Simplex projection visualization for observable triads

[jc-macdonald]

Simplex projection visualization for observable triads

Implement the simplex projection visualization from both notebooks. This is the primary figure type for the structured observables manuscript — projecting model performance onto a 2-simplex defined by 3 observables.

Implementation

• plot_simplex_projection(data, triad, ax=None, norm='twoslope', cmap='RdYlGn_r') — 2D ternary projection
• plot_simplex_projection_3D(data, triad, ax=None) — 3D elevated simplex
• prepare_simplex_data(results, triad) → barycentric coordinates + color values
• generate_simplex_panels(results, triads, ncols=3) → multi-panel figure
• TwoSlopeNorm support for diverging colormaps centered at pass/fail threshold
• ROPE region overlay (shaded region of practical equivalence)
• ConvexHull overlay showing fill ratio

Source code reference

• Thoery_1_Code.ipynb: plot_simplex_projection with TwoSlopeNorm
• Chemostat_Simulator.ipynb: plot_simplex_projection_3D (duplicated ~5x), prepare_simplex_data (~4x), generate_all_simplex_panels (~3x)

Deduplication note

The Chemostat notebook contains 5+ near-identical copies of simplex projection code with minor variations. This issue consolidates them into a single parametric implementation.

Tests

• Barycentric coordinates sum to 1
• Known triangle vertices map to correct simplex corners
• Figure smoke test (renders without error)