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DOI:
Journal of Software:2010.21(zk):60-66

三次ω-Bézier 曲线的形状分析
吴晓勤,韩旭里
(湖南科技大学 数学与计算科学学院,湖南 湘潭 411201;中南大学 数学科学与计算技术学院,湖南 长沙 410083)
Shape Analysis of Cubic ω-Bézier Curve
WU Xiao-Qin,HAN Xu-Li
(School of Mathematics and Computation Science, Hu’nan University of Science and Technology, Xiangtan 411201, China;School of Mathematical Science and Computing Technology, Central South University, Changsha 410083, China)
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Received:May 15, 2010    Revised:August 16, 2010
> 中文摘要: 基于包络理论与拓扑映射的方法对三次ω-Bézier 曲线进行了形状分析,得出了曲线上含有奇点、拐点和曲线为局部凸或全局凸的充分必要条件.这些条件完全由控制多边形的顶点和频率参数所决定.进一步讨论了频率参数对形状分布图的影响及其对曲线形状的调节能力.
Abstract:To investigate effects of the frequency parameter on the curve shape, this paper analyzes the shape features of the cubic ω-Bézier curve by using the method based on the theory of envelope and topological mapping. Necessary and sufficient conditions are derived for this curve having one or two inflection points, a loop or a cusp, or be locally or globally convex. Those conditions are completely characterized by the vertex of the control polygon and frequency parameter. Furthermore, it discusses the influences of frequency parameter on the shape diagram and the ability for adjusting the shape of the curve.
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基金项目:Supported by the National Natural Science Foundation of China under Grant No.10871208 (国家自然科学基金); the Scientific Research Fund of Hu’nan Provincial Education Department of China under Grant No.08B027 (湖南省教育厅资助科研项目) Supported by the National Natural Science Foundation of China under Grant No.10871208 (国家自然科学基金); the Scientific Research Fund of Hu’nan Provincial Education Department of China under Grant No.08B027 (湖南省教育厅资助科研项目)
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吴晓勤,韩旭里.三次ω-Bézier 曲线的形状分析.软件学报,2010,21(zk):60-66

WU Xiao-Qin,HAN Xu-Li.Shape Analysis of Cubic ω-Bézier Curve.Journal of Software,2010,21(zk):60-66