控制边长成等比的一类三次空间Bézier曲线的挠率分析
PDF下载 (381)姚 燕,王亚丽,徐晨东 *.控制边长成等比的一类三次空间Bézier曲线的挠率分析[J].宁波大学学报(理工版),2018,31(1):69-75.DOI:
YAO Yan,Wang Ya-li,Xu Chen-dong *.Analysis on the torsion of a kind of cubic-spatial Bézier curves with geometric proportion control polygon sides[J].Journal of Ningbo University(Natural Science & Engineering Edition),2018,31(1):69-75.DOI:
| Title: | Analysis on the torsion of a kind of cubic-spatial Bézier curves with geometric proportion control polygon sides |
| 作者: | 姚 燕, 王亚丽, 徐晨东 * |
| Author(s): | YAO Yan, Wang Ya-li, Xu Chen-dong * |
| 关键词: | 三次空间Bézier曲线; 挠率; Descartes符号法则; cubic spatial Bézier curve |
| Keywords: | torsion; Descartes sign rule |
| 分类号: | O183.1 |
| 文献标识码: | A |
| 摘要: | 本文针对控制边长成等比、相邻控制边的夹角相等的三次空间Bézier曲线, 根据仿射不变性建立空间直角坐标系, 得到曲线挠率的表达式. 然后通过换元简化计算, 得到挠率导数的表达式. 再结合控制多边形的边角几何特征, 利用Descartes符号法则分析挠率导数为零时根的分布情况. 从而给出了这类三次空间Bézier曲线挠率单调递增和有极小值的参数域刻画. 最后给出了几个典型数值实例. |
| Abstract: | This paper focuses on a kind of cubic spatial Bézier curves with geometric proportion control polygon sides and equal angles between adjacent control polygons. And a rectangular space coordinate system is established according to the affine invariance to obtain the expression of curve deflection rate. In order to simplify calculation, the corresponding expression for the derivative of this torsion is derived by changing variables. Based on geometric features of the control polygon, the distribution of roots where torsion derivative equals zero is analyzed by using the Descartes sign rule. Thus the parametric domains, where the torsion of the corresponding Bézier curve is monotonic increasing or reaches its minimum value, are described. Finally, several typical numerical examples are given. |
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| 备注/Memo: | 收稿日期: 2017－05－18. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/基金项目: 国家自然科学基金（11101230; 11371209）.第一作者: 姚燕（1991－）, 女, 安徽铜陵人, 在读硕士研究生, 主要研究方向: 计算几何. E-mail: 1511071419@nbu.edu.cn*通信作者: 徐晨东（1977－）, 男, 浙江慈溪人, 副教授, 主要研究方向: 计算机辅助几何设计、计算几何. E-mail: xuchendong@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
