Reconstruct NeuralFoil's surface pressure from edge velocity in arc length

[1-Bart-1]

The bug

NeuralFoil samples ue/u∞ at the cell centres of a uniform chordwise grid
(compute_optimal_x_points), so with 32 stations per surface the first sits at
1.5625% chord and the last at 98.4375%. Nothing is reported at either end.
neuralfoil_contour_solution filled those gaps by extrapolating Cp linearly off
the end of each surface, independently.

Through a stagnation point the inviscid surface speed is linear in arc length, so
Cp = 1 − ue² is quadratic. Extrapolating Cp runs a straight line backwards
through the curve's own turning point. On an SK100 mid-span section at 5°:

	old	new	XFoil, same contour
max Cp (stagnation, must be 1)	0.689	1.000	0.999
Cp at the leading edge	−1.595	+0.766	+0.413
Cp at TE, upper / lower	0.057 / 0.117	0.093 / 0.093	0.181 / 0.181
integrated drag (reported 0.0276)	−0.0199	+0.0269	—

Cp cannot exceed 1, and the two trailing-edge values must be equal on a sharp
edge (Kutta). Chord fraction is also the wrong coordinate across a blunt nose: the
unsampled region is 4.1% of arc against 1.6% of chord.

The fix

Interpolate ue, in arc length, over both surfaces as one curve:

• Signing the lower surface negative joins them through the stagnation point, where
  ue = 0 by definition. The nose is then interpolated between the innermost
  station on each side rather than extrapolated off the end of one, and Cp
  reaches exactly 1 at stagnation without that being imposed — including the fact
  that stagnation sits on the lower surface at positive incidence, not at the nose.
• The stagnation point goes in as its own knot, where the two innermost stations
  interpolate linearly to zero. That placement is the stagnation-point-flow result,
  not a fit, and it stops the cubic guessing the region's width from two distant
  samples.
• The trailing edge takes the mean of the two surfaces' extrapolated speeds — Kutta.
• Between stations, a shape-preserving monotone cubic (FritschButland), the family
  NeuralFoil's own training pipeline resamples XFoil boundary layers with.

neuralfoil_section now also returns ue_upper/ue_lower.

No new dependencies; FritschButlandMonotonicInterpolation is in Interpolations.

Honest limits

The lift integral loses about a point (Cl_int 0.934 → 0.919 against a reported
0.949), and on smooth sections whose true drag is small the traction integral now
overshoots (0.027 against 0.009) rather than coming out negative. Both are much
smaller than the sign inversion they replace, but they are real.

This changes nothing about NeuralFoil's integrated CL/CD/CM, only the
distribution reconstructed on the contour — which matters to anything integrating
the surface traction, e.g. a structural coupling.

Not verified locally

Both changed files parse and the reconstruction was exercised against XFoil on four
SK100 section variants. The suite is left to CI.

🤖 Generated with Claude Code

[codecov]

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