Okay, but we can't apply the math unless the system is well defined. The descriptions I've seen of how to use the edge-to-A,B,C and CTE lines leave much to be desired. Just getting your eyes and body in some position, guided by those lines, does not specify where the cue is to be pointed before the pivot. For instance, take the case of cut angles in the range of about 15 to 30 degrees (edge-to-B and CTE lines as guides). Here are some possible interpretations of how the cue should be aligned prior to pivoting.
The first two (figs. 1a and 1b) show the cue aligned parallel (in actuality) to the edge-to-B line. The two diagrams are exactly the same constructions using Google's Sketchup, but seen from the shooter's perspective (roughly), and then from above (non-perspective view).
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The next one (fig. 2a) shows the cue aligned
apparently parallel to the edge-to-B line, that is, in the image plane of the eye (field of view). Figure 2b shows the actual cue alignment in the non-perspective view.
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Figure 3a shows the cue aligned parallel to a line which splits the difference between the edge-to-B and CTE lines in the image plane (field of view), figure 3b the actual alignment (see next post - limit of 5 files per post).
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These are three "natural" interpretations, I think, but others are possible. Obviously, you'll produce different cueball directions - and therefore cut angles - depending on which one you employ. And with the last two, where 'parallel' is judged in the field of view, alignment also depends on where your head is positioned and where your eyes are "pointing" (orientation of the optic axis).
In order to look at the mathematics underlying it, these things have to be specified. As far as I know, they're very loose ends as the system now stands. That's not to say that the math will contradict the logical arguments presented by Patrick, Jsp, Atlarge, etc. If you clearly define the cue's pre-pivot alignments, because they don't take the more-or-less continuous nature of the required cut angles into account, you're going to have a paucity of generated cueball directions. In the case of cut angles from about 15 to 30 degrees, you'll only see two for a given CB-OB separation distance, one for a left cut and one for a right cut.
Jim