I think Rick was pointing out that there are only a finite number of cut angles out of the object ball by using a CTE method. I agree with that. I also believe that CTE isn't used 'to aim at will' at a precise spot you happen to need. For example a bank into a frozen ball cluster to make one of them. Not as I understand it but I'm still a noob at this.
These are my assumptions and I may be wrong on both points. I'll wait and make sure I'm not barking up the wrong tree.
I was not saying that there is a small finite number of angles that can be had from any "CTE" method.
What I was saying is that in 'Stan's' two lines 'system' those visuals that utilize the defined 'objective' points & the lines between them 'objectively' put the shooter on that ONE SINGULAR LINE where both visual lines can be seen equally & simultaneously.
From that SINGLE PHYSICAL LINE...
IF the pivot is precisely defined (such as a 1/2 tip offset & pivot to CCB) & IT is the ONLY one available
& THE ONLY ONE USED then only one line to the OB for each side of pivot can be had for a total of ONLY TWO LINES from that objective visual.
Anything more is simply NOT obtained by an objective means but is instead obtained & delivered from out of the subjective realm.
I'll just stop there other than to say...
I welcome anyone to show otherwise... but ONLY with SCIENCE & not any speculation of matters that simply are not true, such as that "the balls present themselves differently depending on where they are on the table" & that means that the edge is different & that the points on the balls are different.
Those points & lines are defined by the SINGULAR LINE where both can be seen equally & simultaneously.
Hence they will yield the same Singular Physical Line where the TWO Lines can be seen Equally & Simultaneously every time regardless of where they are in the Universe or on any size & shape of table.
If an individual can not realize these simple facts then any discussion with them is futile & basically useless.
I sincerely hope that any post regarding this will be ON the subject matter & not attacks of the messenger... because the poster has nothing of significant substance to offer.
All the Best for You & Yours & ALL.
Rick