May I proffer “Aparallel” CTCP (Center of CB to Contact Point on object ball [OB] “aparallel” shift to center of OB then pivot back to the center of the CB – method of aiming.
The bridge remains constant at say 14" or what ever is comfortable. This works for all distances between the CB and CB – with practice.
What I interject that is new, to me, is the appreciation for perspective, foreshortening and converging parallel lines as they approach infinity - to be a bit hyperbolic.
Two dimensional drawings from a top view of traditional CTCP would conclude that your bridge needs to be in back of the CB the same distance as the distance between the OB and CB – proven by geometry with identical triangles.
This works until the OB and CB are 7 feet apart or longer than your cue etc.
In practice though, one needs to get to the table and get down on the shot. You will immediately notice that the appearance of the OB being down table is smaller than that of the CB.
The disconnect, to me, is that 2D drawings don't show this - the OB and CB are drawn at the same size say 2.25" diameter.
So when I did my parallel shift I was shifting say 1/2 ball at the OB for a 90 degree cut and a corresponding 1/2 at the CB with horrible results. What I did was to ignore the CB and only concentrate on the parallel shift, from a top view of the cue, at the smaller appearing OB, in perspective, which is never the same size as the CB - it is always much smaller...but I said to ignore looking at the CB.
As the object ball goes farther down table, the OB appears smaller and the distance of the shift from the contact point (CP) to the center of the OB gets smaller and thus the included angle has to narrow...or you will fly past the OB to the outside.
What I liked was that the shift is always from the CP to the center of the OB... not to one or the other side of the CB for thick and thin cuts as in CTE.
What I have little problem with is finding 6:00, or contact point, for I am a double distance shooter. What I don't like about CTCP is that you need to be very accurate about the parallel shift.
What I had hoped to find out with CTE was an alternate solution (than double the distance) for thin cuts where the aim point was off of the equator to edge of the OB - somewhere on the felt or rail.
As I said before, parallel lines appear to converge as they travel to infinity…so what I eventually use is “APRALLEL” shifting.
Starting at CTE:
The traditional wisdom for parallel shift/offset for the cue would be to shift the cue say from the edge of the OB at one end of the equator at say, 3:00 to the center of the OB - one would naturally shift the cue to the corresponding 1/2 CB from center to 9:00 on the CB. This would be true from a top view.
When at the table and down on the shot, the OB being down table appears smaller than the CB. I said to disregard the CB during this step and shift the cue parallel from 3:00 on the OB, down table, to its center which would be a smaller shift than on the CB.
[Conventional wisdom would say well, I shifted the cue 1/2 ball from 3:00 to its center, so I will shift the cue the corresponding 1/2 ball from the center of the cue to 9:00 - as said above. This would seem reasonable but, in order to do this, you would be moving the cue in an arc with it's axis at infinity.
This is where I lose the audience LOL].
In fact if the OB was at 9 feet down table, the shift would be very tiny for the OB would appear to be a tiny sphere. If the OB were moved to infinity,
it would not be detectable for it would be but a dot.

The bridge remains constant at say 14" or what ever is comfortable. This works for all distances between the CB and CB – with practice.
What I interject that is new, to me, is the appreciation for perspective, foreshortening and converging parallel lines as they approach infinity - to be a bit hyperbolic.
Two dimensional drawings from a top view of traditional CTCP would conclude that your bridge needs to be in back of the CB the same distance as the distance between the OB and CB – proven by geometry with identical triangles.
This works until the OB and CB are 7 feet apart or longer than your cue etc.
In practice though, one needs to get to the table and get down on the shot. You will immediately notice that the appearance of the OB being down table is smaller than that of the CB.
The disconnect, to me, is that 2D drawings don't show this - the OB and CB are drawn at the same size say 2.25" diameter.
So when I did my parallel shift I was shifting say 1/2 ball at the OB for a 90 degree cut and a corresponding 1/2 at the CB with horrible results. What I did was to ignore the CB and only concentrate on the parallel shift, from a top view of the cue, at the smaller appearing OB, in perspective, which is never the same size as the CB - it is always much smaller...but I said to ignore looking at the CB.
As the object ball goes farther down table, the OB appears smaller and the distance of the shift from the contact point (CP) to the center of the OB gets smaller and thus the included angle has to narrow...or you will fly past the OB to the outside.
What I liked was that the shift is always from the CP to the center of the OB... not to one or the other side of the CB for thick and thin cuts as in CTE.
What I have little problem with is finding 6:00, or contact point, for I am a double distance shooter. What I don't like about CTCP is that you need to be very accurate about the parallel shift.
What I had hoped to find out with CTE was an alternate solution (than double the distance) for thin cuts where the aim point was off of the equator to edge of the OB - somewhere on the felt or rail.
As I said before, parallel lines appear to converge as they travel to infinity…so what I eventually use is “APRALLEL” shifting.
Starting at CTE:
The traditional wisdom for parallel shift/offset for the cue would be to shift the cue say from the edge of the OB at one end of the equator at say, 3:00 to the center of the OB - one would naturally shift the cue to the corresponding 1/2 CB from center to 9:00 on the CB. This would be true from a top view.
When at the table and down on the shot, the OB being down table appears smaller than the CB. I said to disregard the CB during this step and shift the cue parallel from 3:00 on the OB, down table, to its center which would be a smaller shift than on the CB.
[Conventional wisdom would say well, I shifted the cue 1/2 ball from 3:00 to its center, so I will shift the cue the corresponding 1/2 ball from the center of the cue to 9:00 - as said above. This would seem reasonable but, in order to do this, you would be moving the cue in an arc with it's axis at infinity.
This is where I lose the audience LOL].
In fact if the OB was at 9 feet down table, the shift would be very tiny for the OB would appear to be a tiny sphere. If the OB were moved to infinity,
it would not be detectable for it would be but a dot.

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