Version 5.0 The LEDA User Manual

11.6 Planar Maps ( planar map )
1. Definition
An instance M of the data type planar map is the combinatorial embedding of a planar
graph, i.e., M is bidirected (for every edge (v, w) of M the reverse edge (w, v) is also in
M) and there is a planar embedding of M such that for every node v the ordering of the
edges in the adjacency list of v corresponds to the counter-clockwise ordering of these
edges around v in the embedding.
#include < LEDA/graph/planar map.h >
2. Creation
planar map M(const graph& G);
creates an instance M of type planar map and initializes it to the
planar map represented by the directed graph G.
Precondition: G represents a bidirected planar map, i.e. for every
edge (v, w) in G the reverse edge (w, v) is also in G and there is
a planar embedding of G such that for every node v the ordering
of the edges in the adjacency list of v corresponds to the counterclockwise
ordering of these edges around v in the embedding.
3. Operations
edge M.new edge(edge e1 , edge e2 )
inserts the edge e = (source(e 1 ), source(e 2 )) and its
reversal into M and returns e.
Precondition: e 1 and e 2 are bounding the same face
F .
The operation splits F into two new faces.
face M.del edge(edge e) deletes the edge e and its reversal from M. The two
faces adjacent to e are united to one new face which
is returned.
edge M.split edge(edge e) splits edge e = (v, w) and its reversal r = (w, v) into
edges (v, u), (u, w), (w, u), and (u, v). Returns the
edge (u, w).
node
M.new node(const list& el)
splits the face bounded by the edges in el by inserting
a new node u and connecting it to all source nodes
of edges in el.
Precondition: all edges in el bound the same face.
node M.new node(face f) splits face f into triangles by inserting a new node u
and connecting it to all nodes of f. Returns u.