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| <Head> |
| <Title>Boost Graph Library: Chrobak-Payne Straight Line Drawing</Title> |
| <BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b" |
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| <IMG SRC="../../../boost.png" |
| ALT="C++ Boost" width="277" height="86"> |
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| <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> |
