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A Circle Fitting Library for Python

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A Circle Fitting Library for Python

Given a collection of points in 2D space, a common problem is finding the parameters of a circle that best approximate these points. This library implements a collection of different circle fitting algorithms:

- hyperLSQ()      : Least squares circle fit with "hyperaccuracy" by Kenichi Kanatani, Prasanna Rangarajan
- standardLSQ()   : Least squares circle fit, standard version.
- riemannSWFLa()  : Riemann circle fit, SWFL version A
- lm()            : Levenberg-Marquardt in the full (a,b,R) parameter space
- prattSVD()      : Algebraic circle fit by V. Pratt
- taubinSVD()     : Algebraic circle fit by G. Taubin
- hyperSVD()      : Algebraic circle fit with "hyperaccuracy"
- kmh()           : Consistent circle fit by A. Kukush, I. Markovsky, S. Van Huffel

Most of these algorithms are based on the original MATLAB implementations by Nikolai Chernov:

Each algorithm may work better in specific cases. If you are in doubt about which to use, taubinSVD() is a good starting point.


circle-fit is available from PyPi. Run the following in a command line terminal: pip install circle-fit


Fit a circle to four (x,y) points.

from circle_fit import taubinSVD
point_coordinates = [[1, 0], [-1, 0], [0, 1], [0, -1]]
xc, yc, r, sigma = taubinSVD(point_coordinates)

Data format

Your data must have at least two points in 2-D space. The algorithms in circle-fit expects either a 2D List or numpy ndarray of shape (n, 2), where n is the number of points in your dataset.

All the algorithms available in this library return four values:

- xc    : x-coordinate of solution center (float)
- yc    : y-coordinate of solution center (float)
- r     : Radius of solution (float)
- sigma : Residual error of solution (float)

View the fit

The function plot_data_circle(coords, xc, yc, r) can be used to open a plot window which shows you data points with a circle fit overlaid on top. Example use:

xc, yc, r, sigma = taubinSVD(point_coordinates)
plot_data_circle(point_coordinates, xc, yc, r)

Contributors and Maintainers

This library is a community collaboration, all work is voluntary.

To Contribute

Please open a pull request with the changes you would like to contribute (example)


As we are volunteers, please be patient when requesting support. You can either open an issue if you think you've found a bug with the code, or contact one of us directly if you have a user issue:

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