摘要
在光顺点云数据时,为了避免采用多项式曲线拟合点云数据难以取得较好的拟合效果,以及采用分段曲线拟合方法在分段处不满足函数连续性和可导性的缺陷,在传统最小二乘法曲线拟合的基础上,提出了基于拉格朗日乘数法对点云数据光顺处理的算法,对该算法进行了建模、求解及实际算例验证。通过对点云数据处理后结果表明:光顺后的曲线及曲线一阶导数在全域下均连续,且光顺后值与初始值最大偏离误差值不超过0.1mm,偏移幅度小于0.5%。因此,该算法曲线拟合精度高,满足点云数据光顺处理的要求,为点云数据的曲线光顺处理提供了参考依据。
When fitting point cloud data, to avoid the defects that it is hard to obtain a better fitting effect using polynomial curve fitting method, and that it is not satisfied with the continuity and differentiability of a function at the place of segments when using segment curve fitting method, therefore, based on the foundation of traditional least square method curve fitting, this paper propose an algorithm which is based on Lagrange multiplier to implement point cloud data＇ s fairing processing, and then through modeling, solving and practical example to prove the algorithm. The processing result of practical point cloud data indicate that the faired curve and its first differential are continuous at universe, moreover, the maximum deviation amplitude of the faired value and initial value is not more than 0. 1 mm, and the deviation am- plitude is less than 0.5 %. Therefore, the precision of this algorithm is higher, which meet with the re- quirements of point cloud data＇ s fairing and provide reference for the fairing processing of point cloud data.
出处
《组合机床与自动化加工技术》
北大核心
2013年第2期64-66,69,共4页
Modular Machine Tool & Automatic Manufacturing Technique
基金
国家自然科学基金项目(50475170)
关键词
点云数据
光顺
拉格朗日乘数法
分段拟合
逆向工程
point cloud data
fair
lagrange multiplier
segment fitting
reverse engineering
作者简介
王可（1957-），男，山东蓬莱人，沈阳工业大学机械工程学院教授，博士，主要从事复杂曲面数控加工理论与方法等方面的研究（E—mail）wk2222@sina．com。
