四次带参Bzier曲线的形状分析  

Shape Analysis of Quartic Bézier Curve with Shape Parameter

作　　者：吴荣军[1,2] 彭国华[1] 罗卫民[2] 叶正麟[1] 

机构地区：[1]西北工业大学应用数学系,西安710072 [2]西安邮电学院应用数理系,西安710121

出　　处：《计算机辅助设计与图形学学报》2009年第6期725-729,共5页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(60672135);陕西省教育厅专项科研项目(08JK435);西安邮电学院中青年教师科技项目(ZL200813)

摘　　要：为了明确形状参数对四次带参Bzier曲线形状的影响,利用基于包络理论与拓扑映射的方法对其进行了形状分析,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边向量的相对位置所表示;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.To investigate effects of the shape parameter on the curve shape, we analyzed the shape features of the quartic Bezier curve with shape parameter by using the method 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 characterized by the relative position of the edge vectors of the control polygon. Furthermore we discussed the influences of shape parameter on the shape diagram and the ability for adjusting the shape of the curve.

关 键 词：Bzier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]