The invariance of weak convexity conditions of B-nets with respect to subdivision

Abstract In (Grandine, 1989), it is proved that some types of subdivision do not preserve the convexity of Bezier nets and that for most triangulations, C 1 continuous convex Bernstein-Bezier triangular surface with convex Bezier nets must be linear. In this paper, it is first shown that subdivision always preserves weak convexity of Bezier nets, that is, the weak convexity condition of Bezier nets defined on a base triangle T is preserved on any subtriangles inside T . Then the invariance of weak convexity for elevation B-nets is proved. At last a necessary and sufficient condition characterized by the weak convexity of elevation B-net for the strict convexity of Bernstein-Bezier surface is given.