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- <title>Boost Polygon Library: Polygon 45 Concept</title>
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- <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>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 />
- </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 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. In the example
- below CPolygon45 is registered as a model of polygon_45 concept.</p>
- <p> <font face="Courier New">template <><br />
- struct geometry_concept<CPolygon45> { 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. 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. A mutable polygon_45 must also be able to set its geometry
- based on an interator range over such points. A
- std::vector<point_data<int> > or
- std::list<point_data<int> > could be made models of
- polygon_45_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>
- <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 several other polygon concepts through SFINAE
- enable template parameter. 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 <typename T, typename
- enable = gtl_yes><br />
- struct polygon_traits {};<br />
- <br />
- template <typename T><br />
- struct polygon_traits<T, <br />
- typename gtl_or_4<<br />
- typename gtl_same_type<typename
- geometry_concept<T>::type, polygon_concept>::type,<br />
- typename gtl_same_type<typename
- geometry_concept<T>::type, polygon_45_concept>::type,<br />
- typename gtl_same_type<typename
- geometry_concept<T>::type, polygon_with_holes_concept>::type,<br />
- typename gtl_same_type<typename
- geometry_concept<T>::type, polygon_45_with_holes_concept>::type<br />
- >::type> {<br />
- typedef typename T::coordinate_type
- coordinate_type;<br />
- typedef typename T::iterator_type
- iterator_type;<br />
- typedef typename T::point_type point_type;<br />
- static inline iterator_type begin_points(const
- T& t) {<br />
- return t.begin();<br />
- }<br />
- static inline iterator_type end_points(const
- T& t) {<br />
- return t.end();<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, typename
- enable = void><br />
- struct polygon_mutable_traits {<br />
- template <typename iT><br />
- static inline T& set_points(T& t, iT
- input_begin, iT input_end) {<br />
-
- t.set(input_begin, input_end);<br />
- return t;<br />
- }<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. 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_45_object)</font><br />
- <font face="Courier New">view_as<polygon_90_concept>(polygon_45_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 id="table1" border="1" width="100%">
- <tbody>
- <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_45. 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_45. 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_points</b>(T& polygon, iterator b, iterator e)</font></td>
- <td><font face="Times New Roman">Expects a model of
- polygon_45. Sets the polygon to the point data range [b,e)
- that corresponds to vertices of a polygon. Non-45 edges between
- successive input points is disallowed.</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_45
- into left object that models polygon_45.</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_45 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_45. 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_45 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 />
- area_type <b>area</b>(const T& polygon)</font></td>
- <td>Returns the area of an object that models
- polygon_45. 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_45, LOW == CLOCKWISE, HIGH = COUNTERCLOCKWISE. Complexity
- depends upon winding trait.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T><br />
- coordinate_distance <b>perimeter</b>(const T& polygon)</font></td>
- <td>Returns the perimeter length of an object that models
- polygon_45. 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_45 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_45 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_45
- 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_45.
- 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_45. 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<typename T>
- 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.
- 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<T> 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& 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&
- <b>operator=</b>(const polygon_45_data& that)</font></td>
- <td>Assignment operator.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T2><b> <br />
- </b>polygon_45_data& <b>operator=</b>(const T2&
- 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
- <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 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"> </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>
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