Stan's quite clear that the CTE line is to be visualized as running across the top of the cue ball. Here's a bunch of pictures. They were drawn with SketchUp (my thanks to Jal for the table) and captured with Greenshot (this got better images than saving them as .jpg files with SketchUp for some reason).
These are all of one shot: a right cut of about 22-23 degrees, which calls for an outside tip placement relative to the cue ball center, and a left pivot (which is only necessary if you use the outside tip placement, which itself isn't really necessary, but probably is useful as a training aid). I removed the ghost ball for all but the first image.
First, nice diagrams. I'm home and can see them now.
While the CTE orange line is to be visualized running over the top of the CB, I presume that it is also over the center of the CB. The secondary aim chartruse line runs from the 3:00 on the CB equator to the center of the OB. The lateral shift of the bridge and 1/2 cue tip is to the outside of the center of the CB and the CTEL. From there, one pivots/rotates the cue tip at the bridge to the right to get on the shot line (you wrote "left pivot")...no matter.
I have never thoiught about placing my bridge outside of the two aim lines. I thought that the cue and bridge would below the left or right eye or somewhere in between.
Whenever I focus on the secondary aim line, at say the outer 1/8, This forces me to move my eye/s, head and body to move off of the CTEL.
Even if I tilt my head, I cannot resolve the two aim lines simultaniously. I will have to concentrate of contort more?
I will chew on this during dinner.
Thanks to you and JAL.
:thumbup:
The left image is roughly from the player's view before moving to set his bridge; the middle one looks almost directly down on the table; the right one looks along the Edge-to-B line (approximately), but it's still looking down somewhat.
This is from the side, about the middle of the CB-OB line, and about the height of the middle of the balls:
Finally, the most interesting one (to me, at the moment). This is another effort to get the player's view as he moves to set his bridge; it looks along the Edge-to-B line. Note the relationship of the CTE line (orange-ish) and the ghost ball line (white). Also note the black line to the right of the ghost ball line.
The black line is the vertical projection of the visualized orange CTE line onto the table.
Visually, from the player's point of view those lines are pretty far apart horizontally - around an inch apart at around eight inches behind the cue ball along the ghost ball line - i.e., at a reasonable bridge point. Several things come immediately to mind. (See note at end of post.)
When Shuffett refers to the CTE line, which of those lines does he mean? Or does he mean Jal's, which is visualized as being through the centroid of the cue ball and lies between the two I show, though still to the right of the ghost ball line? (Jal's is interesting and possibly the most useful of the three, but it may be too hard for players to visualize. Also, I don't yet know how to draw it with SketchUp.
) To further illustrate the difficulties (that I perceive), here's the image from exactly the same angle (we know this because the Edge-to-B line is still vertical on your screen - well, on mine, anyway) but a different distance and elevation.
The difference is that we are further back and higher. Notice where the orange CTE line has moved to
visually.
Unfortunately, another thing I don't yet know how to do with SketchUp is tell it to put its camera at a certain location in space. I'd like to do that because I'd like to see how all of this looks with the camera at the level of a standing player's eyes (because that's where Shuffett says to get the visuals), which would be about 30-40 inches above the table and mostly around three to four feet behind the cue ball, I think.
I know I said "Several things" above, but it's 0400, I'm rather tired of this right now, and hungry. I'm going to go make a couple of grilled bacon-cheese sandwiches and finish off the Petite Sirah we had for dinner. If anybody is interested, I'll try to go into the other stuff later. Except for the difficulty I perceive in representing most of CTE/ProOne accurately in 2D, which I'm tired of talking about. Oh... and except for "exactness" which was never of much interest to me.
-- jwp
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Note: Here I'm using the phrase "Several things come immediately to mind." in the sense that academics in higher-end research universities use it, which is closely related to the meaning of "It is intuitively obvious to the most casual observer...". The difference is that the former has the lay meaning "I've worked on this 17 hours a day for the last five years and I think I may have finally figured out what some of the problems are, maybe."; whereas the latter means "I've worked on this 17 hours a day for the last five years...." and either (a) "... I understand it but it's really hard and I'm not about to give it away to the likes of
you." or (b, which is more likely) "... I haven't got a clue what the hell is happening in there but this sort of looks right, I hope, and I hope you aren't so gauche as to ask about it, especially if you expect to [graduate/get your PhD/get tenure - as appropriate].".
