:wink:
Let's use my 2D system as an example NOT Stan's Please! Don't know it, can't 'spainit. Here's a thought experiment that may help.
I'll use a watch of 2 1/4" diameter, same size as the balls encased in a transparent sphere. Set the watch to twelve o'clock. Put an object ball one diamond away from the side pocket. Put the watch one diamond away from the side pocket so the 3 o'clock and 9 o'clock line through it defines a straight shot to the side. Get an C visual. Sight down the CTE line and note where it points on the rail. Just a little above the pocket. Place your tip pre-pivot, it will point at 12, 1/2 ball away from 9. (o'clock typing got old quickly) Do a 1/2 ball pivot and the tip is pointing down the 3-9 line and directly at the center of the object ball.
Keep the watch orientation the same and move it straight down 1/2 diamond. Get the same C visual. Sight down the CTE line. The line points much farther up table. You're at different place on the table and the SINGLE PHYSICAL LINE runs at a different angle. The place you put the tip pre-pivot has changed. You are not pointing at 12 but a little before 12. A half ball pivot from here will not be aimed at the center of the object ball but at an angle. This angle is proportional to the difference between the 12 position and the new position a little before 12.
The rotation is small but it's taken from the edge of the ball inward. Near the edge the difference between the point at 75* and the edge is very small. The sine of 90* is 1.00 and the sine of 75* is .966. Multiply by 100 to get percentage. Sin 90 is 100%, sin 75 is 96.6%. The last 3.4% of the radius 'contains' 15 degrees. A small difference will result in a large angle change.
I do not use any subjective adjustments with pivoting. I use it when I shoot CP as I search for the correct angle. I 'feel' the shot is right. When pivoting, I trust my visuals and pivot to put me on the shot line. I'll look at he object ball on occasion to double check I've used the correct one but I DON'T adjust my aim if it looks wrong. I'll try a different visual if it looks way off but if it's close and doesn't look right, I'll stand and take a more careful visual and pivot. If it still doesn't 'feel' right and I'm confident that everything was done correctly I take the shot. It's usually the right choice.
My subjective 'feeling' is not correct sometimes and I've learned to ignore it. Most of the time it's trying to lead me astray. I've said before that some shots I shoot 'blind' by getting a line through CCB and trusting it. If I ignore the OB my subjective is not in play for that shot. Subjective feelings are more likely to hurt my shot making rather than help it.
Good Morning Larry,
That is flawed. You're saying the same type things that Stan's CTEers say.
Boy! Where do I start? Let's start with the word "different" & add in Einstein's Relativity.
We need to put the word "different" into the proper context & I guess the word "angle" too, since it is joined with "different".
Let's set an OB at center pocket sitting on the edge of the shelf at a corner pocket... & then place the CB down the long rail but on the same side of the side pocket & parallel to the rail so that the Center LINE is parallel to the rail.
Now... let's move that CB one 'tic' at a time for 90* of rotation toward the other corner pocket until the shot line gets parallel to the short rail. We then have 90 straight in shots & we could have an infinite number.
They are all "different"... yet they are all the SAME.
They are all on "different" parts of the table. Yet... they are all THE SAME one ball RELATIVE to the other & the
LINES between the balls are ALL the SAME... One Ball RELATIVE to the Other Ball.
Let me say that again.
THEY ARE ON
THE SAME ANGLE & WITH THE SAME LINES RELATIVE ONE BALL TO THE OTHER. THE LINES ARE
SET BY RELATIVITY... ONE BALL TO THE OTHER BALL.... Even though they each are on 'different' parts of the table.
Now do a similar thing... pull the OB straight out of the pocket toward the diagonal side pocket about a diamond's length... then set up a ghost ball on it. We now have a cut shot. Now extend a line through the Ghost Ball/OB center lines to the point on the shelf where the OB sat for ALL 90 (or infinite #) of the straight in shots.
Now rotate the whole mess, the 3 balls & the STRAIGHT LINES between them with that point at the pocket shelf as the apex point.
Rotate that whole set up, the 3 balls & especially the LINES between them 1 'tic' at a time toward the short rail until the LINE through the Ghost Ball/OB gets parallel to the short rail.
I do not know how many degrees of rotation that that actually is. So I do not know how many DIFFERENT shots that it is, but it is a significantly high number & it could be an infinite number.
They are all "DIFFERENT" but the LINES are the SAME... RELATIVE ONE BALL to THE OTHER.
It is the balls that SET the LINES & NOT where they are on the table.
Sorry for the Caps. I'm not yelling. I'm just highlighting certain words.
I certainly hope that you can understand what I am trying to say.
You just received a brief example of Einstein's Relativity.
You need to rotate your watch face.
I hope that you do not have any questions, but if so, I will do my best to answer them... For You.
I'm not inclined to waste time with 'haters' of the scientific truth.
All the Best for You & Yours,
Rick