I would approach it not from an idealized set of equations Jez. Using the interpolation table technique, if you make a fine enough grid, you can remap systems where the ball is not perfect, where you want to concentrate on only a portion of the ball image, and deal with the fact that the CCD plane is not exactly normal to a ray from the center of the sphere. If you went with the idealized mathematical system you would find many system variables that are hard to compute out. The interpolation table technigue on the other hand just needs the initial setup analysis step to derive the correction table from the grid image.

I worked on a laser system one time where we used a 3-D correction table like this to transform a 2D X&Y flat set of draw vectors to an XYZ image on the edge of a contact lens. A small microcontroller generated a set of vectors for a line of text in a straight line. The correction table remapped all the coordinates into a half circle to permit the laser to write around the periphery of the lens. The Z axis was used to control depth of field for the laser beam as it went up around the edge of the lens. The correction table was actually computed on a PC and then fed into the 68000 computer that ran the General Scanning laser galvo head controller. It worked way cool.
Mike Karas