Function hagan_west_integral 

fn hagan_west_integral<R: Scalar>(g0: R, g1: R, x: f64) -> R

∫₀ˣ G, where G is Hagan-West’s shape function on one segment with G(0) = g0, G(1) = g1 and ∫₀¹ G = 0.

The four branches are the paper’s regions: the plain quadratic where it is already monotone, and three repairs that flatten part of the segment and bend the rest, meeting at an interior break η. The region is chosen on the passive g0, g1; the chosen region, its break included, is evaluated in the mode.