Sphere Fit (least squared)

Version 1.1.0.0 (30.7 KB) by Alan Jennings
Fits a sphere to a set of noisy data. Does not require a wide arc or many points.
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Updated 2 Jul 2013

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Editor's Note: This file was selected as MATLAB Central Pick of the Week

Given a set of data points, this function calculates the center and radius of the data in a least squared sense. The least squared equations are used to reduce the matrix that is inverted to a 3x3, opposed to doing it directly on the data set. Does not require a large arc or many data points. Assumes points are not singular (co-planar) and real...
Created on R2010b, but should work on all versions.

Cite As

Alan Jennings (2026). Sphere Fit (least squared) (https://www.mathworks.com/matlabcentral/fileexchange/34129-sphere-fit-least-squared), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2010b
Compatible with any release
Platform Compatibility
Windows macOS Linux
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Version Published Release Notes
1.1.0.0

Since the matrix A is symmetric, I changed the calculation to avoid superfluous calculations. Runs about 25% faster, and even better for large data sets.

1.0.0.0