中文摘要：

构造了2个混合细分模式，一个是基于三次B样条细分的二分混合细分曲线族；另一个是基于一种三分三点逼近细分的三分混合细分曲线族．通过调整混合参数来控制曲线的收缩与膨胀幅度，利用生成函数技术和特征值方法对这2个带参数的细分模式的连续性进行了严格的理论分析．最后，通过选择合适的混合参数给出了一种曲线保长的动态细分方法．

英文摘要：

This paper designs two families of blending subdivisions based on known approximatory subdivisions. One is a binary blending subdivision based on the cubic B-splines, the other is a ternary blending subdivision based on the ternary 3-point subdivision. The approach provides a way to control the length of generated curves by introducing a blending parameter. Continuity analysis based on generating functions demonstrates that two families of blending subdivisions are C2 continuous in most cases. As an application, a length-preserving subdivision strategy is also proposed in the paper.