155 lines
5.0 KiB
HTML
155 lines
5.0 KiB
HTML
<HTML>
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<!-- Copyright 2007 Aaron Windsor
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt)
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-->
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<Head>
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<Title>Boost Graph Library: Chrobak-Payne Straight Line Drawing</Title>
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<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
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ALINK="#ff0000">
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<IMG SRC="../../../boost.png"
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ALT="C++ Boost" width="277" height="86">
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<BR Clear>
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<H1>Chrobak-Payne Straight Line Drawing</H1>
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<p>
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<pre>
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template<typename Graph,
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typename PlanarEmbedding,
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typename ForwardIterator,
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typename PositionMap,
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typename VertexIndexMap>
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void chrobak_payne_straight_line_drawing(const Graph& g,
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PlanarEmbedding perm,
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ForwardIterator ordering_begin,
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ForwardIterator ordering_end,
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PositionMap drawing,
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VertexIndexMap vm
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);
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</pre>
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<br>
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<p>
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A <i>straight line drawing</i> of a <a href="./planar_graphs.html#planar">
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planar graph</a> is a <a href="./planar_graphs.html#plane_drawing">plane
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drawing</a> where each edge is drawn using a straight line segment. Since all
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edges are line segments, the drawing is completely determined by the placement
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of vertices in the plane. <tt>chrobak_payne_straight_line_drawing</tt> uses an
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algorithm of Chrobak and Payne
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[<a href = "./bibliography.html#chrobakpayne95">71</a>]
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to form a straight
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line drawing of a planar graph by mapping all <i>n</i> vertices in a planar
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graph to integer coordinates in a <i>(2n - 4) x (n - 2)</i> grid.
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<center>
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<img src="./figs/straight_line_drawing.png">
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</center>
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<p>
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The input graph passed to <tt>chrobak_payne_straight_line_drawing</tt> must
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be a <a href="make_maximal_planar.html">maximal planar graph</a> with at least
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3 vertices. Self-loops and parallel edges are ignored by this function. Note
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that the restriction that the graph be maximal planar does not
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mean that this function can only draw maximal planar graphs (the graph pictured
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above is not maximal planar, for example). If you want to
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draw a graph <i>g</i>, you can create a copy <i>g'</i> of <i>g</i>, store a
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mapping <i>m</i> of vertices in <i>g'</i> to vertices in <i>g</i>,
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<a href="make_maximal_planar.html">triangulate</a> <i>g'</i>, and then send
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<i>g'</i> in as the input to <tt>chrobak_payne_straight_line_drawing</tt>. The
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drawing returned can then be applied to <i>g</i> using <i>m</i> to translate
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vertices from one graph to another, since <i>g</i> contains a subset of the
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edges in <i>g'</i>.
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<h3>Complexity</h3>
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If the vertex index map provides constant-time access to indices, this
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function takes time <i>O(n + m)</i> for a planar graph with <i>n</i> vertices
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and <i>m</i> edges. Note that
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in a simple planar graph with <i>f</i> faces, <i>m</i> edges, and <i>n</i>
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vertices, both <i>f</i> and <i>m</i> are <i>O(n)</i>.
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<H3>Where Defined</H3>
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<P>
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<a href="../../../boost/graph/chrobak_payne_drawing.hpp">
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<TT>boost/graph/chrobak_payne_drawing.hpp</TT>
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</a>
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<h3>Parameters</h3>
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IN: <tt>Graph& g</tt>
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<blockquote>
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An undirected graph. The graph type must be a model of <a
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href="VertexListGraph.html">Vertex List Graph</a>
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</blockquote>
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IN <tt>PlanarEmbedding embedding</tt>
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<blockquote>
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A <a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map
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</a> that models the <a href="PlanarEmbedding.html">PlanarEmbedding</a>
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concept.
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</blockquote>
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IN <tt>ForwardIterator</tt>
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<blockquote>
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A ForwardIterator that has <tt>value_type</tt> equal to
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<tt>graph_traits<Graph>::vertex_descriptor</tt>.
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</blockquote>
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OUT: <tt>PositionMap</tt>
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<blockquote>
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A <a href="../../property_map/doc/LvaluePropertyMap.html">Writable LValue Property
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Map</a> that models the Position Map concept. The Position Map concept requires
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that the value mapped to be an object that has members <tt>x</tt> and
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<tt>y</tt>. For example, if <tt>p</tt> models PositionMap and <tt>v</tt>
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is a vertex in the graph, <tt>p[v].x</tt> and <tt>p[v].y</tt> are valid
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expressions. The type of <tt>x</tt> and <tt>y</tt> must be implicitly
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convertable to <tt>std::size_t</tt>.
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</blockquote>
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IN: <tt>VertexIndexMap vm</tt>
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<blockquote>
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A <a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map
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</a> that maps vertices from <tt>g</tt> to distinct integers in the range
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<tt>[0, num_vertices(g) )</tt><br>
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<b>Default</b>: <tt>get(vertex_index,g)</tt><br>
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</blockquote>
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<H3>Example</H3>
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<P>
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<a href="../example/straight_line_drawing.cpp">
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<TT>examples/straight_line_drawing.cpp</TT>
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</a>
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<h3>See Also</h3>
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<p>
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<ul>
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<li> <a href="planar_graphs.html">Planar Graphs in the Boost Graph Library</a>
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<li> <a href="is_straight_line_drawing.html"><tt>is_straight_line_drawing</tt>
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</a>
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</ul>
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<br>
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<HR>
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Copyright © 2007 Aaron Windsor (<a href="mailto:aaron.windsor@gmail.com">
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aaron.windsor@gmail.com</a>)
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</BODY>
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</HTML>
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