一种证明二次有理Bezier曲线曲率分布特征的新方法
PDF下载 (177)王亚丽,徐晨东*.一种证明二次有理Bezier曲线曲率分布特征的新方法[J].宁波大学学报(理工版),2023,36(2):82-89.DOI:
WANG Yali,XU Chendong*.A geometric proof of the curvature distribution theorems of the quadratic rational Bezier curves[J].Journal of Ningbo University(Natural Science & Engineering Edition),2023,36(2):82-89.DOI:
| Title: | A geometric proof of the curvature distribution theorems of the quadratic rational Bezier curves |
| 作者: | 王亚丽, 徐晨东* |
| Author(s): | WANG Yali, XU Chendong* |
| 关键词: | 圆锥曲线; 二次有理Bezier曲线; 曲率 |
| Keywords: | conics; rational quadratic B?ezier segment; curvature |
| 分类号: | O187.1 |
| 文献标识码: | A |
| 摘要: | 本文给出了一种证明二次有理Bezier曲线曲率分布特征的新方法. 该方法主要通过利用圆锥曲线的几何特征, 得到圆锥曲线段的对称轴方程; 并基于控制顶点和对称轴的位置, 给出了二次有理Bezier曲线的曲率分布特征定理. 这个方法与其他学者提出的方法相比更简单, 更容易理解. |
| Abstract: | A new method for the proof of the curvature distribution theorems of the quadratic rational Bezier curves is presented. With this method, we derive the line equations of symmetric axes of the conic curves by taking advantage of the geometric features of these curves. Based on the relative position relations between the control points and the symmetric axes, the curvature distribution theorems of the quadratic rational B?ezier segments are derived. This method proves simpler and easier than those previous ones in terms of expression and comprehension. |
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| 备注/Memo: | 收稿日期: 2022－02－16. 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: 王亚丽（1990－）, 女, 河南洛阳人, 在读硕士研究生, 主要研究方向: 计算几何. E-mail: 18892614929@163.com 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/*通信作者: 徐晨东（1977－）, 男, 浙江慈溪人, 博士/副教授, 主要研究方向: 计算几何. E-mail: xuchendong@nbu.edu.cn |
