These are the same old traditional lines people have been showing for years, and they are off by a few degrees. In fact, Stan Shuffett has a video where he sets up a "30° shot" using this 1/2 ball line you show here, where the 30° angle is based on the center-to-center line between the balls, NOT the aim line from center cb to ob edge. The shot is actually a 3/8 and can't be made using a 1/2 ball aim unless you spin it with outside english. Dan White analyzed the stroke on this shot and shows where Stan uses outside spin to account for the fact that this isn't really a dead halfball shot.
Here is Stan's video....
https://youtu.be/AMmmhtZqA1U.
Set the shot up exactly as he describes and you'll see that the ob is on the 1/2 ball line shown in your diagram. The ob is half a diamond away from the center spot and the cb is 1 diamond away from the head spot, lined straight/perpendicular to the end rail. Shoot a halfball shot as he describes, or as your diagram indicates, and the ob hits the end rail, not the pocket. Here's why....
The distance between the cb and ob is 1.5 diamonds, 18.75" on a 9ft table. Stan (and your diagram) reference a 30° angle from a
center cb to center ob perspective. But when you aim ccb to ob edge, you shift your ccb perspective exactly 3.4° to the right.
asin(1.125/18.75) = 3.4°. You create a 30° angle, but it's shifted to the right of the pocket, and once you factor in throw it shifts even farther right of the pocket, sending the ob about half a diamond too thick.
A more accurate line to reference the 1/2 ball shot and other angles must incorporate this change in perspective, the difference between a center cb to center ob perspective and a center cb to required ob aim point perspective, which is shown here.....
https://forums.azbilliards.com/showthread.php?t=502020