Well, I had one exception in mind even as I wrote that, but it's highly doubtful anyone uses it. That would involve simply memorizing the correct aim line relative to, say, the line of centers between the two balls, given some desired OB direction relative to the same line of centers. But then there's a different relative aim line not only for each cut angle, but for every separation distance. If you wanted to severely handicap yourself, that would be the way to go.
Can you describe any legitimate method, that is, one that can stand on its own two legs, that doesn't use some part of the ghostball?
Jim
Well legitimacy is the sticking point now isn't it? From a physioligcal and pyshchological perpsective if some one reports that they are looking at the target in a certain way and basing their body position on what they perceive then you really don't have much choice but to accept their word for it since you can't actually prove or disprove what they are reporting.
The ghost ball method works fine on paper. And it works well enough in the hands of someone with good spatial cognizance. But in the end it relies heavily on estimation and feel. Very heavily. Using the ghost ball method is subject to wide variance in perception and is influenced by otpical illusions related to perception.
The CTE method relies on making a more concrete visual connection between the cueball and the object ball. This causes the shooter to adopt a very narrow approach to the cueball and also a consistent one. This is part of the reason that a player who goes to CTE is often confronted with shots where their formerly ghost-ball using brain is telling them that the line given by the CTE method is wrong. And most often if the player ignores that signal and shoots along the line given by CTE it turns out to be correct. Which indicates that the shooter's perception of what the correct shot line is using ghost ball is flawed. Most likely because of some perceptual problem that the shooter is unaware of.
It is easier however to use the balls one can see. Visually most people can divide a sphere into two equal halves. Most people can see the edge of the sphere clearly enough from their vantage point. So it's not that difficult a task to find a space behind the cue ball that is in line with the center of the cue ball and the edge of the object ball. This simple exercise can be repeated with accuracy by most people. So finding this line and using it to orient the body is a task that is much easier than finding the center of an invisible object to line up to.
Using my earlier example of a laser to double scheck this I am certain that the results of taking normal people off the street would bear out that those people would be much more accurate placing their torso in a position that the CTE line splits them down the middle than they would placing their torso on the GB center line. I might actually attempt to do this experiment with a laser level mounted on a tripod. And of course the more experience that a player has the better they will be able to align themselves to the GB center line but I still firmly believe that even as the skill level increases the use of the CTE line will result in a higher degree of accuracy in initial alignment.
Now, wht are the equations and diagrams that would legitimize this approach for you? I don't know. As I was researching the testimonials I came across something I beleive you created which was the math behind ghost ball. To me it was gibberish and I assume that it was correct. Someone else made the point that no one teaches the GB method using the math. They simply explain the concept of replacing an imaginary ball with the cueball and move on to how to adjust the imaginary ball for throw, cling, spin, deflection, swerve, squirt and gravity.....in other words it's simply a way to have the shooter use his vision and imagination to pick a line to lay the cue down on.
If the shooter's vision is good and his imagination is clear then he can visualize and hold a nearly perfect sphere and use the GB method accurately. If not well then........struggles happen.
Which is why some shooters tend to have better success with methods like CTE or 90/90 which depend on phyical objects and very little imagination to "see" the line.
Lets do another thought experiment.
If I ask a person to stand in the corner and put their nose in it they can do that easily. If I ask them to stand five feet away but at a perfect 45 degrees to the corner with their nose in line they will not be able to do this consistently. If I then place a round wastebasket at 45 degrees to the corner and ask them to stand behind the wastebasket and face the corner with the nose splitting the basket and in line with the corner then they will, I believe, be able to to do this much more consistently. The premise is that the more objects a person has to use as guidance the better that person can orient themselves.
There is a physical reason CTE works that is beyond simply saying it's subconscious adjustment and feel. There has to be because it's so cosistent. Which is obvious because if it were not then there wouldn't be this much debate over it. Notice that there is not debate over the light reflection methods or the shadow methods or the cue stick methods? I personally believe that this is because those methods are not nearly as consistent as CTE is. CTE users know the value of what they are doing and how it works in their game. They don't know the math but they know it works just like any player who is able to use ghost ball knows that it works without needing the math.
So no, if you need the math to consider any method other than Ghost Ball legimate then at the moment there isn't any that I know of and frankly I wouldn't know if it were right even if I saw the math. From a practical task-result perspective though the use of CTE gets the job done consistently so to me that is legitimate.