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1 | <HTML> |
2 | <!-- Copyright 2007 Aaron Windsor | |
3 | ||
4 | Distributed under the Boost Software License, Version 1.0. | |
5 | (See accompanying file LICENSE_1_0.txt or copy at | |
6 | http://www.boost.org/LICENSE_1_0.txt) | |
7 | ||
8 | --> | |
9 | <Head> | |
10 | <Title>Boost Graph Library: Chrobak-Payne Straight Line Drawing</Title> | |
11 | <BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b" | |
12 | ALINK="#ff0000"> | |
13 | <IMG SRC="../../../boost.png" | |
14 | ALT="C++ Boost" width="277" height="86"> | |
15 | ||
16 | <BR Clear> | |
17 | ||
18 | <H1>Chrobak-Payne Straight Line Drawing</H1> | |
19 | ||
20 | <p> | |
21 | <pre> | |
22 | template<typename Graph, | |
23 | typename PlanarEmbedding, | |
24 | typename ForwardIterator, | |
25 | typename PositionMap, | |
26 | typename VertexIndexMap> | |
27 | void chrobak_payne_straight_line_drawing(const Graph& g, | |
28 | PlanarEmbedding perm, | |
29 | ForwardIterator ordering_begin, | |
30 | ForwardIterator ordering_end, | |
31 | PositionMap drawing, | |
32 | VertexIndexMap vm | |
33 | ); | |
34 | </pre> | |
35 | ||
36 | <br> | |
37 | <p> | |
38 | A <i>straight line drawing</i> of a <a href="./planar_graphs.html#planar"> | |
39 | planar graph</a> is a <a href="./planar_graphs.html#plane_drawing">plane | |
40 | drawing</a> where each edge is drawn using a straight line segment. Since all | |
41 | edges are line segments, the drawing is completely determined by the placement | |
42 | of vertices in the plane. <tt>chrobak_payne_straight_line_drawing</tt> uses an | |
43 | algorithm of Chrobak and Payne | |
44 | [<a href = "./bibliography.html#chrobakpayne95">71</a>] | |
45 | to form a straight | |
46 | line drawing of a planar graph by mapping all <i>n</i> vertices in a planar | |
47 | graph to integer coordinates in a <i>(2n - 4) x (n - 2)</i> grid. | |
48 | ||
49 | <center> | |
50 | <img src="./figs/straight_line_drawing.png"> | |
51 | </center> | |
52 | ||
53 | <p> | |
54 | The input graph passed to <tt>chrobak_payne_straight_line_drawing</tt> must | |
55 | be a <a href="make_maximal_planar.html">maximal planar graph</a> with at least | |
56 | 3 vertices. Self-loops and parallel edges are ignored by this function. Note | |
57 | that the restriction that the graph be maximal planar does not | |
58 | mean that this function can only draw maximal planar graphs (the graph pictured | |
59 | above is not maximal planar, for example). If you want to | |
60 | draw a graph <i>g</i>, you can create a copy <i>g'</i> of <i>g</i>, store a | |
61 | mapping <i>m</i> of vertices in <i>g'</i> to vertices in <i>g</i>, | |
62 | <a href="make_maximal_planar.html">triangulate</a> <i>g'</i>, and then send | |
63 | <i>g'</i> in as the input to <tt>chrobak_payne_straight_line_drawing</tt>. The | |
64 | drawing returned can then be applied to <i>g</i> using <i>m</i> to translate | |
65 | vertices from one graph to another, since <i>g</i> contains a subset of the | |
66 | edges in <i>g'</i>. | |
67 | ||
68 | ||
69 | ||
70 | <h3>Complexity</h3> | |
71 | ||
72 | If the vertex index map provides constant-time access to indices, this | |
73 | function takes time <i>O(n + m)</i> for a planar graph with <i>n</i> vertices | |
74 | and <i>m</i> edges. Note that | |
75 | in a simple planar graph with <i>f</i> faces, <i>m</i> edges, and <i>n</i> | |
76 | vertices, both <i>f</i> and <i>m</i> are <i>O(n)</i>. | |
77 | ||
78 | <H3>Where Defined</H3> | |
79 | ||
80 | <P> | |
81 | <a href="../../../boost/graph/chrobak_payne_drawing.hpp"> | |
82 | <TT>boost/graph/chrobak_payne_drawing.hpp</TT> | |
83 | </a> | |
84 | ||
85 | ||
86 | <h3>Parameters</h3> | |
87 | ||
88 | IN: <tt>Graph& g</tt> | |
89 | ||
90 | <blockquote> | |
91 | An undirected graph. The graph type must be a model of <a | |
92 | href="VertexListGraph.html">Vertex List Graph</a> | |
93 | </blockquote> | |
94 | ||
95 | IN <tt>PlanarEmbedding embedding</tt> | |
96 | ||
97 | <blockquote> | |
98 | A <a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map | |
99 | </a> that models the <a href="PlanarEmbedding.html">PlanarEmbedding</a> | |
100 | concept. | |
101 | </blockquote> | |
102 | ||
103 | IN <tt>ForwardIterator</tt> | |
104 | ||
105 | <blockquote> | |
106 | A ForwardIterator that has <tt>value_type</tt> equal to | |
107 | <tt>graph_traits<Graph>::vertex_descriptor</tt>. | |
108 | </blockquote> | |
109 | ||
110 | OUT: <tt>PositionMap</tt> | |
111 | ||
112 | <blockquote> | |
113 | A <a href="../../property_map/doc/LvaluePropertyMap.html">Writable LValue Property | |
114 | Map</a> that models the Position Map concept. The Position Map concept requires | |
115 | that the value mapped to be an object that has members <tt>x</tt> and | |
116 | <tt>y</tt>. For example, if <tt>p</tt> models PositionMap and <tt>v</tt> | |
117 | is a vertex in the graph, <tt>p[v].x</tt> and <tt>p[v].y</tt> are valid | |
118 | expressions. The type of <tt>x</tt> and <tt>y</tt> must be implicitly | |
119 | convertable to <tt>std::size_t</tt>. | |
120 | </blockquote> | |
121 | ||
122 | IN: <tt>VertexIndexMap vm</tt> | |
123 | ||
124 | <blockquote> | |
125 | A <a href="../../property_map/doc/ReadablePropertyMap.html">Readable Property Map | |
126 | </a> that maps vertices from <tt>g</tt> to distinct integers in the range | |
127 | <tt>[0, num_vertices(g) )</tt><br> | |
128 | <b>Default</b>: <tt>get(vertex_index,g)</tt><br> | |
129 | </blockquote> | |
130 | ||
131 | ||
132 | ||
133 | <H3>Example</H3> | |
134 | ||
135 | <P> | |
136 | <a href="../example/straight_line_drawing.cpp"> | |
137 | <TT>examples/straight_line_drawing.cpp</TT> | |
138 | </a> | |
139 | ||
140 | <h3>See Also</h3> | |
141 | ||
142 | <p> | |
143 | <ul> | |
144 | <li> <a href="planar_graphs.html">Planar Graphs in the Boost Graph Library</a> | |
145 | <li> <a href="is_straight_line_drawing.html"><tt>is_straight_line_drawing</tt> | |
146 | </a> | |
147 | </ul> | |
148 | ||
149 | <br> | |
150 | <HR> | |
151 | Copyright © 2007 Aaron Windsor (<a href="mailto:aaron.windsor@gmail.com"> | |
152 | aaron.windsor@gmail.com</a>) | |
153 | </BODY> | |
154 | </HTML> |