B样条曲线逼近的一种新方法  

A Novel Method for Approximation Using B-spline Curve

作　　者：林子植[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350007

出　　处：《福建师范大学学报（自然科学版）》2008年第2期22-28,共7页Journal of Fujian Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(60673014);福建省自然科学基金资助项目(A0610007);福建省教育厅A类基金项目(JA05207)

摘　　要：基于B样条曲线拟合出现的问题和困难,提出了一种新的B样条曲线拟合方法.该方法成功地避免了数据点参数化的问题,并使得逼近曲线具有较好的形状和接近弧长参数化的节点向量.本方法基本思想是:先用易于控制形状的低阶曲线拟合数据点,此曲线称为控制曲线,然后用高次曲线逼近该控制曲线,此高次曲线称为逼近曲线.根据本方法,设计新的拟合目标函数,通过求解二次优化系统来求解逼近曲线,并充分利用控制曲线提出一种新的接近弧长参数化的节点向量的设置方法.A novel method for approximating data points using B-spline curves is proposed. Firstly, the data points are fitted using a B-spline curve with low degree, which is named controlling curve. Secondly, another B-spline curve is finded to approximate the controlling curve, which is named approximating curve. The approach completely avoids the parametrization problem. Futhermore, the approximating curve has a good shape, and the knots are nearly arc-length parametrization. A new placement of knots according to the controlling curve is also proposed.

关 键 词：B样条曲线 逼近 参数化 最佳平方逼近 

分 类 号：O177.7[理学—数学]