## How to fit a quadric to three 3D points: x^T Qx = 0

Hi all,

My problem is the following:
I have three points in R3 that belong to a quadric (https://en.wikipedia.org/wiki/Quadric), that is, they satisfy the equation xTQx=0, where x is the 3D point (in homogeneous coordinates, so x=[x1 x2 x3 1]) and Q is the 4x4 symmetric matrix of the quadric parameters.

How do I compute the matrix Q from three such points?

My guess is that since the number of parameters to compute is 9 (the matrix is symmetric and the last element is fixed to 1), three 3D points should be enough. Of course, I maybe wrong .
I'd like to know how to set the problem in algebraic form!

Thanks.