A new binary four-point subdivision scheme is presented, which keeps the second-order divided difference at the old vertices unchanged when the new vertices are inserted. Using the symbol of the subdivision scheme, we show that the limit curve is at least C 3 continuous. Furthermore, the conditions imposed on the initial points are also discussed, thus the given limit functions are both monotonicity preserving and convexity preserving 
A new four-point shape-preserving C 3 subdivision scheme