Typically 9 points are the minimum number of points required to fit an ellipsoid. In my research I have begun working with methods of fitting models to points while using the surface normal. This offers more information and can dramatically reduce the needed number of points to fit the model. I have not found and am struggling to do something similar for ellipsoids. I am not an expert but I am wondering if there is a way to leverage the fact that the normal is proportional to the gradient at a given point on the ellipsoid.
The ellipsoid to be fit should not be limited to the origin on the center or being axis aligned.