Fast code to fit circular arcs

Abstract
We present a fast code to fit circular arcs to measured points. Our algorithm is based on an explicit solution of a non-linear least-squares problem to fit the circle curvature, direction and position parameters. The code includes error estimation of the circle parameters as well as the transformation of parameters and error matrix to another point of reference. The formalism is valid for any arc lenght up to a full circle.

Title of program: CIRCLEFIT
Catalogue Id: ACBZ_v1_0

Nature of problem
Least squares parametrisation and error estimation of circular arc with measured points.

Versions of this program held in the CPC repository in Mendeley Data
ACBZ_v1_0; CIRCLEFIT; 10.1016/0010-4655(92)90134-K

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要
本文提出一款用于将圆弧拟合至实测点集的快速代码。本算法基于非线性最小二乘问题的显式解，用于拟合圆的曲率、方向与位置参数。该代码支持圆参数的误差估计，同时可实现参数与误差矩阵向另一参考点的转换。本形式化方法适用于任意长度的圆弧，直至整圆。

程序名称：CIRCLEFIT
目录编号：ACBZ_v1_0

问题本质
基于实测点集的圆弧最小二乘参数化与误差估计。

Mendeley数据中CPC库存储的该程序版本：
ACBZ_v1_0; CIRCLEFIT; 10.1016/0010-4655(92)90134-K

本程序源自贝尔法斯特女王大学所持有的CPC程序库（1969-2019）

搜集汇总

背景与挑战

背景概述

该数据集提供了一种快速拟合圆形弧线的代码算法，基于非线性最小二乘方法，能精确计算圆的曲率、方向和位置参数，并包含误差估计和参数转换功能。它适用于计算物理领域，支持从部分弧线到完整圆形的任何弧长拟合。