Moving sphere elastic collision

[HarryW]

Hi all. Hope you can help me with this, I've been puzzling over it a while.

The problem is this: two moving uniform spheres collide perfectly elastically (for now, I may change this later) and bounce off, changing their velocities and conserving energy and momentum. This is a realistic physics thing. The physics I have no trouble with, I am having some trouble with establishing where the spheres actually were when the collision occurred.

The collision is never going to be detected until the spheres overlap and occupy the same space. The collision is easy to detect, but I want to trace their paths back so that I know the position of both spheres at the moment of impact. This obviously makes a difference to the angle that the spheres bounce off at.

I'm basically trying to model collision between two pool balls realistically, in case you hadn't realised what I was doing yet

So anyway, I figured it out for one moving ball hitting a stationary ball, after a lot of head-scratching, but I'm a bit stumped with both balls moving. If this proves to be more trouble than it's worth then I could use this existing model with a bit of modification but I'd rather do it realistically.

This is the image:

The picture shows a diagram of the problems. Fig. 1 is the original problem I had which I've now solved (more or less). Fig. 2 is the problem with both balls moving. The red outlines are the positions of the balls at the moment of impact, and the vertices E and F are their centres. The distance between E and F must be (R+r), where R and r are the radii of the spheres. The vertices marked in blue are known.

So, anybody got any ideas? Thanks