I have a set of geographic (longitude,latitude,value) data to which I would like to fit surface functions, specifically, the set of quadratic surfaces:
At the moment, I am converting the spherical (or rather, WGS84 geodesic) data to planar data using the Lambert Conformal Conic projection. I then fit my surface functions to the planar data, do whatever other calculations I need, and then invert the projection.
But the planar projection incorporates distortions into the data, and thus the fitting process. It would be nice if it were possible to fit the quadratic surface around the sphere/ellipsoid, but I'm not sure how to go about doing this.