A new four-point shape-preserving C3C3 subdivision scheme

• We present a new relaxation of binary four-point subdivision scheme.
• The scheme keeps the second-order divided difference at the old vertices unchanged when inserting new vertices.
• Our limit functions are both monotonicity preserving and convexity preserving.
• Our limit curve is at least C3C3 continuous when using the symbol of the scheme.

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 C3C3 continuous. Furthermore, the conditions imposed on the initial points are also discussed, thus the given limit functions are both monotonicity preserving and convexity preserving