Fitting an ellipsoid to 3D data points

math geometry least-squares
Hannesh picture Hannesh · Sep 1, 2011 · Viewed 20.8k times · Source

I have a large set of 3D data points to which I want to fit to an ellipsoid.

My maths is pretty poor, so I'm having trouble implementing the least squares method without any math libraries.

Does anyone know of or have a piece of code that can fit an ellipsoid to data which I can plug straight into my project? In C would be best, but it should be no problem for me to convert from C++, Java, C#, python etc.

EDIT: Just being able to find the centre would be a huge help too. Note that the points aren't evenly spaced so taking the mean won't result in the centre.

Answer

Nick Levesque picture Nick Levesque · Nov 21, 2011

here you go:

This paper describes fitting an ellipsoid to multiple dimensions AS WELL AS finding the center for the ellipois. Hope this helps,

http://www.physics.smu.edu/~scalise/SMUpreprints/SMU-HEP-10-14.pdf

(btw, I'm assuming this answer is a bit late, but I figured I would add this solution for anyone who stumbles across your question in search for the same thing :)

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