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- <title>Boost Polygon Library: Interval Concept</title>
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- <td style="background-color: rgb(238, 238, 238);" nowrap="1"
- valign="top">
- <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>Interval Concept</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 />
- </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>
- </td>
- <td
- style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;"
- valign="top" width="100%">
- <!-- End Header --><br />
- <p>
- </p>
- <h1>Interval Concept</h1>
- <p> </p>
- <p>The interval concept tag is <font face="Courier New">
- interval_concept</font></p>
- <p> To register a user defined type as a model of interval
- concept, specialize the geometry concept meta-function for that
- type. In the example below CInterval is registered as a model of
- interval concept.</p>
- <p> <font face="Courier New">template <><br />
- struct geometry_concept<CInterval> { typedef interval_concept
- type; };</font></p>
- <p> <font face="Times New Roman">The semantic of an interval is
- that it has a low and high coordinate and there is an invariant that
- low is less than or equal to high. This invariant is enforced by
- the generic library functions that operate on intervals, and is not
- expected of the data type itself or the concept mapping of that data
- type to the interval concept through its traits. In this way a
- std::pair<int, int>, boost::tuple<int, int> or
- boost::array<int, 2> could all be made models of interval by
- simply providing indirect access to their elements through traits.</font></p>
- <p> <font face="Times New Roman">Below is shown the default
- interval traits. Specialization of these traits is required for
- types that don't conform to the default behavior.</font></p>
- <p> <font face="Courier New">template <typename T><br />
- struct interval_traits {<br />
- typedef typename T::coordinate_type coordinate_type;<br />
- <br />
- static inline coordinate_type get(const T& interval,
- direction_1d dir) {<br />
- return interval.get(dir); <br />
- }<br />
- };<br />
- <br />
- template <typename T><br />
- struct interval_mutable_traits {<br />
- </font><font face="Courier New">typedef typename
- T::coordinate_type coordinate_type;</font><br />
- <font face="Courier New"><br />
- static inline void set(T& interval, direction_1d dir, </font>
- <br />
- <font face="Courier New">
- typename interval_traits<T>::coordinate_type value) {<br />
-
- interval.set(dir, value); <br />
-
- }<br />
-
- static inline T construct(typename
- interval_traits<T>::coordinate_type low_value,
- <br />
-
- typename interval_traits<T>::coordinate_type high_value) {<br />
-
- return T(low_value, high_value); <br />
-
- }<br />
- };</font></p>
- <h2>Functions</h2>
- <table id="table1" border="1" width="100%">
- <tbody>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T><br />
- coordinate_type <b>get</b>(const T& interval, direction_1d)</font></td>
- <td><font face="Times New Roman">Expects a model of
- interval. Returns the low or high coordinate of the interval,
- depending on the direction_1d value.</font><font face="Courier New"><br />
- </font></td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T, typename coordinate_type><br />
- void <b>set</b>(T& interval, direction_1d, coordinate_type)</font></td>
- <td><font face="Times New Roman">Expects a model of
- interval. Sets the low or high coordinate of the interval
- to the coordinate, depending on the direction_1d value. If low
- would be greater than high after this change then both are set to the
- input coordinate value.</font></td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T><br />
- T <b>construct</b>(coordinate_type low, coordinate_type high)</font></td>
- <td>Construct an object that is a model of interval given
- low and high coordinate values.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T1, typename T2><br />
- T1& <b>assign</b>(T1& left, const T2& right)</font></td>
- <td>Copies data from right object that models interval into
- left object that models interval.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T, typename T2><br />
- bool <b>equivalence</b>(const T& interval1, const T2&
- interval2)</font></td>
- <td>Given two objects that model interval, compares and
- returns true if their low and high values are respectively equal to
- each other.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T><br />
- bool <b>contains</b>(const T&, coordinate_type, <br />
-
- bool consider_touch=true)</font></td>
- <td>Given an object that models interval and a coordinate,
- returns true if the interval contains the coordinate. If the
- consider_touch flag is true will return true if the coordinate is equal
- to one of the interval ends.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T1, typename T2><br />
- bool <b>contains</b>(const T1& a, const T2& b, <br />
-
- bool consider_touch = true) </font></td>
- <td>Returns true if model of interval a contains both ends
- of model of interval b. If the consider_touch flag is true will
- consider the end of b contained within a even if it is equal to an end
- of a.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename interval_type><br />
- coordinate_type <b>low</b>(const interval_type& interval)</font></td>
- <td>Returns the low end of an object that models interval.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename interval_type><br />
- coordinate_type <b>high</b>(const interval_type& interval)</font></td>
- <td>Returns the high end of an object that models interval.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">// get the center
- coordinate<br />
- template <typename interval_type><br />
- coordinate_type <b>center</b>(const interval_type& interval)</font></td>
- <td>Returns the center coordinate of an object that models
- interval.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename interval_type><br />
- void <b>low</b>(interval_type& interval, coordinate_type )</font></td>
- <td>Sets the low end of the object that models interval to
- the coordinate value. If the low end would be set to larger than
- high end then both are set to the coordinate value.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename interval_type><br />
- void <b>high</b>(interval_type& interval, coordinate_type )</font></td>
- <td>Sets the high end of the object that models interval to
- the coordinate value. If the high end would be set to less than
- low end then both are set to the coordinate value.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename interval_type><br />
- coordinate_difference <b>delta</b>(const interval_type& interval)</font></td>
- <td>Returns the distance from low to high end of an object
- that models interval.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename interval_type><br />
- interval_type& <b>flip</b>(interval_type& interval,<br />
-
- coordinate_type axis = 0)</font></td>
- <td>Flips an object that models interval about the axis
- coordinate. If no axis is provided the interval is flipped across
- the the origin.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename interval_type><br />
- interval_type& <b>scale_up</b>(interval_type& interval, <br />
-
- unsigned_area_type factor)</font></td>
- <td>Multiplies low and high ends of an object that models
- interval by unsigned factor.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename interval_type><br />
- interval_type& <b>scale_down</b>(interval_type& interval, <br />
-
- unsigned_area_type factor)</font></td>
- <td>Divides low and high ends of an object that models
- interval by unsigned factor.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename interval_type><br />
- interval_type& <b>scale</b>(interval_type& interval,<br />
-
- double factor) </font></td>
- <td>Multiplies low and high ends of an object that models
- interval by floating point value.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename interval_type><br />
- interval_type& <b>move</b>(interval_type& interval,<br />
-
- coordinate_difference displacement)</font></td>
- <td>Adds displacement value to low and high ends of an
- object that models interval.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename interval_type><br />
- interval_type& <b>convolve</b>(interval_type& interval,<br />
-
- coordinate_type b)</font></td>
- <td>Adds coordinate value to low and high ends of an object
- that models interval.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename interval_type><br />
- interval_type& <b>deconvolve</b>(interval_type& interval,<br />
-
- coordinate_type b)</font></td>
- <td>Subtracts coordinate value from low and high ends of an
- object that models interval.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T1, typename T2><br />
- T1& <b>convolve</b>(T1& a, const T2& b)</font></td>
- <td>Adds low end of b to low end of a and adds high end of
- b to high end of a.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T1, typename T2><br />
- T1& <b>deconvolve</b>(T1& a, const T2& b)</font></td>
- <td>Subtracts low end of b from low end of a and subtracts
- high end of b from high end of a. </td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T1, typename T2><br />
- T1& <b>reflected_convolve</b>(T1& a, const T2& b)</font></td>
- <td>Adds high end of b to low end of a and adds low end of
- b to high end of a.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T1, typename T2><br />
- T1& <b>reflected_deconvolve</b>(T1& a, const T2& b)</font></td>
- <td>Subtracts high end of b from low end of a and subtracts
- low end of b from high end of a.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T><br />
- coordinate_difference <b>euclidean_distance</b>(const T&,<br />
-
- coordinate_type)</font></td>
- <td>Returns the distance from an object that models
- interval to a coordinate. Returns zero if the coordinate is equal
- to an end of the interval or contained within the interval.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T1, typename T2><br />
- bool <b>intersects</b>(const T1& interval, const T2& b, <br />
-
- bool consider_touch = true)</font></td>
- <td>Returns true if two objects that model interval
- overlap. If the consider_touch flag is true touching at the
- endpoints is considered overlap.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T1, typename T2><br />
- bool <b>boundaries_intersect</b>(const T1& interval, const T2&
- b, <br />
-
- bool consider_touch = true)</font></td>
- <td>Returns true is two objects that model interval
- partially overlap such that one end point of each is contained within
- the other. If the consider_touch flag is true a coordinate is
- considered contained even if it is equal to an end.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T1, typename T2><br />
- bool <b>abuts</b>(const T1& a, const T2& b,<br />
-
- direction_1d dir) </font></td>
- <td>Returns true if interval b abuts but down not overlap
- interval a on the end of interval a specified by dir.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T1, typename T2><br />
- bool <b>abuts</b>(const T1& a, const T2& b)</font></td>
- <td>Returns true if interval b abuts but down not overlap
- interval a.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T1, typename T2><br />
- bool <b>intersect</b>(T1& a, const T2& b,<br />
-
- bool consider_touch = true) </font></td>
- <td>Sets interval a to the intersection of interval a and
- interval b and return true. If the two intervals do not intersect
- interval a is unchanged and the function returns false. 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
- <typename T1, typename T2><br />
- T& <b>generalized_intersect</b>(T1& a, const T2& b)</font></td>
- <td>Same as intersect, but if they do not intersect set a
- to the interval between a and b.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T><br />
- T& <b>bloat</b>(T& interval, coordinate_type)</font></td>
- <td>Adds the coordinate value to high end of interval and
- subtracts it from low end of interval.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T><br />
- T& <b>bloat</b>(T& interval, direction_1d, coordinate_type)</font></td>
- <td>Adds the coordinate value to high end of interval or
- subtracts it from low end of interval depending on the direction_1d.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T><br />
- T& <b>shrink</b>(T& interval, coordinate_type)</font></td>
- <td>Subtracts the coordinate value from high end of
- interval and adds it to low end of interval.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T><br />
- T& <b>shrink</b>(T& interval, direction_1d, coordinate_type)</font></td>
- <td>Subtracts the coordinate value from high end of
- interval or adds it to low end of interval depending on the
- direction_1d.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T1, typename T2><br />
- bool <b>encompass</b>(T1& a, const T2& b)</font></td>
- <td>Sets low of a to min of low of a and low of b and sets
- high of a to max of high of a and high of b. Returns true if b
- was not contained within a to begin with.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">template
- <typename T><br />
- bool <b>encompass</b>(T& a, coordinate_type)</font></td>
- <td>Sets low of a to min of low of a and coordinate value
- and sets high of a to max of high of a and coordinate value.
- Returns true if coordinate value was not contained within a to begin
- with.</td>
- </tr>
- </tbody>
- </table>
- <h1>Interval Data</h1>
- <p> </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 id="table2" border="1" width="100%">
- <tbody>
- <tr>
- <td width="586"><b><font face="Courier New">geometry_type</font></b></td>
- <td><font face="Times New Roman">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 IntervalType><b> <br />
- </b>interval_data& <b>operator=</b>(</font><font
- face="Courier New">const IntervalType</font><font face="Courier New">&
- 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"><b>bool<b>
- operator==</b>(const </b></font><b><font face="Courier New">interval_data</font><font
- face="Courier New">& that) const</font></b></td>
- <td>Equality operator overload.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">bool<b> operator!=</b>(const
- </font><font face="Courier New">interval_data</font><font
- face="Courier New">& that) const</font></td>
- <td>Inequality operator overload.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">bool<b>
- operator<</b>(const </font><font face="Courier New">interval_data</font><font
- face="Courier New">& that) const</font></td>
- <td>Compares low coordinates then high coordinates to break
- ties.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">bool<b>
- operator<=</b>(const </font><font face="Courier New">interval_data</font><font
- face="Courier New">& that) const</font></td>
- <td>Compares low coordinates then high coordinates to break
- ties.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">bool<b>
- operator></b>(const </font><font face="Courier New">interval_data</font><font
- face="Courier New">& that) const</font></td>
- <td>Compares low coordinates then high coordinates to break
- ties.</td>
- </tr>
- <tr>
- <td width="586"><font face="Courier New">bool<b>
- operator>=</b>(const </font><font face="Courier New">interval_data</font><font
- face="Courier New">& 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 style="vertical-align: top;"><font face="Courier New">T
- <span style="font-weight: bold;">low</span>() const</font></td>
- <td style="vertical-align: top;">Retrieves the low value.</td>
- </tr>
- <tr>
- <td style="vertical-align: top;"><font face="Courier New">T
- <span style="font-weight: bold;">high</span>() const</font></td>
- <td style="vertical-align: top;">Retrieves the high
- endpoint.</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>
- <tr>
- <td style="vertical-align: top;"><font face="Courier New">interval_data&
- <span style="font-weight: bold;">low</span>(T value)</font></td>
- <td style="vertical-align: top;">Sets the low value.</td>
- </tr>
- <tr>
- <td style="vertical-align: top;"><font face="Courier New">interval_data&
- <span style="font-weight: bold;">high</span>(T value)</font></td>
- <td style="vertical-align: top;">Sets the high value.</td>
- </tr>
- </tbody>
- </table>
- </td>
- </tr>
- <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" id="table3" 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 © 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>
- </html>
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