Fits an ellipsoid into a 3D set of points, allows some constraints, like orientation constraint and equal radii constraint. E.g., you can use it to fit a rugby ball, or a sphere. 'help ellipsoid_fit' says it all. Returns both the algebraic description of the ellipsoid (the nine coefficients of the quadratic form) and the geometric description (center, radii, principal axes).
This is well done. I especially appreciate the multiple input methods.
The flag=0 method can easily return imaginary results for noisy data. Note that the flag=0 method is also trying to find the primary axes of the ellipsoid. For those getting imaginary results when using flat=0 (the default), if your ellipsoid is expected to already be aligned with x, y, and z, then just use flag=1. This works quite well even when flag=0 falls apart.
I see some folks are using this for magnetometer data, which has a "hard iron" offset. To convert from raw data to points on a unit sphere:
[c, r] = ellipsoid_fit(raw, 1);
% For a single point, k:
unit_sphere(:, k) = (raw(:, k) - c)./r
% For multiple points, vectorized:
unit_sphere = diag(1./r) * (m - c * ones(1, size(m, 2)));
% Just for kicks using bsxfun:
unit_sphere = bsxfun(@times, 1./r, bsxfun(@minus, m, c))
I used your code but the results are not correct with my data. The eigen values are very big. Should you normalise the Covariance matrix? I would also want to ask how did you derive from the 9 parameters of ellipsoid, the covariance matrix, center etc.. which book, notes did u use?
If the ellipsoid passes through the origin (0,0,0), how can the default equation "Ax^2 + By^2 + Cz^2 + 2Dxy + 2Exz + 2Fyz + 2Gx + 2Hy + 2Iz = 1" represent that? Thanks!
Hi, nice and efficient piece of code.
Nevertheless, I believe that the polynomial expression that you compute in a first step is not guaranteed to be one of an ellipsoid. I think that it could be any quadric (hyperboloid, paraboloid, etc), right?
It is probably no problem if you have much data (corresponding to a real ellipsoid) to fit your quadric on.
But in case of sparse data (for instance, data points only on a couple of planes), you could have bad surprises (and in particular negative eigenvalues).
I have a question: we can find the center, the radii of the ellipsoid and also the 3*3 direction matrix "evecs" using this program. Then how do you determine the three rotation angles using "evecs"?
Thanks for your help!