平面参数曲线的凸性分析  

Convexity Analysis of Closed Parametric Curve

作　　者：方逵[1] 姚杰[1] 

机构地区：[1]长沙大学计算机科学与技术系,湖南长沙410003

出　　处：《长沙大学学报》2006年第2期58-61,共4页Journal of Changsha University

基　　金：湖南省自然科学基金(批准号:03JJY3106);长沙市高新技术(批准号:K051127-72)项目资助

摘　　要：从几何和凸集的角度,系统地给出了平面闭参数曲线全局凸和局部凸定义,并且证明了这两个定义是等价的.证明了一条不含二重点的C2正则平面全局闭凸曲线是局部闭凸曲线,并给出了n次的平面Bézier曲线局部凸的判别条件.Based on geometry and convex set methods, this paper gives systemically the definitions of global and local convexity for planar closed parametric curve, and proves the two definitions are equivalent. This paper proves that rifled planar global closed convex curves with no lap points are local closed convex curves, and obtains that the planar convex degree n Bezier curves are local convex curves.

关 键 词：凸曲线 凸集 局部闭凸曲线 全局闭凸曲线 平面n次Bezier曲线 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]