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  <title>Boost Polygon Library: Polygon 45 Concept</title>
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      <div style="padding: 5px;" align="center"> <img
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      <div style="margin: 5px;">
      <h3 class="navbar">Contents</h3>
      <ul>
        <li><a href="index.htm">Boost.Polygon Main Page</a></li>
        <li><a href="gtl_design_overview.htm">Design Overview</a></li>
        <li><a href="gtl_isotropy.htm">Isotropy</a></li>
        <li><a href="gtl_coordinate_concept.htm">Coordinate Concept</a></li>
        <li><a href="gtl_interval_concept.htm">Interval Concept</a></li>
        <li><a href="gtl_point_concept.htm">Point Concept</a></li>
        <li><a href="gtl_segment_concept.htm">Segment Concept</a></li>
        <li><a href="gtl_rectangle_concept.htm">Rectangle Concept</a></li>
        <li><a href="gtl_polygon_90_concept.htm">Polygon 90 Concept</a></li>
        <li><a href="gtl_polygon_90_with_holes_concept.htm">Polygon 90
With Holes Concept</a></li>
        <li>Polygon 45 Concept</li>
        <li><a href="gtl_polygon_45_with_holes_concept.htm">Polygon 45
With Holes Concept</a></li>
        <li><a href="gtl_polygon_concept.htm">Polygon Concept</a></li>
        <li><a href="gtl_polygon_with_holes_concept.htm">Polygon With
Holes Concept</a></li>
        <li><a href="gtl_polygon_90_set_concept.htm">Polygon 90 Set
Concept</a></li>
        <li><a href="gtl_polygon_45_set_concept.htm">Polygon 45 Set
Concept</a></li>
        <li><a href="gtl_polygon_set_concept.htm">Polygon Set Concept</a></li>
        <li><a href="gtl_connectivity_extraction_90.htm">Connectivity
Extraction 90</a></li>
        <li><a href="gtl_connectivity_extraction_45.htm">Connectivity
Extraction 45</a></li>
        <li><a href="gtl_connectivity_extraction.htm">Connectivity
Extraction</a></li>
        <li><a href="gtl_property_merge_90.htm">Property Merge 90</a></li>
        <li><a href="gtl_property_merge_45.htm">Property Merge 45</a></li>
        <li><a href="gtl_property_merge.htm">Property Merge</a></li>
        <li><a href="voronoi_main.htm">Voronoi Main Page<br />
          </a></li>
        <li><a href="voronoi_benchmark.htm">Voronoi Benchmark</a><br />
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        <li><a href="voronoi_builder.htm">Voronoi Builder</a></li>
        <li><a href="voronoi_diagram.htm">Voronoi Diagram</a></li>
      </ul>
      <h3 class="navbar">Other Resources</h3>
      <ul>
        <li><a href="GTL_boostcon2009.pdf">GTL Boostcon 2009 Paper</a></li>
        <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
Presentation</a></li>
        <li><a href="analysis.htm">Performance Analysis</a></li>
        <li><a href="gtl_tutorial.htm">Layout Versus Schematic Tutorial</a></li>
        <li><a href="gtl_minkowski_tutorial.htm">Minkowski Sum Tutorial</a></li>
        <li><a href="voronoi_basic_tutorial.htm">Voronoi Basic Tutorial</a></li>
        <li><a href="voronoi_advanced_tutorial.htm">Voronoi Advanced
Tutorial</a></li>
      </ul>
      </div>
      <h3 class="navbar">Polygon Sponsor</h3>
      <div style="padding: 5px;" align="center"> <img
 src="images/intlogo.gif" border="0" height="51" width="127" /><a
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<!-- End Header --><br />
      <p>
      </p>
      <h1>Polygon 45 Concept</h1>
      <p> </p>
      <p>The polygon_45 concept tag is <font face="Courier New">
polygon_45_concept</font></p>
      <p> To register a user defined type as a model of <font
 face="Times New Roman">polygon_45 </font>concept, specialize the
geometry concept meta-function for that type.&nbsp; In the example
below CPolygon45 is registered as a model of polygon_45&nbsp; concept.</p>
      <p> <font face="Courier New">template &lt;&gt;<br />
struct geometry_concept&lt;CPolygon45&gt; { typedef polygon_45_concept
type; };</font></p>
      <p> <font face="Times New Roman">The semantic of a polygon_45 is
that it can provide iterators over the points that represent its
vertices, angles formed as these vertices must be multiple of 45-degree
relative to the coordinate axis.&nbsp; It is acceptable to have the
last edge explict with the first and last point equal to each other or
implied by this segement that would connect the first and last
point.&nbsp; A mutable polygon_45 must also be able to set its geometry
based on an interator range over such points.&nbsp;&nbsp; A
std::vector&lt;point_data&lt;int&gt; &gt; or
std::list&lt;point_data&lt;int&gt; &gt; could be made models of
polygon_45_concept by simply providing access to their iterators
through traits.&nbsp; Library functions that create polygon objects
require that those objects provide a default constructor.</font></p>
      <p> <font face="Times New Roman">Below is shown the default
polygon traits.&nbsp; Specialization of these traits is required for
types that don't conform to the default behavior.&nbsp; Note that these
traits are also used by several other polygon concepts through SFINAE
enable template parameter.&nbsp; The SFINAE enable parameter also
allows the library to provide default specialization that work for any
object that models the 90 degree polygon concepts.</font></p>
      <p><font face="Courier New">template &lt;typename T, typename
enable = gtl_yes&gt;<br />
struct polygon_traits {};<br />
      <br />
template &lt;typename T&gt;<br />
struct polygon_traits&lt;T, <br />
&nbsp; typename gtl_or_4&lt;<br />
&nbsp;&nbsp;&nbsp; typename gtl_same_type&lt;typename
geometry_concept&lt;T&gt;::type, polygon_concept&gt;::type,<br />
&nbsp;&nbsp;&nbsp; typename gtl_same_type&lt;typename
geometry_concept&lt;T&gt;::type, polygon_45_concept&gt;::type,<br />
&nbsp;&nbsp;&nbsp; typename gtl_same_type&lt;typename
geometry_concept&lt;T&gt;::type, polygon_with_holes_concept&gt;::type,<br />
&nbsp;&nbsp;&nbsp; typename gtl_same_type&lt;typename
geometry_concept&lt;T&gt;::type, polygon_45_with_holes_concept&gt;::type<br />
&nbsp; &gt;::type&gt; {<br />
&nbsp;&nbsp;&nbsp;&nbsp; typedef typename T::coordinate_type
coordinate_type;<br />
&nbsp;&nbsp;&nbsp;&nbsp; typedef typename T::iterator_type
iterator_type;<br />
&nbsp;&nbsp;&nbsp;&nbsp; typedef typename T::point_type point_type;<br />
&nbsp;&nbsp;&nbsp;&nbsp; static inline iterator_type begin_points(const
T&amp; t) {<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return t.begin();<br />
&nbsp;&nbsp;&nbsp;&nbsp; }<br />
&nbsp;&nbsp;&nbsp;&nbsp; static inline iterator_type end_points(const
T&amp; t) {<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return t.end();<br />
&nbsp;&nbsp;&nbsp;&nbsp; }<br />
&nbsp;&nbsp;&nbsp;&nbsp; static inline unsigned int size(const T&amp;
t) {<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return t.size();<br />
&nbsp;&nbsp;&nbsp;&nbsp; }<br />
&nbsp;&nbsp;&nbsp;&nbsp; static inline winding_direction winding(const
T&amp; t) {<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return
unknown_winding;<br />
&nbsp;&nbsp;&nbsp;&nbsp; }<br />
};</font></p>
      <p><font face="Courier New">template &lt;typename T, typename
enable = void&gt;<br />
struct polygon_mutable_traits {<br />
&nbsp;&nbsp;&nbsp;&nbsp; template &lt;typename iT&gt;<br />
&nbsp;&nbsp;&nbsp;&nbsp; static inline T&amp; set_points(T&amp; t, iT
input_begin, iT input_end) {<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
t.set(input_begin, input_end);<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return t;<br />
&nbsp;&nbsp;&nbsp;&nbsp; }<br />
};</font></p>
      <p>An object that is a model of <font face="Courier New">
polygon_45_concept</font> can be viewed as a model of any of its
refinements if it is determined at runtime to conform to the
restriction of those concepts.&nbsp; This concept casting is
accomplished through the
      <font face="Courier New">view_as&lt;&gt;()</font> function.</p>
      <p><font face="Courier New">view_as&lt;rectangle_concept&gt;(polygon_45_object)</font><br />
      <font face="Courier New">view_as&lt;polygon_90_concept&gt;(polygon_45_object)</font></p>
      <p>The return value of <font face="Courier New">view_as&lt;&gt;()</font>
can be passed into any interface that expects an object of the
conceptual type specified in its template parameter.</p>
      <h2>Functions</h2>
      <table id="table1" border="1" width="100%">
        <tbody>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename T&gt;<br />
point_iterator_type <b>begin_points</b>(const T&amp; polygon)</font></td>
            <td><font face="Times New Roman">Expects a model of
polygon_45.&nbsp; Returns the begin iterator over the range of points
that correspond to vertices of the polygon.</font></td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename T&gt;<br />
point_iterator_type <b>end_points</b>(const T&amp; polygon)</font></td>
            <td><font face="Times New Roman">Expects a model of
polygon_45.&nbsp; Returns the end iterator over the range of points
that correspond to vertices of the polygon.</font></td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename T, typename iterator&gt;<br />
void <b>set_points</b>(T&amp; polygon, iterator b, iterator e)</font></td>
            <td><font face="Times New Roman">Expects a model of
polygon_45.&nbsp;&nbsp; Sets the polygon to the point data range [b,e)
that corresponds to vertices of a polygon.&nbsp; Non-45 edges between
successive input points is disallowed.</font></td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename T&gt;<br />
unsigned int <b>size</b>(const T&amp; polygon)</font></td>
            <td><font face="Times New Roman">Returns the number of
edges in the polygon.</font></td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename T1, typename T2&gt;<br />
T1&amp; <b>assign</b>(T1&amp; left, const T2&amp; right)</font></td>
            <td>Copies data from right object that models polygon_45
into left object that models polygon_45.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename T, typename point_type&gt;<br />
bool <b>contains</b>(const T&amp;, const point_type&amp; point, <br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
bool consider_touch=true)</font></td>
            <td>Given an object that models polygon_45 and an object
that models point, returns true if the polygon contains the
point.&nbsp; If the consider_touch flag is true will return true if the
point lies along the boundary of the polygon.&nbsp; Linear wrt.
vertices.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">// get the center
coordinate<br />
template &lt;typename T, typename point_type&gt;<br />
void <b>center</b>(point_type&amp; p, const T&amp; polygon)</font></td>
            <td>Sets object that models point to the center point of
the bounding box of an object that models polygon_45.&nbsp; Linear wrt.
vertices.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename T, typename rectangle_type&gt;<br />
bool <b>extents</b>(rectangle_type&amp; bbox, const T&amp; polygon)</font></td>
            <td>Sets object that models rectangle to the bounding box
of an object that models polygon_45 and returns true.&nbsp; Returns
false and leaves bbox unchanged if polygon is empty.&nbsp; Linear wrt.
vertices.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename T&gt;<br />
area_type <b>area</b>(const T&amp; polygon)</font></td>
            <td>Returns the area of an object that models
polygon_45.&nbsp; Linear wrt. vertices.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename T&gt;<br />
direction_1d <b>winding</b>(const T&amp; polygon)</font></td>
            <td>Returns the winding direction of an object that models
polygon_45, LOW == CLOCKWISE, HIGH = COUNTERCLOCKWISE.&nbsp; Complexity
depends upon winding trait.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename T&gt;<br />
coordinate_distance <b>perimeter</b>(const T&amp; polygon)</font></td>
            <td>Returns the perimeter length of an object that models
polygon_45.&nbsp; Linear wrt. vertices.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename T, typename transform_type&gt;<br />
T&amp; <b>transform</b>(T&amp; polygon, const transform_type&amp;)</font></td>
            <td>Applies transform() on the vertices of polygon and sets
the polygon to that described by the result of transforming its
vertices.&nbsp; Linear wrt. vertices.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename T&gt;<br />
T&amp; <b>scale_up</b>(T&amp; polygon, unsigned_area_type factor)</font></td>
            <td>Scales up coordinate of an object that models
polygon_45 by unsigned factor.&nbsp; Linear wrt. vertices.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename T&gt;<br />
T&amp; <b>scale_down</b>(T&amp; polygon, unsigned_area_type factor)</font></td>
            <td>Scales down coordinates of an object that models
polygon_45 by unsigned factor.&nbsp; Linear wrt. vertices.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename T, scaling_type&gt;<br />
T&amp; <b>scale</b>(T&amp; rectangle, double scaling) </font></td>
            <td>Scales coordinates of an object that models polygon_45
by floating point factor.&nbsp; Linear wrt. vertices.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename T&gt;<br />
T&amp; <b>move</b>(T&amp; polygon, orientation_2d,<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; coordinate_difference
displacement)</font></td>
            <td>Adds displacement value to coordinate indicated by
orientation_2d of vertices of an object that models polygon_45.&nbsp;
Linear wrt. vertices.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename polygon_type, typename point_type&gt;<br />
polygon_type&amp; <b>convolve</b>(polygon_type&amp; polygon,<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
const point_type&amp; point)</font></td>
            <td>Convolves coordinate values of point with vertices of
an object that models polygon_45.&nbsp; Linear wrt. vertices.</td>
          </tr>
        </tbody>
      </table>
      <h1>Polygon 45 Data</h1>
      <p> </p>
      <p>The library provides a model of polygon 45 concept declared
      <font face="Courier New">template&lt;typename T&gt;
polygon_45_data </font>where T is the coordinate type.</p>
      <p>This data type is used internally when a 45-degree polygon is
needed and is available to the library user who finds it convenient to
use a library polygon data type instead of providing their own.&nbsp;
The data type is implemented to be convenient to use with the library
traits.</p>
      <h2>Members</h2>
      <table id="table2" border="1" width="100%">
        <tbody>
          <tr>
            <td width="586"><b><font face="Courier New">geometry_type</font></b></td>
            <td><font face="Times New Roman">polygon_45_concept</font></td>
          </tr>
          <tr>
            <td width="586"><b><font face="Courier New">coordinate_type</font></b></td>
            <td><font face="Times New Roman">T</font></td>
          </tr>
          <tr>
            <td width="586"><b><font face="Courier New">iterator_type</font></b></td>
            <td>Iterator over vertices point_data&lt;T&gt; vertices of
polygon</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New"><b>polygon_45_data</b>()</font></td>
            <td><font face="Times New Roman">Default constructs the </font>polygon.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New"><b>polygon_45_data</b>(const
polygon_45_data&amp; that)</font></td>
            <td><font face="Times New Roman">Copy construct</font></td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">polygon_45_data&amp;
            <b>operator=</b>(const polygon_45_data&amp; that)</font></td>
            <td>Assignment operator.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename T2&gt;<b>&nbsp; <br />
            </b>polygon_45_data&amp; <b>operator=</b>(const T2&amp;
that) const</font></td>
            <td>Assign from an object that is a model of polygon 45.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">iterator_type <b>begin</b>()
const</font></td>
            <td>Get the begin iterator over vertices of the polygon.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">iterator_type <b>end</b>()
const</font></td>
            <td>Get the end iterator over vertices of the polygon.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">std::size_t <b>size</b>()
const</font></td>
            <td>Get the number of elements in the sequence stored to
the polygon, usually equal to the number of edges of the polygon.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename iT&gt;<b>&nbsp; <br />
            </b>void <b>set</b>(iT begin_points, iT end_points)</font></td>
            <td>Sets the polygon to the iterator range of points.&nbsp;
No check is performed to ensure the points describe corners that are
multiples of 45 degrees relative to the coordinate axis.</td>
          </tr>
        </tbody>
      </table>
      </td>
    </tr>
    <tr>
      <td style="background-color: rgb(238, 238, 238);" nowrap="1"
 valign="top"> &nbsp;</td>
      <td
 style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;"
 valign="top" width="100%">
      <table class="docinfo" id="table3" frame="void" rules="none">
        <colgroup> <col class="docinfo-name" /><col
 class="docinfo-content" /> </colgroup> <tbody valign="top">
          <tr>
            <th class="docinfo-name">Copyright:</th>
            <td>Copyright © Intel Corporation 2008-2010.</td>
          </tr>
          <tr class="field">
            <th class="docinfo-name">License:</th>
            <td class="field-body">Distributed under the Boost Software
License, Version 1.0. (See accompanying file <tt class="literal"> <span
 class="pre">LICENSE_1_0.txt</span></tt> or copy at <a
 class="reference" target="_top"
 href="http://www.boost.org/LICENSE_1_0.txt">
http://www.boost.org/LICENSE_1_0.txt</a>)</td>
          </tr>
        </tbody>
      </table>
      </td>
    </tr>
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