与给定多边形相切的四次Q-Bézier闭曲线  

Closed quartic Q-Bézier curves with given tangent polygon

作　　者：刘植[1] 姜婉 路智明 陈晓彦[1] LIU Zhi;JIANG Wan;LU Zhiming;CHEN Xiaoyan(School of Mathematics, Hefei University of Technology, Hefei 230009, China)

机构地区：[1]合肥工业大学数学学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2018年第12期1724-1728,共5页Journal of Hefei University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(11471093);安徽省教育厅自然科学重大研究资助项目(KJ2014ZD30);国家级大学生创新训练计划资助项目(201610359063)

摘　　要：文章构造了一类与给定切线多边形相切的组合四次Q-Bézier闭曲线;所生成的曲线满足C2连续,且对切线多边形是保形的;曲线段的所有控制顶点均由给定的切线多边形顶点直接计算产生;通过调整形状参数的取值,可以灵活控制组合曲线的形状。数值实例表明该文方法简单、灵活、有效,更能够适合计算机辅助几何设计(computer aided geometric design,CAGD)系统的造型要求。A class of closed combined quartic Q-Bézier curves with all edges tangent to a given control polygon are constructed.The constructed combination curves are of C2-continuity and are shape preserving to tangent polygon.The control points of the Q-Bézier curve segments are computed simply by the vertices of the given tangent polygon directly.The shape of curves can be controlled flexibly by adjusting the values of shape parameters.Numerical examples show that the presented method is simple,intuitive,effective and easy to control.It will suit better for modeling demands in computer aided geometric design(CAGD).

关 键 词：Q-Bézier曲线 形状参数 C2连续 切线多边形 组合曲线 

分 类 号：O241.3[理学—计算数学]