A new four-point shape-preserving subdivision scheme.

Abstract: 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 continuous. Furthermore, the conditions imposed on the initial points are also discussed, thus the given limit functions are both monotonicity preserving and convexity preserving [Copyright &y& Elsevier]