triangle in 12 subtriangles the authors analyse the convexity of finite elements over such triangles and of differentiable surfaces obtained by assembling such elements in a triangulated polygonal convex domain [see \textit{M. J. D. Powell} and \textit{M. A. Sabin}, ACM Trans. Math. Software 3, 316-325 (1977; Zbl 0375.41010)]. Necessary and sufficient conditions for the convexity of Bézier nets of the triangles of the foregoing type and of the associated composed surfaces are obtained.
scientific article; zbMATH DE number 1423331