SPS参数化有理Bézier曲线的几何性质
PDF下载 (303)朱如媛,徐晨东.SPS参数化有理Bézier曲线的几何性质[J].宁波大学学报(理工版),2016,29(1):59-63.DOI:
ZHU Ru-yuan,XU Chen-dong*.Geometric Properties of Rational Bézier Curves with SPS Parameter[J].Journal of Ningbo University(Natural Science & Engineering Edition),2016,29(1):59-63.DOI:
| Title: | Geometric Properties of Rational Bézier Curves with SPS Parameter |
| 作者: | 朱如媛, 徐晨东 |
| Author(s): | ZHU Ru-yuan, XU Chen-dong* |
| 关键词: | 有理Bézier曲线; SPS参数化; 升阶; 曲率; rational Bézier curves |
| Keywords: | SPS parameterization; degree elevation; curvature |
| 分类号: | O183.1 |
| 文献标识码: | A |
| 摘要: | SPS(Scalar Projection Scale)参数化有理Bézier曲线在几何造型中有重要应用. 为研究其几何性质, 首先分析了当SPS参数化有理Bézier曲线退化为Bézier曲线时, 其所具有的几何性质; 其次证明了SPS参数化有理Bézier曲线升阶后仍为SPS参数化; 最后在求导的基础上利用笛卡尔符号法则分析SPS参数化二次有理Bézier曲线曲率的单调性, 并得到了其曲率分布的规律. |
| Abstract: | Rational Bézier curves with SPS (scalar projection scale) parameterization are useful in geometric molding. In order to study their geometric properties, the following three steps are carried out. In the first step, we note that, when a rational Bézier curve degenerates into Bézier curve, it will present an intuitive geometric character. In the second step, we demonstrate that a rational Bézier curve with SPS parameterization is still SPS parameterized after degree elevation. Finally, by Descartes’ rule of signs, the monotonicity of curvature is discussed for a rational quadratic Bézier curve parameterized by SPS in a bid to obtain the curvature distribution |
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| 备注/Memo: | 收稿日期: 2014?09?22. 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）; 宁波大学学科项目（XKL11D2051）. 第一作者: 朱如媛（1988－）, 女, 江西萍乡人, 在读硕士研究生, 主要研究方向: 计算几何. E-mail: zhuruyuan1214@qq.com * 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及计算几何 . E-mail: xuchendong@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
