ceph/src/boost/libs/graph/doc/make_maximal_planar.html

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  10 <Title>Boost Graph Library: make_maximal_planar</Title>
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  18 <H1><tt>make_maximal_planar</tt></H1>
  19
  20 <p>
  21
  22 <pre>
  23 template &lt;typename Graph, typename PlanarEmbedding, typename VertexIndexMap, typename EdgeIndexMap, typename AddEdgeVisitor&gt;
  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 &lt;typename Graph, typename Vertex&gt;
  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&amp; 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 &copy; 2007 Aaron Windsor (<a href="mailto:aaron.windsor@gmail.com">
 126 aaron.windsor@gmail.com</a>)
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