四次带参Ball曲线的形状分析  

Shape Analysis of Quartic Ball Curve with Shape Parameter

作　　者：吴晓勤[1] 韩旭里[2] 

机构地区：[1]湖南科技大学数学与计算科学学院,湘潭411201 [2]中南大学数学科学与计算技术学院,长沙410083

出　　处：《应用数学学报》2011年第4期671-682,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10871208);湖南省教育厅资助科研项目(08B027)

摘　　要：基于包络理论与拓扑映射的方法对四次带参Ball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;并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.研究表明,四次带参Ball曲线的形状调控能力要优于四次带参Bezier曲线.This paper considers the shape features of the quartic Ball curve with shape parameter 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 we discussed the influences of shape parameter on the shape distribution diagram and the ability for adjusting the shape of the curve.The results show that the shape adjustment of quartic Ball curve with shape parameter is superior to the quartic Bezier curve with shape parameter.

关 键 词：BALL曲线 形状参数 奇点 拐点 局部凸 全局凸 

分 类 号：O241.5[理学—计算数学] TP391[理学—数学]