Function cut_at_poles 

pub fn cut_at_poles(
    branch: Traced,
    a: &SurfaceGeometry,
    b: &SurfaceGeometry,
    reach: f64,
    tol: Tolerances,
) -> Vec<Traced>

A branch cut where it runs through a pole of either surface’s chart: the pieces between the poles, each ending on the pole, its image there on the line of the chart it arrives or leaves along.

At a pole the chart’s free parameter turns (half a turn round a sphere’s pole) where the curve does not, so no one image follows a curve through it: fitted whole, the image swings across the chart between two samples, or a loop closing on the pole joins two ends a half turn apart. A pole lying on the other surface, within the chord of the branch’s polyline, is a point of the section the branch passes through; it is put among the samples there (or a sample on it taken for it), and the branch cut. Each piece’s end on the pole is read on the line of the free parameter its curve leaves along, the section’s tangent there oriented into the piece.

reach is how far the pole may stand off the other surface and off the polyline and still be a point of the section: the march’s chord as it traces, or a fitted section’s stated tolerance where the fit passes the pole within it (see passes_a_pole).