curver.kernel.curvegraph.CurveGraph

class curver.kernel.curvegraph.CurveGraph(triangulation)

Bases: object

This represents the curve complex of a surface.

See [Bowditch08] and [Webb15] for many of the constants set during initialisation.

all_tight_geodesic_multicurves(a, b)

Return a set that contains all multicurves in any tight geodesic from a to b.

From the first half of Algorithm 4 of [BellWebb16].

distance(a, b)

Return the distance from a to b in the curve complex.

geodesic(a, b)

Return a geodesic in the curve complex from a to b.

The geodesic will always come from a tight geodesic. From Algorithm 5 of [BellWebb16].

quasiconvex(a, b)

Return a polynomial-sized K–quasiconvex subset of the curve complex that contains a and b.

From Algorithm 1 of [BellWebb16].

tight_geodesic(a, b)

Return a tight geodesic in the (multi)curve complex from a to b.

From the second half of Algorithm 4 of [BellWebb16].

tight_paths(a, b, length)

Return the set of all tight paths from a to b that are of the given length.

From Algorithm 3 of [BellWebb16].