基于广义瑞利商的已知点约束圆弧拟合算法  

Algorithm Based on General Rayleigh Quotient for Arc Fitting Subjected to One Known Point

作　　者：王维 Wang Wei(SGIDI Engineering Consulting(Group)Co.,Ltd,Shanghai 200438,China)

机构地区：[1]上海勘察设计研究院(集团)有限公司,上海200438

出　　处：《城市勘测》2020年第6期142-146,共5页Urban Geotechnical Investigation & Surveying

摘　　要：圆弧拟合算法广泛应用在各种任务的数据处理中。在一些特殊的数据处理中,已知圆弧上一点的约束下拟合圆弧参数。本文结合代数拟合的Taubin算法的思路,将其推广到已知端点约束的情况,提出了一种基于广义瑞利商圆弧参数求解算法,并利用AutoCAD的二次开发语言Visual Lisp实现了该算法。从拟合残差、圆心偏差、半径偏差及算法速度等方面综合分析比较了其他几种算法,验证该方法的可靠性和精度。The arc fitting algorithm is widely used in data processing of various surveying tasks.In some surveying data processing,arc parameters are fitted subjected to one known point.This paper inspired by the idea of the algebraic fitting Taubin algorithm and generalizes the idea to the case of known endpoint constraints.We proposed an arc parameter solving algorithm based on generalized Rayleigh quotient which implemented by Visual Lisp customized language of AutoCAD.The method and several other algorithms were analyzed and compared from fitting residual error,circle center error,radius and algorithm speed to verify the reliability and accuracy.

关 键 词：最小二乘法 已知端点 圆弧拟合 广义瑞利商 

分 类 号：P207[天文地球—测绘科学与技术]