CTEPro One, as its teachers describe it: two sight lines seen together, then a small pivot to center.
Drag the balls or click a pocket.
CTE lineedge to A / B / C (best fit)shot lineghost ballcue after pivotpaths that pocket
At the table
Pick a perception for the shot: 15°, 30° or 45°.
Sight the CTE line (for 15° and 30°): from the center of the cue ball to the object ball's outside edge (the right edge for a cut to the left). The 45° perception skips it and uses only the second line.
Also sight the second line: from the cue ball's inside edge to point A, B or C on the object ball. A is the inside quarter, B the center, C the outside quarter. A goes with 15°, B with 30°, C with 45°.
Move straight into the shot keeping both visuals, with the tip half a tip off center, then pivot or sweep to center and shoot. From the inside makes the cut thinner, from the outside thicker. Straight-in shots use 15° with an outside pivot.
The visuals
The visuals, from behind the cue ball. Orange: the CTE line from the cue-ball center to the object ball's outside edge, faint for 45°, which doesn't use it. Green: the line from the cue ball's inside edge to the chosen point. Faint lines: the other two perceptions. Dashed blue: the shot line, where the cue-ball center actually needs to go.
How it works
Each perception on its own. An edge-to-point line is parallel to a center line one radius further out. So edge-to-A is a ¾-ball hit (about 14.5°), edge-to-B a ½-ball hit (30°), edge-to-C a ¼-ball hit (about 48.6°). These shift slightly with distance.
What the pivot must add: the gap between the shot's cut and the perception's cut. An inside pivot thins the shot; an outside pivot thickens it.
Not modelled: the pivot itself. Public descriptions don't say where the cue points before the pivot. Taken literally, a half-tip pivot at an 8–9″ bridge turns the cue about 1.7°, far more than most shots need. Dr. Dave concludes players adjust the setup without noticing; teachers credit the perception step. The Point to Edge (PTE) page shows a purely mechanical version.
Other versions add thin-cut perceptions (60°, edge-to-edge) or use different points. This page covers A, B and C.
Pure geometry. These pages draw the ideal lines. Two things shift real shots: throw, friction between the balls that pushes the object ball slightly toward the thick side, and perspective, your eye misjudging distances on the balls depending on where you look from. Players learn to adjust for both with practice.