Pythagorean Hodograph C-曲线的几何构造方法  

Geometric Construction of Pythagorean Hodograph C-curves

作　　者：李毓君 方林聪[2] Yu Jun LI;Lin Cong FANG(Information Institute,Zhejiang University of Finance&Economics Dongfang College,Haining 314408,P.R.China;School of Information Management and Artificial Intelligence,Zhejiang University of Finance&Economics,Hangzhou 310018,P.R.China)

机构地区：[1]浙江财经大学东方学院信息学院,海宁314408 [2]浙江财经大学信息管理与人工智能学院,杭州310018

出　　处：《数学学报（中文版）》2023年第2期353-362,共10页Acta Mathematica Sinica：Chinese Series

基　　金：浙江财经大学东方学院院级重点项目(2021dfyz006)。

摘　　要：本文研究具有Pythogorean Hodograph(PH)性质的C Bézier曲线的几何性质.以PH C-曲线的代数性质为基础,应用平面参数曲线的复表示方法,本文证明一条C Bézier曲线是PH C-曲线的充分必要条件是其控制多边形的两内角相等,且其第2条边长为首末边长的等比中项.该性质与三次多项式PH曲线相类似,可以用于PHC-曲线的判别.此外,该性质可以很好地应用于解决PH C-曲线的Hermite插值问题,本文构造了PH C-曲线的G^(1)Hermite插值实例,指出对于给定的G^(1)Hermite端点条件,存在不超过2条PH C-曲线满足约束.We study the geometric characteristics of C-Bezier curves that possess the Pythagorean Hodograph(PH)property.Based on the algebraic necessary and sufficient conditions for PH C-curves,we prove that a C-Bezier curve is a PH C-curve if and only if the interior angles of its control polygon are equal,and the second leg length of the control polygon is the geometric mean of the first and the last ones.Our main idea is to represent a planar parametric curve in complex form.We claim that the geometric characteristics of PH C-curves are quite similar to polynomial PH curves,which can be used to identify PH C-curves and their constructions.As an application,we give some examples of G^(1)Hermite interpolation using PH C-curves.We point out that there are no more than two PH C-curves for any given G^(1)Hermite conditions.

关 键 词：几何构造 几何连续 HERMITE插值 C-BÉZIER PH曲线 

分 类 号：O241.3[理学—计算数学]