<HTML> <!-- Copyright 2007 Aaron Windsor Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) --> <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>