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1 | <HTML> |
| 2 | <!-- Copyright 2007 Aaron Windsor | |
| 3 | ||
| 4 | Distributed under the Boost Software License, Version 1.0. | |
| 5 | (See accompanying file LICENSE_1_0.txt or copy at | |
| 6 | http://www.boost.org/LICENSE_1_0.txt) | |
| 7 | ||
| 8 | --> | |
| 9 | <Head> | |
| 10 | <Title>Boost Graph Library: make_maximal_planar</Title> | |
| 11 | <BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b" | |
| 12 | ALINK="#ff0000"> | |
| 13 | <IMG SRC="../../../boost.png" | |
| 14 | ALT="C++ Boost" width="277" height="86"> | |
| 15 | ||
| 16 | <BR Clear> | |
| 17 | ||
| 18 | <H1><tt>make_maximal_planar</tt></H1> | |
| 19 | ||
| 20 | <p> | |
| 21 | ||
| 22 | <pre> | |
| 23 | template <typename Graph, typename PlanarEmbedding, typename VertexIndexMap, typename EdgeIndexMap, typename AddEdgeVisitor> | |
| 24 | void make_maximal_planar(Graph& g, PlanarEmbedding embedding, VertexIndexMap vm, EdgeIndexMap em, AddEdgeVisitor vis); | |
| 25 | </pre> | |
| 26 | ||
| 27 | <p> | |
| 28 | A <a href="planar_graphs.html">planar graph</a> <i>G</i> is | |
| 29 | <i>maximal planar</i> if no additional edges (except parallel edges and | |
| 30 | self-loops) can be added to <i>G</i> without creating a non-planar graph. By | |
| 31 | <a href="planar_graphs.html#EulersFormula">Euler's formula</a>, a maximal | |
| 32 | planar graph on <i>n</i> vertices (<i>n > 2</i>) always has <i>3n - 6</i> edges | |
| 33 | and | |
| 34 | <i>2n - 4</i> faces. The input graph to <tt>make_maximal_planar</tt> must be a | |
| 35 | <a href="make_biconnected_planar.html">biconnected</a> planar graph with at | |
| 36 | least 3 vertices. | |
| 37 | <p> | |
| 38 | The default behavior of <tt>make_maximal_planar</tt> is to modify the graph | |
| 39 | <tt>g</tt> by calling <tt>add_edge(u,v,g)</tt> for every pair of vertices | |
| 40 | <i>(u,v)</i> where an edge needs to be added to make <tt>g</tt> maximal planar. | |
| 41 | This behavior can be overriden by providing a vistor as the | |
| 42 | <tt>AddEdgeVisitor</tt> parameter. The only requirement for an | |
| 43 | <tt>AddEdgeVisitor</tt> is that it define a member function with the following | |
| 44 | signature: | |
| 45 | <pre> | |
| 46 | template <typename Graph, typename Vertex> | |
| 47 | void visit_vertex_pair(Vertex u, Vertex v, Graph& g); | |
| 48 | </pre> | |
| 49 | This event point can also be used as a hook to update the underlying edge | |
| 50 | index map automatically as edges are added. See the | |
| 51 | documentation for the <a href="./AddEdgeVisitor.html">AddEdgeVisitor</a> | |
| 52 | concept for more information. | |
| 53 | ||
| 54 | <H3>Where Defined</H3> | |
| 55 | ||
| 56 | <P> | |
| 57 | <a href="../../../boost/graph/make_maximal_planar.hpp"> | |
| 58 | <TT>boost/graph/make_maximal_planar.hpp</TT> | |
| 59 | </a> | |
| 60 | ||
| 61 | <h3>Parameters</h3> | |
| 62 | ||
| 63 | IN/OUT: <tt>Graph& g</tt> | |
| 64 | ||
| 65 | <blockquote> | |
| 66 | An undirected graph. The graph type must be a model of <a | |
| 67 | href="VertexListGraph.html">Vertex List Graph</a>, <a | |
| 68 | href="IncidenceGraph.html">Incidence Graph</a>, and | |
| 69 | a <a href="MutableGraph.html">Mutable Graph</a><br> | |
| 70 | </blockquote> | |
| 71 | ||
| 72 | IN: <tt>PlanarEmbedding embedding</tt> | |
| 73 | ||
| 74 | <blockquote> | |
| 75 | A <a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map | |
| 76 | </a> that models the <a href="PlanarEmbedding.html">PlanarEmbedding</a> | |
| 77 | concept. | |
| 78 | </blockquote> | |
| 79 | ||
| 80 | IN: <tt>VertexIndexMap vm</tt> | |
| 81 | ||
| 82 | <blockquote> | |
| 83 | A <a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map | |
| 84 | </a> that maps vertices from <tt>g</tt> to distinct integers in the range | |
| 85 | <tt>[0, num_vertices(g) )</tt><br> | |
| 86 | <b>Default</b>: <tt>get(vertex_index,g)</tt><br> | |
| 87 | </blockquote> | |
| 88 | ||
| 89 | IN: <tt>EdgeIndexMap vm</tt> | |
| 90 | ||
| 91 | <blockquote> | |
| 92 | A <a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map | |
| 93 | </a> that maps edges from <tt>g</tt> to distinct integers in the range | |
| 94 | <tt>[0, num_edges(g) )</tt><br> | |
| 95 | <b>Default</b>: <tt>get(edge_index,g)</tt><br> | |
| 96 | </blockquote> | |
| 97 | ||
| 98 | IN: <tt>AddEdgeVisitor vis</tt> | |
| 99 | ||
| 100 | <blockquote> | |
| 101 | A model of <a href="AddEdgeVisitor.html">AddEdgeVisitor</a>.<br> | |
| 102 | <b>Default</b>: <tt>default_add_edge_visitor</tt>, a class defines | |
| 103 | <tt>visit_vertex_pair</tt> to dispatch its calls to <tt>add_edge</tt>. | |
| 104 | </blockquote> | |
| 105 | ||
| 106 | ||
| 107 | <h3>Complexity</h3> | |
| 108 | ||
| 109 | On a graph with <i>n</i> vertices and <i>m</i> edges, | |
| 110 | <tt>make_maximal_planar</tt> runs in time <i>O(n + m)</i> | |
| 111 | ||
| 112 | <H3>Example</H3> | |
| 113 | ||
| 114 | <P> | |
| 115 | <a href="../example/make_maximal_planar.cpp"> | |
| 116 | <TT>examples/make_maximal_planar.cpp</TT> | |
| 117 | </a> | |
| 118 | ||
| 119 | <h3>See Also</h3> | |
| 120 | ||
| 121 | <a href="planar_graphs.html">Planar Graphs in the Boost Graph Library</a> | |
| 122 | ||
| 123 | <br> | |
| 124 | <HR> | |
| 125 | Copyright © 2007 Aaron Windsor (<a href="mailto:aaron.windsor@gmail.com"> | |
| 126 | aaron.windsor@gmail.com</a>) | |
| 127 | </BODY> | |
| 128 | </HTML> |