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  <title>Boost Polygon Library: Coordinate Concept</title>
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      <div style="padding: 5px;" align="center"> <img
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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>Coordinate Concept</li>
        <li><a href="gtl_interval_concept.htm">Interval Concept</a></li>
        <li><a href="gtl_point_concept.htm">Point Concept</a></li>
        <li><a href="gtl_segment_concept.htm">Segment Concept</a></li>
        <li><a href="gtl_rectangle_concept.htm">Rectangle Concept</a></li>
        <li><a href="gtl_polygon_90_concept.htm">Polygon 90 Concept</a></li>
        <li><a href="gtl_polygon_90_with_holes_concept.htm">Polygon 90
With Holes Concept</a></li>
        <li><a href="gtl_polygon_45_concept.htm">Polygon 45 Concept</a></li>
        <li><a href="gtl_polygon_45_with_holes_concept.htm">Polygon 45
With Holes Concept</a></li>
        <li><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>
      </div>
      <h3 class="navbar">Polygon Sponsor</h3>
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      <p>
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      <h1>Coordinate Concept</h1>
      <p> The coordinate concept tag is <font face="Courier New">
coordinate_concept</font></p>
      <p> To register a user defined type as a model of coordinate
concept, specialize the geometry concept meta-function for that
type.&nbsp; In the example below CCoordinate is registered as a model
of coordinate concept.</p>
      <p> <font face="Courier New">template &lt;&gt;<br />
struct geometry_concept&lt;CCoordinate&gt; { typedef coordinate_concept
type; };</font></p>
      <p> The coordinate type is expected to be integral and built-in
numerical data types such as float and int already have concept type
traits specializations in the library.&nbsp; In the coordinate traits
are type definitions for related types are provided to allow the
library to choose the best type to cast to under various
circumstances.&nbsp; The definition of coordinate_traits and its
specialization for int are shown below.</p>
      <p> <font face="Courier New">template &lt;typename T&gt;<br />
struct coordinate_traits {};<br />
      <br />
template &lt;&gt;<br />
struct coordinate_traits&lt;int&gt; {<br />
&nbsp;&nbsp;&nbsp;&nbsp; typedef int coordinate_type;<br />
&nbsp;&nbsp;&nbsp;&nbsp; typedef long double area_type;<br />
&nbsp;&nbsp;&nbsp;&nbsp; typedef long long manhattan_area_type;<br />
&nbsp;&nbsp;&nbsp;&nbsp; typedef unsigned long long unsigned_area_type;<br />
&nbsp;&nbsp;&nbsp;&nbsp; typedef long long coordinate_difference;<br />
&nbsp;&nbsp;&nbsp;&nbsp; typedef long double coordinate_distance;<br />
};</font></p>
      <p> By making use of the coordinate traits of int the library is
able to avoid overflow and handle the normal issues encountered when
programming integer geometry.&nbsp; For the out of the ordinary issues
there is a special meta-function that provides the library with a
numerical type suitable for exact numerical calculations.&nbsp; It
defaults to the highest precision data type available in most
compilers, long double, but can be overridden by specializing for a
particular coordinate type.&nbsp; Use of gmp multi-precision rational
or similar data type is recommended for numerically robust calculations
in the general polygon algorithms.</p>
      <p> <font face="Courier New">template &lt;typename T&gt;<br />
struct high_precision_type {<br />
&nbsp;&nbsp;&nbsp;&nbsp; typedef long double type;<br />
};</font></p>
      <p> There is only one generic function on coordinate concepts,
Euclidean distance.</p>
      <p> <font face="Courier New">template &lt;typename
coordinate_type_1, typename coordinate_type_2&gt;<br />
coordinate_difference euclidean_distance(coordinate_type_1,
coordinate_type_2)</font></p>
      <p> This function returns the absolution value of the difference
between the two coordinates.</p>
      <p> Note: older versions of the stl define a fully generic
distance(T, T) function for computing the difference between two
iterators.&nbsp; We were forced to name our distance function
euclidean_distance to avoid name collision.</p>
      <p> The
      <a
 href="http://www.mentor.com/products/esl/high_level_synthesis/ac_datatypes">
Algorithmic C</a> ac_int&lt;128&gt; is an example of a user defined
coordinate data type that satisfies the coordinate concept.&nbsp; In
general a data type should define std::numeric_limits and be
integer-like.&nbsp; Floating point coordinate types are not supported
by all the algorithms and generally not suitable for use with the
library at present.</p>
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