中文摘要：

为了精确表示分别由{1，x，x^2，x^3}，{1，x，e^sx，e^-sx}和{1，x，e^isx，e^-isx）张成的线性空间，提出一类Hermite插值的动态细分格式，并证明了它至少是C^1收敛的．该细分格式提供了一个松弛参数，当恰当地选择松弛参数时，该细分格式可以生成三次多项式曲线、三角曲线和双曲曲线；特别地，能够精确描述圆锥曲线．最后给出一些实例来说明松弛参数和切向量对细分曲线的影响．

英文摘要：

For representing elements of the linear spaces spanned respectively by the functions {1 ,x, x^2,x^3}, {1,x, e^sx, e^-sx} and {1,x, e^isx, e^-isx}, the paper presents a C^1 non-stationary Hermiteinterpolatory subdivision scheme which provides users with a tension parameter that, through proper adjustment within its range of definition can reproduce cubic polynomials, trigonometric functions and hyperbolic functions. Moreover, for certain given parameters, all conic sections can be reproduced exactly by this scheme. The convergence analysis of the subdivision method is given as well. Finally, we illustrate the effects of using the tension parameter and tangent vectors to generate subdivision curves.