boost_1_45_0/libs/polygon/doc/index.htm - nest-learning-thermostat/5.0/boost - Git at Google

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     <div style="margin: 5px;">
         <h3 class="navbar">Contents</h3>
         <ul>
             <li>Boost.Polygon Main Page</li>
 			<li><a href="gtl_design_overview.htm">Design Overview</a></li>
 			<li><a href="gtl_isotropy.htm">Isotropy</a></li>
             <li><a href="gtl_coordinate_concept.htm">Coordinate Concept</a></li>
             <li><a href="gtl_interval_concept.htm">Interval Concept</a></li>
             <li>
 			<a href="gtl_point_concept.htm">Point Concept</a></li>
 			<li><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>
         </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>
         </ul>
     </div>
         <h3 class="navbar">Polygon Sponsor</h3>
     <div style="padding: 5px;" align="center">
         <img border="0" src="images/intlogo.gif" width="127" height="51">
     </div>
 </td>
 <td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%">

 <!-- End Header -->

 <br>
 <p>
 </p><h1>THE BOOST.POLYGON LIBRARY</h1>
 <p>The Boost.Polygon library provides algorithms focused on manipulating planar
 polygon geometry data.&nbsp; Specific algorithms provided are the polygon set
 operations (intersection, union, difference, disjoint-union) and related
 algorithms such as polygon connectivity graph extraction, offsetting and map-overlay.&nbsp;
 An example of the disjoint-union (XOR) of figure a and figure b is shown below
 in figure c.&nbsp;
 These so-called Boolean algorithms are of significant interest in GIS (Geospatial Information
 Systems), VLSI CAD as well al other fields of CAD, and many more application
 areas, and providing them is the primary focus of this library.&nbsp; The
 Boost.Polygon library is not intended to cover all of computational
 geometry in its scope, and provides a set of capabilities for working with
 coordinates, points, intervals and rectangles that are needed to support
 implementing and interacting with polygon data structures and algorithms.&nbsp; </p><img border="0" src="images/hand.png" width="837" height="277"><p>
 The coordinate data type is a template parameter of all data types and
 algorithms provided by the library, and is expected to be integral.&nbsp;
 Floating point coordinate data types are not supported by the algorithms
 implemented in the library due to the fact that the achieving floating point
 robustness implies a different set of algorithms and generally platform specific
 assumptions about floating point representations.&nbsp;
 For additional detailed discussion of the library and its implementation
 including benchmark comparisons with other open source alternatives please see
 the <a href="GTL_boostcon2009.pdf">paper</a> and
 <a href="GTL_boostcon_draft03.pdf">presentation</a> from
 <a href="http://www.boostcon.com/home">boostcon</a> 2009 as well as a detailed
 <a href="analysis.htm">analysis</a> of the runtime complexity of
 the library's core algorithms. </p>
 <p>The design philosophy behind the polygon library was to create an API for
 invoking the library algorithms it provides on user geometry data types that is maximally
 intuitive, minimally error-prone and easy to integrate into pre-existing
 applications.&nbsp; C++-concepts based template meta-programming combined with
 generic operator overloading meets these design goals without sacrificing the
 runtime or memory efficiency of the underlying algorithms.&nbsp; The API is
 intended to demonstrate what could be achieved with ease by a C++-concepts based
 library interface, but is implemented based on current language features.&nbsp; This API makes
 the following code snippet that operates on non-library geometry types possible:</p>
 <p:colorscheme
  colors="#ffffff,#000000,#808080,#000000,#bbe0e3,#333399,#009999,#99cc00"/>

 <div v:shape="_x0000_s1026" class="O">
 	<div style="text-align:justify;mso-char-wrap:1;mso-kinsoku-overflow:1">
 		<nobr>
 		<span style="font-family: Courier New; mso-ascii-font-family: Courier New; mso-bidi-font-family: Arial; mso-hansi-font-family: Courier New">
 		void foo(list&lt;CPolygon&gt;&amp; result, const list&lt;CPolygon&gt;&amp; a, </span></nobr><br>
 		<span style="font-family: Courier New">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 		</span><nobr>
 		<span style="font-family: Courier New; mso-ascii-font-family: Courier New; mso-bidi-font-family: Arial; mso-hansi-font-family: Courier New">
 		const list&lt;CPolygon&gt;&amp;
 		b, int deflateValue) { </span></nobr></div>
 	<div style="text-align:justify;mso-char-wrap:1;mso-kinsoku-overflow:1">
 		<nobr>
 <span style="font-family: Courier New; mso-ascii-font-family: Courier New; mso-bidi-font-family: Arial; mso-hansi-font-family: Courier New">&nbsp;&nbsp;&nbsp;&nbsp;
 		CBoundingBox domainExtent; </span></nobr></div>
 	<div style="text-align:justify;mso-char-wrap:1;mso-kinsoku-overflow:1">
 		<nobr>
 		<span style="font-family: Courier New; mso-ascii-font-family: Courier New; mso-bidi-font-family: Arial; mso-hansi-font-family: Courier New">
 		<span style="mso-spacerun:yes">&nbsp; </span>&nbsp;&nbsp; using namespace boost::polygon::operators; </span></nobr></div>
 	<div style="text-align:justify;mso-char-wrap:1;mso-kinsoku-overflow:1">
 		<nobr>
 		<span style="font-family: Courier New; mso-ascii-font-family: Courier New; mso-bidi-font-family: Arial; mso-hansi-font-family: Courier New">
 		<span style="mso-spacerun:yes">&nbsp; </span>&nbsp;&nbsp;
 		boost::polygon::extents(domainExtent, a); </span></nobr></div>
 	<div style="text-align:justify;mso-char-wrap:1;mso-kinsoku-overflow:1">
 		<nobr>
 		<span style="font-family: Courier New; mso-ascii-font-family: Courier New; mso-bidi-font-family: Arial; mso-hansi-font-family: Courier New">
 		<span style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp; </span>result += (b &amp;
 		domainExtent) ^ (a - deflateValue); </span></nobr></div>
 	<div style="text-align:justify;mso-char-wrap:1;mso-kinsoku-overflow:1">
 		<nobr>
 		<span style="font-family: Courier New; mso-ascii-font-family: Courier New; mso-bidi-font-family: Arial; mso-hansi-font-family: Courier New">
 		}</span></nobr></div>
 </div>
 <p>In the code snippet above the hypothetical polygon type CPolygon has been
 mapped to the library polygon concept and is used with library APIs to clip
 polygon list <i>b</i> against the bounding box of polygon list <i>a</i> and apply the
 disjoint-union of that with polygon list <i>a</i> deflated by some integer amount.&nbsp;
 The end result is accumulated into a list of polygons with a union operation.&nbsp;
 It is considerably more typing to describe this usage of the API than to code
 it, and the description is not much clearer than the code itself.&nbsp;
 A picture is worth a thousand words.</p>
 <p><img border="0" src="images/foo.PNG" width="432" height="371"></p>
 <p>In Boost.Polygon operations such as those shown above are free functions named for what they do, or are overloads of C++ operators that make it
 easy to infer from reading the code what to expect.&nbsp; Operators are
 contained in the namespace <font face="Courier New">boost::polygon::operators</font>
 so that they can be used outside the <font face="Courier New">boost::polygon</font>
 namespace without bringing in the entire <font face="Courier New">boost::polygon</font>
 namespace.&nbsp; Following the
 principle of least astonishment, the inferred behavior should generally match
 the actual behavior.&nbsp; Conventions such as argument ordering (output
 arguments come first) and consistently applying the same semantics across
 different functions (accumulate) reduces the learning curve for new users while reducing the
 need to memorize semantics and argument ordering of many different functions for
 advanced users.</p>
 <p>While the internal library code that implements this API is usually complex and
 cryptic due to heavy use of template meta-programming, the application of the library
 API in user code is usually simple and clear because it is free of any
 extraneous syntax.&nbsp; The one exception to this is the mapping of user types
 to library concepts, which necessitates that the user perform some simple
 template programming and understand some of the internals of how the library
 concept type system works.&nbsp; The examples below should aid the user in
 performing these programming tasks.</p>
 <ul>

 <li>Example files:
     <ul>
         <li><a href="gtl_point_usage.htm">point_usage.cpp</a> Using the
 		library provided point data type and functions</li>
 		<li><a href="gtl_custom_point.htm">custom_point.cpp</a> Mapping a
 		user defined point class to the library point_concept</li>
         <li><a href="gtl_polygon_usage.htm">polygon_usage.cpp</a> Using
 		the library provided polygon data types and functions</li>
         <li><a href="gtl_custom_polygon.htm">custom_polygon.cpp</a> Mapping a
 		user defined polygon class to the library polygon_concept</li>
         <li><a href="gtl_polygon_set_usage.htm">polygon_set_usage.cpp</a> Using
 		the library provided polygon set data types and functions</li>
 		<li><a href="gtl_custom_polygon_set.htm">custom_polygon_set.cpp</a>
 		Mapping a user defined class to the library polygon_set_concept</li>
 		<li><a href="gtl_connectivity_extraction_usage.htm">connectivity_extraction_usage.cpp</a>
 		Using the connectivity extraction algorithm to build a connectivity
 		graph on polygons</li>
 		<li><a href="gtl_property_merge_usage.htm">property_merge_usage.cpp</a>
 		Using the n-layer map-overlay algorithm on polygon data</li>
     </ul>

 <li>Tutorials:
 <ul>
 	<li><a href="gtl_tutorial.htm">Layout Versus Schematic</a> Learn how to
 	apply Boost.Polygon capabilities to implement a simplified circuit
 	extraction application</li>
 	<li><a href="gtl_minkowski_tutorial.htm">Minkowski Sum</a> Learn how to
 	apply Boost.Polygon capabilities to implement Minkowski sum of polygon sets</li>
 </ul>

 </ul>


 <p>We would like to thank: Thomas Klimpel, Frank Mori Hess, Barend Gehrels,
 Andreas Fabri, Jeffrey Hellrung, Tim Keitt, Markus Werle, Paul A. Bristow,
 Robert Stewart, Mathias Gaunard, Michael Fawcett, Steven Watanabe, Joachim
 Faulhaber, John Bytheway, Sebastian Redl, Mika Heiskanen, John Phillips, Kai
 Benndorf, Hartmut Kaiser, Arash Partow, Maurizio Vitale, Brandon Kohn, David
 Abrahams, Gordon Woodhull, Daniel James, John Maddock, Tom Brinkman, Bo Persson,
 Mateusz Loskot, Christian Henning, Jean-Sebastien Stoezel, for providing
 feedback and or formal review of the library as part of the boost submission
 process and Fernando Cacciola for graciously serving as review manager.</p>


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 		<col class="docinfo-name"><col class="docinfo-content">
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 		<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>
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	<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"><head><!--
	Copyright 2009-2010 Intel Corporation
	license banner
	-->
	<title>Boost Polygon Library: Main Page</title>
	<meta http-equiv="content-type" content="text/html;charset=ISO-8859-1">
	<table style="margin: 0pt; padding: 0pt; width: 100%;" border="0" cellpadding="0" cellspacing="0"><tbody><tr>
	<td style="background-color: rgb(238, 238, 238);" nowrap="1" valign="top">
	<div style="padding: 5px;" align="center">
	<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 ;">
	</a>
	</div>
	<div style="margin: 5px;">
	<h3 class="navbar">Contents</h3>
	<ul>
	<li>Boost.Polygon Main Page</li>
	<li><a href="gtl_design_overview.htm">Design Overview</a></li>
	<li><a href="gtl_isotropy.htm">Isotropy</a></li>
	<li><a href="gtl_coordinate_concept.htm">Coordinate Concept</a></li>
	<li><a href="gtl_interval_concept.htm">Interval Concept</a></li>
	<li>
	<a href="gtl_point_concept.htm">Point Concept</a></li>
	<li><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>
	</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>
	</ul>
	</div>
	<h3 class="navbar">Polygon Sponsor</h3>
	<div style="padding: 5px;" align="center">
	<img border="0" src="images/intlogo.gif" width="127" height="51">
	</div>
	</td>
	<td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%">

	<!-- End Header -->

	<br>
	<p>
	</p><h1>THE BOOST.POLYGON LIBRARY</h1>
	<p>The Boost.Polygon library provides algorithms focused on manipulating planar
	polygon geometry data.  Specific algorithms provided are the polygon set
	operations (intersection, union, difference, disjoint-union) and related
	algorithms such as polygon connectivity graph extraction, offsetting and map-overlay.
	An example of the disjoint-union (XOR) of figure a and figure b is shown below
	in figure c.
	These so-called Boolean algorithms are of significant interest in GIS (Geospatial Information
	Systems), VLSI CAD as well al other fields of CAD, and many more application
	areas, and providing them is the primary focus of this library.  The
	Boost.Polygon library is not intended to cover all of computational
	geometry in its scope, and provides a set of capabilities for working with
	coordinates, points, intervals and rectangles that are needed to support
	implementing and interacting with polygon data structures and algorithms.  </p><img border="0" src="images/hand.png" width="837" height="277"><p>
	The coordinate data type is a template parameter of all data types and
	algorithms provided by the library, and is expected to be integral.
	Floating point coordinate data types are not supported by the algorithms
	implemented in the library due to the fact that the achieving floating point
	robustness implies a different set of algorithms and generally platform specific
	assumptions about floating point representations.
	For additional detailed discussion of the library and its implementation
	including benchmark comparisons with other open source alternatives please see
	the <a href="GTL_boostcon2009.pdf">paper</a> and
	<a href="GTL_boostcon_draft03.pdf">presentation</a> from
	<a href="http://www.boostcon.com/home">boostcon</a> 2009 as well as a detailed
	<a href="analysis.htm">analysis</a> of the runtime complexity of
	the library's core algorithms. </p>
	<p>The design philosophy behind the polygon library was to create an API for
	invoking the library algorithms it provides on user geometry data types that is maximally
	intuitive, minimally error-prone and easy to integrate into pre-existing
	applications.  C++-concepts based template meta-programming combined with
	generic operator overloading meets these design goals without sacrificing the
	runtime or memory efficiency of the underlying algorithms.  The API is
	intended to demonstrate what could be achieved with ease by a C++-concepts based
	library interface, but is implemented based on current language features.  This API makes
	the following code snippet that operates on non-library geometry types possible:</p>
	<p:colorscheme
	colors="#ffffff,#000000,#808080,#000000,#bbe0e3,#333399,#009999,#99cc00"/>

	<div v:shape="_x0000_s1026" class="O">
	<div style="text-align:justify;mso-char-wrap:1;mso-kinsoku-overflow:1">
	<nobr>
	<span style="font-family: Courier New; mso-ascii-font-family: Courier New; mso-bidi-font-family: Arial; mso-hansi-font-family: Courier New">
	void foo(list<CPolygon>& result, const list<CPolygon>& a, </span></nobr><br>
	<span style="font-family: Courier New">
	</span><nobr>
	<span style="font-family: Courier New; mso-ascii-font-family: Courier New; mso-bidi-font-family: Arial; mso-hansi-font-family: Courier New">
	const list<CPolygon>&
	b, int deflateValue) { </span></nobr></div>
	<div style="text-align:justify;mso-char-wrap:1;mso-kinsoku-overflow:1">
	<nobr>
	<span style="font-family: Courier New; mso-ascii-font-family: Courier New; mso-bidi-font-family: Arial; mso-hansi-font-family: Courier New">
	CBoundingBox domainExtent; </span></nobr></div>
	<div style="text-align:justify;mso-char-wrap:1;mso-kinsoku-overflow:1">
	<nobr>
	<span style="font-family: Courier New; mso-ascii-font-family: Courier New; mso-bidi-font-family: Arial; mso-hansi-font-family: Courier New">
	<span style="mso-spacerun:yes">  </span>   using namespace boost::polygon::operators; </span></nobr></div>
	<div style="text-align:justify;mso-char-wrap:1;mso-kinsoku-overflow:1">
	<nobr>
	<span style="font-family: Courier New; mso-ascii-font-family: Courier New; mso-bidi-font-family: Arial; mso-hansi-font-family: Courier New">
	<span style="mso-spacerun:yes">  </span>
	boost::polygon::extents(domainExtent, a); </span></nobr></div>
	<div style="text-align:justify;mso-char-wrap:1;mso-kinsoku-overflow:1">
	<nobr>
	<span style="font-family: Courier New; mso-ascii-font-family: Courier New; mso-bidi-font-family: Arial; mso-hansi-font-family: Courier New">
	<span style="mso-spacerun:yes">     </span>result += (b &
	domainExtent) ^ (a - deflateValue); </span></nobr></div>
	<div style="text-align:justify;mso-char-wrap:1;mso-kinsoku-overflow:1">
	<nobr>
	<span style="font-family: Courier New; mso-ascii-font-family: Courier New; mso-bidi-font-family: Arial; mso-hansi-font-family: Courier New">
	}</span></nobr></div>
	</div>
	<p>In the code snippet above the hypothetical polygon type CPolygon has been
	mapped to the library polygon concept and is used with library APIs to clip
	polygon list <i>b</i> against the bounding box of polygon list <i>a</i> and apply the
	disjoint-union of that with polygon list <i>a</i> deflated by some integer amount.
	The end result is accumulated into a list of polygons with a union operation.
	It is considerably more typing to describe this usage of the API than to code
	it, and the description is not much clearer than the code itself.
	A picture is worth a thousand words.</p>
	<p><img border="0" src="images/foo.PNG" width="432" height="371"></p>
	<p>In Boost.Polygon operations such as those shown above are free functions named for what they do, or are overloads of C++ operators that make it
	easy to infer from reading the code what to expect.  Operators are
	contained in the namespace <font face="Courier New">boost::polygon::operators</font>
	so that they can be used outside the <font face="Courier New">boost::polygon</font>
	namespace without bringing in the entire <font face="Courier New">boost::polygon</font>
	namespace.  Following the
	principle of least astonishment, the inferred behavior should generally match
	the actual behavior.  Conventions such as argument ordering (output
	arguments come first) and consistently applying the same semantics across
	different functions (accumulate) reduces the learning curve for new users while reducing the
	need to memorize semantics and argument ordering of many different functions for
	advanced users.</p>
	<p>While the internal library code that implements this API is usually complex and
	cryptic due to heavy use of template meta-programming, the application of the library
	API in user code is usually simple and clear because it is free of any
	extraneous syntax.  The one exception to this is the mapping of user types
	to library concepts, which necessitates that the user perform some simple
	template programming and understand some of the internals of how the library
	concept type system works.  The examples below should aid the user in
	performing these programming tasks.</p>
	<ul>

	<li>Example files:
	<ul>
	<li><a href="gtl_point_usage.htm">point_usage.cpp</a> Using the
	library provided point data type and functions</li>
	<li><a href="gtl_custom_point.htm">custom_point.cpp</a> Mapping a
	user defined point class to the library point_concept</li>
	<li><a href="gtl_polygon_usage.htm">polygon_usage.cpp</a> Using
	the library provided polygon data types and functions</li>
	<li><a href="gtl_custom_polygon.htm">custom_polygon.cpp</a> Mapping a
	user defined polygon class to the library polygon_concept</li>
	<li><a href="gtl_polygon_set_usage.htm">polygon_set_usage.cpp</a> Using
	the library provided polygon set data types and functions</li>
	<li><a href="gtl_custom_polygon_set.htm">custom_polygon_set.cpp</a>
	Mapping a user defined class to the library polygon_set_concept</li>
	<li><a href="gtl_connectivity_extraction_usage.htm">connectivity_extraction_usage.cpp</a>
	Using the connectivity extraction algorithm to build a connectivity
	graph on polygons</li>
	<li><a href="gtl_property_merge_usage.htm">property_merge_usage.cpp</a>
	Using the n-layer map-overlay algorithm on polygon data</li>
	</ul>

	<li>Tutorials:
	<ul>
	<li><a href="gtl_tutorial.htm">Layout Versus Schematic</a> Learn how to
	apply Boost.Polygon capabilities to implement a simplified circuit
	extraction application</li>
	<li><a href="gtl_minkowski_tutorial.htm">Minkowski Sum</a> Learn how to
	apply Boost.Polygon capabilities to implement Minkowski sum of polygon sets</li>
	</ul>

	</ul>


	<p>We would like to thank: Thomas Klimpel, Frank Mori Hess, Barend Gehrels,
	Andreas Fabri, Jeffrey Hellrung, Tim Keitt, Markus Werle, Paul A. Bristow,
	Robert Stewart, Mathias Gaunard, Michael Fawcett, Steven Watanabe, Joachim
	Faulhaber, John Bytheway, Sebastian Redl, Mika Heiskanen, John Phillips, Kai
	Benndorf, Hartmut Kaiser, Arash Partow, Maurizio Vitale, Brandon Kohn, David
	Abrahams, Gordon Woodhull, Daniel James, John Maddock, Tom Brinkman, Bo Persson,
	Mateusz Loskot, Christian Henning, Jean-Sebastien Stoezel, for providing
	feedback and or formal review of the library as part of the boost submission
	process and Fernando Cacciola for graciously serving as review manager.</p>


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	<th class="docinfo-name">Copyright:</th>
	<td>Copyright © Intel Corporation 2008-2010.</td>
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	<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">
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