A kind of interpolatory convexity-preserving subdivision scheme for the generation of smooth curves

Based on the analysis for the convexity of planar discrete data points, a kind of interpolatory convexity-preserving subdivision scheme for the generation of smooth curves is presented in this paper. The proposed scheme is local and it makes the schemes in [1][2] be the special cases. Furthermore, when the suitable shape parameters are chosen, the limit curve is smooth and tangent continuous. In addition, some useful and interesting properties are discussed, and finally, some numerical examples are given.