Ok, there's my overthinking for the day. Lol
Should be a safe place to do it.
Without adding spin effects the cut angles start from 0 and move through roughly 90°.
The visible part of the equator when viewed through center ball takes is to what is call half ball.
That is the 2 dimensional description.
The 3 dimensional reality is that it only takes us to 30 of those degrees or ⅓ of the possible.
The 2 dimensional description of a quarter ball adds about 19° to the total.
At this point the line from cue ball center along an equatorial line extends a quarter ball outside the extreme perimeter.
Adding an eighth of a ball farther outside, the actual cut angle is 60°, for the 1/8 cut.
The last ⅛ ball to edge to edge, has the last 30° of angles.
Wrapping my head around using a fraction in 2 dimensions to get to a 3 dimensional angle is an overthink for me.
i estimate the contact point from the cue ball.
Holding that point visually I make the 3 dimensional shift to the ob to pocket line.
I compare my estimate to the actual center of the ob on the pocket line.
If need be I bookmark any difference and hold that new point visually as I return to the cue ball.
There is only one point on the cue ball that can contact that point in a 3D world.
If needed a parallel line through the cue ball referenced to the ob to pocket line locates that point.
Joining those two points with a cue line and executing a parallel shift to cb center is the same as the ghost ball line.
All 3 D reasoning.
Welcome to overthink central