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| <Head> |
| <Title>Boost Graph Library: make_maximal_planar</Title> |
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| |
| <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>) |
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