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<title>Boost Polygon Library: Rectangle 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>Rectangle Concept</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><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>
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<h3 class="navbar">Polygon Sponsor</h3>
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<br>
<p>
</p><h1>Rectangle Concept</h1>
<p>
<p>The rectangle concept tag is <font face="Courier New">
rectangle_concept</font></p>
<p>
To register a user defined type as a model of
<font face="Times New Roman">rectangle </font>concept, specialize the
geometry concept meta-function for that type.&nbsp; In the example below CRectangle is registered as a model of
rectangle&nbsp; concept.<p>
<font face="Courier New">template &lt;&gt;<br>
struct geometry_concept&lt;CRectangle&gt; { typedef rectangle_concept type; };</font><p>
<font face="Times New Roman">The semantic of a rectangle is that it has an x and
a y interval and these intervals conform to the semantic of an interval
including its invariant.&nbsp; This invariant on the intervals of a rectangle is enforced by the generic library functions that
operate on rectangles, and is not expected of the data type itself or the concept
mapping of that data type to the rectangle concept through its traits.&nbsp; In
this way a boost::tuple&lt;int, int, int, int&gt; or boost::array&lt;int, 4&gt;
could be made models of rectangle by simply providing indirect access to their
elements through traits.</font><p>
<font face="Times New Roman">Below is shown the default rectangle traits.&nbsp;
Specialization of these traits is required for types that don't conform to the
default behavior.&nbsp; The interested reader will note SFINAE is used on the
traits to allow only an object that provides a member type definition of
interval_type to work with the default read only traits.&nbsp; This becomes
necessary when refinements of concepts are used and it is undesirable to attempt
to match default traits to non-rectangle types at compile time.&nbsp;
Specializing rectangle_traits can be done easily by simply providing gtl_yes as
the enable parameter.</font><p>
<font face="Courier New">template &lt;typename T, typename enable = gtl_yes&gt;<br>
struct rectangle_traits {};</font><p>
<font face="Courier New">template &lt;typename T&gt;<br>
struct rectangle_traits&lt;T, gtl_no&gt; {};<br>
<br>
template &lt;typename T&gt;<br>
struct rectangle_traits&lt;T, typename gtl_same_type&lt;typename T::interval_type,
typename T::interval_type&gt;::type&gt; {<br>
&nbsp;&nbsp;&nbsp;&nbsp; typedef typename T::coordinate_type coordinate_type;<br>
&nbsp;&nbsp;&nbsp;&nbsp; typedef typename T::interval_type interval_type;<br>
&nbsp;&nbsp;&nbsp;&nbsp; static inline interval_type get(const T&amp; rectangle,
orientation_2d orient) {<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return
rectangle.get(orient); }<br>
};<br>
<br>
template &lt;typename T&gt;<br>
struct rectangle_mutable_traits {<br>
&nbsp;&nbsp;&nbsp;&nbsp; template &lt;typename T2&gt;<br>
&nbsp;&nbsp;&nbsp;&nbsp; static inline void set(T&amp; rectangle, orientation_2d
orient, const T2&amp; interval) {<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; rectangle.set(orient,
interval); }<br>
&nbsp;&nbsp;&nbsp;&nbsp; template &lt;typename T2, typename T3&gt;<br>
&nbsp;&nbsp;&nbsp;&nbsp; static inline T construct(const T2&amp; interval_horizontal,
const T3&amp; interval_vertical) {<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return
T(interval_horizontal, interval_vertical); }<br>
};</font><h2>Functions</h2>
<table border="1" width="100%" id="table1">
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
interval_type <b>get</b>(const T&amp; rectangle, orientation_2d)</font></td>
<td><font face="Times New Roman">Expects a model of rectangle.&nbsp;
Returns the x interval or y interval of the rectangle, depending on the
orientation_2d value.</font><font face="Courier New"><br>
&nbsp;</font></td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T, typename
coordinate_type&gt;<br>
void <b>set</b>(T&amp; rectangle, orientation_2d, coordinate_type)</font></td>
<td><font face="Times New Roman">Expects a model of rectangle.&nbsp;&nbsp;
Sets the x interval or y interval of the rectangle to the
coordinate, depending on the orientation_2d value.</font></td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
interval_type <b>get</b>(const T&amp; rectangle, orientation_2d,
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; direction_1d)</font></td>
<td><font face="Times New Roman">Expects a model of rectangle.&nbsp;
Returns the coordinate specificed by the direction_1d value of the x interval or y interval of the rectangle, depending on the
orientation_2d value.</font><font face="Courier New"><br>
&nbsp;</font></td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T, typename
coordinate_type&gt;<br>
void <b>set</b>(T&amp; rectangle, orientation_2d, direction_1d, <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; coordinate_type)</font></td>
<td><font face="Times New Roman">Expects a model of rectangle.&nbsp;&nbsp;
Sets the coordinate specified by the direction_1d value of the x interval or y interval of the rectangle to the
coordinate, depending on the orientation_2d value.</font></td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T, typename
T2&gt;<br>
T <b>construct</b>(const T2&amp; h, const T2&amp; v)</font></td>
<td>Construct an object that is a model of rectangle given x interval
and y intervals.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T, typename
T2&gt;<br>
T <b>construct</b>(coordinate_type xl, coordinate_type yl, <br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; coordinate_type
xh, coordinate_type yh)</font></td>
<td>Construct an object that is a model of rectangle given four coordinate values.</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 rectangle into left object
that models rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T, typename
T2&gt;<br>
bool <b>equivalence</b>(const T&amp; rectangle1, </font>
<br><font face="Courier New">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; const T2&amp; rectangle2)</font></td>
<td>Given two objects that model rectangle, compares and returns true if
their x and y intervals are respectively equivalent.</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 rectangle and an object that models
point, returns true
if the rectangle contains the point.&nbsp; If the consider_touch
flag is true will return true if the point lies along the boundary of
the rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T1, typename
T2&gt;<br>
bool <b>contains</b>(const T1&amp; a, const T2&amp; b, <br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
bool consider_touch = true) </font></td>
<td>Returns true if model of rectangle a contains both intervals of
model of rectangle b.&nbsp; If the consider_touch flag is true will
consider rectangle b contained even if it touches the boundary of a.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
interval_type <b>horizontal</b>(const T&amp; rectangle)</font></td>
<td>Returns the x interval of an object that models rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
interval_type <b>vertical</b>(const T&amp; rectangle)</font></td>
<td>Returns the y interval of an object that models rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
coordinate_type <b>xl</b>(const T&amp; rectangle)</font></td>
<td>Returns the west coordinate of an object that models rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
coordinate_type <b>xh</b>(const T&amp; rectangle)</font></td>
<td>Returns the east coordinate of an object that models rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
coordinate_type <b>yl</b>(const T&amp; rectangle)</font></td>
<td>Returns the south coordinate of an object that models rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
coordinate_type <b>yh</b>(const T&amp; rectangle)</font></td>
<td>Returns the north coordinate of an object that models rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
point_type <b>ll</b>(const T&amp; rectangle)</font></td>
<td>Returns the lower left corner point of an object that models rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
point_type <b>lr</b>(const T&amp; rectangle)</font></td>
<td>Returns the lower right corner point of an object that models rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
point_type <b>ul</b>(const T&amp; rectangle)</font></td>
<td>Returns the upper left corner point of an object that models rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
point_type <b>ur</b>(const T&amp; rectangle)</font></td>
<td>Returns the upper right corner point of an object that models rectangle.</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; rectangle)</font></td>
<td>Sets object that models point to the center point of an object that models rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T,
typename interval_type&gt;<br>
void <b>horizontal</b>(T&amp; rectangle, const interval_type&amp; i)</font></td>
<td>Sets the x interval of the object that models rectangle to be equal
to the value of an object that models interval.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T,
typename interval_type&gt;<br>
void <b>vertical</b>(T&amp; rectangle, const interval_type&amp; i )</font></td>
<td>Sets the y interval of the object that models rectangle to be equal
to the value of an object that models interval.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename
rectangle_type&gt;<br>
void <b>xl</b>(rectangle_type&amp; rectangle, coordinate_type )</font></td>
<td>Sets the west coordinate of the object that models rectangle to be equal
to the coordinate value.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename
rectangle_type&gt;<br>
void <b>xh</b>(rectangle_type&amp; rectangle, coordinate_type )</font></td>
<td>Sets the east coordinate of the object that models rectangle to be equal
to the coordinate value.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename
rectangle_type&gt;<br>
void <b>yl</b>(rectangle_type&amp; rectangle, coordinate_type )</font></td>
<td>Sets the south coordinate of the object that models rectangle to be equal
to the coordinate value.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename
rectangle_type&gt;<br>
void <b>yh</b>(rectangle_type&amp; rectangle, coordinate_type )</font></td>
<td>Sets the north coordinate of the object that models rectangle to be equal
to the coordinate value.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T,
typename T1, typename T2&gt;<br>
T&amp; <b>set_points</b>(T&amp; rectangle, const T1&amp; p1, const T2&amp; p2)</font></td>
<td>Sets the rectangle to the rectangle fully described by the points p1
and p2.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
coordinate_difference <b>delta</b>(const T&amp; rectangle,
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; orientation_2d)</font></td>
<td>Returns the delta of the interval specified by orientation_2d of an object
that models rectangle.</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; rectangle)</font></td>
<td>Returns the area of an object
that models rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
coordinate_difference <b>half_perimeter</b>(const T&amp; rectangle)</font></td>
<td>Returns the length plus width of an object
that models rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
coordinate_difference <b>perimeter</b>(const T&amp; rectangle)</font></td>
<td>Returns the perimeter length of an object
that models rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
orientation_2d <b>quess_orientation</b>(const T&amp; rectangle)</font></td>
<td>Returns the orientation in which the rectangle has a longer delta.&nbsp;
Returns HORIZONTAL if the rectangle is a square.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename
rectangle_type&gt;<br>
rectangle_type&amp; <b>transform</b>(rectangle_type&amp; rectangle,<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; coordinate_type axis = 0)</font></td>
<td>Applies transform() on the two points that fully describe the
rectangle and sets the rectangle to that described by the result of
transforming those points.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename
rectangle_type&gt;<br>
rectangle_type&amp; <b>scale_up</b>(rectangle_type&amp; rectangle, <br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; unsigned_area_type factor)</font></td>
<td>Scales up x interval and y interval&nbsp; of an object that models
rectangle by unsigned factor.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename
rectangle_type&gt;<br>
rectangle_type&amp; <b>scale_down</b>(rectangle_type&amp; rectangle, <br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; unsigned_area_type factor)</font></td>
<td>Scales down x interval and y interval&nbsp; of an object that models
rectangle by unsigned factor.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename
rectangle_type, scaling_type&gt;<br>
rectangle_type&amp; <b>scale</b>(rectangle_type&amp; rectangle,<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
const scaling_type&amp; scaling) </font></td>
<td>Applies scale() on the two points that fully describe the rectangle
and sets the rectangle to that described by the result of transforming
those points.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
T&amp; <b>move</b>(T&amp; rectangle, orientation_2d,<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; coordinate_difference displacement)</font></td>
<td>Adds displacement value to interval indicated by orientation_2d of an
object that models rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename
rectangle_type, typename point_type&gt;<br>
rectangle_type&amp; <b>convolve</b>(rectangle_type&amp; rectangle,<br>
&nbsp;&nbsp;&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 x interval and y interval&nbsp; of an
object that models rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename
rectangle_type, typename point_type&gt;<br>
rectangle_type&amp; <b>deconvolve</b>(rectangle_type&amp; rectangle,<br>
&nbsp;&nbsp;&nbsp;&nbsp;&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>Deconvolves coordinate values of point withx interval and y interval&nbsp; of
an object that models rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T1, typename
T2&gt;<br>
T1&amp; <b>convolve</b>(T1&amp; a, const T2&amp; b)</font></td>
<td>Convolves x interval&nbsp; of b with x interval&nbsp; of a and
convolves y
interval&nbsp; of b with y interval&nbsp; of a.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T1, typename
T2&gt;<br>
T1&amp; <b>deconvolve</b>(T1&amp; a, const T2&amp; b)</font></td>
<td>Deconvolves x interval&nbsp; of b with x interval&nbsp; of a and
deconvolves y interval&nbsp; of b with y interval&nbsp; of a. </td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T1, typename
T2&gt;<br>
T1&amp; <b>reflected_convolve</b>(T1&amp; a, const T2&amp; b)</font></td>
<td>Reflected convolves y interval&nbsp; of b with x interval&nbsp; of a and
reflected convolves x
interval&nbsp; of b with y interval&nbsp; of a.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T1, typename
T2&gt;<br>
T1&amp; <b>reflected_deconvolve</b>(T1&amp; a, const T2&amp; b)</font></td>
<td>Reflected deconvolves y interval&nbsp; of b with x interval&nbsp; of a and
reflected deconvolves x interval&nbsp; of b with y interval&nbsp; of a.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T,
typename point_type&gt;<br>
coordinate_difference <b>euclidean_distance</b>(const T&amp;,<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; const point_type&amp; point,
orienation_2d)</font></td>
<td>Returns the distance from an object that models rectangle to an
object that models point along the given orientation.&nbsp; Returns zero
if the point is contained within the rectangle along that orientation.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T1,
typename T2&gt;<br>
coordinate_difference <b>euclidean_distance</b>(const T1&amp; a,<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; const T2&amp; b, orienation_2d)</font></td>
<td>Returns the distance from an object that models rectangle to an
object that models rectangle along the given orientation.&nbsp; Returns
zero if the intervals of the rectangles overlap along that orientation.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T,
typename point_type&gt;<br>
coordinate_difference <b>square_euclidean_distance</b>(const T&amp;,<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; const point_type&amp; point)</font></td>
<td>Returns the square of the Euclidean distance between a point and a
rectangle.&nbsp; Returns zero if the point is contained within the
rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T1,
typename T2&gt;<br>
coordinate_difference <b>square_euclidean_distance</b><br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (const T1&amp; a, const T2&amp; b)</font></td>
<td>Returns the square of the Euclidean distance between rectangles a
and b.&nbsp; Returns zero if the rectangles intersect.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T,
typename point_type&gt;<br>
coordinate_difference <b>manhattan_distance</b>(const T&amp;,<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; const point_type&amp; point)</font></td>
<td>Returns the Manhattan distance between a point and a rectangle.&nbsp;
Returns zero if the point is contained within the rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T1,
typename T2&gt;<br>
coordinate_difference <b>manhattan_distance</b>(const T1&amp; a, <br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
const T2&amp; b)</font></td>
<td>Returns the Manhattan distance between rectangles a and b.&nbsp;
Returns zero if the rectangles intersect.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T,
typename point_type&gt;<br>
coordinate_distance <b>euclidean_distance</b>(const T&amp;,<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; const point_type&amp; point)</font></td>
<td>Returns the Euclidean distance between a point and a rectangle.&nbsp;
Returns zero if the point is contained within the rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T1,
typename T2&gt;<br>
coordinate_distance <b>euclidean_distance</b>(const T1&amp; a, <br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
const T2&amp; b)</font></td>
<td>Returns the Euclidean distance between rectangles a and b.&nbsp;
Returns zero if the rectangles intersect.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T1, typename
T2&gt;<br>
bool <b>intersects</b>(const T1&amp; a, const T2&amp; b, <br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
bool consider_touch = true)</font></td>
<td>Returns true if two objects that model rectangle overlap.&nbsp; If
the consider_touch flag is true touching at the sides or corners is
considered overlap.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T1, typename
T2&gt;<br>
bool <b>boundaries_intersect</b>(const T1&amp; a, const T2&amp; b, <br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
bool consider_touch = true)</font></td>
<td>Returns true is two objects that model rectangle partially overlap
such that one there is an intersection between the edges of the two
rectangles&nbsp; If the consider_touch flag is true a coordinate is
considered contained even if the two rectangles touch only along a side
or corner.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T1, typename
T2&gt;<br>
bool <b>abuts</b>(const T1&amp; a, const T2&amp; b,<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; direction_2d dir)
</font></td>
<td>Returns true if rectangle b abuts but down not overlap rectangle a
on the side of rectangle a specified by dir.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T1, typename
T2&gt;<br>
bool <b>abuts</b>(const T1&amp; a, const T2&amp; b,<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; orientation_2d)
</font></td>
<td>Returns true if rectangle b abuts but down not overlap rectangle a
on either side of rectangle a specified by the orientation_2d.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T1, typename
T2&gt;<br>
bool <b>abuts</b>(const T1&amp; a, const T2&amp; b)</font></td>
<td>Returns true if rectangle b abuts but down not overlap rectangle a
on any side.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T1, typename
T2&gt;<br>
bool <b>intersect</b>(T1&amp; a, const T2&amp; b, orientation_2d<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
bool consider_touch = true) </font></td>
<td>Sets rectangle a to the intersection of rectangle a and interval b
along the orientation_2d
and returns true.&nbsp; If the does not intersect the interval, the
rectangle is unchanged and the function returns false.&nbsp; If the flag consider_touch is true
intervals that abut are considered to intersect.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T1, typename
T2&gt;<br>
bool <b>intersect</b>(T1&amp; a, const T2&amp; b,<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
bool consider_touch = true) </font></td>
<td>Sets rectangle a to the intersection of rectangle a and rectangle b
and return true.&nbsp; If the two rectangles do not intersect rectangle
a is unchanged and the function returns false.&nbsp; If the flag
consider_touch is true rectangles that abut are considered to intersect.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T1, typename
T2&gt;<br>
T&amp; <b>generalized_intersect</b>(T1&amp; a, const T2&amp; b)</font></td>
<td>Same as intersect, but if they do not intersect set a to the
rectangle between a and b by applying generalized_intersect() on the
intervals of the rectangles.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
T&amp; <b>bloat</b>(T&amp; rectangle, coordinate_type)</font></td>
<td>Bloats x and y intervals of rectangle by coordinate value.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
T&amp; <b>bloat</b>(T&amp; rectangle, direction_2d, coordinate_type)</font></td>
<td>Bloats side of rectangle specified by direction_2d by coordinate
value.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
T&amp; <b>bloat</b>(T&amp; rectangle, orientation_2d, coordinate_type)</font></td>
<td>Bloats interval of rectangle specified by orientation_2d by
coordinate value.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
T&amp; <b>shrink</b>(T&amp; rectangle, coordinate_type)</font></td>
<td>Shrinks x and y intervals of rectangle by coordinate value.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
T&amp; <b>shrink</b>(T&amp; rectangle, direction_2d, coordinate_type)</font></td>
<td>Shrinks side of rectangle specified by direction_2d by coordinate
value.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T&gt;<br>
T&amp; <b>shrink</b>(T&amp; rectangle, orientation_2d, coordinate_type)</font></td>
<td>Shrinks interval of rectangle specified by orientation_2d by
coordinate value.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T1, typename
T2&gt;<br>
bool <b>encompass</b>(T1&amp; a, const T2&amp; b)</font></td>
<td>The x and y intervals of a are set to encompass the x and y
intervals of b respectively.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T, typename
point_type&gt;<br>
bool <b>encompass</b>(T&amp; rectangle, const point_type&amp; point)</font></td>
<td>The x and y intervals of rectangle are set to encompass the x and y
coordinates of point respectively.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T, typename
interval_type&gt;<br>
bool <b>encompass</b>(T&amp; rectangle, const interval_type&amp; i,
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; orientation_2d)</font></td>
<td>The interval of rectangle specified by orientation_2d is set to encompass the
interval i.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T, typename
point_type&gt;<br>
bool <b>get_corner</b>(point_type&amp; point, const T&amp; rectangle,&nbsp;
<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
direction_2d, direction_1d)</font></td>
<td>Sets point to the corner of the rectangle you reach if you look at
its side specified by direction_2d from within the rectangle and turn in
the direction_1d direction (low == left, high = right).&nbsp; Always
returns true.</td>
</tr>
</table>
<h1>Rectangle Data</h1>
<p>
<p>The library provides a model of rectangle concept declared
<font face="Courier New">
template&lt;typename T&gt; rectangle_data </font>where T is the coordinate type.</p>
<p>This data type is used internally when a rectangle is needed and is available
to the library user who finds it convenient to use a library rectangle 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">rectangle_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"><font face="Courier New"><b>interval_type</b></font></td>
<td><font face="Times New Roman">interval_data&lt;T&gt;</font></td>
</tr>
<tr>
<td width="586"><font face="Courier New"><b>rectangle_data</b>(T xl, T
yl, T xh, T yh)</font></td>
<td><font face="Times New Roman">Constructs a rectangle with four
coordinates.</font></td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T1, typename
T2&gt;<b><br>
rectangle_data</b>(const T1&amp; horizontal_interval,<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
const T2&amp; vertical_interval)</font></td>
<td><font face="Times New Roman">Constructs a rectangle with two objects
that model interval.</font></td>
</tr>
<tr>
<td width="586"><font face="Courier New"><b>rectangle_data</b>(const
rectangle_data&amp; that)</font></td>
<td><font face="Times New Roman">Copy construct</font></td>
</tr>
<tr>
<td width="586"><font face="Courier New">rectangle_data&amp; <b>operator=</b>(const
rectangle_data&amp; that)</font></td>
<td>Assignment operator.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T2&gt;<b>
<br> </b>rectangle_data& <b>
operator=</b>(const T2&amp; that) const</font></td>
<td>Assign from an object that is a model of rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T2&gt;<b>
<br> </b>bool<b>
operator==</b>(const T2&amp; that) const</font></td>
<td>Compare equality to an object that is a model of rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T2&gt;<b>
<br> </b>bool<b>
operator!=</b>(const T2&amp; that) const</font></td>
<td>Compare inequality to an object that is a model of rectangle.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">interval_data&lt;T&gt; <b>get</b>(orientation_2d
orient) const</font></td>
<td>Get the interval in the given orientation.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template &lt;typename T2&gt;<br>
void <b>set</b>(orientation_2d orient, const T2&amp; value)</font></td>
<td>Sets the interval in the given orientation to the value of an object
that models interval.</td>
</tr>
</table>
<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" rules="none" frame="void" id="table3">
<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>
</table>
</html>