Merge logic

[raymondwjang]

🔍 Type of Change

✨ New Feature: Introducing new functionality
🧪 Improvement: Enhancements or optimizations to existing code

📝 Description

1. Optimization: Taking some shortcuts in calculations and using Sparse arrays for Footprints to drastically reduce calculation time. Still not very close to real-time (ranging 0.1~1 second per frame).
2. Footprint: Expansion now stops after a few iterations. The logic is "if it was supposed to be covered by expansion, it should've been searched and merged in detect step."
3. Merge: As a part of deprecation effort, we implemented merging. Merging mechanism is largely divided into two rhythms - short and long. short-term merging occurs when the component is first uncovered, to make sure it's not a part of a known component, or a group of neighbors comprise a single cell.
4. Visualize pod added for colored footprints

++ I can probably remove the validation steps (no nans, no negatives, etc. for movie arrays, for example.) since i do it a lot, and shave off time. It makes me super nervous, however, since removing validations introduces brittleness.

🧪 Testing

• Unit tests
• Integration tests
• Existing tests update

🛠️ Dependencies

✅ Checklist

• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation

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📚 Documentation preview 📚: https://cala--141.org.readthedocs.build/en/141/