The conditions of convexity for Bernstein–Bézier surfaces over triangles Original Research Article

This paper derives a convexity condition for Bernstein–Bézier surfaces defined on triangles. The condition for triangular Bézier surfaces to be convex is a linear sufficient condition on the control points. This condition is stronger than that for B-nets to be weak convex, but weaker than known linear conditions. The inequalities in this condition are symmetric with respect to the three barycentric coordinates. Moreover, geometric interpretations are provided. Example shows that this method is feasible and effective in geometric modeling.