On the interpolating 5-point ternary subdivision scheme: A revised proof of convexity-preservation and an application-oriented extension

In this paper we provide the conditions that the free parameter of the interpolating 5-point ternary subdivision scheme and the vertices of a strictly convex initial polygon have to satisfy to guarantee the convexity preservation of the limit curve. Furthermore, we propose an application-oriented extension of the interpolating 5-point ternary subdivision scheme which allows one to construct . C2 limit curves where locally convex segments as well as conic pieces can be incorporated simultaneously. The resulting subdivision scheme generalizes the non-stationary ternary interpolatory 4-point scheme and improves the quality of its limit curves by raising the smoothness order from . 1 to . 2 and by introducing the additional property of convexity preservation