两类特殊三次空间Bézier曲线的挠率特征分析
PDF下载 (306)王秋霞,朱如媛,徐晨东*.两类特殊三次空间Bézier曲线的挠率特征分析[J].宁波大学学报(理工版),2016,29(3):13-18.DOI:
WANG Qiu-xia,ZHU Ru-yuan,XU Chen-dong*.Analysis on Torsion Characteristics of Two Kinds of Special Cubic-spatial Bézier Curves[J].Journal of Ningbo University(Natural Science & Engineering Edition),2016,29(3):13-18.DOI:
| Title: | Analysis on Torsion Characteristics of Two Kinds of Special Cubic-spatial Bézier Curves |
| 作者: | 王秋霞, 朱如媛, 徐晨东* |
| Author(s): | WANG Qiu-xia, ZHU Ru-yuan, XU Chen-dong* |
| 关键词: | 三次空间Bézier曲线; 笛卡尔符号法则; 挠率; 单调; cubic-spatial Bézier curve |
| Keywords: | Descartess rule of signs; torsion; monotone |
| 分类号: | O186.1 |
| 文献标识码: | A |
| 摘要: | 空间Bézier曲线的挠率在几何造型中被广泛应用. 文中利用笛卡尔符号法则讨论了两种特殊三次空间Bézier曲线的挠率单调性问题, 最后得出当空间三次Bézier曲线的控制边相等且中间控制边和相邻两控制边的夹角相等时, 挠率仅有一个极小值; 而当两夹角相等但控制边长成等差数列时, 文中给出了挠率单调及极值存在的充分条件. |
| Abstract: | The torsion of the spatial Bézier curve is widely used in geometrical modelling. In this paper, we mainly discuss the torsion monotonicity problem of two special cubic Bézier curves by use of Descartes’ rule of signs. Based on the study, it is concluded that when the control sides are of equal length and the angles between two adjacent control sides are equal, the only minimum of torsion is always available; and in the case that the two angles are equal while the control side lengths are in arithmetic progression, the sufficient conditions can be determined for the torsion monotony and the existence of extremum. |
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| 备注/Memo: | 收稿日期: 2015?10?27. 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）; 浙江省自然科学基金（LY13A010013）. 第一作者: 王秋霞（1989－）, 女, 河南信阳人, 在读硕士研究生, 主要研究方向: 计算几何. E-mail: 879204064@qq.com *通信作者: 徐晨东（1977－）, 男, 浙江宁波人, 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/ |
