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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_rectangle_concept.htm">Rectangle Concept</a></li>
 			<li>Polygon 90 Concept</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><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>
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 <br>
 <p>
 </p><h1>Polygon 90 Concept</h1>

 <p>
 <p>The polygon_90 concept tag is <font face="Courier New">
 polygon_90_concept</font></p>
 <p>
 To register a user defined type as a model of
 <font face="Times New Roman">polygon_90 </font>concept, specialize the
 geometry concept meta-function for that type.&nbsp; In the example below CPolygon90 is registered as a model of
 polygon_90&nbsp; concept.<p>
 <font face="Courier New">template &lt;&gt;<br>
 struct geometry_concept&lt;CPolygon90&gt; { typedef polygon_90_concept type; };</font><p>
 <font face="Times New Roman">The semantic of a polygon_90 is that it can provide
 iterators over the x and y coordinates that correspond to its horizontal and
 vertical sides, starting with an x coordinate.&nbsp; A mutable polygon_90 must
 also be able to set its geometry based on an interator range over such
 coordinates.&nbsp; Since most polygons use vertex points in internal storage
 iterator adaptors for converting to and from point sequences are provided in
 iterator_points_to_compact.hpp and iterator_compact_to_points.hpp to aid in the
 specialization of polygon_90_traits.&nbsp; A std::vector&lt;int&gt; or std::list&lt;int&gt;
 could be made models of polygon_90_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>
 <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 the
 polygon_90_with_holes concept.</font><p><font face="Courier New">template &lt;typename
 T&gt;<br>
 struct polygon_90_traits {<br>
 &nbsp;&nbsp;&nbsp;&nbsp; typedef typename T::coordinate_type coordinate_type;<br>
 &nbsp;&nbsp;&nbsp;&nbsp; typedef typename T::compact_iterator_type
 compact_iterator_type;<br>
 &nbsp;&nbsp;&nbsp;&nbsp; static inline compact_iterator_type begin_compact(const
 T&amp; t) {<br>
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return t.begin_compact();<br>
 &nbsp;&nbsp;&nbsp;&nbsp; }<br>
 &nbsp;&nbsp;&nbsp;&nbsp; static inline compact_iterator_type end_compact(const
 T&amp; t) {<br>
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return t.end_compact();<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&gt;<br>
 struct polygon_90_mutable_traits { <br>
 &nbsp;&nbsp;&nbsp;&nbsp; template &lt;typename iT&gt;<br>
 &nbsp;&nbsp;&nbsp;&nbsp; static inline T&amp; set_compact(T&amp; t, iT input_begin, iT
 input_end) {<br>
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; t.set_compact(input_begin,
 input_end);<br>
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return t;<br>
 &nbsp;&nbsp;&nbsp;&nbsp; }</font><br>
 <font face="Courier New">};</font></p>
 <p>An object that is a model of <font face="Courier New">
 polygon_90_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_90_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 border="1" width="100%" id="table1">
 	<tr>
 		<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
 		compact_iterator_type <b>begin_compact</b>(const T&amp; polygon)</font></td>
 		<td><font face="Times New Roman">Expects a model of polygon_90.&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>
 		compact_iterator_type <b>end_compact</b>(const T&amp; polygon)</font></td>
 		<td><font face="Times New Roman">Expects a model of polygon_90.&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&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_90.&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_90.&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_compact</b>(T&amp; polygon, iterator b, iterator e)</font></td>
 		<td><font face="Times New Roman">Expects a model of polygon_90.&nbsp;&nbsp;
 		Sets the polygon to the coordinate data range [b,e) that corresponds 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_90.&nbsp;&nbsp;
 		Sets the polygon to the point data range [b,e) that corresponds to
 		vertices of a manhattan polygon.&nbsp; Non-manhattan edges between
 		successive input points results in undefined behavior.</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_90 into left object
 		that models polygon_90.</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_90 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_90.&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_90 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>
 		manhattan_area_type <b>area</b>(const T&amp; polygon)</font></td>
 		<td>Returns the area of an object
 		that models polygon_90.&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_90, 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_difference <b>perimeter</b>(const T&amp; polygon)</font></td>
 		<td>Returns the perimeter length of an object
 		that models polygon_90.&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_90 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_90 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_90 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_90 .&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_90.&nbsp; Linear wrt. vertices.</td>
 	</tr>
 	</table>
 	<h1>Polygon 90 Data</h1>

 <p>
 <p>The library provides a model of polygon 90 concept declared
 <font face="Courier New">
 template&lt;typename T&gt; polygon_90_data </font>where T is the coordinate type.</p>
 <p>This data type is used internally when a Manhattan 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 border="1" width="100%" id="table2">
 	<tr>
 		<td width="586"><b><font face="Courier New">geometry_type</font></b></td>
 		<td><font face="Times New Roman">polygon_90_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">compact_iterator_type</font></b></td>
 		<td><font face="Times New Roman">Iterator over non-redundant coordinates
 		of the polygon, alternating x, y, x, y starting with an x, where each x
 		corresponds to a vertical edge and each y corresponds to a horizontal
 		edge.</font></td>
 	</tr>
 	<tr>
 		<td width="586"><font face="Courier New"><b>polygon_90_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_90_data</b>(const
 		polygon_90_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_90_data&amp; <b>operator=</b>(const
 		polygon_90_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_90_data&amp; <b>operator=</b>(const T2&amp; that) const</font></td>
 		<td>Assign from an object that is a model of polygon 90.</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">compact_iterator_type <b>
 		begin_compact</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">compact_iterator_type <b>
 		end_compact</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">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 Manhattan figure, every other
 		x and y value of the points is used to initialize the polygon.</td>
 	</tr>
 	<tr>
 		<td width="586"><font face="Courier New">template &lt;typename iT&gt;<b>&nbsp;
 		<br> </b>void <b>set_compact</b>(iT begin_coords, iT end_coords)</font></td>
 		<td>Sets the polygon to the iterator range of coordinates.&nbsp; These
 		coordinates correspond to the x values of vertical edges and y values of
 		horizontal edges.&nbsp; It is expected that the sequence start with an x
 		value and proceed x then y then x then y.</td>
 	</tr>
 </table>
 	<tr>
 <td style="background-color: rgb(238, 238, 238);" nowrap="1" valign="top">
     &nbsp;</td>
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 			<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">
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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_rectangle_concept.htm">Rectangle Concept</a></li>
	<li>Polygon 90 Concept</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><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>
	</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>
	</ul>
	</div>
	<h3 class="navbar">Polygon Sponsor</h3>
	<div style="padding: 5px;" align="center">
	<img border="0" src="images/intlogo.gif" width="127" height="51">
	</div>
	</td>
	<td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%">

	<!-- End Header -->

	<br>
	<p>
	</p><h1>Polygon 90 Concept</h1>

	<p>
	<p>The polygon_90 concept tag is <font face="Courier New">
	polygon_90_concept</font></p>
	<p>
	To register a user defined type as a model of
	<font face="Times New Roman">polygon_90 </font>concept, specialize the
	geometry concept meta-function for that type.  In the example below CPolygon90 is registered as a model of
	polygon_90  concept.<p>
	<font face="Courier New">template <><br>
	struct geometry_concept<CPolygon90> { typedef polygon_90_concept type; };</font><p>
	<font face="Times New Roman">The semantic of a polygon_90 is that it can provide
	iterators over the x and y coordinates that correspond to its horizontal and
	vertical sides, starting with an x coordinate.  A mutable polygon_90 must
	also be able to set its geometry based on an interator range over such
	coordinates.  Since most polygons use vertex points in internal storage
	iterator adaptors for converting to and from point sequences are provided in
	iterator_points_to_compact.hpp and iterator_compact_to_points.hpp to aid in the
	specialization of polygon_90_traits.  A std::vector<int> or std::list<int>
	could be made models of polygon_90_concept by simply providing access to their
	iterators through traits.  Library functions that create polygon objects
	require that those objects provide a default constructor.</font><p>
	<font face="Times New Roman">Below is shown the default polygon traits.
	Specialization of these traits is required for types that don't conform to the
	default behavior.  Note that these traits are also used by the
	polygon_90_with_holes concept.</font><p><font face="Courier New">template <typename
	T><br>
	struct polygon_90_traits {<br>
	typedef typename T::coordinate_type coordinate_type;<br>
	typedef typename T::compact_iterator_type
	compact_iterator_type;<br>
	static inline compact_iterator_type begin_compact(const
	T& t) {<br>
	return t.begin_compact();<br>
	}<br>
	static inline compact_iterator_type end_compact(const
	T& t) {<br>
	return t.end_compact();<br>
	}<br>
	static inline unsigned int size(const T& t) {<br>
	return t.size();<br>
	}<br>
	static inline winding_direction winding(const T& t) {<br>
	return unknown_winding;<br>
	}<br>
	};</font></p>
	<p><font face="Courier New">template <typename T><br>
	struct polygon_90_mutable_traits { <br>
	template <typename iT><br>
	static inline T& set_compact(T& t, iT input_begin, iT
	input_end) {<br>
	t.set_compact(input_begin,
	input_end);<br>
	return t;<br>
	}</font><br>
	<font face="Courier New">};</font></p>
	<p>An object that is a model of <font face="Courier New">
	polygon_90_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.  This concept casting is accomplished through the
	<font face="Courier New">view_as<>()</font> function.</p>
	<p><font face="Courier New">view_as<rectangle_concept>(polygon_90_object)</font></p>
	<p>The return value of <font face="Courier New">view_as<>()</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 border="1" width="100%" id="table1">
	<tr>
	<td width="586"><font face="Courier New">template <typename T><br>
	compact_iterator_type <b>begin_compact</b>(const T& polygon)</font></td>
	<td><font face="Times New Roman">Expects a model of polygon_90.
	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 <typename T><br>
	compact_iterator_type <b>end_compact</b>(const T& polygon)</font></td>
	<td><font face="Times New Roman">Expects a model of polygon_90.
	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 <typename T><br>
	point_iterator_type <b>begin_points</b>(const T& polygon)</font></td>
	<td><font face="Times New Roman">Expects a model of polygon_90.
	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 <typename T><br>
	point_iterator_type <b>end_points</b>(const T& polygon)</font></td>
	<td><font face="Times New Roman">Expects a model of polygon_90.
	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 <typename T, typename
	iterator><br>
	void <b>set_compact</b>(T& polygon, iterator b, iterator e)</font></td>
	<td><font face="Times New Roman">Expects a model of polygon_90.
	Sets the polygon to the coordinate data range [b,e) that corresponds to
	.horizontal and vertical edges.</font></td>
	</tr>
	<tr>
	<td width="586"><font face="Courier New">template <typename T, typename
	iterator><br>
	void <b>set_points</b>(T& polygon, iterator b, iterator e)</font></td>
	<td><font face="Times New Roman">Expects a model of polygon_90.
	Sets the polygon to the point data range [b,e) that corresponds to
	vertices of a manhattan polygon.  Non-manhattan edges between
	successive input points results in undefined behavior.</font></td>
	</tr>
	<tr>
	<td width="586"><font face="Courier New">template <typename T><br>
	unsigned int <b>size</b>(const T& 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 <typename T1, typename
	T2><br>
	T1& <b>assign</b>(T1& left, const T2& right)</font></td>
	<td>Copies data from right object that models polygon_90 into left object
	that models polygon_90.</td>
	</tr>
	<tr>
	<td width="586"><font face="Courier New">template <typename T,
	typename point_type><br>
	bool <b>contains</b>(const T&, const point_type& point, <br>

	bool consider_touch=true)</font></td>
	<td>Given an object that models polygon_90 and an object that models
	point, returns true
	if the polygon contains the point.  If the consider_touch
	flag is true will return true if the point lies along the boundary of
	the polygon.  Linear wrt. vertices.</td>
	</tr>
	<tr>
	<td width="586"><font face="Courier New">// get the center coordinate<br>
	template <typename T, typename point_type><br>
	void <b>center</b>(point_type& p, const T& polygon)</font></td>
	<td>Sets object that models point to the center point of the bounding
	box of an object that models polygon_90.  Linear wrt. vertices.</td>
	</tr>
	<tr>
	<td width="586"><font face="Courier New">template <typename T,
	typename rectangle_type><br>
	bool <b>extents</b>(rectangle_type& bbox, const T& polygon)</font></td>
	<td>Sets object that models rectangle to the bounding box of an object
	that models polygon_90 and returns true.  Returns false and leaves
	bbox unchanged if polygon is empty.  Linear wrt. vertices.</td>
	</tr>
	<tr>
	<td width="586"><font face="Courier New">template <typename T><br>
	manhattan_area_type <b>area</b>(const T& polygon)</font></td>
	<td>Returns the area of an object
	that models polygon_90.  Linear wrt. vertices.</td>
	</tr>
	<tr>
	<td width="586"><font face="Courier New">template <typename T><br>
	direction_1d <b>winding</b>(const T& polygon)</font></td>
	<td>Returns the winding direction of an object
	that models polygon_90, LOW == CLOCKWISE, HIGH = COUNTERCLOCKWISE.
	Complexity depends upon winding trait.</td>
	</tr>
	<tr>
	<td width="586"><font face="Courier New">template <typename T><br>
	coordinate_difference <b>perimeter</b>(const T& polygon)</font></td>
	<td>Returns the perimeter length of an object
	that models polygon_90.  Linear wrt. vertices.</td>
	</tr>
	<tr>
	<td width="586"><font face="Courier New">template <typename T,
	typename transform_type><br>
	T& <b>transform</b>(T& polygon, const transform_type&)</font></td>
	<td>Applies transform() on the vertices of polygon and sets the polygon to that described by the result of
	transforming its vertices.  Linear wrt. vertices.</td>
	</tr>
	<tr>
	<td width="586"><font face="Courier New">template <typename T><br>
	T& <b>scale_up</b>(T& polygon, unsigned_area_type factor)</font></td>
	<td>Scales up coordinate of an object that models
	polygon_90 by unsigned factor.  Linear wrt. vertices.</td>
	</tr>
	<tr>
	<td width="586"><font face="Courier New">template <typename T><br>
	T& <b>scale_down</b>(T& polygon, unsigned_area_type factor)</font></td>
	<td>Scales down coordinates of an object that models
	polygon_90 by unsigned factor.  Linear wrt. vertices.</td>
	</tr>
	<tr>
	<td width="586"><font face="Courier New">template <typename T, scaling_type><br>
	T& <b>scale</b>(T& rectangle, double scaling) </font></td>
	<td>Scales coordinates of an object that models polygon_90 by floating
	point factor.  Linear wrt. vertices.</td>
	</tr>
	<tr>
	<td width="586"><font face="Courier New">template <typename T><br>
	T& <b>move</b>(T& polygon, orientation_2d,<br>
	coordinate_difference displacement)</font></td>
	<td>Adds displacement value to coordinate indicated by orientation_2d of
	vertices of an object that models polygon_90 .  Linear wrt.
	vertices.</td>
	</tr>
	<tr>
	<td width="586"><font face="Courier New">template <typename polygon_type, typename point_type><br>
	polygon_type& <b>convolve</b>(polygon_type& polygon,<br>

	const point_type& point)</font></td>
	<td>Convolves coordinate values of point with vertices of an
	object that models polygon_90.  Linear wrt. vertices.</td>
	</tr>
	</table>
	<h1>Polygon 90 Data</h1>

	<p>
	<p>The library provides a model of polygon 90 concept declared
	<font face="Courier New">
	template<typename T> polygon_90_data </font>where T is the coordinate type.</p>
	<p>This data type is used internally when a Manhattan 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.  The data type is implemented to
	be convenient to use with the library traits.</p>
	<h2>Members</h2>
	<table border="1" width="100%" id="table2">
	<tr>
	<td width="586"><b><font face="Courier New">geometry_type</font></b></td>
	<td><font face="Times New Roman">polygon_90_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<T> vertices of polygon</td>
	</tr>
	<tr>
	<td width="586"><b><font face="Courier New">compact_iterator_type</font></b></td>
	<td><font face="Times New Roman">Iterator over non-redundant coordinates
	of the polygon, alternating x, y, x, y starting with an x, where each x
	corresponds to a vertical edge and each y corresponds to a horizontal
	edge.</font></td>
	</tr>
	<tr>
	<td width="586"><font face="Courier New"><b>polygon_90_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_90_data</b>(const
	polygon_90_data& that)</font></td>
	<td><font face="Times New Roman">Copy construct</font></td>
	</tr>
	<tr>
	<td width="586"><font face="Courier New">polygon_90_data& <b>operator=</b>(const
	polygon_90_data& that)</font></td>
	<td>Assignment operator.</td>
	</tr>
	<tr>
	<td width="586"><font face="Courier New">template <typename T2><b>
	<br> </b>polygon_90_data& <b>operator=</b>(const T2& that) const</font></td>
	<td>Assign from an object that is a model of polygon 90.</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">compact_iterator_type <b>
	begin_compact</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">compact_iterator_type <b>
	end_compact</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">template <typename iT><b>
	<br> </b>void <b>set</b>(iT begin_points, iT end_points)</font></td>
	<td>Sets the polygon to the iterator range of points.  No check is
	performed to ensure the points describe a Manhattan figure, every other
	x and y value of the points is used to initialize the polygon.</td>
	</tr>
	<tr>
	<td width="586"><font face="Courier New">template <typename iT><b>
	<br> </b>void <b>set_compact</b>(iT begin_coords, iT end_coords)</font></td>
	<td>Sets the polygon to the iterator range of coordinates.  These
	coordinates correspond to the x values of vertical edges and y values of
	horizontal edges.  It is expected that the sequence start with an x
	value and proceed x then y then x then y.</td>
	</tr>
	</table>
	<tr>
	<td style="background-color: rgb(238, 238, 238);" nowrap="1" valign="top">
	</td>
	<td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%">


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	<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>
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