Abstract: As extension of the classical 4-point interpolating subdivision scheme，an improved scheme to design subdivision curves using three control parameters is presented.The sufficient conditions of the uniform convergence property and Ck continuity properties of this subdivision scheme are proved.At the same time，it is extended to surface design.Given the condition of the initial data，it’s very easy to adjust and control the surface shape through selecting appropriate parameters.The scheme can solve the problems of position adjustment and shape control of curves and surfaces that exist in engineering.

Key words: subdivision scheme, limit surface, surface modeling

摘要： 在经典四点细分法的基础上，通过在曲线细分过程中引入三个参数，给出一种改进的细分曲线构造的算法，利用生成多项式等方法对细分法的一致收敛性、Ck连续性进行了分析。并把该方法扩展到曲面上，进而提出了曲面三参数binary细分法。在给定初始控制数据的条件下，可以通过对形状参数的适当选择来实现对细分极限曲面形状的调控。数值实验表明该算法较容易控制曲面形状，可方便地应用于工程实际，解决曲线、曲面位置调整和控制问题。

关键词: 细分法, 极限曲面, 曲面造型