Circle Fitting Program Using Least Squares Method

In this article, we discuss the development of a circle fitting program using the least squares method for your graduation project. The program implements mathematical optimization to minimize the sum of squared residuals between observed data points and the fitted circle model. Through this application, you will obtain the circle's center coordinates (x, y) and radius (r) as output parameters, enabling comprehensive dataset analysis and geometric pattern recognition. The implementation involves key computational steps including Jacobian matrix calculation for partial derivatives and iterative parameter updates using Gauss-Newton optimization. You will learn practical techniques for handling edge cases such as outlier detection through residual analysis and singularity handling in matrix inversion operations. We provide detailed explanations of the core algorithm's mathematical foundation, ensuring thorough understanding of error minimization principles and their application in computational geometry. This knowledge will equip you with transferable skills for implementing regression models in future engineering or research projects.