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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 R^{3} that belong to a quadric (https://en.wikipedia.org/wiki/Quadric), that is, they satisfy the equation x^{T}Qx=0, where x is the 3D point (in homogeneous coordinates, so x=[x_{1 }x_{2 }x_{3 }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.
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