| 一个分析计算平面曲线拐点的可靠判据 |
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| 引用本文： | 王兴波 石金龙 文锦. 一个分析计算平面曲线拐点的可靠判据[J]. 湖南理工学院学报：自然科学版, 2004, 17(2): 1-6 |
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| 作者姓名： | 王兴波 石金龙 文锦 |
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| 作者单位： | [1]国防科技大学机电工程与自动化学院湖南长沙410073 [2]湖南理工学院湖南岳阳414000 |
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| 基金项目： | 国家自然科学基金 (5 10 75 0 16)，国防科技大学博士基金项目 (KDBSJJ3— 0 3 0 0 0 1)。 |
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| 摘 要： | 拐点是平面曲线重要的特征点之一，在工程应用中有着特殊的意义，但是长期以来在理论上缺乏统一与完备的数学描述，导致分析计算的混乱。该文首先综述了目前有关拐点研究的一些成果，指出了拐点研究中尚存在的一些问题与不足，然后给出了拐点的一个数学定义，并在此基础上演绎推导出曲线在拐点处若干性质。其研究结果为工程上分析计算拐点提供了科学依据。
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| 关 键 词： | 几何 CAD 曲线 拐点 |
| 文章编号： | 1672-5298(2004)02-0001-06 |
| 修稿时间： | 2003-11-15 |
A reliable criterion for analysis and calculation of inflection points on plane curves |
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| WANG Xing bo ,SHI Jin long ,WEN Jin. A reliable criterion for analysis and calculation of inflection points on plane curves[J]. Journal of Hunan Institute of Science and Technology, 2004, 17(2): 1-6 |
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| Authors: | WANG Xing bo SHI Jin long WEN Jin |
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| Affiliation: | WANG Xing bo 1,SHI Jin long 1,WEN Jin 2 |
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| Abstract: | Inflection points are important characteristic points of plane curves with speical meanings in engineering,but have little been systematically and completely described in mathematics,and this leads to many confusions in analysis and calculations.Thus this paper first points out some problems and confusions in study of inflection points through a survey of the historical researches,then gives a mathematical definition of inflection point,and induces several properties of plane curves at their inflection points.The study of this paper can provide a complete and unite resolution in researches of inflection points as well as a scientific criterion for analysis and calculation of inflection points. |
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| Keywords: | geometry CAD curve inflection point |
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