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- <Head>
- <Title>Boost Graph Library: make_maximal_planar</Title>
- <BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
- ALINK="#ff0000">
- <IMG SRC="../../../boost.png"
- ALT="C++ Boost" width="277" height="86">
- <BR Clear>
- <H1><tt>make_maximal_planar</tt></H1>
- <p>
- <pre>
- template <typename Graph, typename PlanarEmbedding, typename VertexIndexMap, typename EdgeIndexMap, typename AddEdgeVisitor>
- 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 <typename Graph, typename Vertex>
- 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& 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>
- <HR>
- Copyright © 2007 Aaron Windsor (<a href="mailto:aaron.windsor@gmail.com">
- aaron.windsor@gmail.com</a>)
- </BODY>
- </HTML>
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