Aparallel CTCP aiming method

[LAMas]

LAMas,

I'm running out the door, but I read your post. I'll clarify what I'm getting at later. I'm trying to tie in the pivot relationship with ghostball and other systems. I've got a few thoughts I would like to discuss and expand on your method possibly. Hence, all my questions.

One thing jumps out at me with your answer. 90/90 does not vary the bridge length or use any CP at all in its setup. You must use a consistent bridge distance and vary the 3 aiming points on the OB (edge, center, opposite edge) not use a CP (as in ghostball aiming). There is some adjustment or tweeking only on very close to OB shots which is done with almost all systems.

Mike,
I thought that I understood 90/90 from dr_dave's colostate diagrams, but you say that I don't.

The diagram shows the aim prepivot to be the obverse CP on the OB and a corresponding obverse CP on the CB. This is results for a single trajectory after the pivot as drawn. if you move the OB down table, the CB will eventually roll past the OB to the left. This is diagramed from a top view and is dimensionally accurate.

Things change with perspective when you are down on the shot/table; the CB will appear smaller than 2.25" and the OB will appear eve smaller than the CB etc.....but you already knew that.

In order to satisfy the diagram, you must point the tip of the cue and the length of the cue (at the obverse contact point) at the CB toward the vanishing point.





After the first alignment, one pivots to the center of the CB and shoots to the GB location....how it works for this cut angle at this distance between the CB and OB.



This makes sense to me from the info given, but you say that there is more to learn as you understand 90/90.
Are you going to proffer your interpretation to this august though tiny audience?

Thanks.

 

[pooltchr]

This entire thread is proof positive that some people make this game far more complicated than it needs to be!

Steve

 

[Mikjary]

Mike,
I thought that I understood 90/90 from dr_dave's colostate diagrams, but you say that I don't.

The diagram shows the aim prepivot to be the obverse CP on the OB and a corresponding obverse CP on the CB. This is results for a single trajectory after the pivot as drawn. if you move the OB down table, the CB will eventually roll past the OB to the left. This is diagramed from a top view and is dimensionally accurate.

Things change with perspective when you are down on the shot/table; the CB will appear smaller than 2.25" and the OB will appear eve smaller than the CB etc.....but you already knew that.

In order to satisfy the diagram, you must point the tip of the cue and the length of the cue (at the obverse contact point) at the CB toward the vanishing point.



View attachment 139503

After the first alignment, one pivots to the center of the CB and shoots to the GB location....how it works for this cut angle at this distance between the CB and OB.

View attachment 139504

This makes sense to me from the info given, but you say that there is more to learn as you understand 90/90.
Are you going to proffer your interpretation to this august though tiny audience?

Thanks.

Quick answer, home for lunch. First thing Dr. Dave is never wrong. :grin: His links may be, but he's spot on. Anyway this drawing is correct. With a consistent bridge and pivot you can pocket this shot. If you want to bank it you move to the 90/half or 90 reverse setup. It is what I use on cuts to the left. The drawing is for a cut to the right. I use Cte when I cut to the right to always be able to pivot from left to right. Changing your 90/90 aiming setup can change your cut angle or adjust for closer shots. Same bridge, same pivot unless balls are really close. I don't use any CP except the 90/90 aiming CP.

I will be back later. I have some thoughts and ideas about your offset and pivot in aparallel aiming.
Thanks,
Mike

 

[Jal]

Hi Jal,
What you show is correct and the "aparallel" shift is not parallel to the converging perspective lines in the cloth on the slate.

I contend though that, when down on the shot with the eye behind the bridge, and CB, and further down table the OB, that you can move the cue the same short distance on the smaller appearing OB, say from the CP to the center of the OB, at the tip and butt and it will be parallel by definition, but "aparallel" when viewed in perspective.

Thanks

LAmas,

When you say "parallel by definition," which of these do you mean?

1. You mark the initial direction of the cue with a line on the cloth. You then do a parallel shift with respect to the cloth, as in rolling a dowel. You then mark this "new" direction with a line on the cloth. With a ruler, you measure the separation of those lines at various locations up and down the table. You find that they are all the same distance apart.

2. You mark the initial direction of the cue with a line on the cloth. With your eye somewhere behind the tip of your cue, you move the cue such that it appears to be a parallel shift. By "appears to be a parallel shift," I mean all points of the cue move the same amount sideways across your field of view. That is, you ignore any other information reported by your eye as you perform the shift, such as the relative distances from your eye of each point on the cue. You simply make sure that each one moves the same apparent "distance" laterally across the uninterpreted image field. You mark this new direction on the table and then measure as before. You find that the lines diverge in the forward direction.

3. Something else.

What you can't do is both 1 and 2 simultaneously. That's where I think we're having trouble agreeing on what is meant by parallel (or "aparallel" ).

I have to confess that I was wrong in saying (a few days ago) that for some given impact direction with respect to the CB-OB line of centers, with regard to CTCP method, the parallel shift is exactly the same at all CB-OB distances. This is the distance "b" in the diagram below (see the red line shown in step 2 in particular).



It does get smaller at increasing separations along the line of centers, but not by much at more typical separations than shown above. (For the sake of compactness, the diagram shows the CB as unusually close to the OB.) With a more normal initial separation, as you move the OB farther away (along the line of centers), "b" hardly changes at all--not anywhere near enough to account for the diminishing apparent angular size of the OB in the perspective view. (The relevant trigonometry confirms this.)

But you were right to contend that it does get smaller. I concede that point to you sir!

Jim

 

[Mikjary]

Mike,
I thought that I understood 90/90 from dr_dave's colostate diagrams, but you say that I don't.

The diagram shows the aim prepivot to be the obverse CP on the OB and a corresponding obverse CP on the CB. This is results for a single trajectory after the pivot as drawn. if you move the OB down table, the CB will eventually roll past the OB to the left. This is diagramed from a top view and is dimensionally accurate.

Things change with perspective when you are down on the shot/table; the CB will appear smaller than 2.25" and the OB will appear eve smaller than the CB etc.....but you already knew that.

In order to satisfy the diagram, you must point the tip of the cue and the length of the cue (at the obverse contact point) at the CB toward the vanishing point.



View attachment 139503

After the first alignment, one pivots to the center of the CB and shoots to the GB location....how it works for this cut angle at this distance between the CB and OB.

View attachment 139504

This makes sense to me from the info given, but you say that there is more to learn as you understand 90/90.
Are you going to proffer your interpretation to this august though tiny audience?

Thanks.

LAMas,

This is so huge and and parallels your aparallel :wink: in meaning. Your work shows what perspective does for a pivot system and this I believe is the feel of CTE based systems. I want to explore a bit deeper on your setup and ask a few more questions about the shift and pivot. But first I have to think about how to phrase them. Not sure yet. I know I don't have your capability to draw them so I will have to figuratively post my thoughts.

On 90/90...I aim left cuts sighting with my left eye on the left edges of the CB and OB. On right cuts I sight with my right eye. Not straight in type cuts or small angles, but cuts approaching 20-30 degrees. I use my dominant eye on these straighter shots left or right. The reason I mention this is because of the big difference in perspective if you do not sight this way. It completely changes the edge you aim to and why so many people say the system is hogwash. They are not sighting correctly and with a little knowledge they would get it. You have to look across the aiming line, kind of 'poke your head out' as Spidey says and all of a sudden your feel alarm goes ding, ding, ding because you lock in on the aiming line. Alot of times I don't look at the pocket, I feel it with the right perspective.

That is what I think you have explained with your drawings, but there is a connection there to other pivot systems and the perspective portion is the key. It's why the CTE critics argue that the pivoters are using feel devloped with fractional, ghostball or other traditional systems. The idea of perspective is well, in a word, aparallel to straight lines and angles. It's subjective and a concept that is different for each player.

Enough for now. Let me read some more of your posts and come up with a question or two for you.

One thought I had was your shift distance x, is the pivot distance less, equal or more?

Thanks,
Mike

 

[LAMas]

"One thought I had was your shift distance x, is the pivot distance less, equal or more?"
Mike

Aim the cue at a line from the center of the CB to the contact point CP (in this case the edge of the OB for a 90 degree cut) aparallel shift the cue to the center of the small OB which we will call "X" (less than 1.125" for a 2.250" OB)- like rolling a dowel.

As you shift the cue to this new line, the bridge hand moves as well the same distance "X" - moving the axis of your pivot.

Thanks.

 

[LAMas]

"It does get smaller at increasing separations along the line of centers, but not by much"
Jal

Jim,
On a long table, place a cue ball 2 feet from the edge and then an OB 2 feet further down table from the CB or 4 feet from the edge of the table.

Take a scale and place it atop the near end of the table near your eye and measure the height of the CB; then measure the height of the OB down table - it (OB) will be smaller by aprroximately 1/2 - that's significant.

Thanks

 

[Jal]

On a long table, place a cue ball 2 feet from the edge and then an OB 2 feet further down table from the CB or 4 feet from the edge of the table.

Take a scale and place it atop the near end of the table near your eye and measure the height of the CB; then measure the height of the OB down table - it (OB) will be smaller by aprroximately 1/2 - that's significant.

LAmas,

I fully agree that the apparent size (angular diameter) of the OB does change just as you indicate. But the offset used in CTCP while 'parallel' shifting to OB center hardly changes at all. Let's say you have to propel the OB at 60 degrees with respect to the line of centers between the CB and OB. And let's do this for CB-OB separations of centers of 1', 2', 4' and 8'. The corresponding cut angles, which is the OB direction measured with respect to the pre-impact CB direction (as opposed to the line of centers) are:

1' (12") - 70.15833 degrees
2' (24") - 64.86886
4' (48") - 62.38037
8' (96") - 61.17658

If the center of the lens of your eye was 2' behind the center of the CB, its apparent angular diameter would be 5.37345 degrees. The apparent angular diameters of the OB in each case (distances of 3', 4', 6' and 10' from your eye) would be:

3' (36") - 3.58157 degrees
4' (48") - 2.68599
6' (72") - 1.79057
10' (120") - 1.07431

Undeniably, they get smaller with distance.

Nevertheless, the parallel offsets needed to shift to OB center ("b" in the previous diagrams) are nearly the same. These are identical at both the OB and CB (Of course, this depends on a true parallel shift being performed.) :

1' (12") - 1.01851 inches
2' (24") - 0.99680
4' (48") - 0.98562
8' (96") - 0.97997

They are based on the geometry shown below. "b" is labeled as bcp here, while P is 60 degrees in our example. Equations 6 and 8 are the relevant ones:



I don't have the time now to show how the angular sizes of the balls are calculated (hurray!), but then we all agree that they get smaller (almost linearly) with distance.

Jim

 

[LAMas]

"If the center of the lens of your eye was 2' behind the center of the CB, its apparent angular diameter would be 5.37345 degrees. The apparent angular diameters of the OB in each case (distances of 3', 4', 6' and 10' from your eye) would be:

3' (36") - 3.58157 degrees
4' (48") - 2.68599
6' (72") - 1.79057
10' (120") - 1.07431
..."
This is as viewed from above and not in perspective from a focal/viewing plane at and relative to the CB.


"Nevertheless, the parallel offsets needed to shift to OB center ("b" in the previous diagrams) are nearly the same. These are identical at both the OB and CB (Of course, this depends on a true parallel shift being performed.) :

1' (12") - 1.01851 inches
2' (24") - 0.99680
4' (48") - 0.98562
8' (96") - 0.97997
......."
Jal

I concur with you except for the above, The difference is so small that the result would be the almost the same included angle created by the pivot to the center of the OB.

Take a cut angle of 80 to 90 degrees (line of centers) where the CB must contact the OB from 1.1" to 1.125" or 1/2 the diameter of a 2.25" GB outside of the edge of the OB.

Using a trig calculator with round off to .X" so that 1/2 of a OB or GB should be 1.125" (r) but is entered as 1.1' - a small deviation.

The included angle from the center of the CB to an GB 12" away:
creates a triangle with 2 sides of 12" and the 3rd side of 1.1" is 5.24 degrees

The included angle from the center of the CB to an GB 24" away:
creates a triangle with 2 sides of 24" and the 3rd side of 1.1" is 2.62 degrees

The included angle from the center of the CB to an GB 36" away:
creates a triangle with 2 sides of 36" and the 3rd side of 1.1" is 1.75 degrees

The included angle from the center of the CB to an GB 48" away:
creates a triangle with 2 sides of 48" and the 3rd side of 1.1" is 1.31 degrees

So the included angle must decrease from 5.24 degrees @ 12" to 1.31 degrees at 48"
for a delta of almost 4 degrees.

I contend that the aparallel offset is greater than from your post of 1.01851 inches
@ 12" to 0.98562" @ 48"
or 0.033" difference between or about the diameter of a small metal wire paper clip.

I contend that this isn't enough to accomplish the 4 degrees necesary from 12" to 48".

Thanks.

 

[LAMas]

"On 90/90...I aim left cuts sighting with my left eye on the left edges of the CB and OB. On right cuts I sight with my right eye. Not straight in type cuts or small angles, but cuts approaching 20-30 degrees. I use my dominant eye on these straighter shots left or right. The reason I mention this is because of the big difference in perspective if you do not sight this way. It completely changes the edge you aim to and why so many people say the system is hogwash. They are not sighting correctly and with a little knowledge they would get it. You have to look across the aiming line, kind of 'poke your head out' as Spidey says and all of a sudden your feel alarm goes ding, ding, ding because you lock in on the aiming line. Alot of times I don't look at the pocket, I feel it with the right perspective."
Mikjary
-----------------

Mike,
How did Hal instruct this head shifting over the phone?

I am not a good candidate for CTE then for my dominant eye changes from time to time so I must calibrate my stroke with a series of straight in shots to get into the alignment of the day.

 

[LAMas]

[B].ppt deleted in favor of the Acad drawing below.
Please look at the next post for Acad[/B]

Thanks

 

[LAMas]

Acad drawing of the relative size of the OB as viewed from the CB focal/viewing plane.

The OB appears smaller as it moves farther away from the CB

In Aparallel CTCP, one aims the center of the CB at the contact point on the OB that sends it to the pocket. In this case the cut is a 90 degree cut to a pocket on the left. The contact point for this is the right edge (3:00) of the OB.

Next step is to aparallel shift to the center of the OB.

Then pivot back to the center of the CB and shoot.

The aparallel shift for the OB moving down table, and appearing smaller, from the CB is for separations between the CB and OB of:

1 foot .750"
2 feet .562"
3 feet .450"
4 feet .375"

 

[Jal]

Acad drawing of the relative size of the OB as viewed from the CB focal/viewing plane.

The OB appears smaller as it moves farther away from the CB

In Aparallel CTCP, one aims the center of the CB at the contact point on the OB that sends it to the pocket. In this case the cut is a 90 degree cut to a pocket on the left. The contact point for this is the right edge (3:00) of the OB.

Next step is to aparallel shift to the center of the OB.

Then pivot back to the center of the CB and shoot.

The aparallel shift for the OB moving down table, and appearing smaller, from the CB is for separations between the CB and OB of:

1 foot .750"
2 feet .562"
3 feet .450"
4 feet .375"

View attachment 139638

LAmas,

I'm not really following the method behind your carefully done drawings.

You begin with the CB lined up with the right edge (contact point in this case for a 90 degree cut) of the OB's. You then show lines emanating from the eye to the left edge of each OB. Can you describe how you're relating this to the shift over to OB center? Can you elaborate a little more on what you mean by an "aparallel shift"? I've been taking this to mean a "parallel" shift as the eye sees it, i.e., across the uninterpreted (raw) image presented to it, but I'm not sure we're in sync with this. If you pivoted the cue about the eye position shown in your drawing, all points along its central axis would indeed be displaced sideways in the image plane by the same amount, since their angular offsets are the same. Is this in fact what you mean by an "aparallel shift"? If so, I'm not sure why you're shifting over to the left edge of the OB, as opposed to its center?

You show a bridge distance of 12" behind the CB. Is this where the pivot back to CB/GB center is to be performed?

Also, I don't know what is meant by a "focal plane" at the CB?

Thanks.

As an aside, I have to re-assert that the numbers offered for the offsets when doing a parallel shift to OB center with respect to the table's frame of reference are correct. They may be irrelevant to an "aparallel shift," but as indicated, I'm still not sure we're on the same page as far as that goes.

Jim

 

[LAMas]

Jal,
We are at an impasse.
You are in a 2D paradigm.

I am looking at "what is" from a the perspective of the shooter who is down on the shot.

I have put your 2D trigonometry picture into perspective and you can see that the 2 triangles that are equal in your 2D picture cannot be overlaid on each other for they are fore shortened.

Let's agree that you can exist with your 2D world viewed from above (I have been there) while I venture in my perspective one - which works for me, probably Mike and at least one other that PMd me.



Thanks for humoring me but this is a conundrum.

Adios

 

[pooltchr]

this is a conundrum.

Adios

But does it help you shoot any better?

Steve

 

[Mikjary]

Acad drawing of the relative size of the OB as viewed from the CB focal/viewing plane.

The OB appears smaller as it moves farther away from the CB

In Aparallel CTCP, one aims the center of the CB at the contact point on the OB that sends it to the pocket. In this case the cut is a 90 degree cut to a pocket on the left. The contact point for this is the right edge (3:00) of the OB.

Next step is to aparallel shift to the center of the OB.

Then pivot back to the center of the CB and shoot.

The aparallel shift for the OB moving down table, and appearing smaller, from the CB is for separations between the CB and OB of:

1 foot .750"
2 feet .562"
3 feet .450"
4 feet .375"

View attachment 139638

LAMas.

Sorry about not getting back to you. Looks like you've been busy! This set of drawings is what I was talking about. This is what perspective is to me and illustrates the point that makes these pivot systems work in a 2D world. I always viewed the pool table as a length and width shape with straight lines and spheres that were consistent in shape no matter where they sat in relation to the CB. This shows how we use our telescopic vision even though our brains tell us there is no difference in the size of the balls and that lines are parallel.

This leads to the toughest question I can think of (besides how to stop the oil spill). It is Dr. Dave's drawing of the table with several shots lined up in a straight line and positioned where the distance between the CB and OB doesn't change. As they are progressively moved toward the short rail the angle increases to pocket a ball in the corner. Do you remember that diagram? It was posted about 20 times. J/K Dr. Dave.

With 90/90 I have no problem adjusting because of the different aiming point on the OB to compensate for angles, but how do you compensate with only one CTE pivot? Your aparallel system will have no problem pocketing any of the shots because of its basis on the OB CP. When you are looking at only the edge of the OB how does it differ or change as it moves further away from you, but still on the same line and the CB distance a constant? 2D logic (new aiming term) says the OB will track on the same angle for each shot with the constant CB distance. The 3D perspective ( as wierd outer limits music comes on ) or aparallel aiming doesn't fit this example or does it? Does the CB have to be stationary or does the perspective change only because the OB has moved further away?

I believe this is the heart of the CTE debate and I would be interested in any thoughts you or Jim might have on my rambling post. :wink:

Thanks,
Mike

 

[Spike8ball]

Randy...Simply put....SAM 3 and SAM 4.

You're welcome!


Steve

Ah thanks Steve... NOW I get it. SAM 3 and SAM 4. Whew, for a minute there I thought I was going crazy...

Mike

 

[LAMas]

Mike,
"....It is Dr. Dave's drawing of the table with several shots lined up in a straight line and positioned where the distance between the CB and OB doesn't change. As they are progressively moved toward the short rail the angle increases to pocket a ball in the corner...."

Yes, many times on the CTE threads and never succinctly answered there. In CTE if the offset is one tip diameter, at the CB, that is one cut angle; if it is 1/2 ball in is another different angle. Both will work for their dedicated angle, but move the OB down table and it misses the pocket or the CB sails past the OB.

That is because in CTE, the only relationship to the OB is its edge. The other relationship is the where to aim the tip of the cue at the CB.

In Aparallel CTCP, one doesn't care about the CB, except it's center at the start (CTCP) and only the CP and center of the smaller OB.

In CTE, if the shift was a little more than one tip or 1/2 ball, then the cut angle would increase and may go to the pocket...but by how much (the converse is also true) - the tweek that is learned?

This is where aiming at the CP, the GB contact/impact point or where the line from the pocket exits the OB,
to start (not CTE) adds a direct relationhip to the angle (you know that). What is added to address that the included angle must decrease as the OB goes down table is the shift to the center of the OB. As my diagram shows, the appearance of the OB gets smaller the farther it is from the CB (focal plane reference) - this decreases the aparallel offset in direct proportion to
that distance (smaller OB = smaller offset), and after the pivot, the included angle has also decreased.

Again, in Aparallel CTCP, one aims not at the edge of the OB but the GB contact/impact point or where the line from the pocket exits the OB - the CP

Sorry if I am too verbose and repeat myself

"...The 3D perspective ( as wierd outer limits music comes on ) or aparallel aiming doesn't fit this example or does it? Does the CB have to be stationary or does the perspective change only because the OB has moved further away?..."

No, Aparallel CTCP doesn't fit the CTE paradigm,
You ask a good question - if the CB also moves down table, the distance between it and the smaller appearing OB is what is in play - 1 foot apart in the kitchen or 1 foot apart down table are the same.

Thanks.

 

[Jal]

Jal,
We are at an impasse.
You are in a 2D paradigm.

I am looking at "what is" from a the perspective of the shooter who is down on the shot.

I have put your 2D trigonometry picture into perspective and you can see that the 2 triangles that are equal in your 2D picture cannot be overlaid on each other for they are fore shortened.

Let's agree that you can exist with your 2D world viewed from above (I have been there) while I venture in my perspective one - which works for me, probably Mike and at least one other that PMd me.

View attachment 139706

Thanks for humoring me but this is a conundrum.

Adios

Well, I guess this is the end of a beautiful friendship?

As a parting thought, you might consider working out why a nickel held at arms length is not actually larger than the moon.

Jim

 

[LAMas]

Beauty is to the beholder.