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