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=========================================================================== This shows where the curvature method shines - no trig in the inner loop! --------------------------------------------------------------------------- Ellipse: a=150, b=100 (Moderate eccentricity) --------------------------------------------------------------------------- N points Curvature Newton Speedup --------------------------------------------------------- 1000 0.210 ms 0.504 ms 2.40x Curv wins! 10000 1.222 ms 3.732 ms 3.05x Curv wins! 100000 14.496 ms 40.999 ms 2.83x Curv wins! Accuracy (max deviation from ellipse): Curvature: 4.44e-16 Newton: 4.44e-16 --------------------------------------------------------------------------- Ellipse: a=200, b=50 (High eccentricity) --------------------------------------------------------------------------- N points Curvature Newton Speedup --------------------------------------------------------- 1000 0.310 ms 0.568 ms 1.83x Curv wins! 10000 1.163 ms 3.726 ms 3.20x Curv wins! 100000 10.348 ms 41.531 ms 4.01x Curv wins! Accuracy (max deviation from ellipse): Curvature: 4.44e-16 Newton: 4.44e-16 --------------------------------------------------------------------------- Ellipse: a=100, b=10 (Extreme eccentricity) --------------------------------------------------------------------------- N points Curvature Newton Speedup --------------------------------------------------------- 1000 0.247 ms 0.605 ms 2.45x Curv wins! 10000 0.885 ms 3.692 ms 4.17x Curv wins! 100000 11.002 ms 40.572 ms 3.69x Curv wins! Accuracy (max deviation from ellipse): Curvature: 6.66e-16 Newton: 4.44e-16
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