Function fit_polyline 

pub fn fit_polyline(
    points: &[Vec3],
    tolerance: f64,
    maximum_points: usize,
    local_interpolation: bool,
) -> Result<PolylineFit, String>

Interpolate a curve through a polyline and REFINE it until the curve itself is within tolerance of that polyline.

tolerance is the deviation the RESULT must reach; maximum_points is where the station ladder STARTS, not where it ends. Rung zero is exactly the fit this routine returned before the ladder existed — same simplification, same conditioning, same decimation, same parameters — so a section that already met its tolerance returns the identical curve, to the bit. Only a MEASURED miss spends anything: the budget doubles, each rung is measured, and the best is kept, up to MAX_FIT_STATIONS or the input’s own station count.

Where it cannot get there it says so, in PolylineFit::report, rather than returning silently — the interpolant becomes a trim boundary and every mass property downstream is read off it, so “within a step of the marched points” is not good enough. This is the same contract offset::fold_locus::fit_locus_pcurve already keeps for a traced locus and crate::PcurveFitReport for a pcurve.

THE LANE IS ALSO MEASURED. local_interpolation is the lane the ladder STARTS in, not the lane that is returned: where the caller’s own ladder ends unmet, the other lane’s ladder is run on the same input and the better MEASURED result is returned. Neither lane wins in general and the two fail differently — measured on the exact-circle bench and the kink bench below:

• on a SMOOTH section the global cubic converges at h⁴ and the local lane at h², so at the 96 stations offset_shell asks for the local lane delivers 286 control points 2.179e-3 from the input and the global one delivers 96 at 3.700e-6 — 589x better with a third of the controls, and the local lane cannot reach 1e-7 there at any station count;
• at a KINK — a rim through a corner — the local lane’s monotonicity limiter holds the corner where the global cubic rings across it: 8.377e-2 against 4.095e-1 at the same 32 stations, 4.9x.

So the flag is a caller’s PREFERENCE — which ladder is paid for first — and never a decision about which curve is delivered. offset_shell asks for the global lane since 2026-09-13 because its sections are mostly smooth and the global rungs are three times cheaper per station; its corner sections reach the local lane through this fallback instead. This is the same shape as degenerate_apex_frustum’s branch selection in geometry/analytic_surface/intersect.rs: a deterministic choice between two constructions on their measured error, never a tolerance, and it can only return the more accurate of the two.

Escape hatch: BREP_POLYLINE_FIT_REFINE=0 fits rung zero alone, for bisecting a moved number against the pre-ladder tree.