| 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. |
| 关键词: ω-Bézier 曲线 频率参数 奇点 拐点 局部凸 全局凸 |
| DOI： |
| 分类号: |
| 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) |
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| Shape Analysis of Cubic ω-Bézier Curve |
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WU Xiao-Qin1, HAN Xu-Li2
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1.School of Mathematics and Computation Science, Hu’nan University of Science and Technology, Xiangtan 411201, China;2.School of Mathematical Science and Computing Technology, Central South University, Changsha 410083, China
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| 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. |
| Key words: ω-Bézier curve frequency parameter singular point inflection point local convexity global convexity |
