Wow you guys have gone a long way down the road with this.
I think it's best to stay away from mathematics unless you have actually 3D data something Brian Gordon has developed. But I try to stay to descriptions of positions. I think we can say some very valuable things about the strokes in this fashion and about the effects that making certain positions have on the ball and the shot.
The first thing I want to clarify is what extension means to me.
Since the swing is on an arc, there is technically no such thing as swinging directly along the line of the shot.
The hand and racket don't extend directly out to the target.
They move upward and forward across the body.
The point at which the hand and racket have moved the furthest forward (and usually furtherest upward or close to furthest upward) I call the extension point.
Now go back and look at the original video:
http://www.tennisplayer.net/public/tw/fed/
Go to about the frame where the ball leaves the view. That is what I call extension. Notice how flat Roger's swing arc is (not from low to high but from left to right to the contact and then back to the left.) Notice how far it travels forward or outward as it (also) travels back to the left across the body. This position he makes is characteristic of a basic, aggressive drive.
The hand comes across to about the left edge of the torso and the wrist is about at eye level.
Make the full turn and the extension position--usually everything else will take care of itself.
I think the way to do this is thru phyiscal modeling and the creation of mental imagery of these positions. Talking about them is interesting and necessary but not necessarily (and usually not) the path to change.