boost-react-native-bundle

<html><head><title>Boost Graph Library: Planar Canonical Ordering</title> </head> <body alink="#ff0000" bgcolor="#ffffff" link="#0000ee" text="#000000" vlink="#551a8b"> <img src="../../../boost.png" alt="C++ Boost" height="86" width="277"> <h1>Planar Canonical Ordering</h1> <pre>template <typename Graph, typename PlanarEmbedding, typename OutputIterator, typename VertexIndexMap> void planar_canonical_ordering(const Graph& g, PlanarEmbedding embedding, OutputIterator ordering, VertexIndexMap vm); </pre> A planar canonical ordering is an ordering v1, v2, ..., vn of the vertices of a <a href="make_maximal_planar.html">maximal</a> <a href="planar_graphs.html">planar</a> graph having the property that, for each k, 3 <= k < n, the graph induced by v1, v2, ..., vk <ul> <li>is biconnected and contains the edge {v1, v2} on its outer face. </li><li>has any vertices in the range v1, v2, ..., vk that are adjacent to v(k+1) on its outer face, and these vertices form a path along the outer face. </li></ul> Let Gk be the graph induced by the first k vertices in the canonical ordering, along with all edges between any of the first k vertices. After Gk has been drawn, the (k+1)st vertex can be drawn easily without edge crossings, since it's adjacent only to a consecutive sequence of vertices on the outer face of Gk. <blockquote> <center> <img src="./figs/canonical_ordering.png"> </center> </blockquote> A planar canonical ordering exists for every maximal planar graph with at least 2 vertices. <tt>planar_canonical_ordering</tt> expects the input graph to have at least 2 vertices. The planar canonical ordering is used as an input in some planar graph drawing algorithms, particularly those that create a straight line embedding. de Fraysseix, Pach, and Pollack [<a href="./bibliography.html#defraysseixpachpollack90">72</a>] first proved the existence of such an ordering and showed how to compute one in time O(n) on a maximal planar graph with n vertices. <h3>Complexity</h3> If the vertex index map provides constant-time access to indices, this function takes time O(n + m) for a planar graph with n vertices and m edges. Note that in a simple planar graph with f faces, m edges, and n vertices, both f and m are O(n). <h3>Where Defined</h3> <a href="../../../boost/graph/planar_canonical_ordering.hpp"> <tt>boost/graph/planar_canonical_ordering.hpp</tt></a> <h3>Parameters</h3> IN: <tt>Graph& g</tt> <blockquote> An undirected graph. The graph type must be a model of <a href="VertexAndEdgeListGraph.html">VertexAndEdgeListGraph</a>. The graph must: <ul> <li>Be maximal planar.</li> <li>Have at least two vertices.</li> </ul> </blockquote> IN: <tt>PlanarEmbedding</tt> <blockquote> A model of <a href="PlanarEmbedding.html">PlanarEmbedding</a>. </blockquote> IN: <tt>OutputIterator</tt> <blockquote> An OutputIterator with <tt>value_type</tt> equal to <tt>graph_traits<Graph>::vertex_descriptor</tt>. The canonical ordering will be written to this iterator. </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> Default: <tt>get(vertex_index,g)</tt> </blockquote> <h3>Example</h3> <a href="../example/canonical_ordering.cpp"> <tt>examples/canonical_ordering.cpp</tt></a> <h3>See Also</h3> <a href="planar_graphs.html">Planar Graphs in the Boost Graph Library</a> <hr> Copyright � 2007 Aaron Windsor (<a href="mailto:aaron.windsor@gmail.com"> aaron.windsor@gmail.com</a>) </body></html>