Ellipse Curve Fitting via Least Squares Method by Solving Generalized Matrix Eigenvalues and Eigenvectors
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Resource Overview
This MATLAB program implements ellipse curve fitting using the least squares method through generalized matrix eigenvalue and eigenvector computation. The input variables x and y represent the horizontal and vertical coordinates of sample points respectively. The resulting coefficient matrix contains parameters [a, b, c, d, e, f] for the elliptical equation aX² + bXY + cY² + dX + eY + f = 0.
Detailed Documentation
This program utilizes the least squares method to perform ellipse curve fitting by solving generalized matrix eigenvalues and eigenvectors. The algorithm processes input coordinates where x and y represent the horizontal and vertical positions of sampling points respectively. The output coefficient matrix corresponds to the parameters in the elliptical equation aX² + bXY + cY² + dX + eY + f = 0. The implementation involves constructing a scatter matrix from sample points and solving the generalized eigenvalue problem to determine optimal ellipse parameters. This method ensures accurate calculation of elliptical curve coefficients, making it valuable for various engineering and scientific applications. Additionally, the program can be effectively used for data analysis, mathematical computations, and numerous practical computational applications, demonstrating broad utility in technical domains.
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