Replace arbitrary grid sampling with principled geometric intersection detection.
Previous approach (sampling):
- 11×11 grid = 121 point tests
- Arbitrary density - had to guess how dense to make it
- Wasteful - most points tested empty space
New approach (geometric):
- 9 strategic points: 4 corners + center + 4 edge midpoints of detection box
- Additional check: if region center is inside box, verify it's in region fill
- Total: ~10 point tests (vs 121 before)
- Based on geometric reasoning, not arbitrary density
Why this works:
- Tests the boundary of the detection box (corners + edges)
- Catches regions that intersect the box from any angle
- Catches tiny regions entirely contained in box (center check)
- More efficient and more correct
This properly handles:
- Large regions intersecting box (corners/edges catch them)
- Tiny regions inside box (center check catches them)
- Irregularly shaped regions (boundary points catch them)
🤖 Generated with [Claude Code](https://claude.com/claude-code)
Co-Authored-By: Claude <noreply@anthropic.com>
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