Definition
An instance M of the data type planarmap 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 >
Creation
planar_map | M(const graph& G) | creates an instance M of type
planarmap 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 counter-clockwise ordering of these edges around v in the embedding. |
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. |
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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<edge>& 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. |
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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. |
list<edge> | M.triangulate() | triangulates all faces of M by inserting new edges. The list of inserted edges is returned. |
Implementation
Planar maps are implemented by parameterized directed graph. All operations take constant time, except for new_edge and del_edge which take time O(f ) where f is the number of edges in the created faces and triangulate and straight_line_embedding which take time O(n) where n is the current size (number of edges) of the planar map.