In order to enrich the modeling methods of subdivision curves and surfaces,a new three-point binary approximating subdivision scheme with a parameter is constructed.The continuity of the subdivision scheme is studied and the corresponding parameter ranges are given when the scheme has uniform continuity and each order continuity by using the generating polynomi-al method proposed by Dyn.At the same time,the convexity preservation of the subdivision scheme is studied.The range of the parameter for the property of convexity preservation of the limiting curves is also provided.Numerical examples show that the values of parameters have an important effect on the continuity of the generated limit curve,and the proposed subdivision scheme is reasonable and effective.
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