一类三次曲线的形状分析  

Shape analysis of class of cubic curves

作　　者：吴晓勤[1] 陈福来[1] 朱秀云[1] 

机构地区：[1]湖南科技大学数学与计算科学学院,湖南湘潭411201

出　　处：《计算机工程与应用》2012年第3期165-168,共4页Computer Engineering and Applications

基　　金：湖南省教育厅资助科研项目(No.08B027)

摘　　要：基于包络理论与拓扑映射的方法,对一类带有形状参数的三次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和形状参数所决定。进一步讨论了形状参数对形状分布图的影响及其对曲线形状的调节能力。This paper considers the shape features of the class of cubic curves based on the theory of envelop 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 decided by control polygon and the shape parameter.Furthermore,it discusses the influences of shape parameter on the shape distribution diagram and the ability for adjusting the shape of the curve.

关 键 词：三次曲线 形状参数 奇点 拐点 局部凸 全局凸 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]