closure

Closure of an open knot (knotoid).

Provides underpass, overpass, and double-sided (over+under) closures by routing a path through faces in the dual planar diagram.

closure(k, over=False, under=False)

Close a knotoid by routing through the dual graph between its two degree-1 vertices.

You must choose at least one of over or under. If both are True, a double-sided closure is performed (one overpass and one underpass).

Parameters:

• k (PlanarDiagram) – Planar diagram with exactly two leaves (degree-1 vertices).

• over (bool) – Use overpass closure.

• under (bool) – Use underpass closure.

Returns:

A new PlanarDiagram with the chosen closure applied.

Raises:

• ValueError – If neither over nor under is selected.

• ValueError – If the diagram does not have exactly two leaves.

Return type:

PlanarDiagram