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@@ -27,9 +27,9 @@ This document explains how the Python pipeline creates the **500 aircraft-style
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  ## 1) Inputs & Reproducibility
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- - **Airfoil geometry**: Each airfoil file contains two columns $(x, y)$ forming a closed perimeter ordered **TE → upper → LE → lower → TE**.
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- - On load, $x$ is normalized to $[0,1]$; the perimeter is rotated so the first point is closest to the **trailing edge** $(1,0)$ and the **upper surface** comes first.
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- - **Polars (optional)**: QBlade/XFOIL exports with $(\alpha, C_l, C_d, C_m)$.
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  - Files are matched to airfoils by flexible filename heuristics.
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  - Polars are parsed (3–4 numeric columns), **deduplicated in $\alpha$**, and **sorted by $\alpha$**.
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  - **Random seed**: We use `np.random.default_rng(42)` so all 500 wings are reproducible bit-for-bit.
 
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  ## 1) Inputs & Reproducibility
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+ - **Airfoil geometry**: Each airfoil file contains two columns \\(x, y\\) forming a closed perimeter ordered **TE → upper → LE → lower → TE**.
31
+ - On load, \\(x\\) is normalized to \\([0,1]\\); the perimeter is rotated so the first point is closest to the **trailing edge** \\(1,0\\) and the **upper surface** comes first.
32
+ - **Polars (optional)**: QBlade/XFOIL exports with \\(\alpha, C_l, C_d, C_m\\).
33
  - Files are matched to airfoils by flexible filename heuristics.
34
  - Polars are parsed (3–4 numeric columns), **deduplicated in $\alpha$**, and **sorted by $\alpha$**.
35
  - **Random seed**: We use `np.random.default_rng(42)` so all 500 wings are reproducible bit-for-bit.