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高校应用数学学报
高校应用数学学报  2014, Vol. 29 Issue (4): 419-430    
    
圆锥曲线的三次有理多项式参数化
吴伟栋, 杨勋年
浙江大学 数学系, 浙江杭州 310027
Cubic rational polynomial parametrization of conics
WU Wei-dong, YANG Xun-nian
Department of Mathematics, Zhejiang University, Hangzhou 310027, China
 全文: PDF 
摘要： 圆锥曲线重新参数化可以提高曲线参数的均匀性, 且增强在拼接点处的光滑性. 常用的参数化方法是采用一次有理多项式或二次有理多项式. 采用三次有理多项式对圆锥曲线重新参数化, 使曲线的次数由二次升到六次. 以圆弧为例所得的实验结果表明, 在两段圆弧的公共点处的连续性为$C^{3}$, 而且三次有理多项式参数化与弧长参数化的弦长偏差相比二次有理多项式参数化减小两个数量级.
关键词： 圆锥曲线;  三次有理多项式参数化;  连续性;  弦长偏差    
Abstract: Reparametrization of conics can make the parameter as uniform as possible and improve the smoothness at the junction points. The common ways are to use linear rational polynomials or quadratic rational polynomials. In the paper, a cubic rational polynomial is used to reparametrize the conic section, which triples the degree of quadratic rational curve. Experimental results obtained by the parametrization of the circular arcs show that the continuity at the junction point of two circular arcs can reach $C^3$ and the deviation between the parametrization presented in the paper and the arc length parametrization has been reduced about two orders of magnitude, compared with the quadratic rational polynomial parametrization.
Key words: conic section    cubic rational polynomial parametrization    continuity    chordal deviation
收稿日期: 2014-02-24 出版日期: 2018-06-08
CLC:  TP391.72  
基金资助: 国家自然科学基金(11290142; 61272300)
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引用本文:

吴伟栋, 杨勋年. 圆锥曲线的三次有理多项式参数化[J]. 高校应用数学学报, 2014, 29(4): 419-430.

WU Wei-dong, YANG Xun-nian. Cubic rational polynomial parametrization of conics. Applied Mathematics A Journal of Chinese Universities, 2014, 29(4): 419-430.

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http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2014/V29/I4/419

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