三点插值的三次PH曲线构造方法  

Construction of Cubic PH Curves Interpolating Three Points

作　　者：方林聪[1] 李毓君 Fang Lincong;Li Yujun(School of Information and Artificial Intelligence,Zhejiang University of Finance and Economics,Hangzhou 310018;Zhejiang University of Finance&Economics Dongfang College,Haining 314408)

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

出　　处：《计算机辅助设计与图形学学报》2020年第3期385-391,共7页Journal of Computer-Aided Design & Computer Graphics

基　　金：浙江省自然科学基金(LY18F020023).

摘　　要：为推广三次PH曲线的实际应用,研究在给定3个平面型值点条件下的三次PH曲线构造方法.三次PH曲线具有鲜明的几何性质和代数特征,采用平面参数曲线的复数表示方法,三次PH曲线的充分必要条件被表述为复代数系统.通过对给定型值点进行参数化,将复代数系统转化为一元二次复方程,求解方程即得三次PH曲线的控制顶点,从而得到2条构造曲线.应用该方法对模拟给定的若干平面型值点数据进行实验,比较了均匀参数化、弦长参数化、弧长参数化方法的不同效果,并计算弧长、弯曲能量、绝对旋转数来选取最优构造曲线.实验结果表明,该方法有效且易于计算,可应用于三次PH样条构造.This paper introduces a novel method to construct cubic PH curves by interpolating three planar points, which broadens their practical applications. Since these curves possess prominent geometric characteristics and algebraic properties, their necessary and sufficient conditions can be expressed by a complex system by employing complex representation of planar parametric curves. Following parametrization of given points, we get a quadratic complex equation from the complex system, which gives the control points of two cubic PH curves. We do experiments by constructing cubic PH curves for some given planar points. We compare different parametrization methods including uniform parametrization, chord length, and arc-length parametrization methods. In order to select the best solution, we further compute arc lengths, bending energies, and absolute rotation numbers of curves. Finally, as an application we use the proposed method to construct a cubic PH spline curve.

关 键 词：BÉZIER曲线 参数化 插值 三次PH曲线 等距线 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]