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Add flyby geometry, cubic spline method, and sample count sweep - #5

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emilymfoley wants to merge 2 commits into
kgklein:mainfrom
emilymfoley:new-methods
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Add flyby geometry, cubic spline method, and sample count sweep#5
emilymfoley wants to merge 2 commits into
kgklein:mainfrom
emilymfoley:new-methods

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Added flyby geometry, cubic spline method, and sample count sweep.

  • Wired up flyby and tetrahedron_like geometries that were defined in geometries.py but unreachable via generate_sampling_points
  • Added CubicSplineMethod (Clough-Tocher 2D) following the existing base class pattern
  • Added scripts/run_sample_count_sweep.py comparing RBF, linear, nearest, and cubic spline across n = 10, 25, 50, 100, 200 random samples
  • Added tests for all geometry functions including flyby in 2D and 3D

Found:

  • RBF covers 100% of the domain at all sample counts and reaches rel L2 = 0.077 at n=200
  • Cubic spline has lower error than RBF within the convex hull, but only covers ~84% of the domain at n=200 — same coverage limitation as linear interpolation
  • Nearest neighbor is consistently the weakest method
  • Linear and cubic spline have identical domain coverage at every sample count since both are triangulation-based

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