Comparison between Gregory-Qu Algorithm and Hermite Interpolatory Subdivision Scheme

The subdivision rules of Gregory-Qu algorithm and Hermite interpolatory subdivision scheme,including the conditions of C¹ continuity,are presented.Analysing the two schemes,we conclude that stationary Gregory-Qu algorithm is a special case of stationary Hermite interpolatory subdivision.And Hermite interpolatory subdivision scheme not only has the weaker conditions of C¹ continuity,but also generates the limit curve more flexibly.