Summary

Jason Sachs shows how Green’s theorem can be applied to compute swept areas for collision detection and occupancy tasks in constrained systems. The article walks through the mathematical derivation, discrete implementation details, and practical optimizations that make swept-area detection efficient on microcontrollers.

Key Takeaways

• Apply Green's theorem to compute the signed area swept by moving edges or polygons for collision/occupancy checks
• Implement swept-area detection with discrete polygon operations suitable for embedded systems
• Optimize the algorithm for low CPU and memory by using integer/fixed-point arithmetic and early-reject heuristics
• Integrate swept-area checks into real-time loops for collision avoidance and sensor-based mapping

Who Should Read This

Embedded firmware engineers and developers working on motion, collision detection, or sensor-based mapping who need practical, microcontroller-friendly algorithms.

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