Editing Openai/6959ed27-accc-800e-8e87-21aa81e93c07 (section)

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The curvature-based method (0xfaded's approach) offers:
# Faster execution (fewer iterations needed)
# No trigonometric functions in the main loop
# Robust convergence across different eccentricities
# Simple implementation

The key insight is approximating the ellipse locally as a circle using
the center of curvature. This gives very good updates per iteration,
typically converging in just 3 iterations.

Newton's method can be faster per iteration but may need more iterations
and can have convergence issues near the ellipse axes.

Interesting results! The benchmark shows some key findings. Let me create a better summary with the key insights and also fix the bisection method which seems broken (it's reporting issues). Let me also add a more focused micro-benchmark that shows the efficiency more clearly.

The benchmark reveals some interesting results! Let me create a more focused micro-benchmark to isolate the per-call performance:

bash
cd /home/claude && python micro_benchmark.py

Output