平面三次PH曲线偶C^1 Hermite插值解的构造和形状分析  

CONSTRUCTION AND SHAPE ANALYSIS OF THE COUPLE OF PLANAR PH CUBIC C^1 HERMITE INTERPOLATION

作　　者：马元魁[1] 张天平[2] 康宝生[3] 

机构地区：[1]西安工业学院数理系,陕西西安710032 [2]陕西师范大学数学与信息科学学院,陕西西安710062 [3]西北大学信息科学与技术学院,陕西西安710069

出　　处：《计算机应用与软件》2006年第8期109-111,138,共4页Computer Applications and Software

摘　　要：一般情况下,三次PH曲线偶的C1Herm ite插值问题有四个不同的解。在这四个解中,只有一条曲线能很好地满足几何设计的要求。已有的插值算法都是依赖于构造出所有四个解,利用绝对旋转指标或弹性弯曲能量来找出这条“好”的插值曲线。本文提出一种新的方法以区分这些解,即用由三次PH曲线偶和惟一经典三次插值曲线的速端曲线形成的闭环的弯曲数来区分。对于“合理”的Herm ite数据,本文还给出了不需计算和比较所有的四个解便可直接构造“好”的三次PH曲线偶的方法。In general, the problem of interpolating given first-order Hermite data（ end points and derivatives ） by the couple of planar Pythagorean-hodograph （PH） cubic curves has four distinct formal solutions. Ordinarily, only one of these interpolants is of acceptable shape. Previous interpolation algorithms have relied on explicitly constructing all four solutions, and invoking a suitable measure of shape, the absolute rotation index or elastic bending energy-to select the＂ good＂ interpolant. A new means to differentiate among the solutions is introduced here, namely, the winding number of the closed loop formed by a union of the hodographs of the couple of PH cubics and of the unique ＂ordinary＂ cubic interpolant. It also shows that, for＂ reasonable＂ Hermite data, the ＂good＂ couple of PH cubics can be directly constructed, obviating the need to compute and compare all four solutions.

关 键 词：PH曲线 HERMITE插值 弯曲数 

分 类 号：TP391.7[自动化与计算机技术—计算机应用技术] O174.42[自动化与计算机技术—计算机科学与技术]