基于切矢控制的B样条曲线逼近的PIA算法  

PIA for B-spline Curve Approximation with Tangent Constraint

作　　者：黄丽琴[1] 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）》2015年第2期32-41,共10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：提出了一种基于切矢控制的B样条曲线逼近的渐进迭代逼近(PIA)算法.一方面该方法将离散数据点的切失、曲率等几何特征充分应用到离散数据点的逼近问题上,利用切矢约束引导逼近曲线的走势,避免不必要的波动现象,获得较好的逼近效果.另一方面由于选取主特征点作为控制顶点,算法中控制顶点的数目小于数据点的数目,所以允许拟合较大规模的数据点.而且PIA算法的每次迭代过程中的各个步骤都是完全独立的,很容易被应用到并行计算上,可提高计算效率.最后给出了一些实例来证明方法的有效性.It proposes a progressive iterative approximation（ PIA） algorithm for B-spline curve approximation with tangent constraint.On the one hand the discrete data points of the tangent vector,curvature and other geometric characteristics are fully applied to the approximation problem of discrete data points,using tangent constraint can avoid unnecessary fluctuations,and obtain better approximation effect.On the other hand,the number of selecting feature points is less than the number of data points,so the PIA algorithm can be used for the approximation of the mass of discrete data points.The steps in the process of each iteration of the algorithm are independent,which is easy to be applied to the parallel computing,which greatly improve the computational efficiency.Some examples are given to show the validity of the algorithm.

关 键 词：渐进迭代逼近 B样条曲线 主特征点 切矢 调整差向量 曲率 

分 类 号：O177.7[理学—数学]