Module pole 

Degenerate edges restored where a face’s boundary crosses a pole.

Where closed_at_poles lays a straight run across every pole of a wire whose other joints all meet, this solves a wire whose joints also jump whole periods, and says which way round each pole is crossed.

Where a surface collapses a whole row of its chart to one point (a sphere’s pole, a cone’s apex), a boundary through that point arrives at the row at one parameter and leaves it at another. In space the two are the same place; in the chart they are a stretch of the row apart, and the edge that spans it is a degenerate one: no curve in space, a pcurve along the row. Without it the stretch is left to whoever reads the chart, and on a row that repeats it is ambiguous: the boundary of a sphere walking its seam up and down crosses each pole by a whole turn, which a reader taking the shortest way across reads as no turn at all, and the face meshes to nothing. check passes such a boundary, since its two ends meet on the surface.

Functions

pole_crossings

The wires of face whose crossings of poles a reader of the chart takes the wrong way, each paired with a rebuilt wire holding a degenerate edge across every pole it crosses; empty where none is.