I have a spherical surface defined by four points on an ellipsoid centered at (0,0,0). That is, the four points define a bounding box projected onto the ellipsoid. I have another point, P at some location (x,y,z). I need to find the minimum and maximum distances between this point and the surface.
The equation of an ellipsoid is given by:
$r^2=\frac{x^2}{A} + \frac{y^2}{B} + \frac{z^2}{C} $
Here's a terribly drawn picture that might help: