基于二次代数曲线端点几何信息的最优有理参数化  

Optimal Rational Parameterization Based on the Geometry of Quadratic Curves's Ends

作　　者：厉玉蓉[1] 姜丽[2] 

机构地区：[1]山东工商学院计算机科学与技术学院,山东烟台264005 [2]山东师范大学信息科学与工程学院,山东济南250014

出　　处：《图学学报》2014年第1期21-25,共5页Journal of Graphics

基　　金：国家自然科学基金资助项目(60803048;61272244);山东省自然科学基金资助项目(Y2007A28)

摘　　要：利用参数化曲线段端点处的几何信息,根据端点处参数速率相等构造并确定最优或逼近最优的有理参数化方程。方法计算简单、效率高,由曲线端点处的几何信息可直接得到最优有理参数化方程。大量实验数据表明方法准确度更高、自适应性更强。若参数化曲线段端点处的参数速率相等且是最值,则得到的参数化是最优的;其余情形逼近于最优。In this paper, the equation of algebraic curve segment with the geometric information of both ends is rewritten. The optimal or nearly optimal rational parameterization formula is determined according to the principle that parametric speeds at both ends are equal. Comparing with literature [8] and literature [9], the method in this paper has advantage in efficiency and is easy to realize. The equation of optimal rational parameterization can be obtained directly by the information of both ends. A lot of number of numerical experimental data shows that our method has more self-adaptability and accuracy than that of literature [10], and if the parametric speed at any end reaches its maximum or minimum value, the parameterization is optimal; otherwise it's nearly optimal rational parameterization.

关 键 词：代数曲线 参数曲线 最优参数化 弧长参数化 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]