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ALGORITHM_REDESIGN.md

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Alpha/Beta Generation Algorithm Redesign

Major Change: Stroke-Relative → Global Center

Previous Algorithm (Stroke-Relative)

Motion was created around each individual stroke's center point:

center = (end_p + start_p) / 2  # Stroke midpoint
r = (start_p - end_p) / 2       # Half stroke range
x = center + r * np.cos(theta)  # Relative to stroke center
y = r * np.sin(theta) + 0.5     # Beta centered at 0.5

Problem:

  • A stroke from 0.2→0.8 created motion centered at 0.5
  • With max radius_scale, alpha/beta still only oscillated 0.2-0.8
  • Never reached the edges (0,0) or (1,1)

New Algorithm (Global Center)

All motion is from the global center (0.5, 0.5):

# Scale radius: 0 to 0.5 (circle boundary at edges)
target_radius = 0.5 * radius_scale

# Map funscript position to angle
position_angles = (1.0 - current_positions) * np.pi

# Generate from global center (0.5, 0.5)
x = 0.5 + target_radius * np.cos(position_angles)
y = 0.5 + target_radius * np.sin(position_angles)

Result:

  • With radius_scale = 1.0: radius = 0.5 → reaches circle edge
  • Position 1.0 → (1.0, 0.5) - right edge
  • Position 0.0 → (0.0, 0.5) - left edge
  • Position 0.5 → (0.5, 1.0) - top edge

Behavior Comparison

Example: Stroke from position 0.2 to 0.8

Old Algorithm (max speed):

center = 0.5, r = 0.3
Alpha range: 0.5 ± 0.3 = 0.2 to 0.8
Beta range: 0.5 ± 0.3 = 0.2 to 0.8
NEVER reaches 0 or 1

New Algorithm (max speed):

target_radius = 0.5
Position 0.2 → angle = 144° → Alpha ≈ 0.09, Beta ≈ 0.79
Position 0.8 → angle = 36° → Alpha ≈ 0.90, Beta ≈ 0.79
CAN reach near 0 and 1

Speed Threshold Scaling

Min Distance from Center (0.1)

  • Slow speeds (below threshold): Stay near center
  • radius = 0.5 * 0.1 = 0.05 (very small circle)
  • Alpha/Beta range: ~0.45 to 0.55

Max Distance (1.0)

  • Fast speeds (at/above threshold): Reach circle edge
  • radius = 0.5 * 1.0 = 0.5 (full circle)
  • Alpha/Beta range: 0.0 to 1.0 (full range!)

50% Speed Threshold Example

Speed Value Radius Scale Radius Alpha Range Beta Range
0% 0.1 0.05 0.45-0.55 0.45-0.55
25% 0.55 0.275 0.225-0.775 0.225-0.775
50%+ 1.0 0.5 0.0-1.0 0.0-1.0

Angle Mapping

Circular Algorithm (0°-180°)

  • Position 1.0 → 0° → (1.0, 0.5) - right
  • Position 0.5 → 90° → (0.5, 1.0) - top
  • Position 0.0 → 180° → (0.0, 0.5) - left

Top-Left-Right (0°-270°)

  • Position 1.0 → 0° → (1.0, 0.5) - right
  • Position 0.67 → 90° → (0.5, 1.0) - top
  • Position 0.33 → 180° → (0.0, 0.5) - left
  • Position 0.0 → 270° → (0.5, 0.0) - bottom

Top-Right-Left (0°-90°)

  • Position 1.0 → 0° → (1.0, 0.5) - right
  • Position 0.5 → 45° → (0.85, 0.85) - top-right
  • Position 0.0 → 90° → (0.5, 1.0) - top

Impact on Users

What Changes

  1. Full Range Motion: Fast speeds now reach edges (0,0) and (1,1)
  2. Speed Matters More: Speed threshold has dramatic effect on motion range
  3. Uniform Scaling: All motion scales uniformly from center

What Stays Same

  • Speed threshold percentage control (0-100%)
  • Min distance from center setting (0.1-0.9)
  • Three algorithms: circular, top-left-right, top-right-left
  • Speed funscript used for radius scaling

Migration Notes

  • Existing configurations will work but produce different motion patterns
  • Motion will be more expanded at high speeds
  • May need to adjust min_distance_from_center settings
  • Recommended: Start with default 50% threshold and 0.1 min distance

Testing Recommendations

  1. Test at extremes:

    • Speed threshold 0% → everything at max radius
    • Speed threshold 100% → everything at min radius

  2. Verify full range:

    • Check alpha/beta reach 0.0-1.0 at max speed
    • Check alpha/beta stay near 0.5 at min speed

  3. Test all algorithms:

    • Circular (semicircle)
    • Top-left-right (3/4 circle)
    • Top-right-left (quarter circle)

  4. Visual inspection:

    • Plot alpha vs beta to verify circular patterns
    • Confirm motion is centered at (0.5, 0.5)