Which method is best to fit a 3D surface with a given constrain equation?

Hello all!

I need to fit some 3D data to an ellipsoid. This surface can be arbitrarily oriented, so it will be given by the equation

a11*x^2 + a12*x*y + a13*x*z + a10*x + a22*y^2 + a23*y*z + a20*y + a33*z^2 + a30*z + a00 = 0.

I have solved the problem by using the pseudo-inverse function, which pretty straightforward there is the possibility that the best fitting surface isn't an ellipsoid, which, for this project can't happen. In other words, I have to force the fit to be an ellipsoid, which can be done by

det(A)>0.

Where A is the matrix associated to the quadric (quadratic terms). In essence, its a fully defined expression in terms of the fitting parameters (aij).

Thanks in advance, Jorge.