Function refine_crossing 

pub fn refine_crossing(
    curve: &NurbCurve<4>,
    surface: &NurbSurface<4>,
    t: Scalar,
    uv: Vector2,
) -> (Scalar, Vector2)

Polish one isolated (t, uv) — as returned by curve_surface_intersect — by Newton on C(t) - Scalar(u, v) = 0, three equations in the three unknowns t, u, v (newton::refine).

curve_surface_intersect deliberately does not apply this to everything it returns — most callers only need to know where and how many crossings there are, and refining changes results they already agree with. Call it when the parameter is about to be used as a split point, where the width genuinely matters: a point evaluated at a wide crossing is just as wide, which is how it becomes a fat vertex and a fat sub-curve.

The refined box must still be able to hold a crossing: the curve and the surface evaluated over it have to overlap. Newton only assumes an isolated, regular root; where that fails — a curve lying on the surface’s extension beyond the patch, so the iterate slides along it and gets clamped at the patch’s edge — it can return a narrow box that provably misses, and the honest incoming box is what is kept.