Function elevation_chord_bound 

pub fn elevation_chord_bound(law: &ElevationLaw, a: f64, b: f64) -> Option<f64>

Certified bound on how far an elevation law strays from the chord of its heights over the plan-distance span [a, b]: sup |z(d) - L(d)|, L the straight line through (a, z(a)) and (b, z(b)).

This is the vertical half of flattening an elevated curve: (b - a)^2 / 8 * sup |z''| with z'' = k / cos^3 t for a curve in (d, z) of curvature k, bounded in closed form per law:

• polynomial: sum i (i - 1) |c_i| m^(i - 2), m = max(|a|, |b|);
• circular arc: 1 / (|R| cos^3 t), cos t least at the span end with the larger |sin t|, since sin t is linear in d;
• intrinsic: the curvature supremum over a certified arc-length span containing [s(a), s(b)], over the cube of the certified cos t floor there.

None – unbounded, never a guess – when the span is not finite, a piecewise seam lies strictly inside it (the grade may jump there), the span leaves a law’s domain, or the law or its curvature law is a family this function does not bound.