一类由Laurent多项式诱导的带参数二重细分

基金项目:

国家自然科学基金（61472466）；中央高校基本科研业务费专项经费（JZ2015HGXJ0175）.

详细信息

A Class of Binary Subdivision Schemes Derived by the Laurent Polynomial with Parameters

1. School of Mathematics, Hefei University of Technology, Hefei 230009;
2. School of Computer and Information, Hefei University of Technology, Hefei 230009

摘要: 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.
- 二重细分 /
- 极限曲线 /
- 参数 /
- C^k连续性
Abstract: 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 symmetric 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.
- binary subdivision /
- limit curve /
- parameter /
- C^k continuity