与给定多边形相切的可调二、三次Bézier曲线  

Adjustable Quadratic and Cubic Bézier Curves with Given Tangent Polygons

作　　者：刘植[1,2] 檀结庆[1,2] 陈晓彦[2] 张莉[1,2] 时军[2] 

机构地区：[1]合肥工业大学计算机与信息学院,安徽合肥230009 [2]合肥工业大学数学系,安徽合肥230009

出　　处：《工程图学学报》2010年第6期45-50,共6页Journal of Engineering Graphics

基　　金：国家自然科学基金资助项目(60773043);教育部博士点新教师基金资助项目(2008JYXJ0828);安徽省自然科学基金资助项目(070416273X);安徽省高校优秀青年人才基金资助项目(2009SQRZ008);合肥工业大学科研基金资助项目(071003F)

摘　　要：讨论与给定多边形相切的分段二、三次Bézier曲线,所构造的曲线C1连续,且对切线多边形是保形的。曲线上的所有Bézier曲线段的控制点由切线多边形的顶点直接计算产生。在一定范围内,可以通过调节控制参数对切线多边形作整体或局部逼近。实例表明,该文方法计算简单、控制灵活,方便有效。This paper proposes an approach to constructing planar piecewise quadratic and cubic Bézier curve with all edges tangent to a given polygon and the curve segments are joined together with C1-continuity.The segmented Bézier curves are all shape preserving to their tangent polygon.All control points of the Bézier curve segments can be calculated simply by the vertices of the given polygon.The curve can locally or globally approximate the tangent polygon by the adjustment of the control parameters.Experiments show that the method given in this paper is simple,intuitive,effective and easy to control.

关 键 词：计算机辅助几何设计 切线多边形 BÉZIER曲线 C1连续 保形 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]