How many angles would you say there are on a regulation table that deliver the object ball to a pocket?
The number of possible cut angles to center pocket is infinite -- everything (including all fractions of a degree) from 0° to about 90° (or more than 90° with a massé). But the number of cut angles needed to pocket all shots is less than that because of pocket slop.
BTW, would you care to share with us which aiming method you use for a half-ball hit?
Is this a trick question? If I knew for certain that I needed a half-ball hit with no spin, I'd aim the center of the CB at the edge of the OB and try to stroke straight on that line of aim. Often, however, one doesn't know for sure that a half-ball hit is required (even when it is), and other aiming methods (many choices available) are used.