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- <Head>
- <Title>Boost Graph Library: make_biconnected_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_biconnected_planar</tt></H1>
- <p>
- <pre>
- template <typename Graph, typename PlanarEmbedding, typename EdgeIndexMap, typename AddEdgeVisitor>
- void make_biconnected_planar(Graph& g, PlanarEmbedding embedding, EdgeIndexMap em, AddEdgeVisitor& vis);
- </pre>
- <p>
- A graph <i>G</i> is biconnected if, for every pair of vertices <i>u,v</i> in
- <i>G</i>, there is a cycle containing both <i>u</i> and <i>v</i>.
- Alternatively, a graph is biconnected if it is connected and cannot be made
- disconnected by removing any single vertex. <tt>make_biconnected_planar</tt>
- takes a <a href="./make_connected.html">connected</a>
- <a href="planar_graphs.html">planar</a> graph <tt>g</tt> as input and adds zero
- or more edges to make <tt>g</tt> biconnected while preserving planarity.
- <p>
- The default behavior of <tt>make_biconnected_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>
- biconnected. 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_biconnected_planar.hpp">
- <TT>boost/graph/make_biconnected_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 model of <a href="PlanarEmbedding.html">PlanarEmbedding</a>.
- </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</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 planar graph with <i>n</i> vertices, <tt>make_biconnected_planar</tt>
- runs in time <i>O(n)</i>
- <H3>Example</H3>
- <P>
- <a href="../example/make_biconnected_planar.cpp">
- <TT>examples/make_biconnected_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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