Effect of the two Hassan-Dodgson Parameters on the Shape of 3-point Ternary Interpolatory Subdivision Curve

摘要

Hassan and Dodgson proposed a 3-point ternary interpolatory subdivision scheme which contains two parameters. It is proved that when the two parameters are kept within a proper range, it is C{sup}1-continuous. But their clear meanings and how they affect the shape of the subdivision curve are still unknown, which limit the application of the subdivision scheme. This paper focuses on the role of the two Hassan-Dodgson parameters. Based on the equivalent descriptions of the C{sup}0 and C{sup}1 ranges of the subdivision scheme, a novel method is proposed to analyze the effect of the parameters on the shape of the subdivision curve theoretically. Some examples are given to illustrate that the present theory provides with a clear way to control the shape of the 3-point ternary interpolatory subdivision curve.