三次均匀B样条曲线插值数据点及其切矢的PIA算法  

PIA for Uniform Cubic B-spline Curve Interpolation with Prescribed Tangent Vector

作　　者：星蓉生 潘日晶[1] 

机构地区：[1]福建师范大学数学与计算机科学学院,福建福州350117

出　　处：《福建师范大学学报（自然科学版）》2014年第1期25-32,共8页Journal of Fujian Normal University：Natural Science Edition

基　　金：福建省自然科学基金资助项目(2010J01318)

摘　　要：基于渐进迭代逼近算法生成插值数据点及其切矢的三次均匀B样条曲线.其基本思想是用偶数项控制顶点来对应拟合数据点,用奇数项控制顶点控制相应切矢逼近,根据迭代公式不断调整控制顶点,当迭代次数趋于无穷时,一系列迭代曲线的极限曲线插值于给定的数据点及其相应的切矢.用该方法构造插值曲线是一个迭代过程,不必解线性方程组.An uniform cubic B-spline curve is generated to interpolate the data points with prescribed tangent vectors based on the progressive iterative approximation. It starts with an initial B-spline curve which takes the given data points as the control points with even indexes and takes the end points of the tangent vectors as the control points with odd indexes. Then by adjusting its control points gradually with iterative formulas, a sequence of curves is obtained . The limit curve of the sequence will interpolate the data points with prescribed tangent vectors. The curve fits a given ordered point set and corresponding tangent vectors without solving a linear system.

关 键 词：渐进迭代逼近 B样条 切矢 调整差向量 

分 类 号：O177.7[理学—数学]