Rick:
I can tell you that I don't align CTC/CTE...since the very beginning, I've aligned my way, using back of the ball aiming (like I have for 25 years), but aimed slightly thick, at the near side of the pocket. After a while, it looks like I'm aiming at the same place on the OB that I always did before, but it's all "recalibrated" to account for the delfection and thick hit aim. Now I see the angle, connecting the dots between the pocket/OB/CB and just drop down into the TOI alignment. CJ is describing HIS perception of the connection/angle, as he perceives a difference between his eye line and the stick line (as I understand it, anyway). I was messing around with that the other day and I could see what he was describing, but it still "looked wrong" to me. When I'm down lined up correctly, I can visualize the CTC or CTE line, but I choose my own perception alignment, which works perfectly for me. As we've all said, TOI isn't an aiming system...it's an alignment/address system that "anchors" your stickline to the CB in an absolutely predictable and repeatable place, with all of any potential stroke/deflection error directed in one direction--toward the center of the pocket. And it's a brilliant way to control the cueball without as little spin as possible while putting collision induced spin on the OB that makes it hug rails and avoid rattling. It's also very hard to scratch with this method, as the CB post collision path is so easy to see.
I also use a light touch as well as firm touch as you see in this video...acceleration straight through the CB is the key, not necessarily a hard hit. As long as the cue is not slowing down during the stroke, the deflection will take and the TOI will work. A firmer hit needs a little thicker aim and vice versa, that takes some time to dial in. I use the L drill (15 balls lined up in a box around the corner pocket, two diamonds out, start at one end and put them all in the corner pocket in a row, without touching a ball) to test this out. It's a nightmare, but it proves TOI works with finesse as well as muscle. You have to use BHE from the TOI alignment a lot more, though, which is fine and will prove to you that you can still spin the CB if you have to off the TOI alignment and still drill the pocket.