I was one of the fortunate ones that got a phone call from Hal back in the late 90s. I have used CTE in the past, as well as Ghost Ball, as well as fractional aiming, Equal/Opposite method, etc..
The method he taught me, which still works to this day with no adjustments, is different than what has been posted (or I haven't seen the correct version yet). You need to know which way you're cutting the ball, and there are a few magic starting points you need to know. You, first off, need to be able to identify a half ball hit.
The direction of the pivot, and the starting point, are determined by the angle of the cut. This is why you need to know the half ball hit angle. The alignment point on the object ball is always the outer edge. The starting point on the cueball is always the edge. However, it can be the inside or outside edge. That is determined by the cut angle.
For shots less than 30 degrees, line up the centre of the cueball with the edge of the object ball. Start with the outside edge of your cue tip lined up with the outside edge of the cueball. Pivot towards centre. Your pivot should be leading you towards the centre of the object ball.
For cuts greater than 30 degrees, but less than 65, the pivot comes from the inside edge of the cueball. When you pivot to centre, you should be going towards the outside edge of the object ball, away from the centre.
For thin cuts, the pivots are edge to edge. Thinner than 80, pivot from outside edge to centre on the cueball, with the starting alignment being cutting edge of cueball to the cutting edge of the object ball. For razor cuts, line up outside edge to outside edge, and pivot away from the edge.
Feel free to hack and slash the system. I thought Hal was completely full of shit when he was on the phone with me. However, this version takes into account the angle of the shot, and gives you reference starting points for each cut. Do I use this system today? Sometimes. I've got most of these shots in my memory bank. However, I struggle with some thinner cuts, seeing the right point of contact. So, I go back to this system, and I rarely miss.
Certain things cannot be explained on paper. If you need a diagram to show you a system works, stick with Virtual Pool. You will have a chance of winning there, but not on a real table that has elements like chalk dust, humidity, and friction between surfaces. If I was to draw all the vector diagrams associated with a pool shot, I'd have to account for rotational force transferred to the object ball, jump/bounce affecting the aim on shots struck with force, and a multitude of others.
I struggled with the mathematical explanation for why it works. Then, you reach an age where you really don't care about the why, and come to grips with the fact that it seems to work.
Well...
Thanks for supplying details. They sound similar to ones I've read. Hopefully, Dr. Dave can include your details in his CTE resource area.
The trouble with the system you outline is that it only produces, I don't know, 4, 5, 6, 8 or so different actual "shots." But there are far more than that for all possible shots at less than 60 (or 65, or 80) degrees. The system simply DOESN'T provide any information for all the others.
It's obvious to me that the others (well, ALL of them, really, since nobody I know can distinguish 30 degree shots from 28 degree shots by estimation alone) are made by "feel" or "pool player estimation." So, if they're made by estimation, I have to wonder why you just don't ADMIT THAT, and why you don't just go ahead and MAKE shots purely by estimation--and forget all the "edge-lining" and pivot waving stuff--since THAT IS WHAT YOU'RE DOING, ANYWAY!
As far as "Then, you reach an age where you really don't care about the why, and come to grips with the fact that it seems to work."
I haven't reached that age yet. I'm thinking I might hit it around 110-115. I'll let you know what I think about it, then....but something tells me at that point I won't "really care" about letting you know, either.