有理二次Bézier曲线的几何Hermite插值新方法  

New Method for Geometric Hermite Interpolation Problem of Rational Quadratic Bézier Curve

作　　者：林建兵[1] 陈小雕[1] 王毅刚[2] 

机构地区：[1]杭州电子科技大学计算机学院,杭州310018 [2]杭州电子科技大学数字媒体与艺术设计学院,杭州310018

出　　处：《计算机科学与探索》2013年第7期667-671,共5页Journal of Frontiers of Computer Science and Technology

基　　金：国防基础科研计划;浙江省自然科学基金 No.Y1090004~~

摘　　要：给定两个点以及相应的两个切向,Femiani等人提出了基于最小离心率椭圆的插值方法。同一椭圆上不同位置的椭圆弧,对应的形状与圆弧的接近程度是不一样的。椭圆弧的最小曲率半径和最大曲率半径之比,可以反映对应的椭圆弧与圆弧的接近程度,称之为椭圆弧的拟离心率。给出了基于拟离心率的新方法,使获取的椭圆弧具有最小拟离心率。与Femiani的方法相比,采用新方法得到的插值椭圆弧更加接近于圆弧。最后举例说明了新方法及其效果。Given two points and their directional tangent vectors, Femiani et al. proposed a method for obtaining an interpolation elliptic arc with least eccentricity. The elliptic arcs from different positions of a same ellipse have dif- ferent deviations from a circle. The ratio between the minimum curvature radius and the maximum curvature radius of an elliptic arc can be used to measure the corresponding deviation from a circle, which is called pseudo-eccentricity. This paper presents a new method to achieve an interpolation elliptic arc with least pseudo-eccentricity, which means that the resulting elliptic arc has less deviation from a circle than that of Femiani＇ s method. Examples illus- trate the new method and its effectiveness as well.

关 键 词：有理二次曲线 几何Hermite插值 最小离心率 椭圆弧拟离心率 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]