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  <title>Boost Polygon Library: Polygon 45 With Holes Concept</title>
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      <div style="padding: 5px;" align="center"> <img
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      <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><a href="gtl_polygon_45_concept.htm">Polygon 45 Concept</a></li>
        <li>Polygon 45 With Holes Concept</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 />
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        <li><a href="voronoi_diagram.htm">Voronoi Diagram</a></li>
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      <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>
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<!-- End Header --><br />
      <p>
      </p>
      <h1>Polygon 45 With Holes Concept</h1>
      <p> </p>
      <p>The polygon_45_with_holes concept tag is <font
 face="Courier New">
polygon_45_with_holes_concept</font></p>
      <p> To register a user defined type as a model of <font
 face="Times New Roman">polygon_45_with_holes </font>concept,
specialize the geometry concept meta-function for that type.&nbsp; In
the example below CPolygon45WithHoles is registered as a model of
polygon<font face="Times New Roman">_45_with_holes&nbsp;</font> concept.</p>
      <p> <font face="Courier New">template &lt;&gt;<br />
struct geometry_concept&lt;CPolygon45WithHoles&gt; { typedef
polygon_45_with_holes_concept type; };</font></p>
      <p> <font face="Times New Roman">The semantic of a
polygon_45_with_holes is a polygon_45 that it can provide iterators
over holes that are also polygon_45.&nbsp; A mutable
polygon_45_with_holes must also be able to set its geometry based on an
interator range over polygon_45 holes.&nbsp; There is no convention of
winding of holes enforced within the library. </font></p>
      <p> <font face="Times New Roman">Below is shown the default
polygon with holes traits.&nbsp; Specialization of these traits is
required for types that don't conform to the default behavior.</font></p>
      <p><font face="Courier New">template &lt;typename T, typename
enable = void&gt;<br />
struct polygon_with_holes_traits {<br />
&nbsp;&nbsp;&nbsp;&nbsp; typedef typename T::iterator_holes_type
iterator_holes_type;<br />
&nbsp;&nbsp;&nbsp;&nbsp; typedef typename T::hole_type hole_type;<br />
&nbsp;&nbsp;&nbsp;&nbsp; static inline iterator_holes_type
begin_holes(const T&amp; t) {<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return
t.begin_holes();<br />
&nbsp;&nbsp;&nbsp;&nbsp; }<br />
&nbsp;&nbsp;&nbsp;&nbsp; static inline iterator_holes_type
end_holes(const T&amp; t) {<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return
t.end_holes();<br />
&nbsp;&nbsp;&nbsp;&nbsp; }<br />
&nbsp;&nbsp;&nbsp;&nbsp; static inline unsigned int size_holes(const
T&amp; t) {<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return
t.size_holes();<br />
&nbsp;&nbsp;&nbsp;&nbsp; }<br />
};</font></p>
      <p><font face="Courier New">template &lt;typename T, typename
enable = void&gt;<br />
struct polygon_with_holes_mutable_traits {<br />
&nbsp;&nbsp;&nbsp;&nbsp; template &lt;typename iT&gt;<br />
&nbsp;&nbsp;&nbsp;&nbsp; static inline T&amp; set_holes(T&amp; t, iT
inputBegin, iT inputEnd) {<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
t.set_holes(inputBegin, inputEnd);<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_with_holes_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_with_holes_object)</font><br />
      <font face="Courier New">view_as&lt;polygon_90_concept&gt;(polygon_45_with_holes_object)</font><br />
      <font face="Courier New">view_as&lt;polygon_90_with_holes_concept&gt;(polygon_45_with_holes_object)</font><br />
      <font face="Courier New">view_as&lt;polygon_45_concept&gt;(polygon_45_with_holes_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_with_holes.&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_with_holes.&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&gt;<br />
hole_iterator_type <b>begin_holes</b>(const T&amp; polygon)</font></td>
            <td><font face="Times New Roman">Expects a model of
polygon_45_with_holes.&nbsp; Returns the begin iterator over the range
of coordinates that correspond to horizontal and vertical edges.</font></td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename T&gt;<br />
hole_iterator_type <b>end_holes</b>(const T&amp; polygon)</font></td>
            <td><font face="Times New Roman">Expects a model of
polygon_45_with_holes.&nbsp; Returns the end iterator over the range of
coordinates that correspond to horizontal and vertical edges.</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_with_holes.&nbsp;&nbsp; Sets the polygon to the point data
range [b,e) that corresponds to vertices of a polygon.&nbsp; </font></td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename T, typename iterator&gt;<br />
void <b>set_holes</b>(T&amp; polygon, iterator b, iterator e)</font></td>
            <td><font face="Times New Roman">Expects a model of
polygon_45_with_holes.&nbsp;&nbsp; Sets the polygon holes to the hole
data range [b,e)</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 outer shell of the polygon_45_with_holes.&nbsp; Does not
include sizes of the holes.</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_with_holes or one of its refinements into left object that
models polygon_45_with_holes.</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_with_holes and
an object that models point, returns true if the polygon shell contains
the point and one of its holes does not contain the point.&nbsp; If the
consider_touch flag is true will return true if the point lies along
the boundary of the polygon or one of its holes.</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_with_holes.</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_with_holes and returns true.&nbsp;
Returns false and leaves bbox unchanged if polygon is empty.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename T&gt;<br />
manhattan_area_type <b>area</b>(const T&amp; polygon)</font></td>
            <td>Returns the area of an object that models
polygon_45_with_holes including subtracting the area of its holes from
the area of the outer shell polygon.</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_with_holes, LOW == CLOCKWISE, HIGH = COUNTERCLOCKWISE.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename T&gt;<br />
coordinate_difference <b>perimeter</b>(const T&amp; polygon)</font></td>
            <td>Returns the perimeter length of an object that models
polygon_45, including the perimeters of the holes.</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; Also applies transform() on the holes of the polygon.</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 outer shell and holes of an object that
models polygon_45 by unsigned factor.</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 outer shell and holes of an object that
models polygon_45 by unsigned factor.</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 outer shell and holes of an object that models
polygon_45 by floating point factor.</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 .</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 the outer
shell and holes of an object that models polygon_45_with_holes.</td>
          </tr>
        </tbody>
      </table>
      <h1>Polygon 45 With Holes Data</h1>
      <p> </p>
      <p>The library provides a model of polygon 45 with holes concept
declared
      <font face="Courier New">template&lt;typename T&gt;
polygon_45_with_holes_data </font>where T is the coordinate type.</p>
      <p>This data type is used internally when a 45 degree polygon
with holes 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_with_holes_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"><b><font face="Courier New">iterator_holes_type</font></b></td>
            <td><font face="Times New Roman">Iterator over hole
polygons of type polygon_45_data&lt;T&gt;.</font></td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New"><b>polygon_45_with_holes_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_with_holes_data</b>(const
polygon_45_with_holes_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_with_holes_data&amp;
            <b> <br />
operator=</b>(const polygon_45_with_holes_data&amp; that)</font></td>
            <td>Assignment operator.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename T2&gt;<b> </b> polygon_45_with_holes_data&amp;<b>&nbsp; <br />
operator=</b>(const T2&amp; that) const</font></td>
            <td>Assign from an object that is a model of polygon 45
with holes.</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">iterator_hole_type
            <b>begin_holes</b>() const</font></td>
            <td>Get the begin compact iterator over non-redundant
coordinates of the polygon.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">iterator_hole_type
            <b>end_holes</b>() const</font></td>
            <td>Get the end compact iterator over non-redundant
coordinates 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">std::size_t <b>size_holes</b>()
const</font></td>
            <td>Get the number of holes in 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 a 45 degree figure.</td>
          </tr>
          <tr>
            <td width="586"><font face="Courier New">template
&lt;typename iT&gt;<b>&nbsp; <br />
            </b>void <b>set_holes</b>(iT begin_holes, iT end_choless)</font></td>
            <td>Sets the polygon holes the iterator range of hole
polygons.&nbsp; These polygons in the input range may be either
polygon_45_data or polygon_45_with_holes_data or any type that provides
begin and end member functions to iterate over point_data&lt;T&gt;.</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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