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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:(null)1="http://www.w3.org/TR/REC-html40" lang="en"> <head> <!-- Copyright 2009-2010 Intel Corporation license banner --> <title>Boost Polygon Library: Polygon Concept</title> <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /> <!-- <link type="text/css" rel="stylesheet" href="adobe_source.css"> --> </head> <body> <table style="margin: 0pt; padding: 0pt; width: 100%;" border="0" cellpadding="0" cellspacing="0"> <tbody> <tr> <td style="background-color: rgb(238, 238, 238);" nowrap="1" valign="top"> <div style="padding: 5px;" align="center"> <img src="images/boost.png" border="0" height="86" width="277" /><a title="www.boost.org home page" href="http://www.boost.org/" tabindex="2" style="border: medium none ;"> </a> </div> <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><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>Polygon Concept</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 /> </li> <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 title="www.adobe.com home page" href="http://www.adobe.com/" tabindex="2" style="border: medium none ;"> </a> </div> </td> <td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%"> <!-- End Header --><br /> <p> </p> <h1>Polygon Concept</h1> <p> </p> <p>The polygon concept tag is <font face="Courier New"> polygon_concept</font></p> <p> To register a user defined type as a model of <font face="Times New Roman">polygon </font>concept, specialize the geometry concept meta-function for that type.&nbsp; In the example below CPolygon is registered as a model of polygon&nbsp; concept.</p> <p> <font face="Courier New">template &lt;&gt;<br /> struct geometry_concept&lt;CPolygon&gt; { typedef polygon_concept type; };</font></p> <p> <font face="Times New Roman">The semantic of a polygon is that it can provide iterators over the points that represent its vertices.&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 must also be able to set its geometry based on an interator range over such points.&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_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 same traits are also used by several other polygon concepts through SFINE enable template parameter.&nbsp; The SFINE 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_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_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>Example code <a href="gtl_custom_polygon.htm">custom_polygon.cpp</a> demonstrates mapping a user defined polygon class to the library polygon_concept</p> <p>An object that is a model of <font face="Courier New"> polygon_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_object)</font><br /> <font face="Courier New">view_as&lt;polygon_90_concept&gt;(polygon_object)</font><br /> <font face="Courier New">view_as&lt;polygon_45_concept&gt;(polygon_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.&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.&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.&nbsp;&nbsp; Sets the polygon to the point data range [b,e) that corresponds to vertices of a manhattan polygon.</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 into left object that models polygon.</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 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.&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 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.&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, 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.&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 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 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 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 .&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.&nbsp; Linear wrt. vertices.</td> </tr> </tbody> </table> <h1>Polygon Data</h1> <p> </p> <p>The library provides a model of polygon concept declared <font face="Courier New">template&lt;typename T&gt; polygon_data </font>where T is the coordinate type.</p> <p>This data type is used internally when a 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> <p>Example code <a href="gtl_polygon_usage.htm">polygon_usage.cpp</a> demonstrates using the library provided polygon data types and functions</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_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_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_data</b>(const polygon_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_data&amp; <b>operator=</b>(const polygon_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_data&amp; <b>operator=</b>(const T2&amp; that) const</font></td> <td>Assign from an object that is a model of polygon.</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; </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> </tbody> </table> </body> </html>