To improve the flexibility for the design of subdivision curves, a Laurent polynomial is constructed by means of its relationship with the generated polynomial of the subdivision scheme. The Laurent polynomial can generate a family of subdivision schemes with several parameters, which not only include some existing symmet-ric schemes, but also can be used to construct asymmetric schemes. The continuity and smoothness of the limit curve are analyzed for a five-point scheme with three parameters. Numerical examples are given to demonstrate the influence of parameters on the limit curves in some special cases and to show that sometimes the asymmetric subdivision has better approximating effect than symmetric one.%为了提高细分曲线的设计灵活性，根据Laurent多项式与细分生成多项式的关系，构造一个可以生成一类多参数细分格式的 Laurent多项式。该多项式生成的格式包含许多现有的对称细分，可以用来构造非对称细分；针对一种三参数五点细分格式，分析其产生的极限曲线的光滑性和连续性。通过数值实例分析特定情形下参数对极限曲线的影响，并说明非对称细分有时比对称细分逼近效果更好。
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