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<title>Boost Polygon Library: Polygon 45 Concept</title>
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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>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>
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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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<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>
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<td>Copyright � Intel Corporation 2008-2010.</td>
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<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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