a vector of (oriented) edges giving the boundary in the correct order

the set of vertices

Forced version of turnLeft, for geodesics and edgepaths

Forced version of turnRight, for geodesics and edgepaths

Forced version of slightLeft, for geodesics and edgepaths

Forced version of slightRight, for geodesics and edgepaths

Forced swivelLeft, for geodesics and edgepaths

Forced swivelRight, for geodesics and edgepaths

Given a set of edges eds gives the TwoComplex got by adding eds and there flips to the existing twoComplex.

Given a set of faces fcs gives the TwoComplex got by adding fcs to the existing twoComplex.

Gives the result of adding the given set of twocomplexes to the existing one.

Given a set of vertices vs gives the TwoComplex got by adding vs to the existing twoComplex. If vs is already inside gives the same twoComplex

all edges to the left of the edge e including itself

all edges to the left of the edge e including itself

Given two edges e1 and e2 says what is the angle between them. Where angle is the number of turns to reach e2 from e1. Left turns are considered positive and right turns are considered negative. For this method to work both e1 and e2 need to end at the same vertex

Finds the connected component of a vertex

The degree of a vertex

the boundary as a formal sum

Occurences of edges in faces, counting multiplicity

the set of edges

set of all edges ending at v

Checks if the complex is connected

Checks if the given edge is at the boundary. That is exactly one of e and e.flip is inside a face of the twocomplex

Checks if the twoComplex is a surface with boundary

auxilliary function to start with an edge and take all edges by rotating left

given an edge, find a face whose boundary contains e (if it exists, it is unique); take the previous edge along the boundary

gives the edge with same terminal vertex obtained by left rotation.

gives the edge with same terminal vertex obtained by right rotation.

Given e rotates left twice and flips it. This is same as rotating left once and then taking the successor.

Given e takes two right rotations and flips it.

Given a set of vertices gives the subcomplex on the vertices

given an edge, find a face whose boundary contains e (if it exists, it is unique); take the next edge along the boundary

checks if we start with an edge e with v == e.terminal, using left rotations, (by iterating) we should get all edges with terminal vertex v. The naming is slightly misleading. Do give suggestions for better names

Gives the succeeding edge associated to a previous edge and a turning index

Gives the designated index (1 L, 2 SL, -1 R, -2 SR, higher values by turn distance) associated to a turn

Turns left in an EdgePath

Turns right in an EdgePath

Vector of edges to the left of an edge

Vector of edges to the right of an edge

Vector of flips of edges to the left of an edge

Vector of edges related by a function opt to an edge, modified version of orbit

Vector of flips of edges to the right of an edge

Finds neighbours of a vertex