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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en" xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:(null)1="http://www.w3.org/TR/REC-html40"><head><!--
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Copyright 2009-2010 Intel Corporation
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license banner
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-->
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<title>Boost Polygon Library: Interval Concept</title>
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<meta http-equiv="content-type" content="text/html;charset=ISO-8859-1">
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<table style="margin: 0pt; padding: 0pt; width: 100%;" border="0" cellpadding="0" cellspacing="0"><tbody><tr>
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<td style="background-color: rgb(238, 238, 238);" nowrap="1" valign="top">
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<div style="padding: 5px;" align="center">
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<img border="0" src="images/boost.png" width="277" height="86"><a title="www.boost.org home page" href="http://www.boost.org/" tabindex="2" style="border: medium none ;">
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</a>
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</div>
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<div style="margin: 5px;">
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<h3 class="navbar">Contents</h3>
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<ul>
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<li><a href="index.htm">Boost.Polygon Main Page</a></li>
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<li><a href="gtl_design_overview.htm">Design Overview</a></li>
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<li><a href="gtl_isotropy.htm">Isotropy</a></li>
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<li><a href="gtl_coordinate_concept.htm">Coordinate Concept</a></li>
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<li>Interval Concept</li>
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<li><a href="gtl_point_concept.htm">Point Concept</a></li>
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<li><a href="gtl_rectangle_concept.htm">Rectangle Concept</a></li>
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<li><a href="gtl_polygon_90_concept.htm">Polygon 90 Concept</a></li>
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<li><a href="gtl_polygon_90_with_holes_concept.htm">Polygon 90 With Holes Concept</a></li>
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<li><a href="gtl_polygon_45_concept.htm">Polygon 45 Concept</a></li>
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<li><a href="gtl_polygon_45_with_holes_concept.htm">Polygon 45 With Holes Concept</a></li>
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<li><a href="gtl_polygon_concept.htm">Polygon Concept</a></li>
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<li><a href="gtl_polygon_with_holes_concept.htm">Polygon With Holes Concept</a></li>
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<li><a href="gtl_polygon_90_set_concept.htm">Polygon 90 Set Concept</a></li>
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<li><a href="gtl_polygon_45_set_concept.htm">Polygon 45 Set Concept</a></li>
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<li><a href="gtl_polygon_set_concept.htm">Polygon Set Concept</a></li>
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<li><a href="gtl_connectivity_extraction_90.htm">Connectivity Extraction 90</a></li>
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<li><a href="gtl_connectivity_extraction_45.htm">Connectivity Extraction 45</a></li>
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<li><a href="gtl_connectivity_extraction.htm">Connectivity Extraction</a></li>
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<li><a href="gtl_property_merge_90.htm">Property Merge 90</a></li>
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<li><a href="gtl_property_merge_45.htm">Property Merge 45</a></li>
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<li><a href="gtl_property_merge.htm">Property Merge</a></li>
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</ul>
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<h3 class="navbar">Other Resources</h3>
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<ul>
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<li><a href="GTL_boostcon2009.pdf">GTL Boostcon 2009 Paper</a></li>
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<li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
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Presentation</a></li>
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<li><a href="analysis.htm">Performance Analysis</a></li>
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<li><a href="gtl_tutorial.htm">Layout Versus Schematic Tutorial</a></li>
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<li><a href="gtl_minkowski_tutorial.htm">Minkowski Sum Tutorial</a></li>
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</ul>
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</div>
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<h3 class="navbar">Polygon Sponsor</h3>
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<div style="padding: 5px;" align="center">
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<img border="0" src="images/intlogo.gif" width="127" height="51">
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</div>
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</td>
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<td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%">
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<!-- End Header -->
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<br>
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<p>
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</p><h1>Interval Concept</h1>
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<p>
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<p>The interval concept tag is <font face="Courier New">
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interval_concept</font></p>
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<p>
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To register a user defined type as a model of interval concept, specialize the
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geometry concept meta-function for that type. In the example below
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CInterval is registered as a model of interval concept.<p>
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<font face="Courier New">template <><br>
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struct geometry_concept<CInterval> { typedef interval_concept type; };</font><p>
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<font face="Times New Roman">The semantic of an interval is that it has a low
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and high coordinate and there is an invariant that low is less than or equal to
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high. This invariant is enforced by the generic library functions that
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operate on intervals, and is not expected of the data type itself or the concept
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mapping of that data type to the interval concept through its traits. In
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this way a std::pair<int, int>, boost::tuple<int, int> or boost::array<int, 2>
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could all be made models of interval by simply providing indirect access to their
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elements through traits.</font><p>
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<font face="Times New Roman">Below is shown the default interval traits.
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Specialization of these traits is required for types that don't conform to the
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default behavior.</font><p>
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<font face="Courier New">template <typename T><br>
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struct interval_traits {<br>
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typedef typename T::coordinate_type coordinate_type;<br>
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<br>
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static inline coordinate_type get(const T& interval, direction_1d dir) {<br>
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return interval.get(dir); <br>
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}<br>
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};<br>
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<br>
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template <typename T><br>
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struct interval_mutable_traits {<br>
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static inline void set(T& interval, direction_1d dir, </font>
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<br>
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<font face="Courier New"> typename interval_traits<T>::coordinate_type value) {<br>
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interval.set(dir, value); <br>
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}<br>
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static inline T construct(typename interval_traits<T>::coordinate_type low_value,
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<br>
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typename interval_traits<T>::coordinate_type high_value) {<br>
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return T(low_value, high_value); <br>
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}<br>
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};</font><h2>Functions</h2>
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<table border="1" width="100%" id="table1">
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<tr>
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<td width="586"><font face="Courier New">template <typename T><br>
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coordinate_type <b>get</b>(const T& interval, direction_1d)</font></td>
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<td><font face="Times New Roman">Expects a model of interval.
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Returns the low or high coordinate of the interval, depending on the
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direction_1d value.</font><font face="Courier New"><br>
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</font></td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T, typename
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coordinate_type><br>
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void <b>set</b>(T& interval, direction_1d, coordinate_type)</font></td>
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<td><font face="Times New Roman">Expects a model of interval.
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Sets the low or high coordinate of the interval to the coordinate,
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depending on the direction_1d value. If low would be greater than
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high after this change then both are set to the input coordinate value.</font></td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T><br>
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T <b>construct</b>(coordinate_type low, coordinate_type high)</font></td>
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<td>Construct an object that is a model of interval given low and high
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coordinate values.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T1, typename
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T2><br>
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T1& <b>assign</b>(T1& left, const T2& right)</font></td>
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<td>Copies data from right object that models interval into left object
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that models interval.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T, typename
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T2><br>
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bool <b>equivalence</b>(const T& interval1, const T2& interval2)</font></td>
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<td>Given two objects that model interval, compares and returns true if
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their low and high values are respectively equal to each other.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T><br>
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bool <b>contains</b>(const T&, coordinate_type, <br>
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bool consider_touch=true)</font></td>
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<td>Given an object that models interval and a coordinate, returns true
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if the interval contains the coordinate. If the consider_touch
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flag is true will return true if the coordinate is equal to one of the
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interval ends.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T1, typename
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T2><br>
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bool <b>contains</b>(const T1& a, const T2& b, <br>
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bool consider_touch = true) </font></td>
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<td>Returns true if model of interval a contains both ends of model of
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interval b. If the consider_touch flag is true will consider the
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end of b contained within a even if it is equal to an end of a.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename
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interval_type><br>
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coordinate_type <b>low</b>(const interval_type& interval)</font></td>
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<td>Returns the low end of an object that models interval.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename
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interval_type><br>
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coordinate_type <b>high</b>(const interval_type& interval)</font></td>
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<td>Returns the high end of an object that models interval.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">// get the center coordinate<br>
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template <typename interval_type><br>
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coordinate_type <b>center</b>(const interval_type& interval)</font></td>
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<td>Returns the center coordinate of an object that models interval.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename
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interval_type><br>
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void <b>low</b>(interval_type& interval, coordinate_type )</font></td>
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<td>Sets the low end of the object that models interval to the
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coordinate value. If the low end would be set to larger than high
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end then both are set to the coordinate value.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename
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interval_type><br>
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void <b>high</b>(interval_type& interval, coordinate_type )</font></td>
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<td>Sets the high end of the object that models interval to the
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coordinate value. If the high end would be set to less than low
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end then both are set to the coordinate value.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename
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interval_type><br>
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coordinate_difference <b>delta</b>(const interval_type& interval)</font></td>
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<td>Returns the distance from low to high end of an object that models
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interval.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename
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interval_type><br>
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interval_type& <b>flip</b>(interval_type& interval,<br>
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coordinate_type axis = 0)</font></td>
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<td>Flips an object that models interval about the axis coordinate.
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If no axis is provided the interval is flipped across the the origin.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename
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interval_type><br>
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interval_type& <b>scale_up</b>(interval_type& interval, <br>
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unsigned_area_type factor)</font></td>
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<td>Multiplies low and high ends of an object that models interval by
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unsigned factor.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename
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interval_type><br>
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interval_type& <b>scale_down</b>(interval_type& interval, <br>
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unsigned_area_type factor)</font></td>
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<td>Divides low and high ends of an object that models interval by
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unsigned factor.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename
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interval_type><br>
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interval_type& <b>scale</b>(interval_type& interval,<br>
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double factor) </font></td>
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<td>Multiplies low and high ends of an object that models interval by
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floating point value.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename
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interval_type><br>
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interval_type& <b>move</b>(interval_type& interval,<br>
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coordinate_difference displacement)</font></td>
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<td>Adds displacement value to low and high ends of an object that
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models interval.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename
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interval_type><br>
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interval_type& <b>convolve</b>(interval_type& interval,<br>
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coordinate_type b)</font></td>
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<td>Adds coordinate value to low and high ends of an object that models
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interval.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename
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interval_type><br>
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interval_type& <b>deconvolve</b>(interval_type& interval,<br>
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coordinate_type b)</font></td>
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<td>Subtracts coordinate value from low and high ends of an object that
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models interval.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T1, typename
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T2><br>
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T1& <b>convolve</b>(T1& a, const T2& b)</font></td>
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<td>Adds low end of b to low end of a and adds high end of b to high end
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of a.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T1, typename
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T2><br>
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T1& <b>deconvolve</b>(T1& a, const T2& b)</font></td>
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<td>Subtracts low end of b from low end of a and subtracts high end of b
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from high end of a. </td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T1, typename
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T2><br>
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T1& <b>reflected_convolve</b>(T1& a, const T2& b)</font></td>
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<td>Adds high end of b to low end of a and adds low end of b to high end
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of a.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T1, typename
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T2><br>
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T1& <b>reflected_deconvolve</b>(T1& a, const T2& b)</font></td>
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<td>Subtracts high end of b from low end of a and subtracts low end of b
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from high end of a.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T><br>
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coordinate_difference <b>euclidean_distance</b>(const T&,<br>
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coordinate_type)</font></td>
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<td>Returns the distance from an object that models interval to a
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coordinate. Returns zero if the coordinate is equal to an end of
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the interval or contained within the interval.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T1, typename
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T2><br>
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bool <b>intersects</b>(const T1& interval, const T2& b, <br>
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bool consider_touch = true)</font></td>
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<td>Returns true if two objects that model interval overlap. If
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the consider_touch flag is true touching at the endpoints is considered
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overlap.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T1, typename
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T2><br>
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bool <b>boundaries_intersect</b>(const T1& interval, const T2& b, <br>
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bool consider_touch = true)</font></td>
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<td>Returns true is two objects that model interval partially overlap
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such that one end point of each is contained within the other. If
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the consider_touch flag is true a coordinate is considered contained
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even if it is equal to an end.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T1, typename
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T2><br>
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bool <b>abuts</b>(const T1& a, const T2& b,<br>
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direction_1d dir)
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</font></td>
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<td>Returns true if interval b abuts but down not overlap interval a on
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the end of interval a specified by dir.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T1, typename
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T2><br>
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bool <b>abuts</b>(const T1& a, const T2& b)</font></td>
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<td>Returns true if interval b abuts but down not overlap interval a.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T1, typename
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T2><br>
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bool <b>intersect</b>(T1& a, const T2& b,<br>
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bool consider_touch = true) </font></td>
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<td>Sets interval a to the intersection of interval a and interval b and
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return true. If the two intervals do not intersect interval a is
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unchanged and the function returns false. If the flag
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consider_touch is true intervals that abut are considered to intersect.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T1, typename
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T2><br>
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T& <b>generalized_intersect</b>(T1& a, const T2& b)</font></td>
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<td>Same as intersect, but if they do not intersect set a to the
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interval between a and b.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T><br>
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T& <b>bloat</b>(T& interval, coordinate_type)</font></td>
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<td>Adds the coordinate value to high end of interval and subtracts it
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from low end of interval.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T><br>
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T& <b>bloat</b>(T& interval, direction_1d, coordinate_type)</font></td>
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<td>Adds the coordinate value to high end of interval or subtracts it
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from low end of interval depending on the direction_1d.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T><br>
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T& <b>shrink</b>(T& interval, coordinate_type)</font></td>
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<td>Subtracts the coordinate value from high end of interval and adds it
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to low end of interval.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T><br>
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T& <b>shrink</b>(T& interval, direction_1d, coordinate_type)</font></td>
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<td>Subtracts the coordinate value from high end of interval or adds it
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to low end of interval depending on the direction_1d.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T1, typename
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T2><br>
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bool <b>encompass</b>(T1& a, const T2& b)</font></td>
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<td>Sets low of a to min of low of a and low of b and sets high of a to
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max of high of a and high of b. Returns true if b was not
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contained within a to begin with.</td>
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</tr>
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<tr>
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<td width="586"><font face="Courier New">template <typename T><br>
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bool <b>encompass</b>(T& a, coordinate_type)</font></td>
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<td>Sets low of a to min of low of a and coordinate value and sets high
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of a to max of high of a and coordinate value. Returns true if
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coordinate value was not contained within a to begin with.</td>
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</tr>
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</table>
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||
<h1>Interval Data</h1>
|
||
|
||
<p>
|
||
<p>The library provides a model of interval concept declared
|
||
<font face="Courier New">
|
||
template<typename T> interval_data </font>where T is the coordinate type.</p>
|
||
<p>This data type is used internally when an interval is needed and is available
|
||
to the library user who finds it convenient to use a library interval 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 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">interval_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_data</b>()</font></td>
|
||
<td><font face="Times New Roman">Default constructs the two coordinate
|
||
values of the interval.</font></td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New"><b>interval_data</b>(T low, T
|
||
high)</font></td>
|
||
<td><font face="Times New Roman">Constructs an interval with two
|
||
coordinates.</font></td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New"><b>interval_data</b>(const
|
||
interval_data& that)</font></td>
|
||
<td><font face="Times New Roman">Copy construct</font></td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">interval_data& <b>operator=</b>(const
|
||
interval_data& that)</font></td>
|
||
<td>Assignment operator.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">template <typename T2><b>
|
||
<br> </b>interval_data& <b>operator=</b>(const T2& that) const</font></td>
|
||
<td>Assign from an object that is a model of interval.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">template <typename T2><b>
|
||
<br> </b>bool<b>
|
||
operator==</b>(const T2& that) const</font></td>
|
||
<td>Compare equality to an object that is a model of interval.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">template <typename T2><b>
|
||
<br> </b>bool<b>
|
||
operator!=</b>(const T2& that) const</font></td>
|
||
<td>Compare inequality to an object that is a model of interval.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">template <typename T2><b>
|
||
<br> </b>bool<b>
|
||
operator<</b>(const T2& that) const</font></td>
|
||
<td>Compares low coordinates then high coordinates to break ties.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">template <typename T2><b>
|
||
<br> </b>bool<b>
|
||
operator<=</b>(const T2& that) const</font></td>
|
||
<td>Compares low coordinates then high coordinates to break ties.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">template <typename T2><b>
|
||
<br> </b>bool<b>
|
||
operator></b>(const T2& that) const</font></td>
|
||
<td>Compares low coordinates then high coordinates to break ties.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">template <typename T2><b>
|
||
<br> </b>bool<b>
|
||
operator>=</b>(const T2& that) const</font></td>
|
||
<td>Compares low coordinates then high coordinates to break ties.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">T <b>get</b>(direction_1d dir)
|
||
const</font></td>
|
||
<td>Get the coordinate in the given direction.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">void <b>set</b>(direction_1d
|
||
dir, T value)</font></td>
|
||
<td>Sets the coordinate in the given direction to the value.</td>
|
||
</tr>
|
||
</table>
|
||
<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" 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 <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>
|
||
</table>
|
||
|
||
</html> |