This was originally posted as post #211 last night. Somehow the images vanished out of it; they were there when I last looked at it, but are gone now. So let's try again.
Take BOTH the OB and CB and move them together an inch forward, backward, to the left, or to the right. Take your pick as long as the resulting cut angle stays between 15 and 30 degrees. Each CB/OB position has a different cut angle but yet has the EXACT SAME CB/OB alignment (remember you're moving the CB and OB together). How does the system differentiate between those shots?
For an explanation of the 3D perspective images below, see the "A CTE test!" thread, post #209.
The shot shown in the left image has been moved forward about two inches directly toward the end rail to make the right image (Jal, I will be forever thankful for that table). No other change was made. In particular, the camera - which represents the player's eye(s) - was not moved, meaning that the player did not move. [Added later: On reviewing the original SketchUp drawing from which these images were made, it looks like I moved the CB+OB more like four inches rather than two as stated in the first sentence above. This does not affect the principle involved, and the cut is still within the 15-30 degree range. - jwp]
I left the old blue GB-OB-Pocket line in place in the right image to show how far the set up was moved down table, and to clearly indicate that the shot angle changed. Notice the difference in the apparent paths of the CTE and Edge-to-B lines between the two images. In the left image the camera/player is looking directly along the Edge-to-B line (you can tell this because it is vertical on your screen - or, rather, it should be - it is on mine); in the right image, that is no longer true. The image on the right no longer shows the same "visuals" as the left image because the CB and OB have moved with respect to the player, thus causing the centers, edges, and aim point B to "rotate" from the player's perspective. Now, let us suppose that the player moves to bring his "visuals" back in order:
Now the player has the same "visuals" (in this case, is looking directly along the Edge-to-B line) that he had in the left image above. The cut angle is clearly not the same. The fact that the player had to move to restore his visual sight lines realigned him for the new cut angle. (It's probably not exactly the correct alignment for either shot, but that's an issue most likely related to trying to represent binocular vision with a monocular tool. It has no effect on the principle involved.)
This also answers jsp's question about moving the pocket.
NB: The above images do not address, nor are they intended to address, the issue of exactness, however that may, or may not, defined.
If you remain unconvinced that the above images correctly illustrate what happens with regard to cut angles and CB-OB-Pocket relationships, I would be happy to describe the simple experiments that I conducted with some cans and string before I started drawing all this crap. Then you could do them for yourselves and describe the conclusions, perhaps differing from mine, you might draw from them. I, at least, would be quite interested in reading those conclusions.