Reference position: equal distanceD1: distance of the cue ball from the mirror line: 2D2: distance of the ghost ball from the mirror line: 2Start: position of the cue ball along the cushion: 6Arrival: position of the ghost ball along the cushion: 2Aim: 4Start 6, Arrival 2, D1 = D2 = 2 → Aim = 6 + (2 − 6) × 2 ÷ 4 = 4. The aim is exactly midway between the two positions.
Mirror system · Drill cards
Aim = Start + (Arrival − Start) × D1 ÷ (D1 + D2)
Cue ball far from the cushionD1: distance of the cue ball from the mirror line: 3D2: distance of the ghost ball from the mirror line: 1Start: position of the cue ball along the cushion: 7Arrival: position of the ghost ball along the cushion: 3Aim: 4Start 7, D1 3; Arrival 3, D2 1 → Aim = 7 + (3 − 7) × 3 ÷ 4 = 4. The aim point moves toward the target that is closer to the cushion.
Target far from the cushionD1: distance of the cue ball from the mirror line: 1D2: distance of the ghost ball from the mirror line: 3Start: position of the cue ball along the cushion: 6.5Arrival: position of the ghost ball along the cushion: 2.5Aim: 5.5Start 6.5, D1 1; Arrival 2.5, D2 3 → Aim = 6.5 + (2.5 − 6.5) × 1 ÷ 4 = 5.5.
Target close to the cushionD1: distance of the cue ball from the mirror line: 2.5D2: distance of the ghost ball from the mirror line: 0.5Start: position of the cue ball along the cushion: 5Arrival: position of the ghost ball along the cushion: 1Aim: 1.67Start 5, D1 2.5; Arrival 1, D2 0.5 → Aim = 5 + (1 − 5) × 2.5 ÷ 3 = 1.67.
Shallow angle, sliding ballD1: distance of the cue ball from the mirror line: 1D2: distance of the ghost ball from the mirror line: 0.75Start: position of the cue ball along the cushion: 7.5Arrival: position of the ghost ball along the cushion: 0.5Aim: 3.5Start 7.5, D1 1; Arrival 0.5, D2 0.75 → Aim = 7.5 + (0.5 − 7.5) × 1 ÷ 1.75 = 3.5.
Shallow angle, rolling ballSlow, rolling ball (shallow angle): YesD1: distance of the cue ball from the mirror line: 1D2: distance of the ghost ball from the mirror line: 0.75Start: position of the cue ball along the cushion: 7.5Arrival: position of the ghost ball along the cushion: 0.5Aim: 4.12Same position, slow and rolling ball: instead of D1, 0.7 × 1 = 0.7 → Aim = 7.5 + (0.5 − 7.5) × 0.7 ÷ 1.45 = 4.12. The aim point moves 0.62 diamond toward the cue ball.