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<title>Boost Polygon Library: Segment Concept</title>
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<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><br />
</li>
<li>Segment Concept</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><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>
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<td
style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;"
valign="top" width="100%"><!-- End Header --><br />
<p> </p>
<h1>Segment Concept</h1>
<p> </p>
<p> The segment concept tag is <font face="Courier New">segment_concept</font></p>
<p> To register a user defined type as a model of the segment
concept, specialize the geometry concept meta-function for that
type.&nbsp; In the example below CSegment is registered as a model of
the segment concept.</p>
<p style="font-family: Courier New,Courier,monospace;"> template
&lt;&gt;<br />
struct geometry_concept&lt;CSegment&gt;
{ typedef segment_concept type; };</p>
<p> The semantic of a segment is
that it has a low and high point.&nbsp; A
std::pair&lt;Point, Point&gt;,
boost::tuple&lt;Point, Point&gt; or boost::array&lt;Point, 2&gt; could
all be made models of
segment by simply providing indirect access to their elements through
traits, however, these objects cannot be made a model of both segment
and rectangle in the same compilation unit, for obvious reason that
duplicate specialization of the geometry_concept struct is illegal, but
also because it would make overloading generic function by concept
ambiguous if a type modeled more than one concept.</p>
<p> Below is shown the default
segment traits. Specialization of these traits is required for
types that don't conform to the default behavior.</p>
<p><span style="font-family: Courier New,Courier,monospace;"><span
style="font-family: Courier New,Courier,monospace;">template
&lt;typename Segment&gt;</span><br
style="font-family: Courier New,Courier,monospace;" />
<span style="font-family: Courier New,Courier,monospace;">struct
segment_traits {</span><br
style="font-family: Courier New,Courier,monospace;" />
<span style="font-family: Courier New,Courier,monospace;">&nbsp;
typedef typename Segment::coordinate_type coordinate_type;</span><br
style="font-family: Courier New,Courier,monospace;" />
<span style="font-family: Courier New,Courier,monospace;">&nbsp;
typedef typename Segment::point_type point_type;</span><br
style="font-family: Courier New,Courier,monospace;" />
<br style="font-family: Courier New,Courier,monospace;" />
<span style="font-family: Courier New,Courier,monospace;">&nbsp;
static inline point_type get(const Segment&amp; segment, direction_1d
dir) {</span><br style="font-family: Courier New,Courier,monospace;" />
<span style="font-family: Courier New,Courier,monospace;">&nbsp;&nbsp;&nbsp;
return segment.get(dir);</span><br
style="font-family: Courier New,Courier,monospace;" />
<span style="font-family: Courier New,Courier,monospace;">&nbsp; }</span><br
style="font-family: Courier New,Courier,monospace;" />
<span style="font-family: Courier New,Courier,monospace;">};</span><br />
<br />
<span style="font-family: Courier New,Courier,monospace;">template
&lt;typename Segment&gt;<br />
struct segment_mutable_traits {<br />
&nbsp; </span></span><span
style="font-family: Courier New,Courier,monospace;"><span
style="font-family: Courier New,Courier,monospace;">typedef typename
segment_traits&lt;Segment&gt;::coordinate_type </span></span><span
style="font-family: Courier New,Courier,monospace;"><span
style="font-family: Courier New,Courier,monospace;">coordinate_type;</span></span><br />
<span style="font-family: Courier New,Courier,monospace;"><span
style="font-family: Courier New,Courier,monospace;">&nbsp; typedef
typename segment_traits&lt;Segment&gt;::point_type point_type;<br />
<br />
&nbsp; static inline void set(Segment&amp; segment, direction_1d dir,
const point_type&amp; point) {<br />
&nbsp;&nbsp;&nbsp; segment.set(dir, p);<br />
&nbsp; }<br />
<br />
&nbsp; static inline Segment construct(const point_type&amp; low, const
point_type&amp; high) {<br />
&nbsp;&nbsp;&nbsp; return Segment(low, high);<br />
&nbsp; }<br />
};</span></span></p>
<h2>Functions</h2>
<table style="width: 100%;" id="table1" border="1">
<tbody>
<tr>
<td width="586"><font face="Courier New">template
&lt;typename Segment&gt;<br />
point_type <b>get</b>(const Segment&amp; segment, direction_1d dir)</font></td>
<td>Returns the low or high endpoint of an object that
models segment, depending on
the direction_1d value.<font face="Courier New">&nbsp;</font></td>
</tr>
<tr>
<td width="586"><font face="Courier New">template
&lt;typename </font><font face="Courier New">Segment</font><font
face="Courier New">, typename Point&gt;<br />
void <b>set</b>(</font><font face="Courier New">Segment</font><font
face="Courier New">&amp; segment, direction_1d dir,<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; const Point&amp; </font><span
style="font-family: Courier New;">point</span><font face="Courier New">)</font></td>
<td>Sets
the low or high endpoint of an object that models segment to an object
that models point, depending on the direction_1d value.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template
&lt;typename Segment, typename Point1, typename Point2&gt;<br />
Segment<b> construct</b>(const Point1&amp; low, const Point2&amp; high)</font></td>
<td>Constructs an object that is a model of segment given
the two objects that are models of point.</td>
</tr>
<tr>
<td><font face="Courier New">template &lt;typename
Segment1, typename </font><font face="Courier New">Segment2</font><font
face="Courier New">&gt;<br />
</font><font face="Courier New">Segment1</font><font
face="Courier New"> <span style="font-weight: bold;">copy_construct</span>(const
</font><font face="Courier New">Segment2</font><font
face="Courier New">&amp; segment)</font></td>
<td style="text-align: left;">Copy constructs an object
that models segment given another segment.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template
&lt;typename </font><font face="Courier New">Segment1</font><font
face="Courier New">, typename </font><font face="Courier New">Segment2&gt;</font><br />
<font face="Courier New">Segment1</font><font
face="Courier New">&amp; <b>assign</b>(</font><font face="Courier New">Segment1</font><font
face="Courier New">&amp; segment1,<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
const </font><font face="Courier New">Segment2</font><font
face="Courier New">&amp; segment2)</font></td>
<td>Copies data from the second object that models segment
into
the first object that models segment.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template
&lt;typename </font><font face="Courier New">Segment1</font><font
face="Courier New">, typename </font><font face="Courier New">Segment1</font><font
face="Courier New">&gt;<br />
bool <b>equivalence</b>(const </font><font face="Courier New">Segment1</font><font
face="Courier New">&amp; segment1,<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
const </font><font face="Courier New">Segment1</font><font
face="Courier New">&amp; segment2)</font></td>
<td>Given two objects that model segment, compares and
returns true if their low and high values are respectively equal.</td>
</tr>
<tr>
<td><span
style="font-family: Courier New,Courier,monospace;">template
&lt;typename Segment, typename Point&gt;</span><br
style="font-family: Courier New,Courier,monospace;" />
<span style="font-family: Courier New,Courier,monospace;">int
<b>orientation</b></span><span
style="font-family: Courier New,Courier,monospace;">(const </span><span
style="font-family: Courier New,Courier,monospace;">Segment</span><span
style="font-family: Courier New,Courier,monospace;">&amp; segment,</span><br
style="font-family: Courier New,Courier,monospace;" />
<span style="font-family: Courier New,Courier,monospace;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
const Point&amp; point)</span><br />
</td>
<td>Implements
a robust orientation test of two objects that model segment and point.
Returns 0, if the point is collinear to the segment.<br />
Returns 1, if the point lies to the left of the segment.<br />
Returns -1, if the point lies to the right of the segment.<br />
</td>
</tr>
<tr>
<td><span
style="font-family: Courier New,Courier,monospace;">template
&lt;typename Segment1, typename Segment2&gt;</span><br
style="font-family: Courier New,Courier,monospace;" />
<span style="font-family: Courier New,Courier,monospace;">int
<b>orientation</b></span><span
style="font-family: Courier New,Courier,monospace;">(const </span><span
style="font-family: Courier New,Courier,monospace;">Segment1</span><span
style="font-family: Courier New,Courier,monospace;">&amp; segment1,</span><br
style="font-family: Courier New,Courier,monospace;" />
<span style="font-family: Courier New,Courier,monospace;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
const Segment2&amp; segment2)</span></td>
<td>Implements a robust orientation test of two objects
that model segment. Note: segments are treated as math.
vectors.<br />
Returns 0, if segments are collinear.<br />
Returns 1, if the second segment is CCW oriented to the first segment.<br />
Returns -1, if the second segment is CW oriented to the first segment.<br />
</td>
</tr>
<tr>
<td><span
style="font-family: Courier New,Courier,monospace;">template
&lt;typename </span><font face="Courier New">Segment, typename Point</font><span
style="font-family: Courier New,Courier,monospace;">&gt;</span><br
style="font-family: Courier New,Courier,monospace;" />
<span style="font-family: Courier New,Courier,monospace;">bool
</span><span
style="font-weight: bold; font-family: Courier New,Courier,monospace;">contains</span><span
style="font-family: Courier New,Courier,monospace;">(const </span><font
face="Courier New">Segment</font><span
style="font-family: Courier New,Courier,monospace;">&amp; segment,</span><br
style="font-family: Courier New,Courier,monospace;" />
<span style="font-family: Courier New,Courier,monospace;">&nbsp;&nbsp;&nbsp;
const Point&amp; value,</span><span
style="font-family: Courier New,Courier,monospace;"> bool
consider_touch)</span><br />
</td>
<td>Returns true if an object that models segment contains
an object that models point, else false.<br />
</td>
</tr>
<tr>
<td><span
style="font-family: Courier New,Courier,monospace;">template
&lt;typename Segment1, typename Segment2&gt;</span><br
style="font-family: Courier New,Courier,monospace;" />
<span style="font-family: Courier New,Courier,monospace;">bool
</span><span
style="font-weight: bold; font-family: Courier New,Courier,monospace;">contains</span><span
style="font-family: Courier New,Courier,monospace;">(const </span><span
style="font-family: Courier New,Courier,monospace;">Segment1</span><span
style="font-family: Courier New,Courier,monospace;">&amp; segment1,</span><br
style="font-family: Courier New,Courier,monospace;" />
<span style="font-family: Courier New,Courier,monospace;">&nbsp;&nbsp;&nbsp;
const </span><span style="font-family: Courier New,Courier,monospace;">Segment</span><span
style="font-family: Courier New,Courier,monospace;">2&amp; segment2,</span>
<span style="font-family: Courier New,Courier,monospace;">bool
consider_touch)</span></td>
<td>Returns true if the first object contains the second
one, else false. Both objects model segment.<br />
</td>
</tr>
<tr>
<td style="font-family: Courier New,Courier,monospace;">template
&lt;typename <span style="font-family: Courier New,Courier,monospace;">Segment</span>&gt;<br />
point_type <span style="font-weight: bold;">low</span>(const <span
style="font-family: Courier New,Courier,monospace;">Segment</span>&amp;
segment)<br />
</td>
<td>Returns the low endpoint of an object that models
segment.<br />
</td>
</tr>
<tr>
<td style="font-family: Courier New,Courier,monospace;">template
&lt;typename <span style="font-family: Courier New,Courier,monospace;">Segment</span>&gt;<br />
point_type <span style="font-weight: bold;">high</span>(const <span
style="font-family: Courier New,Courier,monospace;">Segment</span>&amp;
segment)</td>
<td>Returns the high endpoint of an object that models
segment.<br />
</td>
</tr>
<tr>
<td style="font-family: Courier New,Courier,monospace;">template
&lt;typename <span style="font-family: Courier New,Courier,monospace;">Segment</span>&gt;<br />
point_type <span style="font-weight: bold;">center</span>(const <span
style="font-family: Courier New,Courier,monospace;">Segment</span>&amp;
segment)</td>
<td>Returns the central point of an object that models
segment.<br />
</td>
</tr>
<tr>
<td style="font-family: Courier New,Courier,monospace;">template
&lt;typename <span style="font-family: Courier New,Courier,monospace;">Segment</span>,
typename Point&gt;<br />
void <span style="font-weight: bold;">low</span>(<span
style="font-family: Courier New,Courier,monospace;">Segment</span>&amp;
segment, const Point&amp; point)</td>
<td>Sets the low endpoint of an object that models segment.<br />
</td>
</tr>
<tr>
<td style="font-family: Courier New,Courier,monospace;">template
&lt;typename <span style="font-family: Courier New,Courier,monospace;">Segment,
typename Point</span>&gt;<br />
void <span style="font-weight: bold;">high</span>(<span
style="font-family: Courier New,Courier,monospace;">Segment</span>&amp;
segment, const Point&amp; point)</td>
<td>Sets the high endpoint of an object that models of
segment.<br />
</td>
</tr>
<tr>
<td><span
style="font-family: Courier New,Courier,monospace;">template
&lt;typename </span><span
style="font-family: Courier New,Courier,monospace;">Segment</span><span
style="font-family: Courier New,Courier,monospace;">&gt;</span><br
style="font-family: Courier New,Courier,monospace;" />
<span style="font-family: Courier New,Courier,monospace;">distance_type
<span style="font-weight: bold;">length</span>(const </span><span
style="font-family: Courier New,Courier,monospace;">Segment</span><span
style="font-family: Courier New,Courier,monospace;">&amp; segment)</span><br />
</td>
<td>Returns length of an object that models segment.<br />
</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template
&lt;typename </font><span
style="font-family: Courier New,Courier,monospace;">Segment</span><font
face="Courier New">&gt;<br />
</font><span
style="font-family: Courier New,Courier,monospace;">Segment</span><font
face="Courier New">&amp; <b>scale_up</b>(</font><span
style="font-family: Courier New,Courier,monospace;">Segment</span><font
face="Courier New">&amp; </font><font face="Courier New">segment</font><font
face="Courier New">, <br />
&nbsp;&nbsp;&nbsp; unsigned_area_type factor)</font></td>
<td>Multiplies x and y coordinates of both endpoints of an
object that models segment by unsigned factor.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template
&lt;typename </font><span
style="font-family: Courier New,Courier,monospace;">Segment</span><font
face="Courier New">&gt;<br />
</font><span
style="font-family: Courier New,Courier,monospace;">Segment</span><font
face="Courier New">&amp; <b>scale_down</b>(</font><span
style="font-family: Courier New,Courier,monospace;">Segment</span><font
face="Courier New">&amp; </font><font face="Courier New">segment</font><font
face="Courier New">, <br />
&nbsp;&nbsp;&nbsp; unsigned_area_type factor)</font></td>
<td>Divides x and y coordinates of both endpoints of an
object that models segment by unsigned factor.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template
&lt;typename </font><span
style="font-family: Courier New,Courier,monospace;">Segment</span><font
face="Courier New">, typename Scale&gt;<br />
</font><span
style="font-family: Courier New,Courier,monospace;">Segment</span><font
face="Courier New">&amp; <b>scale</b>(</font><span
style="font-family: Courier New,Courier,monospace;">Segment</span><font
face="Courier New">&amp; </font><font face="Courier New">segment</font><font
face="Courier New">, const Scale&amp; sc) </font></td>
<td>Calls
the scale member function of the scaling type on the low and high
endpoint of
an object that models segment and updates the segment with the
scaled endpoints.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template
&lt;typename </font><span
style="font-family: Courier New,Courier,monospace;">Segment</span><font
face="Courier New">, typename Transform&gt;<br />
</font><span
style="font-family: Courier New,Courier,monospace;">Segment</span><font
face="Courier New">&amp; <b>transform</b>(</font><span
style="font-family: Courier New,Courier,monospace;">Segment</span><font
face="Courier New">&amp; segment, const </font><font
face="Courier New">Transform</font><font face="Courier New">&amp; tr) </font></td>
<td>Calls the transform member function of transform type
on the low and high endpoints of an object that models segment and
updates the segment with the transformed endpoints.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template
&lt;typename </font><span
style="font-family: Courier New,Courier,monospace;">Segment</span><font
face="Courier New">&gt;<br />
</font><span
style="font-family: Courier New,Courier,monospace;">Segment</span><font
face="Courier New">&amp; <b>move</b>(</font><span
style="font-family: Courier New,Courier,monospace;">Segment</span><font
face="Courier New">&amp; segment, orientation_2d<br />
&nbsp;&nbsp;&nbsp; coordinate_difference displacement)</font></td>
<td>Adds displacement value to the x or y coordinates of
both endpoints of an object
that models segment indicated by the orientation_2d.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template
&lt;</font><span style="font-family: Courier New,Courier,monospace;">Segment,
Point</span><font face="Courier New">&gt;<br />
</font><span
style="font-family: Courier New,Courier,monospace;">Segment</span><font
face="Courier New">&amp; <b>convolve</b>(</font><span
style="font-family: Courier New,Courier,monospace;">Segment</span><font
face="Courier New">&amp; segment, const Point&amp; point)</font></td>
<td>Convolves both endpoints of an object that models
segment with an object that models a point.<br />
</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template
&lt;</font><span style="font-family: Courier New,Courier,monospace;">Segment,
Point</span><font face="Courier New">&gt;<br />
</font><span
style="font-family: Courier New,Courier,monospace;">Segment</span><font
face="Courier New">&amp; <b>deconvolve</b>(</font><span
style="font-family: Courier New,Courier,monospace;">Segment</span><font
face="Courier New">&amp; segment, const Point&amp; point)</font></td>
<td>Deconvolves both endpoints of an object that models
segment with an object that models a point. </td>
</tr>
<tr>
<td style="font-family: Courier New,Courier,monospace;">template
&lt;typename Segment1, typename Segment2&gt;<br />
bool <span style="font-weight: bold;">abuts</span>(const Segment1&amp;
segment1,<br />
&nbsp;&nbsp;&nbsp; const Segment2&amp; segment2, direction_1d dir)</td>
<td>Returns true if two objects that model segment abut,
depending on the direction_1d value.</td>
</tr>
<tr>
<td style="font-family: Courier New,Courier,monospace;">template
&lt;typename Segment1, typename Segment2&gt;<br />
bool <span style="font-weight: bold;">abuts</span>(const Segment1&amp;
segment1,<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; const
Segment2&amp; segment2)</td>
<td>Returns true if two objects that model segment abut:
either the first one to the second one or vice versa.</td>
</tr>
<tr>
<td><span
style="font-family: Courier New,Courier,monospace;">template
&lt;typename Segment1, typename Segment2&gt;</span><br
style="font-family: Courier New,Courier,monospace;" />
<span style="font-family: Courier New,Courier,monospace;">bool
<span style="font-weight: bold;">intersects</span>(const
Segment1&amp; segment1,</span><br
style="font-family: Courier New,Courier,monospace;" />
<span style="font-family: Courier New,Courier,monospace;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
const Segment2&amp; segment2,<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
bool consider_touch)</span><br />
</td>
<td>Returns true if two objects that model segment
intersect, else false.<br />
</td>
</tr>
<tr>
<td style="font-family: Courier New,Courier,monospace;"><font
face="Courier New">template
&lt;typename </font><span
style="font-family: Courier New,Courier,monospace;">Segment, typename
Point</span><font face="Courier New">&gt;<br />
distance_type <b>euclidean_distance</b>(<br />
&nbsp;&nbsp;&nbsp; const </font><span
style="font-family: Courier New,Courier,monospace;">Segment</span><font
face="Courier New">&amp; segment, const Point&amp; point)</font> </td>
<td>Returns distance from an object that models segment
to an object that models point. </td>
</tr>
<tr>
<td style="font-family: Courier New,Courier,monospace;"><font
face="Courier New">template
&lt;typename Segment1, typename </font><font face="Courier New">Segment2</font><font
face="Courier New">&gt;<br />
distance_type <b>euclidean_distance</b>(<br />
&nbsp;&nbsp;&nbsp; const </font><font face="Courier New">Segment1</font><font
face="Courier New">&amp; segment1, const </font><font
face="Courier New">Segment2</font><font face="Courier New">&amp;
segment2)</font> </td>
<td>Returns distance between two objects that model
segment. </td>
</tr>
</tbody>
</table>
<h1>Segment Data</h1>
<p> </p>
<p>The library provides a model of the segment concept declared <font
face="Courier New">template&lt;typename T&gt; segment_data</font>,
where
T is the coordinate type.</p>
<p>This data type is used internally when a segment is needed and
is available to the library user, who finds it convenient to use a
library segment 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 style="width: 100%;" id="table2" border="1">
<tbody>
<tr>
<td width="586"><b><font face="Courier New">geometry_type</font></b></td>
<td>segment_concept</td>
</tr>
<tr>
<td width="586"><b><font face="Courier New">coordinate_type</font></b></td>
<td>T</td>
</tr>
<tr>
<td><b><font face="Courier New">point_type</font></b></td>
<td>point_data&lt;T&gt;<br />
</td>
</tr>
<tr>
<td width="586"><font face="Courier New"><b>segment_data</b>()</font></td>
<td>Default constructor.</td>
</tr>
<tr>
<td width="586"><font face="Courier New"><b>segment_data</b>(const
point_type&amp; low,<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
const point_type&amp; high)</font></td>
<td>Constructs a segment from the given endpoints.</td>
</tr>
<tr>
<td width="586"><font face="Courier New"><b>segment_data</b>(const
segment_data&amp; that)</font></td>
<td>Copy constructor.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">segment_data&amp; <b>operator=</b>(const
segment_data&amp; that)</font></td>
<td>Assignment operator.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">template
&lt;typename SegmentType&gt;<b><br />
</b>segment_data&amp; <b>operator=</b>(const </font><font
face="Courier New">SegmentType</font><font face="Courier New">&amp;
that)
const</font></td>
<td>Assign from an object that is a model of segment.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">bool<b> operator==</b>(const
segment_data&amp; that) const</font></td>
<td>Equality operator overload.</td>
</tr>
<tr>
<td width="586"><font face="Courier New"><b> </b>bool<b>
operator!=</b>(const segment_data&amp; that) const</font></td>
<td>Inequality operator overload.</td>
</tr>
<tr>
<td width="586"><font face="Courier New"><b> </b>bool<b>
operator&lt;</b>(const segment_data&amp; that) const</font></td>
<td>Less operator overload. Compares low endpoints then
high endpoints to break ties.<br />
</td>
</tr>
<tr>
<td width="586"><font face="Courier New"><b> </b>bool<b>
operator&lt;=</b>(const segment_data&amp; that) const</font></td>
<td>Less or equal operator overload. Compares low endpoints
then high endpoints to break ties.<br />
</td>
</tr>
<tr>
<td width="586"><font face="Courier New"><b> </b>bool<b>
operator&gt;</b>(const segment_data&amp; that) const</font></td>
<td>Greater operator overload. Compares low endpoints then
high endpoints to break ties.<br />
</td>
</tr>
<tr>
<td width="586"><font face="Courier New"><b> </b>bool<b>
operator&gt;=</b>(const segment_data&amp; that) const</font></td>
<td>Greater or equal operator overload. Compares low
endpoints then high endpoints to break ties.<br />
</td>
</tr>
<tr>
<td width="586"><font face="Courier New">point_type <b>get</b>(direction_1d
dir) const</font></td>
<td>Retrieves the low/high endpoint considering direction
value.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">point_type <span
style="font-weight: bold;">low</span>() const</font></td>
<td>Retrieves the low endpoint.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">point_type <span
style="font-weight: bold;">high</span>() const</font></td>
<td>Retrieves the high endpoint.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">void <b>set</b></font><font
face="Courier New">(direction_1d dir</font><font face="Courier New">,
const point_type&amp; point)</font></td>
<td>Sets the endpoint in the given direction.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">segment_data&amp; <span
style="font-weight: bold;">low</span>(const point_type&amp; point)</font></td>
<td>Sets the low endpoint.</td>
</tr>
<tr>
<td width="586"><font face="Courier New">segment_data&amp; <span
style="font-weight: bold;">high(</span>const point_type&amp; point)</font></td>
<td>Sets the high endpoint.</td>
</tr>
</tbody>
</table>
<h1>Segment Utils</h1>
<p> </p>
<p>The library provides several algorithms for the manipulation
of sets of segment data. In particular, the generalize line segment
intersection algorithm used for polygon set operations is exposed
through several interfaces to allow it to be used with any collection
or sequence of objects that model the <font face="Courier New">segment_concept</font>.
</p>
<h2>Functions</h2>
<table style="width: 100%;" id="table3" border="1">
<tbody>
<tr>
<td width="586"><font face="Courier New">template
&lt;</font><font face="Courier New">typename SegmentContainer</font><font
face="Courier New">,</font><font face="Courier New"><br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; typename
SegmentIterator</font><font face="Courier New">&gt;<b><br />
</b>void <b>intersect_segments</b>(<br />
&nbsp;&nbsp;&nbsp; </font><font face="Courier New">SegmentContainer*
result,</font><br />
<font face="Courier New">&nbsp;&nbsp;&nbsp; SegmentIterator
first,<br />
&nbsp;&nbsp;&nbsp; SegmentIterator last) </font></td>
<td>Accumulates
the result of splitting the segments in the iterator range at their
intersection points into the result container. Preconditions: segment
type used by all the input structures should model segment
concept.Postconditions: no segments intersect except at their end
points. Useful to satisfy the precondition of voronoi diagram
construction. Expected n log n runtime, worst case quadratic runtime
wrt. vertices + intersections. </td>
</tr>
<tr>
<td width="586"><font face="Courier New">template
&lt;</font><font face="Courier New">typename Segment,</font><font
face="Courier New"><br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </font><font
face="Courier New">typename SegmentIterator</font><font
face="Courier New">&gt;<b><br />
</b>void <b>intersect_segments</b>(<br />
&nbsp;&nbsp;&nbsp; </font><font face="Courier New">vector&lt;pair&lt;size_t,
Segment&gt;* result,</font><br />
<font face="Courier New">&nbsp;&nbsp;&nbsp; SegmentIterator
first,<br />
&nbsp;&nbsp;&nbsp; SegmentIterator last)</font></td>
<td>Accumulates
the result of splitting the segments in the iterator range at their
intersection points into the result container. Preconditions: segment
type used by all the input structures should model segment concept.
Postconditions: no segments intersect except at their end points. The
index of the input segment is paired with each resultant segment that
was split to produce it to associate the result segments with the
inputs segments. Expected n log n runtime, worst case quadratic runtime
wrt. vertices + intersections. </td>
</tr>
<tr>
<td width="586"><font face="Courier New">template
&lt;</font><font face="Courier New">typename Rectangle,<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </font><font
face="Courier New">typename </font><font face="Courier New">SegmentIterator</font><font
face="Courier New">&gt;<b><br />
</b>void <span style="font-weight: bold;">envelope_segments</span>(<br />
&nbsp;&nbsp;&nbsp; </font><font face="Courier New">Rectangle* rect,</font><br />
<font face="Courier New">&nbsp;&nbsp;&nbsp; </font><font
face="Courier New">SegmentIterator first,<br />
&nbsp; &nbsp; SegmentIterator last</font><font face="Courier New">) </font></td>
<td>Computes
the bounding rectangle of the iterator range of line segments.
Preconditions: segment type and rectangle type used by the input
structures should model segment concept and rectangle concept
respectively. Linear runtime. </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="table4" 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 <20> 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>
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