Bézier曲线最优参数化研究  

Research on Optimal Parametrization of Bezier Curve

作　　者：郭凤华[1] 杨兴强[1] 

机构地区：[1]山东大学计算机科学与技术学院,济南250061

出　　处：《计算机科学》2005年第5期195-196,212,共3页Computer Science

摘　　要：本文采用一种重新参数化方法,计算比Mobius变换简单,通用性强。对这种重新参数化方法研究表明,该方法含有单一自由度,重新参数化一条多项式曲线,得到同一条曲线的不同参数化,可以从中找出最接近弧长的参数化,即最优参数化。采用这种重新参数化方法求出的曲线最优参数化与采用Mobius变换求出的最优参数化是一样的。实例表明了该方法的有效性。A rational reparametrization function is used, compared with Mobius transformation, the function is very simple. Rational reparametrization of a polynomial curve is characterized by a single degree of freedom. Like Mobius transformation, further research shows the 'optimal' reparametrization in this faminly(that comes closest under the L_2 norm to arc-length parametrization) can also be identified by solving a quadratic equation. The function is proved to reach the same result with Mobius transformation as identifying the 'optimal' parametrization of the same polyno- mial curve.

关 键 词：BÉZIER曲线 最优 MOBIUS变换 参数化方法 多项式曲线 重新参数化 通用性 自由度 接近 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术] TP301.6[自动化与计算机技术—计算机科学与技术]