提出了一类带两个形状参数的五点二重逼近细分格式.这类格式具有一些优良的性质:高阶连续性、可调性和多项式再生性质.对于参数的某些取值范围极限曲线可以达到$C^k(k=0,1,\cdots ,7)$ 连续,分析了一类特殊情况的多项式再生性质.实例表明该格式的有效性和灵活性.

A new five-point binary approximating subdivision scheme with two parameters is proposed in this paper. The scheme has some good properties, such as high continuity, flexibility and polynomial reproduction property. It is shown that the limiting curves are $C^k(k=0,1,\cdots ,7)$ continuous for certain ranges of the parameters. Polynomial reproduction property is also analyzed for a special case. Experimental results demonstrate the efficiency and flexibility of the scheme.