That's a common fractional overlap: 1/4 ball (~49°) cut to the right.
And we know that right edge of the cueball to the B position on the object ball is another common fractional overlap: 1/2 ball (30°) cut to the right.
The question is how does CTE specify the adjustments needed for shots between the common fractions? What's CTE's objective description of a 45° cut? A 40° cut?
Yeah, we know: "offset and pivot". Pivot how much for 45° vs 40°?
pj
chgo
Is it? What do you think that I said? I didn't instruct you or anyone else to put the cue down on that line and shoot it.
If we were speaking about fractional aiming, full, half, quarter ball overlaps where those lines were used to determine the hit and then the user would consciously/subconsciously adjust thicker and thinner IF it were determined that the fraction chosen wouldn't work then your question would be pertinent.
CTE does not specify adjustments between fractional overlaps because fractional overlaps are not what is used in the CTE method. CTE users don't identify a cut angle and work from there. CTE users identify two visual perception lines from an offset position and using the pivot from the correct edge of the cueball they land on the shot line with no regard to whatever the actual cut angle is. The pivot is a half ball and can be done mechanically through a literal landing of the cuetip addressing the correct edge of the cueball followed by a body movement that brings the cue tip to center ball and the actual correct shot line. Or it can be done visually where the eyes start at the correct side of the cueball and the tip stops at a half tip away from center and then is mechanically pivoted to center ball to be on the accurate shot line. Or it can be done completely visually where the eyes do the work and the shooter swings in from the offset position and the cue lands on the correct shot line. Any of these three methods for going from standing position to shooting position can be used to get to the shot line. All three use the same set of perception lines to to get the shooter into the right alignment before going into the shot. The decision to use a particular combination of perception lines comes through practice to recognize which ones work for which types of shots.
So basically you are talking about a whole different and not actually common (for most players) way to aim. A far less accurate way that does use a ball overlap perception of what the HIT would be at that perception and requires adjustment/estimation for shots that don't fall on one of the fractional HIT shot lines. This method however does work as a useful guide to develop visual acuity which then helps to make those estimation judgements of thicker/thinner for the in-between hits/cut angles that you describe. CTE is just different and better at guiding the shooter to the shot line consistently in my experience.
CTE does not have a description of a 45 degree cut shot. Nor does it have a description of a 33 degree cut. CTE has descriptions of 15, 30, 45 and 60 degree perceptions that begin with a clear perception of the objective center to edge line as an initial orientation. The mechanism by which CTE leads the shooter to the correct shot line is through the application of the method as instructed with no regard for the actual cut angle. WHY this works, mathematically, geometrically, physically, or even psychologically is unknown to me.
I am a user not a programmer. I follow the directions and measure the results. If the results are acceptable to me then I share the method and get feedback from those I share it with. If others figure out better ways to use the method then I will try to learn those ways and apply them and measure the results. If those results are good then I will share those better ways. All innovation is a refinement of what has come before.
For all I know Hal Houle started with pure fractional aiming and discovered that changing the approach visually worked better. A statement that goes "the eyes lead and the body follows" can be confusing and sound hokey but really Pat isn't that what all aiming in pool is? And if so then why is hard to accept that someone somewhere might figure out something that is counterintuitive but which actually works better than conventional methods that have been discovered/created previously?
The bottom line for me isn't that you disagree with certain terminology, "objective" "accurate" and I guess possibly "no imagination shot line". It's that instead of using your clear interest and intelligence to figure out whatever is missing without simply ascribing it to the catch-all of "subconscious adjustment". Taking the time to understand that CTE isn't fractional-overlap aiming despite the usage of 15/30/45 degree terminology and then measuring everything using your analytical skills would only serve to help to answer your question of HOW does a 15 degree perception+a pivot allow the shooter to get onto a shot that is 17.5 degrees of cut AND also a shot that is 18.8 degrees and a shot that is 12.4 degrees of cut. When there are clear instructions and those instructions result in the shooter finding a clear difference in the ability to get on the true shot line accurately as contrasted with prior methods used then there must be an answer as to why and that answer does not have to be subconscious adjustment.
BUT
For the sake of argument let's say that the answer is subconscious adjustment. Let's say in a hypothetical that there is that last moment between standing and shooting position where the subconscious chooses where the body is going to place the cue stick. Everything until that moment has been conscious choice with vocal descriptions of each step as accurately as humanly possible. If that were the case and the results were getting on the shot line accurately at a far higher level of consistency than prior to the adoption of the method being used would that not indicate a much higher level of objective measuring in some way?
I think it's fair to say that the person who uses known quantities to measure with can get more consistent results. A baker who wings it on the ingredient amounts is more likely to have less consistency than one who precisely measures. So, as I have said many times before, if a method of aiming is 99.9% objective in the application and .1% is subjective subconscious choice then why is there a problem with saying that it's objective? A real percentage couldn't be applied anyway.
As Joey earlier when trying to make an equivalency, all aiming using balls is objective because balls are objects. And this is true in the sense that without objective references you would have no idea where you are in space. Objects inform us where we can go and what we can do. Not all aiming is the same level of objectivity though. As Mike Page says a lot more data is better. A player who knows exactly how far up the rail and at what angle he can consistently pocket the ball has an advantage over one who doesn't. He has the knowledge that gives him a larger range of options. Both players are using the same equipment but one of them has discovered an objective reference that he can consciously use. He doesn't need to estimate or guess or hope. He has a wider range of shots to take confidently and greater latitude in playing position consistently merely by knowing that fact about the table.
The instructions that work for CTE are all there Pat. You know this. Trying to discredit so ruthlessly over what is really a quibble in speech and the resulting animosities has been actually tragic to see.