三次DP曲线的形状分析  

Shape analysis of cubic DP curve

作　　者：吴晓勤[1] 朱秀云[1] 陈福来[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：《湖南科技大学学报（自然科学版）》2011年第3期70-74,共5页Journal of Hunan University of Science And Technology：Natural Science Edition

基　　金：湖南省教育厅项目资助(08B027);湖南科技大学博士启动基金(E58126)

摘　　要：基于包络理论与拓扑映射的方法对三次DP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位置所决定.最后,就三次DP曲线和三次Bezier曲线、三次Ball曲线的形状图进行了对比.The shape features were analyzed,that of the cubic DP curve,based on the theory of envelop and topological mapping.Necessary and sufficient conditions were derived for this curve with one or two inflection points,a loop or a cusp,and be locally or globally convex.Those conditions were completely determined by the vertexes the control polygon.At last,the shape diagrams were given,that of cubic Bézier curve and Ball curve.

关 键 词：DP曲线 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]