一类4次OR曲线的几何判别法  

Geometric Discriminate Methods of a Class of Quartic Offset-rational Curves

作　　者：段小娟 汪国昭[2] Duan Xiaojuan;Wang Guozhao(Department of Mathematical Sciences,Zhejiang Sci-Tech University,Hangzhou 310018;School of Mathematical Sciences,Zhejiang University,Hangzhou 310027)

机构地区：[1]浙江理工大学数学科学系,杭州310018 [2]浙江大学数学科学学院,杭州310027

出　　处：《计算机辅助设计与图形学学报》2018年第3期499-504,513,共7页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61272300;11671009)

摘　　要：针对4次Bézier曲线,探讨其是一类具有精确多项式等距线的平面参数曲线(OR curves)的充要条件.根据4次OR曲线的速端曲线在复平面的分解式,将OR曲线分为PH曲线、第1类普通OR曲线和第2类普通OR曲线3种;针对第1类普通OR曲线或PH曲线,利用其速端曲线和二阶导矢曲线之间的关系给出统一的几何判别充要条件,得到了控制多边形上边角分离的几何条件;给出4次第1类普通OR曲线或PH曲线的速端曲线的统一的分解式及判别这2类曲线的方法.最后给出了4次第1类普通OR曲线与PH曲线的等距线实例.The necessary and sufficient conditions for quartic Bézier curves being a class of offset-rational curves are discussed.Quartic offset-rational curves which possess exact rational polynomial offsets can be classified into Pythagorean-hodograph(PH)curves,Class I ordinary OR curves and Class II ordinary OR curves,according to the decompositions of their hodograph curves in complex form.Based on the common factor of the hodograph curve and the second derivative curve,the uniform geometric discriminate methods and geometric explanations based on the control polygon for a quartic Class I ordinary OR curve or PH curve are proved.The uniform decompositions of the hodograph curve are presented and the distinguish method between Class I ordinary OR curves and PH curves is given.Finally,we show the examples of offset curves for quartic Class I ordinary OR curves and PH curves.

关 键 词：具有精确有理等距曲线的参数曲线 重新参数化 判别法 几何内在量 控制多边形 

分 类 号：TP391.7[自动化与计算机技术—计算机应用技术]