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<Title>Boost Graph Library: make_maximal_planar</Title>
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<H1><tt>make_maximal_planar</tt></H1>

<p>

<pre>
template &lt;typename Graph, typename PlanarEmbedding, typename VertexIndexMap, typename EdgeIndexMap, typename AddEdgeVisitor&gt;
void make_maximal_planar(Graph& g, PlanarEmbedding embedding, VertexIndexMap vm, EdgeIndexMap em, AddEdgeVisitor vis);
</pre>

<p>
A <a href="planar_graphs.html">planar graph</a> <i>G</i> is 
<i>maximal planar</i> if no additional edges (except parallel edges and 
self-loops) can be added to <i>G</i> without creating a non-planar graph. By 
<a href="planar_graphs.html#EulersFormula">Euler's formula</a>, a maximal
planar graph on <i>n</i> vertices (<i>n > 2</i>) always has <i>3n - 6</i> edges
 and 
<i>2n - 4</i> faces. The input graph to <tt>make_maximal_planar</tt> must be a 
<a href="make_biconnected_planar.html">biconnected</a> planar graph with at 
least 3 vertices.
<p>
The default behavior of <tt>make_maximal_planar</tt> is to modify the graph 
<tt>g</tt> by calling <tt>add_edge(u,v,g)</tt> for every pair of vertices 
<i>(u,v)</i> where an edge needs to be added to make <tt>g</tt> maximal planar.
This behavior can be overriden by providing a vistor as the 
<tt>AddEdgeVisitor</tt> parameter. The only requirement for an 
<tt>AddEdgeVisitor</tt> is that it define a member function with the following 
signature:
<pre>
template &lt;typename Graph, typename Vertex&gt;
void visit_vertex_pair(Vertex u, Vertex v, Graph& g);
</pre>
This event point can also be used as a hook to update the underlying edge
index map automatically as edges are added. See the 
documentation for the <a href="./AddEdgeVisitor.html">AddEdgeVisitor</a> 
concept for more information.

<H3>Where Defined</H3>

<P>
<a href="../../../boost/graph/make_maximal_planar.hpp">
<TT>boost/graph/make_maximal_planar.hpp</TT>
</a>

<h3>Parameters</h3>

IN/OUT: <tt>Graph&amp; g</tt>

<blockquote>
An undirected graph. The graph type must be a model of <a
href="VertexListGraph.html">Vertex List Graph</a>, <a
href="IncidenceGraph.html">Incidence Graph</a>, and
a <a href="MutableGraph.html">Mutable Graph</a><br>
</blockquote>

IN: <tt>PlanarEmbedding embedding</tt>

<blockquote>
A <a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map
</a> that models the <a href="PlanarEmbedding.html">PlanarEmbedding</a> 
concept.
</blockquote>

IN: <tt>VertexIndexMap vm</tt>

<blockquote>
A <a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map
</a> that maps vertices from <tt>g</tt> to distinct integers in the range 
<tt>[0, num_vertices(g) )</tt><br>
<b>Default</b>: <tt>get(vertex_index,g)</tt><br>
</blockquote>

IN: <tt>EdgeIndexMap vm</tt>

<blockquote>
A <a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map
</a> that maps edges from <tt>g</tt> to distinct integers in the range 
<tt>[0, num_edges(g) )</tt><br>
<b>Default</b>: <tt>get(edge_index,g)</tt><br>
</blockquote>

IN: <tt>AddEdgeVisitor vis</tt>

<blockquote>
A model of <a href="AddEdgeVisitor.html">AddEdgeVisitor</a>.<br>
<b>Default</b>: <tt>default_add_edge_visitor</tt>, a class defines 
<tt>visit_vertex_pair</tt> to dispatch its calls to <tt>add_edge</tt>.
</blockquote>


<h3>Complexity</h3>

On a graph with <i>n</i> vertices and <i>m</i> edges, 
<tt>make_maximal_planar</tt> runs in time <i>O(n + m)</i>

<H3>Example</H3>

<P>
<a href="../example/make_maximal_planar.cpp">
<TT>examples/make_maximal_planar.cpp</TT>
</a>

<h3>See Also</h3>

<a href="planar_graphs.html">Planar Graphs in the Boost Graph Library</a>

<br>
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Copyright &copy; 2007 Aaron Windsor (<a href="mailto:aaron.windsor@gmail.com">
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