How does the “bottom-of-the-ball aiming” aiming system work?
“Bottom-of-the-ball” aiming is a way to visualize the required contact point on the object ball (assuming no throw). First visualize the required cut angle for the shot as shown in “a” in the diagram below. Then visualize this same angle on the face of the object ball, as shown in “b” below. If the vertex of the angle is on the edge of the ball, and one leg of the angle goes through the center of the ball with the other leg vertical, the necessary contact point (CP) is where the vertical leg crosses the ball’s equator.
Below is an example for a 1/2-ball hit, 30° cut shot.
from Patrick Johnson: