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Subject: [Boost-commit] svn:boost r78414 - in trunk/libs/polygon/doc: . images
From: sydorchuk.andriy_at_[hidden]
Date: 2012-05-10 17:45:18

Next message: sydorchuk.andriy_at_[hidden]: "[Boost-commit] svn:boost r78415 - in trunk/libs/polygon/doc: . images"
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Author: asydorchuk
Date: 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
New Revision: 78414
URL: http://svn.boost.org/trac/boost/changeset/78414

Log:
Polygon: updating documentation.
Added:
   trunk/libs/polygon/doc/gtl_segment_concept.htm (contents, props changed)
   trunk/libs/polygon/doc/images/rover.jpg (contents, props changed)
   trunk/libs/polygon/doc/images/vlsi.jpg (contents, props changed)
   trunk/libs/polygon/doc/images/voronoi.png (contents, props changed)
   trunk/libs/polygon/doc/images/voronoi2.png (contents, props changed)
   trunk/libs/polygon/doc/images/voronoi3.png (contents, props changed)
   trunk/libs/polygon/doc/images/voronoi4.png (contents, props changed)
   trunk/libs/polygon/doc/voronoi_advanced_tutorial.htm (contents, props changed)
   trunk/libs/polygon/doc/voronoi_basic_tutorial.htm (contents, props changed)
   trunk/libs/polygon/doc/voronoi_benchmark.htm (contents, props changed)
   trunk/libs/polygon/doc/voronoi_builder.htm (contents, props changed)
   trunk/libs/polygon/doc/voronoi_diagram.htm (contents, props changed)
   trunk/libs/polygon/doc/voronoi_main.htm (contents, props changed)
   trunk/libs/polygon/doc/voronoi_predicates.htm (contents, props changed)
   trunk/libs/polygon/doc/voronoi_robust_fpt.htm (contents, props changed)
   trunk/libs/polygon/doc/voronoi_utils.htm (contents, props changed)
Text files modified:
   trunk/libs/polygon/doc/analysis.htm | 127 +++++++-----
   trunk/libs/polygon/doc/gtl_connectivity_extraction.htm | 84 +++++---
   trunk/libs/polygon/doc/gtl_connectivity_extraction_45.htm | 84 +++++---
   trunk/libs/polygon/doc/gtl_connectivity_extraction_90.htm | 84 +++++---
   trunk/libs/polygon/doc/gtl_coordinate_concept.htm | 113 ++++++----
   trunk/libs/polygon/doc/gtl_design_overview.htm | 55 +++-
   trunk/libs/polygon/doc/gtl_interval_concept.htm | 254 ++++++++++++++------------
   trunk/libs/polygon/doc/gtl_isotropy.htm | 126 +++++++-----
   trunk/libs/polygon/doc/gtl_minkowski_tutorial.htm | 5
   trunk/libs/polygon/doc/gtl_point_concept.htm | 206 +++++++++++---------
   trunk/libs/polygon/doc/gtl_polygon_45_concept.htm | 201 +++++++++++---------
   trunk/libs/polygon/doc/gtl_polygon_45_set_concept.htm | 236 +++++++++++++-----------
   trunk/libs/polygon/doc/gtl_polygon_45_with_holes_concept.htm | 189 ++++++++++---------
   trunk/libs/polygon/doc/gtl_polygon_90_concept.htm | 187 ++++++++++--------
   trunk/libs/polygon/doc/gtl_polygon_90_set_concept.htm | 349 +++++++++++++++++++-----------------
   trunk/libs/polygon/doc/gtl_polygon_90_with_holes_concept.htm | 193 ++++++++++---------
   trunk/libs/polygon/doc/gtl_polygon_concept.htm | 203 +++++++++++---------
   trunk/libs/polygon/doc/gtl_polygon_set_concept.htm | 242 +++++++++++++-----------
   trunk/libs/polygon/doc/gtl_polygon_with_holes_concept.htm | 193 ++++++++++---------
   trunk/libs/polygon/doc/gtl_property_merge.htm | 86 +++++---
   trunk/libs/polygon/doc/gtl_property_merge_45.htm | 86 +++++---
   trunk/libs/polygon/doc/gtl_property_merge_90.htm | 86 +++++---
   trunk/libs/polygon/doc/gtl_rectangle_concept.htm | 382 ++++++++++++++++++++-------------------
   trunk/libs/polygon/doc/index.htm | 201 +++++++++++++-------
   24 files changed, 2204 insertions(+), 1768 deletions(-)

Modified: trunk/libs/polygon/doc/analysis.htm
==============================================================================
--- trunk/libs/polygon/doc/analysis.htm (original)
+++ trunk/libs/polygon/doc/analysis.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -1,64 +1,85 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"><head>
-<title>Boost Polygon Library: Performance Analysis</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>
+--><title>Boost Polygon Library: Performance Analysis</title>
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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>Boost.Polygon Main Page</li>
- <li><a href="gtl_design_overview.htm">Polygon
- Library Design Overview</a></li>
- <li>Isotropy</li>
- <li>Coordinate Concept</li>
- <li>Interval Concept</li>
- <li>
- Point Concept</li>
- <li>Rectangle Concept</li>
- <li>Polygon 90 Concept</li>
- <li>Polygon 90 With Holes Concept</li>
- <li>Polygon 45 Concept</li>
- <li>Polygon 45 With Holes Concept</li>
- <li>Polygon Concept</li>
- <li>Polygon With Holes Concept</li>
- <li>Polygon 90 Set Concept</li>
- <li>Polygon 45 Set Concept</li>
- <li>Polygon Set Concept</li>
- <li>Connectivity Extraction 90</li>
- <li>Connectivity Extraction 45</li>
- <li>Connectivity Extraction</li>
- <li>Property Merge 90</li>
- <li>Property Merge 45</li>
- <li>Property Merge</li>
- </ul>
+ <li>Boost.Polygon Main Page</li>
+ <li>Design Overview</li>
+ <li>Isotropy</li>
+ <li>Coordinate Concept</li>
+ <li>Interval Concept</li>
+ <li>Point Concept</li>
+ <li>Segment Concept</li>
+ <li>Rectangle Concept</li>
+ <li>Polygon 90 Concept</li>
+ <li><a href="gtl_polygon_90_with_holes_concept.htm">Polygon 90
+With Holes Concept</a></li>
+ <li>Polygon 45 Concept</li>
+ <li><a href="gtl_polygon_45_with_holes_concept.htm">Polygon 45
+With Holes Concept</a></li>
+ <li>Polygon Concept</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>Polygon Set Concept</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>Property Merge 90</li>
+ <li>Property Merge 45</li>
+ <li>Property Merge</li>
+ <li>Voronoi Main Page
+ </li>
+ <li>Voronoi Benchmark</li>
+ <li>Voronoi Builder 
+ </li>
+ <li>Voronoi Diagram</li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+</ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
- <li>GTL Boostcon 2009 Paper</li>
- <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
- Presentation</a></li>
- <li>Performance Analysis</li>
- <li>Layout Versus Schematic Tutorial</li>
- <li>Minkowski Sum Tutorial</li>
- </ul>
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+Presentation</a></li>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</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 border="0" src="images/intlogo.gif" width="127" height="51">
+ <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%">



- 
+ 

<h1>Polygon Set Algorithms Analysis</h1>
Most non-trivial algorithms in the Boost.Polygon library are
@@ -86,25 +107,25 @@
constant factor of input vertices we can examine runtime complexity in terms of
input vertices.  The operation performed was a union (Boolean OR) of the
input rectangles by each of the Manhattan, 45-degree and arbitrary angle
-Booleans algorithms, which are labeled "boolean 90", "boolean 45" and "boolean". 
+Booleans algorithms, which are labeled "boolean 90", "boolean 45" and "boolean". 
Also shown in the plot is the performance of the arbitrary angle Booleans
algorithm as prior to the addition of divide and conquer recursive subdivision,
which was described in the paper
<a href="GTL_boostcon_draft03.pdf">presented</a> at
<a href="http://www.boostcon.com/home">boostcon</a> 2009.  Finally, the
time required to sort the input points is shown as a common reference for O(n log n)
-runtime to put the data into context.<img border="0" src="images/perf_graph.PNG" width="391" height="414">
+runtime to put the data into context.<img src="images/perf_graph.PNG" border="0" height="414" width="391" />
We can see in the log-log plot that sorting and the three Booleans algorithms
-provided by the Boost.Polygon library have nearly 45 degree "linear"
+provided by the Boost.Polygon library have nearly 45 degree "linear"
scaling with empirical exponents just slightly larger than 1.0 and can be
observed to scale proportional to O(n log n) for
-these inputs.  The "old boolean" algorithm presented at boostcon 2009
+these inputs.  The "old boolean" algorithm presented at boostcon 2009
exhibits scaling close to the expected O(n1.5)
scaling.  Because the speedup provided by the divide and conquer approach
is algorithmic, the 10X potential performance improvement alluded to in the paper is
realized at inputs of 200,000 rectangles and larger.  Even for small inputs
of 2K rectangles the algorithm is 2X faster and now can be expected to be
-roughly as fast as GPC at small scales,
+roughly as fast as GPC at small scales,
while algorithmically faster at large scales.


@@ -116,10 +137,10 @@
work, 45-degree  Booleans cost roughly

-</body>ten units of O(n log n) work and arbitrary angle Booleans cost roughly
+ten units of O(n log n) work and arbitrary angle Booleans cost roughly
seventy units of O(n log n) work.  Sorting the input vertices is the first
step in a Booleans algorithm and therefore provides a hard lower bound for the
-runtime of an optimal Booleans algorithm.
+runtime of an optimal Booleans algorithm.

One final thing to note about performance of the arbitrary angle Booleans
@@ -137,17 +158,17 @@
intersection point within one integer unit of both line segments.  This
means that there is effectively no runtime penalty for the use of infinite
precision to ensure 100% robustness.  Most inputs will process through the
-algorithm without ever resorting to GMP.<tr>
+algorithm without ever resorting to GMP.</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" rules="none" frame="void" id="table1">
+<table class="docinfo" id="table1" frame="void" rules="none">
 <colgroup>
- <col class="docinfo-name"><col class="docinfo-content">
+ <col class="docinfo-name" /><col class="docinfo-content" />
 </colgroup>
- <tbody vAlign="top">
+ <tbody valign="top">
 <tr>
 <th class="docinfo-name">Copyright:</th>
 <td>Copyright © Intel Corporation 2008-2010.</td>
@@ -160,6 +181,6 @@
 <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt>)</td>
 </tr>
-</table>
+</tbody></table>

-</html>
\ No newline at end of file
+</td></tr></tbody></table></body></html>
\ No newline at end of file

Modified: trunk/libs/polygon/doc/gtl_connectivity_extraction.htm
==============================================================================
--- trunk/libs/polygon/doc/gtl_connectivity_extraction.htm (original)
+++ trunk/libs/polygon/doc/gtl_connectivity_extraction.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -1,14 +1,15 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<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>
-<title>Boost Polygon Library: Connectivity Extraction 45</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>
+--><title>Boost Polygon Library: Connectivity Extraction 45</title>
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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;">
@@ -20,6 +21,8 @@
 <li>Coordinate Concept</li>
 <li>Interval Concept</li>
 <li>Point Concept</li>
+ <li>Segment Concept</li>
+
 <li>Rectangle Concept</li>
 <li>Polygon 90 Concept</li>
 <li>Polygon 90 With Holes Concept</li>
@@ -36,32 +39,47 @@
 <li>Property Merge 90</li>
 <li>Property Merge 45</li>
 <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+</a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+</a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+
 </ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
- <li>GTL Boostcon 2009 Paper</li>
- <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
 Presentation</a></li>
- <li>Performance Analysis</li>
- <li>Layout Versus Schematic Tutorial</li>
- <li>Minkowski Sum Tutorial</li>
- </ul>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</li>
+ <li>Voronoi Advanced Tutorial</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">
+ <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%">



- 
+ 

<h1>Connectivity Extraction</h1>


-The connectivity extraction algorithm constructs the connectivity graph where
+The connectivity extraction algorithm constructs the connectivity graph where
input polygon sets are modeled as graph nodes and assigned node ids and
overlap/touching between input polygon sets is modeled as graph edges.  One
supported graph formats is std::vector<std::set<int> > where node ids index into
@@ -71,33 +89,33 @@
the operator[] is used internally to access the graph   The other
supported graph format is std::map<int, std::set<int> > which is slightly easier to
work with, but potentially more expensive.  Improving the interface to
-support more generic graph concepts is deferred to future work.The following
-is the declaration of the connectivity extraction algorithm.
-template <typename coordinate_type> 
-class connectivity_extraction;
+support more generic graph concepts is deferred to future work.The following
+is the declaration of the connectivity extraction algorithm.
+template <typename coordinate_type> 
+class connectivity_extraction;
Example code connectivity_extraction_usage.cpp
 demonstrates using the connectivity extraction algorithm to build a
-connectivity graph on geometry.<h2>Member Functions</h2>
-<table border="1" width="100%" id="table1">
- <tr>
+connectivity graph on geometry.<h2>Member Functions</h2>
+<table id="table1" border="1" width="100%">
+ <tbody><tr>
 <td width="586">connectivity_extraction()</td>
 <td>Default constructor. </td>
 </tr>
 <tr>
- <td width="586">connectivity_extraction(      const
+ <td width="586">connectivity_extraction(      const
 connectivity_extraction& that)</td>
 <td>Copy construct.</td>
 </tr>
 <tr>
 <td width="586">
-unsigned int insert(const polygon_set_data<coordinate_type>& ps)</td>
+unsigned int insert(const polygon_set_data<coordinate_type>& ps)</td>
 <td>Insert a polygon set graph node, the
 value returned is the id of the graph node.</td>
 </tr>
 <tr>
 <td width="586">

-template <class GeoObjT> 
+template <class GeoObjT> 
unsigned int insert(const GeoObjT& geoObj)</td>
 <td>Insert a geometry object that is a refinement of polygon set as a
 graph node, the return value is the id of the graph node.</td>
@@ -105,24 +123,24 @@
 <tr>
 <td width="586">

-template <class GraphT> 
+template <class GraphT> 
void extract(GraphT& graph)</td>
 <td>Accepts a graph object that conforms to the expectations defined
 above.  Performs connectivity extraction and populates the graph
 object.</td>
 </tr>
- </table>
- <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" rules="none" frame="void" id="table2">
+<table class="docinfo" id="table2" frame="void" rules="none">
 <colgroup>
- <col class="docinfo-name"><col class="docinfo-content">
+ <col class="docinfo-name" /><col class="docinfo-content" />
 </colgroup>
- <tbody vAlign="top">
+ <tbody valign="top">
 <tr>
 <th class="docinfo-name">Copyright:</th>
 <td>Copyright © Intel Corporation 2008-2010.</td>
@@ -135,6 +153,6 @@
 <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt>)</td>
 </tr>
-</table>
+</tbody></table>

-</html>
\ No newline at end of file
+</td></tr></tbody></table></body></html>
\ No newline at end of file

Modified: trunk/libs/polygon/doc/gtl_connectivity_extraction_45.htm
==============================================================================
--- trunk/libs/polygon/doc/gtl_connectivity_extraction_45.htm (original)
+++ trunk/libs/polygon/doc/gtl_connectivity_extraction_45.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -1,14 +1,15 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<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>
-<title>Boost Polygon Library: Connectivity Extraction 45</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>
+--><title>Boost Polygon Library: Connectivity Extraction 45</title>
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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;">
@@ -20,6 +21,8 @@
 <li>Coordinate Concept</li>
 <li>Interval Concept</li>
 <li>Point Concept</li>
+ <li>Segment Concept</li>
+
 <li>Rectangle Concept</li>
 <li>Polygon 90 Concept</li>
 <li>Polygon 90 With Holes Concept</li>
@@ -36,32 +39,47 @@
 <li>Property Merge 90</li>
 <li>Property Merge 45</li>
 <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+</a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+</a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+
 </ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
- <li>GTL Boostcon 2009 Paper</li>
- <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
 Presentation</a></li>
- <li>Performance Analysis</li>
- <li>Layout Versus Schematic Tutorial</li>
- <li>Minkowski Sum Tutorial</li>
- </ul>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</li>
+ <li>Voronoi Advanced Tutorial</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">
+ <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%">



- 
+ 

<h1>Connectivity Extraction 45</h1>


-The connectivity extraction algorithm constructs the connectivity graph where
+The connectivity extraction algorithm constructs the connectivity graph where
input polygon sets are modeled as graph nodes and assigned node ids and
overlap/touching between input polygon sets is modeled as graph edges.  One
supported graph formats is std::vector<std::set<int> > where node ids index into
@@ -71,33 +89,33 @@
the operator[] is used internally to access the graph   The other
supported graph format is std::map<int, std::set<int> > which is slightly easier to
work with, but potentially more expensive.  Improving the interface to
-support more generic graph concepts is deferred to future work.The following
-is the declaration of the connectivity extraction algorithm.
-template <typename coordinate_type> 
-class connectivity_extraction_45;
+support more generic graph concepts is deferred to future work.The following
+is the declaration of the connectivity extraction algorithm.
+template <typename coordinate_type> 
+class connectivity_extraction_45;
Example code connectivity_extraction_usage.cpp
 demonstrates using the connectivity extraction algorithm to build a
-connectivity graph on geometry.<h2>Member Functions</h2>
-<table border="1" width="100%" id="table1">
- <tr>
+connectivity graph on geometry.<h2>Member Functions</h2>
+<table id="table1" border="1" width="100%">
+ <tbody><tr>
 <td width="586">connectivity_extraction_45()</td>
 <td>Default constructor. </td>
 </tr>
 <tr>
- <td width="586">connectivity_extraction_45(      const
+ <td width="586">connectivity_extraction_45(      const
 connectivity_extraction_45& that)</td>
 <td>Copy construct.</td>
 </tr>
 <tr>
 <td width="586">
-unsigned int insert(const polygon_45_set_data<coordinate_type>& ps)</td>
+unsigned int insert(const polygon_45_set_data<coordinate_type>& ps)</td>
 <td>Insert a polygon set graph node, the
 value returned is the id of the graph node.</td>
 </tr>
 <tr>
 <td width="586">

-template <class GeoObjT> 
+template <class GeoObjT> 
unsigned int insert(const GeoObjT& geoObj)</td>
 <td>Insert a geometry object that is a refinement of polygon 45 set as a
 graph node, the return value is the id of the graph node.</td>
@@ -105,24 +123,24 @@
 <tr>
 <td width="586">

-template <class GraphT> 
+template <class GraphT> 
void extract(GraphT& graph)</td>
 <td>Accepts a graph object that conforms to the expectations defined
 above.  Performs connectivity extraction and populates the graph
 object.</td>
 </tr>
- </table>
- <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" rules="none" frame="void" id="table2">
+<table class="docinfo" id="table2" frame="void" rules="none">
 <colgroup>
- <col class="docinfo-name"><col class="docinfo-content">
+ <col class="docinfo-name" /><col class="docinfo-content" />
 </colgroup>
- <tbody vAlign="top">
+ <tbody valign="top">
 <tr>
 <th class="docinfo-name">Copyright:</th>
 <td>Copyright © Intel Corporation 2008-2010.</td>
@@ -135,6 +153,6 @@
 <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt>)</td>
 </tr>
-</table>
+</tbody></table>

-</html>
\ No newline at end of file
+</td></tr></tbody></table></body></html>
\ No newline at end of file

Modified: trunk/libs/polygon/doc/gtl_connectivity_extraction_90.htm
==============================================================================
--- trunk/libs/polygon/doc/gtl_connectivity_extraction_90.htm (original)
+++ trunk/libs/polygon/doc/gtl_connectivity_extraction_90.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -1,14 +1,15 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<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>
-<title>Boost Polygon Library: Connectivity Extraction 90</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>
+--><title>Boost Polygon Library: Connectivity Extraction 90</title>
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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;">
@@ -20,6 +21,8 @@
 <li>Coordinate Concept</li>
 <li>Interval Concept</li>
 <li>Point Concept</li>
+ <li>Segment Concept</li>
+
 <li>Rectangle Concept</li>
 <li>Polygon 90 Concept</li>
 <li>Polygon 90 With Holes Concept</li>
@@ -36,32 +39,47 @@
 <li>Property Merge 90</li>
 <li>Property Merge 45</li>
 <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+</a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+</a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+
 </ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
- <li>GTL Boostcon 2009 Paper</li>
- <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
 Presentation</a></li>
- <li>Performance Analysis</li>
- <li>Layout Versus Schematic Tutorial</li>
- <li>Minkowski Sum Tutorial</li>
- </ul>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</li>
+ <li>Voronoi Advanced Tutorial</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">
+ <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%">



- 
+ 

<h1>Connectivity Extraction 90</h1>


-The connectivity extraction algorithm constructs the connectivity graph where
+The connectivity extraction algorithm constructs the connectivity graph where
input polygon sets are modeled as graph nodes and assigned node ids and
overlap/touching between input polygon sets is modeled as graph edges.  One
supported graph formats is std::vector<std::set<int> > where node ids index into
@@ -71,33 +89,33 @@
the operator[] is used internally to access the graph   The other
supported graph format is std::map<int, std::set<int> > which is slightly easier to
work with, but potentially more expensive.  Improving the interface to
-support more generic graph concepts is deferred to future work.The following
-is the declaration of the connectivity extraction algorithm.
-template <typename coordinate_type> 
-class connectivity_extraction_90;
+support more generic graph concepts is deferred to future work.The following
+is the declaration of the connectivity extraction algorithm.
+template <typename coordinate_type> 
+class connectivity_extraction_90;
Example code connectivity_extraction_usage.cpp
 demonstrates using the connectivity extraction algorithm to build a
-connectivity graph on geometry.<h2>Member Functions</h2>
-<table border="1" width="100%" id="table1">
- <tr>
+connectivity graph on geometry.<h2>Member Functions</h2>
+<table id="table1" border="1" width="100%">
+ <tbody><tr>
 <td width="586">connectivity_extraction_90()</td>
 <td>Default constructor. </td>
 </tr>
 <tr>
- <td width="586">connectivity_extraction_90(      const
+ <td width="586">connectivity_extraction_90(      const
 connectivity_extraction_90& that)</td>
 <td>Copy construct.</td>
 </tr>
 <tr>
 <td width="586">
-unsigned int insert(const polygon_90_set_data<coordinate_type>& ps)</td>
+unsigned int insert(const polygon_90_set_data<coordinate_type>& ps)</td>
 <td>Insert a polygon set graph node, the
 value returned is the id of the graph node.</td>
 </tr>
 <tr>
 <td width="586">

-template <class GeoObjT> 
+template <class GeoObjT> 
unsigned int insert(const GeoObjT& geoObj)</td>
 <td>Insert a geometry object that is a refinement of polygon 90 set as a
 graph node, the return value is the id of the graph node.</td>
@@ -105,24 +123,24 @@
 <tr>
 <td width="586">

-template <class GraphT> 
+template <class GraphT> 
void extract(GraphT& graph)</td>
 <td>Accepts a graph object that conforms to the expectations defined
 above.  Performs connectivity extraction and populates the graph
 object.</td>
 </tr>
- </table>
- <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" rules="none" frame="void" id="table2">
+<table class="docinfo" id="table2" frame="void" rules="none">
 <colgroup>
- <col class="docinfo-name"><col class="docinfo-content">
+ <col class="docinfo-name" /><col class="docinfo-content" />
 </colgroup>
- <tbody vAlign="top">
+ <tbody valign="top">
 <tr>
 <th class="docinfo-name">Copyright:</th>
 <td>Copyright © Intel Corporation 2008-2010.</td>
@@ -135,6 +153,6 @@
 <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt>)</td>
 </tr>
-</table>
+</tbody></table>

-</html>
\ No newline at end of file
+</td></tr></tbody></table></body></html>
\ No newline at end of file

Modified: trunk/libs/polygon/doc/gtl_coordinate_concept.htm
==============================================================================
--- trunk/libs/polygon/doc/gtl_coordinate_concept.htm (original)
+++ trunk/libs/polygon/doc/gtl_coordinate_concept.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -1,14 +1,16 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<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>
-<title>Boost Polygon Library: Coordinate Concept</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>
+--><title>Boost Polygon Library: Coordinate Concept</title>
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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;">
@@ -20,6 +22,8 @@
 <li>Coordinate Concept</li>
 <li>Interval Concept</li>
 <li>Point Concept</li>
+ <li>Segment Concept</li>
+
 <li>Rectangle Concept</li>
 <li>Polygon 90 Concept</li>
 <li>Polygon 90 With Holes Concept</li>
@@ -36,56 +40,71 @@
 <li>Property Merge 90</li>
 <li>Property Merge 45</li>
 <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+</a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+</a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+
 </ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
- <li>GTL Boostcon 2009 Paper</li>
- <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
 Presentation</a></li>
- <li>Performance Analysis</li>
- <li>Layout Versus Schematic Tutorial</li>
- <li>Minkowski Sum Tutorial</li>
- </ul>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</li>
+ <li>Voronoi Advanced Tutorial</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">
+ <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%">



- 
+ 

<h1>Coordinate Concept</h1>


The coordinate concept tag is 
-coordinate_concept
+coordinate_concept
To register a user defined type as a model of coordinate concept, specialize the
geometry concept meta-function for that type.  In the example below
-CCoordinate is registered as a model of coordinate concept.
-template <> 
-struct geometry_concept<CCoordinate> { typedef coordinate_concept type; };
+CCoordinate is registered as a model of coordinate concept.
+template <> 
+struct geometry_concept<CCoordinate> { typedef coordinate_concept type; };
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.  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.  The definition of coordinate_traits and its
-specialization for int are shown below.
-template <typename T> 
-struct coordinate_traits {}; 
- 
-template <> 
-struct coordinate_traits<int> { 
-     typedef int coordinate_type; 
-     typedef long double area_type; 
-     typedef long long manhattan_area_type; 
-     typedef unsigned long long unsigned_area_type; 
-     typedef long long coordinate_difference; 
-     typedef long double coordinate_distance; 
-};
+specialization for int are shown below.
+template <typename T> 
+struct coordinate_traits {}; 
+ 
+template <> 
+struct coordinate_traits<int> { 
+     typedef int coordinate_type; 
+     typedef long double area_type; 
+     typedef long long manhattan_area_type; 
+     typedef unsigned long long unsigned_area_type; 
+     typedef long long coordinate_difference; 
+     typedef long double coordinate_distance; 
+};
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.  For the out of the ordinary issues there is a special
@@ -94,37 +113,37 @@
available in most compilers, long double, but can be overridden by specializing
for a particular coordinate type.  Use of gmp multi-precision rational or
similar data type is recommended for numerically robust calculations in the
-general polygon algorithms.
-template <typename T> 
-struct high_precision_type { 
-     typedef long double type; 
-};
-There is only one generic function on coordinate concepts, Euclidean distance.
+general polygon algorithms.
+template <typename T> 
+struct high_precision_type { 
+     typedef long double type; 
+};
+There is only one generic function on coordinate concepts, Euclidean distance.
template <typename coordinate_type_1, typename
-coordinate_type_2> 
-coordinate_difference euclidean_distance(coordinate_type_1, coordinate_type_2)
+coordinate_type_2> 
+coordinate_difference euclidean_distance(coordinate_type_1, coordinate_type_2)
This function returns the absolution value of the difference between the two
-coordinates.
+coordinates.
Note: older versions of the stl define a fully generic distance(T, T) function
for computing the difference between two iterators.  We were forced to name
-our distance function euclidean_distance to avoid name collision.
+our distance function euclidean_distance to avoid name collision.
The
<a href="http://www.mentor.com/products/esl/high_level_synthesis/ac_datatypes">
Algorithmic C</a> ac_int<128> is an example of a user defined coordinate data
type that satisfies the coordinate concept.  In general a data type should
define std::numeric_limits and be integer-like.  Floating point coordinate
types are not supported by all the algorithms and generally not suitable for use
-with the library at present.<tr>
+with the library at present.</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" rules="none" frame="void" id="table1">
+<table class="docinfo" id="table1" frame="void" rules="none">
 <colgroup>
- <col class="docinfo-name"><col class="docinfo-content">
+ <col class="docinfo-name" /><col class="docinfo-content" />
 </colgroup>
- <tbody vAlign="top">
+ <tbody valign="top">
 <tr>
 <th class="docinfo-name">Copyright:</th>
 <td>Copyright © Intel Corporation 2008-2010.</td>
@@ -137,6 +156,6 @@
 <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt>)</td>
 </tr>
-</table>
+</tbody></table>

-</html>
\ No newline at end of file
+</td></tr></tbody></table></body></html>
\ No newline at end of file

Modified: trunk/libs/polygon/doc/gtl_design_overview.htm
==============================================================================
--- trunk/libs/polygon/doc/gtl_design_overview.htm (original)
+++ trunk/libs/polygon/doc/gtl_design_overview.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -1,14 +1,15 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<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>
-<title>Boost Polygon Library: Overview</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>
+--><title>Boost Polygon Library: Overview</title>
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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;">
@@ -21,6 +22,8 @@
 <li>Interval Concept</li>
 <li>
 <a href="gtl_point_concept.htm">Point Concept</a></li>
+ <li>Segment Concept</li>
+
 <li>Rectangle Concept</li>
 <li>Polygon 90 Concept</li>
 <li>Polygon 90 With Holes Concept</li>
@@ -37,6 +40,18 @@
 <li>Property Merge 90</li>
 <li>Property Merge 45</li>
 <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+</a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+</a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+
 </ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
@@ -46,23 +61,27 @@
 <li>Performance Analysis</li>
 <li>Layout Versus Schematic Tutorial</li>
 <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</li>
+ <li>Voronoi Advanced Tutorial</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">
+ <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%">



- 
+ 

<h1>Polygon Library Design Overview</h1>


-The Polygon library uses C++-Concepts inspired template programming to
+The Polygon library uses C++-Concepts inspired template programming to
provide generic library functions overloaded on concept type.  There are
currently thirteen concepts in the Polygon library type system.  A concept
object in the Polygon library is just an empty struct similar to a tag that
@@ -70,7 +89,7 @@
refinement diagram below.

-</body><img border="0" src="images/refinements.png" width="466" height="369">
+<img src="images/refinements.png" border="0" height="369" width="466" />
The arrows between diagram bubbles show concept refinement relationships.  This is
similar, but not identical to, inheritance relationships between normal classes. 
A refinement of a concept narrows down the definition of a more general concept. 
@@ -123,7 +142,7 @@
as that conceptual type with the library by
specializing the geometry_concept meta-function.  Once mapped and
registered, a user data type can be used interchangeably with library data types
-in the generic free functions that are overloaded on concept.Traits for
+in the generic free functions that are overloaded on concept.Traits for
mapping a data type to a concept are broken down into mutable and read only
traits.  Read only traits are specialized internally to work with any types
that are refinements of a concept.  The mutable traits are defined only for
@@ -135,7 +154,7 @@
traits defined for that triangle type.  This would allow the triangle type
to be passed into any API that expects a const reference to an object that models
polygon. 
-An object that is a model of a given concept can usually be viewed as a model of any of its
+An object that is a model of a given concept can usually be viewed as a model of any of its
refinements if it is determined at runtime to conform to the restrictions of
those concepts.  This concept casting is accomplished through the
view_as<>() function.  For example if
@@ -146,17 +165,17 @@
passed into any interface that expects an object of the conceptual type
specified in its template parameter.  The exception to this ability to
concept cast geometric objects is that polygon set objects cannot be viewed as
-individual polygons or rectangles. <tr>
+individual polygons or rectangles. </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" rules="none" frame="void" id="table1">
+<table class="docinfo" id="table1" frame="void" rules="none">
 <colgroup>
- <col class="docinfo-name"><col class="docinfo-content">
+ <col class="docinfo-name" /><col class="docinfo-content" />
 </colgroup>
- <tbody vAlign="top">
+ <tbody valign="top">
 <tr>
 <th class="docinfo-name">Copyright:</th>
 <td>Copyright © Intel Corporation 2008-2010.</td>
@@ -169,6 +188,6 @@
 <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt>)</td>
 </tr>
-</table>
+</tbody></table>

-</html>
\ No newline at end of file
+</td></tr></tbody></table></body></html>
\ No newline at end of file

Modified: trunk/libs/polygon/doc/gtl_interval_concept.htm
==============================================================================
--- trunk/libs/polygon/doc/gtl_interval_concept.htm (original)
+++ trunk/libs/polygon/doc/gtl_interval_concept.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -1,14 +1,15 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<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>
-<title>Boost Polygon Library: Interval Concept</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>
+--><title>Boost Polygon Library: Interval Concept</title>
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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;">
@@ -20,6 +21,8 @@
 <li>Coordinate Concept</li>
 <li>Interval Concept</li>
 <li>Point Concept</li>
+ <li>Segment Concept</li>
+
 <li>Rectangle Concept</li>
 <li>Polygon 90 Concept</li>
 <li>Polygon 90 With Holes Concept</li>
@@ -36,6 +39,18 @@
 <li>Property Merge 90</li>
 <li>Property Merge 45</li>
 <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+</a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+</a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+
 </ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
@@ -45,30 +60,34 @@
 <li>Performance Analysis</li>
 <li>Layout Versus Schematic Tutorial</li>
 <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</li>
+ <li>Voronoi Advanced Tutorial</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">
+ <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%">



- 
+ 

<h1>Interval Concept</h1>


-The interval concept tag is 
+The interval concept tag is 
interval_concept

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.
-template <> 
-struct geometry_concept<CInterval> { typedef interval_concept type; };
+CInterval is registered as a model of interval  concept.
+template <> 
+struct geometry_concept<CInterval> { typedef interval_concept type; };
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
@@ -76,50 +95,51 @@
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.
+elements through traits.
Below is shown the default interval traits. 
Specialization of these traits is required for types that don't conform to the
-default behavior.
-template <typename T> 
-struct interval_traits { 
-  typedef typename T::coordinate_type coordinate_type; 
- 
-  static inline coordinate_type get(const T& interval, direction_1d dir) { 
-    return interval.get(dir); 
-  } 
-}; 
- 
-template <typename T> 
-struct interval_mutable_traits { 
+default behavior.
+template <typename T> 
+struct interval_traits { 
+  typedef typename T::coordinate_type coordinate_type; 
+ 
+  static inline coordinate_type get(const T& interval, direction_1d dir) { 
+    return interval.get(dir); 
+  } 
+}; 
+ 
+template <typename T> 
+struct interval_mutable_traits { 
  static inline void set(T& interval, direction_1d dir, 
- 
-                         typename interval_traits<T>::coordinate_type value) { 
+ 
+                        
+typename interval_traits<T>::coordinate_type value) { 
   
-interval.set(dir, value); 
+interval.set(dir, value); 
 
-} 
+} 
 
static inline T construct(typename interval_traits<T>::coordinate_type low_value,
- 
+ 
                           
-typename interval_traits<T>::coordinate_type high_value) { 
+typename interval_traits<T>::coordinate_type high_value) { 
   
-return T(low_value, high_value); 
+return T(low_value, high_value); 
 
-} 
-};<h2>Functions</h2>
-<table border="1" width="100%" id="table1">
- <tr>
- <td width="586">template <typename T> 
+} 
+};<h2>Functions</h2>
+<table id="table1" border="1" width="100%">
+ <tbody><tr>
+ <td width="586">template <typename T> 
 coordinate_type get(const T& interval, direction_1d)</td>
 <td>Expects a model of interval. 
 Returns the low or high coordinate of the interval, depending on the
- direction_1d value. 
+ direction_1d value. 
 </td>
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- coordinate_type> 
+ coordinate_type> 
 void set(T& interval, direction_1d, coordinate_type)</td>
 <td>Expects a model of interval.  
 Sets the low or high coordinate of the interval to the coordinate,
@@ -127,28 +147,28 @@
 high after this change then both are set to the input coordinate value.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T construct(coordinate_type low, coordinate_type high)</td>
 <td>Construct an object that is a model of interval given low and high
 coordinate values.</td>
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& assign(T1& left, const T2& right)</td>
 <td>Copies data from right object that models interval into left object
 that models interval.</td>
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- T2> 
+ T2> 
 bool equivalence(const T& interval1, const T2& interval2)</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">template <typename T> 
- bool contains(const T&, coordinate_type, 
+ <td width="586">template <typename T> 
+ bool contains(const T&, coordinate_type, 
             
 bool consider_touch=true)</td>
 <td>Given an object that models interval and a coordinate, returns true
@@ -158,8 +178,8 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
- bool contains(const T1& a, const T2& b, 
+ T2> 
+ bool contains(const T1& a, const T2& b, 
             
 bool consider_touch = true) </td>
 <td>Returns true if model of interval a contains both ends of model of
@@ -168,25 +188,25 @@
 </tr>
 <tr>
 <td width="586">template <typename
- interval_type> 
+ interval_type> 
 coordinate_type low(const interval_type& interval)</td>
 <td>Returns the low end of an object that models interval.</td>
 </tr>
 <tr>
 <td width="586">template <typename
- interval_type> 
+ interval_type> 
 coordinate_type high(const interval_type& interval)</td>
 <td>Returns the high end of an object that models interval.</td>
 </tr>
 <tr>
- <td width="586">// get the center coordinate 
- template <typename interval_type> 
+ <td width="586">// get the center coordinate 
+ template <typename interval_type> 
 coordinate_type center(const interval_type& interval)</td>
 <td>Returns the center coordinate of an object that models interval.</td>
 </tr>
 <tr>
 <td width="586">template <typename
- interval_type> 
+ interval_type> 
 void low(interval_type& interval, coordinate_type )</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
@@ -194,7 +214,7 @@
 </tr>
 <tr>
 <td width="586">template <typename
- interval_type> 
+ interval_type> 
 void high(interval_type& interval, coordinate_type )</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
@@ -202,15 +222,15 @@
 </tr>
 <tr>
 <td width="586">template <typename
- interval_type> 
+ interval_type> 
 coordinate_difference delta(const interval_type& interval)</td>
 <td>Returns the distance from low to high end of an object that models
 interval.</td>
 </tr>
 <tr>
 <td width="586">template <typename
- interval_type> 
- interval_type& flip(interval_type& interval, 
+ interval_type> 
+ interval_type& flip(interval_type& interval, 
                   
 coordinate_type axis = 0)</td>
 <td>Flips an object that models interval about the axis coordinate. 
@@ -218,26 +238,26 @@
 </tr>
 <tr>
 <td width="586">template <typename
- interval_type> 
- interval_type& scale_up(interval_type& interval, 
-                       
- unsigned_area_type factor)</td>
+ interval_type> 
+ interval_type& scale_up(interval_type& interval, 
+                       
+unsigned_area_type factor)</td>
 <td>Multiplies low and high ends of an object that models interval by
 unsigned factor.</td>
 </tr>
 <tr>
 <td width="586">template <typename
- interval_type> 
- interval_type& scale_down(interval_type& interval, 
-                         
- unsigned_area_type factor)</td>
+ interval_type> 
+ interval_type& scale_down(interval_type& interval, 
+                         
+unsigned_area_type factor)</td>
 <td>Divides low and high ends of an object that models interval by
 unsigned factor.</td>
 </tr>
 <tr>
 <td width="586">template <typename
- interval_type> 
- interval_type& scale(interval_type& interval, 
+ interval_type> 
+ interval_type& scale(interval_type& interval, 
                    
 double factor) </td>
 <td>Multiplies low and high ends of an object that models interval by
@@ -245,8 +265,8 @@
 </tr>
 <tr>
 <td width="586">template <typename
- interval_type> 
- interval_type& move(interval_type& interval, 
+ interval_type> 
+ interval_type& move(interval_type& interval, 
                   
 coordinate_difference displacement)</td>
 <td>Adds displacement value to low and high ends of an object that
@@ -254,53 +274,53 @@
 </tr>
 <tr>
 <td width="586">template <typename
- interval_type> 
- interval_type& convolve(interval_type& interval, 
-                       
- coordinate_type b)</td>
+ interval_type> 
+ interval_type& convolve(interval_type& interval, 
+                       
+coordinate_type b)</td>
 <td>Adds coordinate value to low and high ends of an object that models
 interval.</td>
 </tr>
 <tr>
 <td width="586">template <typename
- interval_type> 
- interval_type& deconvolve(interval_type& interval, 
-                         
- coordinate_type b)</td>
+ interval_type> 
+ interval_type& deconvolve(interval_type& interval, 
+                         
+coordinate_type b)</td>
 <td>Subtracts coordinate value from low and high ends of an object that
 models interval.</td>
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& convolve(T1& a, const T2& b)</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">template <typename T1, typename
- T2> 
+ T2> 
 T1& deconvolve(T1& a, const T2& b)</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">template <typename T1, typename
- T2> 
+ T2> 
 T1& reflected_convolve(T1& a, const T2& b)</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">template <typename T1, typename
- T2> 
+ T2> 
 T1& reflected_deconvolve(T1& a, const T2& b)</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">template <typename T> 
- coordinate_difference euclidean_distance(const T&, 
+ <td width="586">template <typename T> 
+ coordinate_difference euclidean_distance(const T&, 
                     
 coordinate_type)</td>
 <td>Returns the distance from an object that models interval to a
@@ -309,8 +329,8 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
- bool intersects(const T1& interval, const T2& b, 
+ T2> 
+ bool intersects(const T1& interval, const T2& b, 
               
 bool consider_touch = true)</td>
 <td>Returns true if two objects that model interval overlap.  If
@@ -319,10 +339,10 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
- bool boundaries_intersect(const T1& interval, const T2& b, 
-                         
- bool consider_touch = true)</td>
+ T2> 
+ bool boundaries_intersect(const T1& interval, const T2& b, 
+                         
+bool consider_touch = true)</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
@@ -330,8 +350,8 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
- bool abuts(const T1& a, const T2& b, 
+ T2> 
+ bool abuts(const T1& a, const T2& b, 
           direction_1d dir)
 </td>
 <td>Returns true if interval b abuts but down not overlap interval a on
@@ -339,14 +359,14 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 bool abuts(const T1& a, const T2& b)</td>
 <td>Returns true if interval b abuts but down not overlap interval a.</td>
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
- bool intersect(T1& a, const T2& b, 
+ T2> 
+ bool intersect(T1& a, const T2& b, 
              
 bool consider_touch = true) </td>
 <td>Sets interval a to the intersection of interval a and interval b and
@@ -356,55 +376,55 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T& generalized_intersect(T1& a, const T2& b)</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">template <typename T> 
+ <td width="586">template <typename T> 
 T& bloat(T& interval, coordinate_type)</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">template <typename T> 
+ <td width="586">template <typename T> 
 T& bloat(T& interval, direction_1d, coordinate_type)</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">template <typename T> 
+ <td width="586">template <typename T> 
 T& shrink(T& interval, coordinate_type)</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">template <typename T> 
+ <td width="586">template <typename T> 
 T& shrink(T& interval, direction_1d, coordinate_type)</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">template <typename T1, typename
- T2> 
+ T2> 
 bool encompass(T1& a, const T2& b)</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">template <typename T> 
+ <td width="586">template <typename T> 
 bool encompass(T& a, coordinate_type)</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>
-</table>
+</tbody></table>
 <h1>Interval Data</h1>


-The library provides a model of interval concept declared
+The library provides a model of interval concept declared

template<typename T> interval_data where T is the coordinate type.
This data type is used internally when an interval is needed and is available
@@ -412,8 +432,8 @@
instead of providing their own.  The data type is implemented to be
convenient to use with the library traits.
<h2>Members</h2>
-<table border="1" width="100%" id="table2">
- <tr>
+<table id="table2" border="1" width="100%">
+ <tbody><tr>
 <td width="586">geometry_type</td>
 <td>interval_concept</td>
 </tr>
@@ -444,42 +464,42 @@
 </tr>
 <tr>
 <td width="586">template <typename T2> 
- interval_data& operator=(const T2& that) const</td>
+ interval_data& operator=(const T2& that) const</td>
 <td>Assign from an object that is a model of interval.</td>
 </tr>
 <tr>
 <td width="586">template <typename T2>
- bool
+ bool
 operator==(const T2& that) const</td>
 <td>Compare equality to an object that is a model of interval.</td>
 </tr>
 <tr>
 <td width="586">template <typename T2>
- bool
+ bool
 operator!=(const T2& that) const</td>
 <td>Compare inequality to an object that is a model of interval.</td>
 </tr>
 <tr>
 <td width="586">template <typename T2>
- bool
+ bool
 operator<(const T2& that) const</td>
 <td>Compares low coordinates then high coordinates to break ties.</td>
 </tr>
 <tr>
 <td width="586">template <typename T2>
- bool
+ bool
 operator<=(const T2& that) const</td>
 <td>Compares low coordinates then high coordinates to break ties.</td>
 </tr>
 <tr>
 <td width="586">template <typename T2>
- bool
+ bool
 operator>(const T2& that) const</td>
 <td>Compares low coordinates then high coordinates to break ties.</td>
 </tr>
 <tr>
 <td width="586">template <typename T2>
- bool
+ bool
 operator>=(const T2& that) const</td>
 <td>Compares low coordinates then high coordinates to break ties.</td>
 </tr>
@@ -493,18 +513,18 @@
 dir, T value)</td>
 <td>Sets the coordinate in the given direction to the value.</td>
 </tr>
- </table>
- <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" rules="none" frame="void" id="table3">
+<table class="docinfo" id="table3" frame="void" rules="none">
 <colgroup>
- <col class="docinfo-name"><col class="docinfo-content">
+ <col class="docinfo-name" /><col class="docinfo-content" />
 </colgroup>
- <tbody vAlign="top">
+ <tbody valign="top">
 <tr>
 <th class="docinfo-name">Copyright:</th>
 <td>Copyright © Intel Corporation 2008-2010.</td>
@@ -517,6 +537,6 @@
 <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt>)</td>
 </tr>
-</table>
+</tbody></table>

-</html>
\ No newline at end of file
+</td></tr></tbody></table></body></html>
\ No newline at end of file

Modified: trunk/libs/polygon/doc/gtl_isotropy.htm
==============================================================================
--- trunk/libs/polygon/doc/gtl_isotropy.htm (original)
+++ trunk/libs/polygon/doc/gtl_isotropy.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -1,14 +1,15 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<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>
-<title>Boost Polygon Library: Isotropy</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>
+--><title>Boost Polygon Library: Isotropy</title>
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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;">
@@ -20,6 +21,8 @@
 <li>Coordinate Concept</li>
 <li>Interval Concept</li>
 <li>Point Concept</li>
+ <li>Segment Concept</li>
+
 <li>Rectangle Concept</li>
 <li>Polygon 90 Concept</li>
 <li>Polygon 90 With Holes Concept</li>
@@ -36,6 +39,18 @@
 <li>Property Merge 90</li>
 <li>Property Merge 45</li>
 <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+</a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+</a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+
 </ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
@@ -45,32 +60,34 @@
 <li>Performance Analysis</li>
 <li>Layout Versus Schematic Tutorial</li>
 <li>Minkowski Sum Tutorial</li>
- </ul>
+ <li>Voronoi Basic Tutorial</li>
+ <li>Voronoi Advanced Tutorial</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">
+ <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%">



- 
+ 

<h1>Isotropy</h1>


-What is isotropy?
-<P:COLORSCHEME
-colors="#ffffff,#000000,#808080,#000000,#bbe0e3,#333399,#009999,#99cc00" />
-<div class="O" style="TEXT-ALIGN: center; mso-line-spacing: '90 0 0'; mso-margin-left-alt: 216; mso-char-wrap: 1; mso-kinsoku-overflow: 1" v:shape="_x0000_s1026">
- 
- Isotropy - Function: adjective Etymology: International
- Scientific Vocabulary 
+What is isotropy?
+<p:colorscheme colors="#ffffff,#000000,#808080,#000000,#bbe0e3,#333399,#009999,#99cc00">
+</p:colorscheme><div class="O" style="text-align: center;" v:shape="_x0000_s1026">
+ 
+ Isotropy - Function: adjective Etymology: International
+ Scientific Vocabulary 
 : exhibiting properties (as velocity of light transmission) with the
 same values when measured along axes in all directions <an isotropic
- crystal></div>
+ crystal></div>
In computational geometry things are often symmetric and
invariant to direction and orientation.  This invariance to direction is
called isotropy.  In such situations it is convenient to parameterize
@@ -95,8 +112,8 @@
describing isotropic situations programmatically.  For instance, to get the
positive direction_2d from an orientation_2d you would call a member function of
orientation_2d and pass a direction_1d:
-orientation_2d orient = HORIZONTAL; 
-direction_2d dir = orient.get_direction(direction_1d(HIGH)); 
+orientation_2d orient = HORIZONTAL; 
+direction_2d dir = orient.get_direction(direction_1d(HIGH)); 
assert(dir == EAST);
The motivation for providing isotropic data types is to
encourage programming at a higher level of abstraction where program behavior is
@@ -114,7 +131,7 @@
<h2>direction_1d</h2>


-The direction_1d data type has two possible states.  These
+The direction_1d data type has two possible states.  These
are the positive and negative directions on a continuum such as the number line.  
These states can be described by one of several direction_1d_enum values: 
We make clockwise and counterclockwise winding orientation of polygons a
@@ -122,24 +139,23 @@
type.  This is because winding orientation can be thought of as positive
and negative directions in a 1d (although cyclic) space.  We assign
counterclockwise to be the positive direction of travel in the 1d cyclic space
-to conform with the mathematical convention frequently described as the "right
-hand rule" which assigns positive normal value to counterclockwise and negative
+to conform with the mathematical convention frequently described as the "right
+hand rule" which assigns positive normal value to counterclockwise and negative
normal value to clockwise as well as the common convention that counterclockwise
polygon winding corresponds to positive polygonal regions where as clockwise
polygon winding corresponds to hole (negative) polygonal regions.
enum direction_1d_enum {LOW = 0, HIGH =
-1, 
-                       
-LEFT = 0, RIGHT = 1, 
-                       
-CLOCKWISE = 0, COUNTERCLOCKWISE = 1, 
-                       
-REVERSE = 0, FORWARD = 1, 
-                       
+1,                        
+LEFT = 0, RIGHT = 1, 
+                       
+CLOCKWISE = 0, COUNTERCLOCKWISE = 1, 
+                       
+REVERSE = 0, FORWARD = 1, 
+                       
NEGATIVE = 0, POSITIVE = 1 };
<h2>Member Functions</h2>
-<table border="1" width="100%" id="table1">
- <tr>
+<table id="table1" border="1" width="100%">
+ <tbody><tr>
 <td width="586">direction_1d(direction_1d_enum
 val = LOW)</td>
 <td>Constructor defaults to LOW. </td>
@@ -193,18 +209,18 @@
 <td>Returns positive 1 if positive direction and negative one if
 negative direction.</td>
 </tr>
- </table>
+ </tbody></table>
<h2>orientation_2d</h2>


-The orientation_2d data type has two possible states. 
+The orientation_2d data type has two possible states. 
These are the horizontal and vertical axis of a 2d Cartesian coordinate system.  
These states can be described by one of the two orientation_2d_enum values:
enum orientation_2d_enum { HORIZONTAL =
0, VERTICAL = 1 };
<h2>Member Functions</h2>
-<table border="1" width="100%" id="table2">
- <tr>
+<table id="table2" border="1" width="100%">
+ <tbody><tr>
 <td width="586">orientation_2d(orientation_2d_enum
 val = HORIZONTAL)</td>
 <td>Constructor defaults to HORIZONTAL. </td>
@@ -261,18 +277,18 @@
 <td>Returns the positive or negative direction_2d depending on the value
 of dir</td>
 </tr>
- </table>
+ </tbody></table>
<h2>direction_2d</h2>


-The direction_2d data type has four possible states.  These
+The direction_2d data type has four possible states.  These
are the cardinal directions of the 2D Cartesian coordinate system.  
These states can be described by one of several direction_2d_enum values:
enum direction_2d_enum { WEST = 0, EAST
= 1, SOUTH = 2, NORTH = 3 };
<h2>Member Functions</h2>
-<table border="1" width="100%" id="table3">
- <tr>
+<table id="table3" border="1" width="100%">
+ <tbody><tr>
 <td width="586">direction_2d(direction_2d_enum
 val = WEST)</td>
 <td>Constructor defaults to WEST. </td>
@@ -342,19 +358,19 @@
 <td>Returns positive 1 if positive direction and negative one if
 negative direction.</td>
 </tr>
- </table>
+ </tbody></table>
<h2>orientation_3d</h2>


-The orientation_3d data type has three possible states. 
+The orientation_3d data type has three possible states. 
These are the horizontal, vertical and proximal (x, y, z) axis of a 3d Cartesian
coordinate system.   These states can be described by one of the
orientation_2d_enum values or by the orientation_3d_enum value:
enum orientation_3d_enum { PROXIMAL = 2
};
<h2>Member Functions</h2>
-<table border="1" width="100%" id="table6">
- <tr>
+<table id="table6" border="1" width="100%">
+ <tbody><tr>
 <td width="586">orientation_3d(orientation_2d_enum
 val = HORIZONTAL)</td>
 <td>Constructor defaults to HORIZONTAL. </td>
@@ -416,19 +432,19 @@
 <td>Returns the positive or negative direction_2d depending on the value
 of dir</td>
 </tr>
- </table>
+ </tbody></table>
<h2>direction_3d</h2>


-The direction_3d data type has six possible states.  These
+The direction_3d data type has six possible states.  These
are the cardinal directions of the 3D Cartesian coordinate system.  
These states can be described by one of the direction_2d_enum values or the
direction_3d_enum values:
enum direction_3d_enum { DOWN = 4, UP =
5 };
<h2>Member Functions</h2>
-<table border="1" width="100%" id="table5">
- <tr>
+<table id="table5" border="1" width="100%">
+ <tbody><tr>
 <td width="586">direction_3d(direction_2d_enum
 val = WEST)</td>
 <td>Constructor defaults to LOW. </td>
@@ -490,18 +506,18 @@
 <td>Returns positive 1 if positive direction and negative one if
 negative direction.</td>
 </tr>
- </table>
- <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" rules="none" frame="void" id="table7">
+<table class="docinfo" id="table7" frame="void" rules="none">
 <colgroup>
- <col class="docinfo-name"><col class="docinfo-content">
+ <col class="docinfo-name" /><col class="docinfo-content" />
 </colgroup>
- <tbody vAlign="top">
+ <tbody valign="top">
 <tr>
 <th class="docinfo-name">Copyright:</th>
 <td>Copyright © Intel Corporation 2008-2010.</td>
@@ -514,6 +530,6 @@
 <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt>)</td>
 </tr>
-</table>
+</tbody></table>

-</html>
\ No newline at end of file
+</td></tr></tbody></table></body></html>
\ No newline at end of file

Modified: trunk/libs/polygon/doc/gtl_minkowski_tutorial.htm
==============================================================================
--- trunk/libs/polygon/doc/gtl_minkowski_tutorial.htm (original)
+++ trunk/libs/polygon/doc/gtl_minkowski_tutorial.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -96,7 +96,7 @@
convolutions.  First we implement a function that convolves all pairs of
edges represented by iterator pairs over points.  We assume that the first
point is equal to the last point in each sequence because we know the polygons
-that gave rise to the iterators were produced by the Boost.Polygon algorithm for
+that gave rise to the iterators were produce by the Boost.Polygon algorithm for
general polygon formation.
template <typename itrT1, typename itrT2> 
void convolve_two_point_sequences(polygon_set& result, itrT1 ab, itrT1 ae, itrT2
@@ -177,7 +177,7 @@
    } 
  } 
}
-We test the convolution of two polygon sets with the code shown below that
+We test the convolution of two polygon set with the code shown below that
produces the first example shown in this tutorial.

polygon_set a, b, c; 
@@ -197,6 +197,7 @@
polygon poly; 
boost::polygon::set_points(poly, pts.begin(), pts.end()); 
b+=poly; 
+polys.clear(); 
convolve_two_polygon_sets(c, a, b);
Output (a is blue, b is green and c is red):
<img border="0" src="images/convolution1.PNG" width="438" height="404">

Modified: trunk/libs/polygon/doc/gtl_point_concept.htm
==============================================================================
--- trunk/libs/polygon/doc/gtl_point_concept.htm (original)
+++ trunk/libs/polygon/doc/gtl_point_concept.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -1,14 +1,15 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<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>
-<title>Boost Polygon Library: Point Concept</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>
+--><title>Boost Polygon Library: Point Concept</title>
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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;">
@@ -20,6 +21,8 @@
 <li>Coordinate Concept</li>
 <li>Interval Concept</li>
 <li>Point Concept</li>
+ <li>Segment Concept</li>
+
 <li>Rectangle Concept</li>
 <li>Polygon 90 Concept</li>
 <li>Polygon 90 With Holes Concept</li>
@@ -36,6 +39,18 @@
 <li>Property Merge 90</li>
 <li>Property Merge 45</li>
 <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+</a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+</a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+
 </ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
@@ -45,30 +60,34 @@
 <li>Performance Analysis</li>
 <li>Layout Versus Schematic Tutorial</li>
 <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</li>
+ <li>Voronoi Advanced Tutorial</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">
+ <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%">



- 
+ 

<h1>Point Concept</h1>


-
+
The point concept tag is 
-point_concept
+point_concept
To register a user defined type as a model of point concept, specialize the
geometry concept meta-function for that type.  In the example below CPoint is registered as a model of
-point  concept.
-template <> 
-struct geometry_concept<CPoint> { typedef point_concept type; };
+point  concept.
+template <> 
+struct geometry_concept<CPoint> { typedef point_concept type; };
The semantic of a point is that it has an x and y
coordinate.  A std::pair<int, int>, boost::tuple<int, int> or boost::array<int, 2>
could all be made models of point by simply providing indirect access to their
@@ -76,116 +95,115 @@
point and interval in the same compilation unit, for obvious reason that
duplicate specialization of the geometry_concept struct is illegal, but also
because it would make overloading generic function by concept ambiguous if a
-type modeled more than one concept.
+type modeled more than one concept.
Below is shown the default point traits. 
Specialization of these traits is required for types that don't conform to the
-default behavior.
-template <typename T> 
-struct point_traits { 
-     typedef typename T::coordinate_type coordinate_type; 
- 
+default behavior.
+template <typename T> 
+struct point_traits { 
+     typedef typename T::coordinate_type coordinate_type; 
+ 
     static inline coordinate_type get(const T& point,
-orientation_2d orient) { 
+orientation_2d orient) { 
          return point.get(orient);
- 
-     } 
-}; 
- 
-template <typename T> 
-struct point_mutable_traits { 
+ 
+     } 
+}; 
+ 
+template <typename T> 
+struct point_mutable_traits { 
     static inline void set(T& point, orientation_2d orient,
-typename point_traits<T>::coordinate_type value) { 
+typename point_traits<T>::coordinate_type value) { 
          point.set(orient, value);
- 
-     } 
+ 
+     } 
     static inline T construct(typename point_traits<T>::coordinate_type
-x_value, typename point_traits<T>::coordinate_type y_value) { 
+x_value, typename point_traits<T>::coordinate_type y_value) { 
          return T(x_value, y_value);
- 
-     } 
-};
+ 
+     } 
+};
Example code custom_point.cpp demonstrates
how to map a
- user defined point class to the library point_concept<h2>Functions</h2>
-<table border="1" width="100%" id="table1">
- <tr>
- <td width="586">template <typename T> 
+ user defined point class to the library point_concept<h2>Functions</h2>
+<table id="table1" border="1" width="100%">
+ <tbody><tr>
+ <td width="586">template <typename T> 
 coordinate_type get(const T& point, orientation_2d)</td>
 <td>Expects a model of point.  Returns
 the x or y coordinate of the point, depending on the orientation_2d
- value. 
+ value. 
 </td>
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- coordinate_type> 
+ coordinate_type> 
 void set(T& point, orientation_2d, coordinate_type)</td>
 <td>Expects a model of point.  
 Sets the x or y coordinate of the point to the coordinate, depending on
 the orientation_2d  value. </td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T construct(coordinate_type x, coordinate_type y)</td>
 <td>Construct an object that is a model of point given x and y
 coordinate values.</td>
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& assign(T1& left, const T2& right)</td>
 <td>Copies data from right object that models point into left object
 that models point.</td>
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- T2> 
+ T2> 
 bool equivalence(const T& point1, const T2& point2)</td>
 <td>Given two objects that model point, compares and returns true if
 their x and y values are respectively equal to each other.</td>
 </tr>
 <tr>
- <td width="586">template <typename point_type> 
+ <td width="586">template <typename point_type> 
 coordinate_type x(const point_type& point)</td>
 <td>Returns the x coordinate of an object that models point.</td>
 </tr>
 <tr>
- <td width="586">template <typename point_type> 
+ <td width="586">template <typename point_type> 
 coordinate_type y(const point_type& point)</td>
 <td>Returns the y coordinate of an object that models point.</td>
 </tr>
 <tr>
- <td width="586">template <typename point_type> 
+ <td width="586">template <typename point_type> 
 void x(point_type& point, coordinate_type )</td>
 <td>Sets the x coordinate of the object that models point to the
 coordinate value.  </td>
 </tr>
 <tr>
- <td width="586">template <typename point_type> 
+ <td width="586">template <typename point_type> 
 void y(point_type& point, coordinate_type )</td>
 <td>Sets the y coordinate of the object that models point to the
 coordinate value.  </td>
 </tr>
 <tr>
- <td width="586">template <typename point_type> 
- point_type& scale_up(point_type& point, 
-                       
- unsigned_area_type factor)</td>
+ <td width="586">template <typename point_type> 
+ point_type& scale_up(point_type& point,                        
+unsigned_area_type factor)</td>
 <td>Multiplies x and y coordinate of an object that models point by
 unsigned factor.</td>
 </tr>
 <tr>
- <td width="586">template <typename point_type> 
- point_type& scale_down(point_type& point, 
-                         
- unsigned_area_type factor)</td>
+ <td width="586">template <typename point_type> 
+ point_type& scale_down(point_type& point, 
+                         
+unsigned_area_type factor)</td>
 <td>Divides x and y coordinate of an object that models point by
 unsigned factor.</td>
 </tr>
 <tr>
 <td width="586">template <typename point_type,
- typename scaling_type> 
- point_type& scale(point_type& point, 
+ typename scaling_type> 
+ point_type& scale(point_type& point, 
                 
 const scaling_type& factor) </td>
 <td>Calls the scale member function of scaling type on the x and y value
@@ -193,8 +211,8 @@
 </tr>
 <tr>
 <td width="586">template <typename point_type,
- typename transform_type> 
- point_type& transform(point_type& point, 
+ typename transform_type> 
+ point_type& transform(point_type& point, 
                     
 const transform_type& transform) </td>
 <td>Calls the transform member function of transform type on the x and y
@@ -202,8 +220,8 @@
 transformed values.</td>
 </tr>
 <tr>
- <td width="586">template <typename point_type> 
- point_type& move(point_type& point, orientation_2d 
+ <td width="586">template <typename point_type> 
+ point_type& move(point_type& point, orientation_2d 
                
 coordinate_difference displacement)</td>
 <td>Adds displacement value to the coordinate of an object that models
@@ -211,30 +229,30 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& convolve(T1& a, const T2& b)</td>
 <td>Adds x coordinate of b to x coordinate of a and adds y coordinate of
 b to y coordinate of a.</td>
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& deconvolve(T1& a, const T2& b)</td>
 <td>Subtracts x coordinate of b from x coordinate of a and subtracts y
 coordinate of b from y coordinate of a. </td>
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
- coordinate_distance euclidean_distance(const T1&, 
-                                      
- const T2&)</td>
+ T2> 
+ coordinate_distance euclidean_distance(const T1&, 
+                                      
+const T2&)</td>
 <td>Returns the distance from an object that models point to a second
 object that models point.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
- coordinate_difference euclidean_distance(const T&, 
+ <td width="586">template <typename T> 
+ coordinate_difference euclidean_distance(const T&, 
           orientation_2d,
 coordinate_type)</td>
 <td>Returns the distance from an object that models point to a
@@ -242,28 +260,28 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
- coordinate_difference manhattan_distance(const T1&, 
-                                      
- const T2&)</td>
+ T2> 
+ coordinate_difference manhattan_distance(const T1&, 
+                                      
+const T2&)</td>
 <td>Returns the distance in x plus the distance in y from an object that
 models point to a second object that models point.</td>
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
- coordinate_difference distance_squared(const T1&, 
-                                      
- const T2&)</td>
+ T2> 
+ coordinate_difference distance_squared(const T1&, 
+                                      
+const T2&)</td>
 <td>Returns the square of the distance in x plus the square of the
 distance in y from an object that models point to a second object that
 models point.</td>
 </tr>
-</table>
+</tbody></table>
<h1>Point Data</h1>


-The library provides a model of point concept declared
+The library provides a model of point concept declared

template<typename T> point_data where T is the coordinate type.
This data type is used internally when a point is needed and is available to
@@ -273,8 +291,8 @@
Example code point_usage.cpp demonstrates using the
 library provided point data type and functions
<h2>Members</h2>
-<table border="1" width="100%" id="table2">
- <tr>
+<table id="table2" border="1" width="100%">
+ <tbody><tr>
 <td width="586">geometry_type</td>
 <td>point_concept</td>
 </tr>
@@ -304,42 +322,42 @@
 </tr>
 <tr>
 <td width="586">template <typename T2> 
- point_data& operator=(const T2& that) const</td>
+ point_data& operator=(const T2& that) const</td>
 <td>Assign from an object that is a model of point.</td>
 </tr>
 <tr>
 <td width="586">template <typename T2>
- bool
+ bool
 operator==(const T2& that) const</td>
 <td>Compare equality to an object that is a model of point.</td>
 </tr>
 <tr>
 <td width="586">template <typename T2>
- bool
+ bool
 operator!=(const T2& that) const</td>
 <td>Compare inequality to an object that is a model of point.</td>
 </tr>
 <tr>
 <td width="586">template <typename T2>
- bool
+ bool
 operator<(const T2& that) const</td>
 <td>Compares y coordinates then x coordinates to break ties.</td>
 </tr>
 <tr>
 <td width="586">template <typename T2>
- bool
+ bool
 operator<=(const T2& that) const</td>
 <td>Compares y coordinates then x coordinates to break ties.</td>
 </tr>
 <tr>
 <td width="586">template <typename T2>
- bool
+ bool
 operator>(const T2& that) const</td>
 <td>Compares low coordinates then high coordinates to break ties.</td>
 </tr>
 <tr>
 <td width="586">template <typename T2>
- bool
+ bool
 operator>=(const T2& that) const</td>
 <td>Compares low coordinates then high coordinates to break ties.</td>
 </tr>
@@ -369,18 +387,18 @@
 <td width="586">void y(T value)</td>
 <td>Sets the coordinate in the vertical orientation to the value.</td>
 </tr>
- </table>
- <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" rules="none" frame="void" id="table3">
+<table class="docinfo" id="table3" frame="void" rules="none">
 <colgroup>
- <col class="docinfo-name"><col class="docinfo-content">
+ <col class="docinfo-name" /><col class="docinfo-content" />
 </colgroup>
- <tbody vAlign="top">
+ <tbody valign="top">
 <tr>
 <th class="docinfo-name">Copyright:</th>
 <td>Copyright © Intel Corporation 2008-2010.</td>
@@ -393,6 +411,6 @@
 <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt>)</td>
 </tr>
-</table>
+</tbody></table>

-</html>
\ No newline at end of file
+</td></tr></tbody></table></body></html>
\ No newline at end of file

Modified: trunk/libs/polygon/doc/gtl_polygon_45_concept.htm
==============================================================================
--- trunk/libs/polygon/doc/gtl_polygon_45_concept.htm (original)
+++ trunk/libs/polygon/doc/gtl_polygon_45_concept.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -1,14 +1,15 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<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>
-<title>Boost Polygon Library: Polygon 45 Concept</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>
+--><title>Boost Polygon Library: Polygon 45 Concept</title>
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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;">
@@ -20,6 +21,8 @@
 <li>Coordinate Concept</li>
 <li>Interval Concept</li>
 <li>Point Concept</li>
+ <li>Segment Concept</li>
+
 <li>Rectangle Concept</li>
 <li>Polygon 90 Concept</li>
 <li>Polygon 90 With Holes Concept</li>
@@ -36,40 +39,55 @@
 <li>Property Merge 90</li>
 <li>Property Merge 45</li>
 <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+</a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+</a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+
 </ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
- <li>GTL Boostcon 2009 Paper</li>
- <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
 Presentation</a></li>
- <li>Performance Analysis</li>
- <li>Layout Versus Schematic Tutorial</li>
- <li>Minkowski Sum Tutorial</li>
- </ul>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</li>
+ <li>Voronoi Advanced Tutorial</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">
+ <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%">



- 
+ 

<h1>Polygon 45 Concept</h1>


-The polygon_45 concept tag is 
+The polygon_45 concept tag is 
polygon_45_concept

To register a user defined type as a model of
polygon_45 concept, specialize the
geometry concept meta-function for that type.  In the example below CPolygon45 is registered as a model of
-polygon_45  concept.
-template <> 
-struct geometry_concept<CPolygon45> { typedef polygon_45_concept type; };
+polygon_45  concept.
+template <> 
+struct geometry_concept<CPolygon45> { typedef polygon_45_concept type; };
The semantic of a polygon_45 is that it can provide
iterators over the points that represent its vertices, angles formed as these
vertices must be multiple of 45-degree relative to the coordinate axis.  It
@@ -80,75 +98,75 @@
or std::list<point_data<int> >
could be made models of polygon_45_concept by simply providing access to their
iterators through traits.  Library functions that create polygon objects
-require that those objects provide a default constructor.
+require that those objects provide a default constructor.
Below is shown the default polygon traits. 
Specialization of these traits is required for types that don't conform to the
default behavior.  Note that these traits are also used by several other
polygon concepts through SFINAE enable template parameter.  The SFINAE enable
parameter also allows the library to provide default specialization that work
-for any object that models the 90 degree polygon concepts.
-template <typename T, typename enable = gtl_yes> 
-struct polygon_traits {}; 
- 
-template <typename T> 
-struct polygon_traits<T, 
-  typename gtl_or_4< 
+for any object that models the 90 degree polygon concepts.
+template <typename T, typename enable = gtl_yes> 
+struct polygon_traits {}; 
+ 
+template <typename T> 
+struct polygon_traits<T, 
+  typename gtl_or_4< 
    typename gtl_same_type<typename geometry_concept<T>::type,
-polygon_concept>::type, 
+polygon_concept>::type, 
    typename gtl_same_type<typename geometry_concept<T>::type,
-polygon_45_concept>::type, 
+polygon_45_concept>::type, 
    typename gtl_same_type<typename geometry_concept<T>::type,
-polygon_with_holes_concept>::type, 
+polygon_with_holes_concept>::type, 
    typename gtl_same_type<typename geometry_concept<T>::type,
-polygon_45_with_holes_concept>::type 
-  >::type> { 
-     typedef typename T::coordinate_type coordinate_type; 
-     typedef typename T::iterator_type iterator_type; 
-     typedef typename T::point_type point_type; 
-     static inline iterator_type begin_points(const T& t) { 
-          return t.begin(); 
-     } 
-     static inline iterator_type end_points(const T& t) { 
-          return t.end(); 
-     } 
-     static inline unsigned int size(const T& t) { 
-          return t.size(); 
-     } 
-     static inline winding_direction winding(const T& t) { 
-          return unknown_winding; 
-     } 
+polygon_45_with_holes_concept>::type 
+  >::type> { 
+     typedef typename T::coordinate_type coordinate_type; 
+     typedef typename T::iterator_type iterator_type; 
+     typedef typename T::point_type point_type; 
+     static inline iterator_type begin_points(const T& t) { 
+          return t.begin(); 
+     } 
+     static inline iterator_type end_points(const T& t) { 
+          return t.end(); 
+     } 
+     static inline unsigned int size(const T& t) { 
+          return t.size(); 
+     } 
+     static inline winding_direction winding(const T& t) { 
+          return unknown_winding; 
+     } 
};
-template <typename T, typename enable = void> 
-struct polygon_mutable_traits { 
-     template <typename iT> 
+template <typename T, typename enable = void> 
+struct polygon_mutable_traits { 
+     template <typename iT> 
     static inline T& set_points(T& t, iT input_begin, iT
-input_end) { 
+input_end) { 
          t.set(input_begin,
-input_end); 
-          return t; 
-     } 
+input_end); 
+          return t; 
+     } 
};
An object that is a model of 
polygon_45_concept can be viewed as a model of any of its
refinements if it is determined at runtime to conform to the restriction of
those concepts.  This concept casting is accomplished through the
view_as<>() function.
-view_as<rectangle_concept>(polygon_45_object) 
+view_as<rectangle_concept>(polygon_45_object) 
view_as<polygon_90_concept>(polygon_45_object)
The return value of view_as<>() can be
passed into any interface that expects an object of the conceptual type
specified in its template parameter.
<h2>Functions</h2>
-<table border="1" width="100%" id="table1">
- <tr>
- <td width="586">template <typename T> 
+<table id="table1" border="1" width="100%">
+ <tbody><tr>
+ <td width="586">template <typename T> 
 point_iterator_type begin_points(const T& polygon)</td>
 <td>Expects a model of polygon_45. 
 Returns the begin iterator over the range of points that correspond to
 vertices of the polygon.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 point_iterator_type end_points(const T& polygon)</td>
 <td>Expects a model of polygon_45. 
 Returns the end iterator over the range of points that correspond to
@@ -156,7 +174,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- iterator> 
+ iterator> 
 void set_points(T& polygon, iterator b, iterator e)</td>
 <td>Expects a model of polygon_45.  
 Sets the polygon to the point data range [b,e) that corresponds to
@@ -164,22 +182,22 @@
 points is disallowed.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 unsigned int size(const T& polygon)</td>
 <td>Returns the number of edges in the
 polygon.</td>
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& assign(T1& left, const T2& right)</td>
 <td>Copies data from right object that models polygon_45 into left object
 that models polygon_45.</td>
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename point_type> 
- bool contains(const T&, const point_type& point, 
+ typename point_type> 
+ bool contains(const T&, const point_type& point, 
             
 bool consider_touch=true)</td>
 <td>Given an object that models polygon_45 and an object that models
@@ -189,85 +207,84 @@
 the polygon.  Linear wrt. vertices.</td>
 </tr>
 <tr>
- <td width="586">// get the center coordinate 
- template <typename T, typename point_type> 
+ <td width="586">// get the center coordinate 
+ template <typename T, typename point_type> 
 void center(point_type& p, const T& polygon)</td>
 <td>Sets object that models point to the center point of the bounding
 box of an object that models polygon_45.  Linear wrt. vertices.</td>
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename rectangle_type> 
+ typename rectangle_type> 
 bool extents(rectangle_type& bbox, const T& polygon)</td>
 <td>Sets object that models rectangle to the bounding box of an object
 that models polygon_45 and returns true.  Returns false and leaves
 bbox unchanged if polygon is empty.  Linear wrt. vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 area_type area(const T& polygon)</td>
 <td>Returns the area of an object
 that models polygon_45.  Linear wrt. vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 direction_1d winding(const T& polygon)</td>
 <td>Returns the winding direction of an object
 that models polygon_45, LOW == CLOCKWISE, HIGH = COUNTERCLOCKWISE. 
 Complexity depends upon winding trait.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 coordinate_distance perimeter(const T& polygon)</td>
 <td>Returns the perimeter length of an object
 that models polygon_45.  Linear wrt. vertices.</td>
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename transform_type> 
+ typename transform_type> 
 T& transform(T& polygon, const transform_type&)</td>
 <td>Applies transform() on the vertices of polygon and sets the polygon to that described by the result of
 transforming its vertices.  Linear wrt. vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& scale_up(T& polygon, unsigned_area_type factor)</td>
 <td>Scales up coordinate of an object that models
 polygon_45 by unsigned factor.  Linear wrt. vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& scale_down(T& polygon, unsigned_area_type factor)</td>
 <td>Scales down coordinates of an object that models
 polygon_45 by unsigned factor.  Linear wrt. vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T, scaling_type> 
+ <td width="586">template <typename T, scaling_type> 
 T& scale(T& rectangle, double scaling) </td>
 <td>Scales coordinates of an object that models polygon_45 by floating
 point factor.  Linear wrt. vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
- T& move(T& polygon, orientation_2d, 
+ <td width="586">template <typename T> 
+ T& move(T& polygon, orientation_2d, 
        coordinate_difference displacement)</td>
 <td>Adds displacement value to coordinate indicated by orientation_2d of
 vertices of an object that models polygon_45.  Linear wrt.
 vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename polygon_type, typename point_type> 
- polygon_type& convolve(polygon_type& polygon, 
-                      
- const point_type& point)</td>
+ <td width="586">template <typename polygon_type, typename point_type> 
+ polygon_type& convolve(polygon_type& polygon,                       
+const point_type& point)</td>
 <td>Convolves coordinate values of point with vertices of an
 object that models polygon_45.  Linear wrt. vertices.</td>
 </tr>
- </table>
+ </tbody></table>
 <h1>Polygon 45 Data</h1>


-The library provides a model of polygon 45 concept declared
+The library provides a model of polygon 45 concept declared

template<typename T> polygon_45_data where T is the coordinate type.
This data type is used internally when a 45-degree polygon is needed and is
@@ -275,8 +292,8 @@
data type instead of providing their own.  The data type is implemented to
be convenient to use with the library traits.
<h2>Members</h2>
-<table border="1" width="100%" id="table2">
- <tr>
+<table id="table2" border="1" width="100%">
+ <tbody><tr>
 <td width="586">geometry_type</td>
 <td>polygon_45_concept</td>
 </tr>
@@ -304,7 +321,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T2> 
- polygon_45_data& operator=(const T2& that) const</td>
+ polygon_45_data& operator=(const T2& that) const</td>
 <td>Assign from an object that is a model of polygon 45.</td>
 </tr>
 <tr>
@@ -324,23 +341,23 @@
 </tr>
 <tr>
 <td width="586">template <typename iT> 
- void set(iT begin_points, iT end_points)</td>
+ void set(iT begin_points, iT end_points)</td>
 <td>Sets the polygon to the iterator range of points.  No check is
 performed to ensure the points describe corners that are multiples of 45
 degrees relative to the coordinate axis.</td>
 </tr>
-</table>
- <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" rules="none" frame="void" id="table3">
+<table class="docinfo" id="table3" frame="void" rules="none">
 <colgroup>
- <col class="docinfo-name"><col class="docinfo-content">
+ <col class="docinfo-name" /><col class="docinfo-content" />
 </colgroup>
- <tbody vAlign="top">
+ <tbody valign="top">
 <tr>
 <th class="docinfo-name">Copyright:</th>
 <td>Copyright © Intel Corporation 2008-2010.</td>
@@ -353,6 +370,6 @@
 <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt>)</td>
 </tr>
-</table>
+</tbody></table>

-</html>
\ No newline at end of file
+</td></tr></tbody></table></body></html>
\ No newline at end of file

Modified: trunk/libs/polygon/doc/gtl_polygon_45_set_concept.htm
==============================================================================
--- trunk/libs/polygon/doc/gtl_polygon_45_set_concept.htm (original)
+++ trunk/libs/polygon/doc/gtl_polygon_45_set_concept.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -1,14 +1,15 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<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>
-<title>Boost Polygon Library: Polygon 45 Set Concept</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>
+--><title>Boost Polygon Library: Polygon 45 Set Concept</title>
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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;">
@@ -20,6 +21,8 @@
 <li>Coordinate Concept</li>
 <li>Interval Concept</li>
 <li>Point Concept</li>
+ <li>Segment Concept</li>
+
 <li>Rectangle Concept</li>
 <li>Polygon 90 Concept</li>
 <li>Polygon 90 With Holes Concept</li>
@@ -36,32 +39,47 @@
 <li>Property Merge 90</li>
 <li>Property Merge 45</li>
 <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+</a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+</a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+
 </ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
- <li>GTL Boostcon 2009 Paper</li>
- <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
 Presentation</a></li>
- <li>Performance Analysis</li>
- <li>Layout Versus Schematic Tutorial</li>
- <li>Minkowski Sum Tutorial</li>
- </ul>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</li>
+ <li>Voronoi Advanced Tutorial</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">
+ <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%">



- 
+ 

<h1>Polygon 45 Set Concept</h1>


-The polygon_45_set concept tag is 
+The polygon_45_set concept tag is 
polygon_45_set_concept

The semantic of a polygon_45_set is zero or more
@@ -75,7 +93,7 @@
intersection point.  In the case that data represented contains no
45-degree angles and is Manhattan a runtime check will default to the Manhattan
algorithm.  The results of which are identical to what the 45-degree
-algorithm would do, but obtained more efficiently.
+algorithm would do, but obtained more efficiently.
The motivation for providing the polygon_45_set is
to extend the special case of Manhattan geometry capability of the library to
encompass the slightly less common, but still important special case of geometry
@@ -84,7 +102,7 @@
and affords many opportunities for optimization.  45-degree algorithms can
be 50X faster than arbitrary angle algorithms and are required to provide a
complete feature set that meets the performance requirements of application
-domains in which Manhattan and 45-degree geometry are a common special case.Users are recommended to use std::vector and std::list of user defined polygons
+domains in which Manhattan and 45-degree geometry are a common special case.Users are recommended to use std::vector and std::list of user defined polygons
or library provided polygon_45_set_data<coordinate_type> objects.  Lists
and vectors of models of polygon_45_concept or polygon_45_with_holes_concept are automatically models of polygon_45_set_concept.
An object that is a model of 
@@ -106,10 +124,10 @@
eliminate temp copies of intermediate results when Boolean operators are chained
together.
Operators are declared inside the namespace boost::polygon::operators.
-<table border="1" width="100%" id="table5">
- <tr>
+<table id="table5" border="1" width="100%">
+ <tbody><tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 polygon_45_set_view operator|(const T1& l, const T2& r)</td>
 <td>Boolean OR operation (polygon set union).  Accepts two objects
 that model polygon_45_set or one of its refinements.  Returns an
@@ -119,7 +137,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 polygon_45_set_view operator+(const T1& l, const T2& r)</td>
 <td>Same as operator|.  The plus sign is also used for OR
 operations in Boolean logic expressions.  O( n log n) runtime
@@ -127,7 +145,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 polygon_45_set_view operator&(const T1& l, const T2& r)</td>
 <td>Boolean AND operation (polygon set intersection).  Accepts two
 objects that model polygon_45_set or one of its refinements.  O( n
@@ -135,7 +153,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 polygon_45_set_view operator*(const T1& l, const T2& r)</td>
 <td>Same as operator&.  The multiplication symbol is also used for
 AND operations in Boolean logic expressions.  O( n log n) runtime
@@ -143,7 +161,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 polygon_45_set_view operator^(const T1& l, const T2& r)</td>
 <td>Boolean XOR operation (polygon set disjoint-union).  Accepts
 two objects that model polygon_45_set or one of its refinements. 
@@ -152,7 +170,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 polygon_45_set_view operator-(const T1& l, const T2& r)</td>
 <td>Boolean SUBTRACT operation (polygon set difference).  Accepts
 two objects that model polygon_45_set or one of its refinements. 
@@ -161,7 +179,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator|=(const T1& l, const T2& r)</td>
 <td>Same as operator|, but with self assignment, left operand must model
 polygon_45_set and not one of it's refinements.  O( n log n)
@@ -169,7 +187,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator+=(T1& l, const T2& r)</td>
 <td>Same as operator+, but with self assignment, left operand must model
 polygon_45_set and not one of it's refinements.  O( n log n)
@@ -177,7 +195,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator&=(const T1& l, const T2& r)</td>
 <td>Same as operator&, but with self assignment, left operand must model
 polygon_45_set and not one of it's refinements.  O( n log n)
@@ -185,7 +203,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator*=(T1& l, const T2& r)</td>
 <td>Same as operator*, but with self assignment, left operand must model
 polygon_45_set and not one of it's refinements.  O( n log n)
@@ -193,7 +211,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator^=(const T1& l, const T2& r)</td>
 <td>Same as operator^, but with self assignment, left operand must model
 polygon_45_set and not one of it's refinements.  O( n log n)
@@ -201,14 +219,14 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator-=(T1& l, const T2& r)</td>
 <td>Same as operator-, but with self assignment, left operand must model
 polygon_45_set and not one of it's refinements.  O( n log n)
 runtime complexity and O(n) memory wrt vertices + intersections.</td>
 </tr>
 <tr>
- <td width="586">template <typename T1> 
+ <td width="586">template <typename T1> 
 T1 operator+(const T1&, coordinate_type bloating)</td>
 <td>Performs resize operation, inflating by bloating ammount.  If
 negative the result is a shrink instead of bloat.  Note: returns
@@ -217,7 +235,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1 operator-(const T1&, coordinate_type shrinking)</td>
 <td>Performs resize operation, deflating by bloating ammount.  If
 negative the result is a bloat instead of shrink.  Note: returns
@@ -226,7 +244,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator+=(const T1&, coordinate_type bloating)</td>
 <td>Performs resize operation, inflating by bloating ammount.  If
 negative the result is a shrink instead of bloat.  Returns
@@ -235,19 +253,19 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator-=(const T1&, coordinate_type shrinking)</td>
 <td>Performs resize operation, deflating by bloating ammount.  If
 negative the result is a bloat instead of shrink.  Returns
 reference to modified argument.  O( n log n) runtime complexity and
 O(n) memory wrt vertices + intersections.</td>
 </tr>
- </table>
+ </tbody></table>
<h2>Functions</h2>
-<table border="1" width="100%" id="table3">
- <tr>
+<table id="table3" border="1" width="100%">
+ <tbody><tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& assign(T1& lvalue, const T2& rvalue)</td>
 <td>Eliminates overlaps in geometry and copies from an object that
 models polygon_45_set or any of its refinements into an object that
@@ -256,7 +274,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 bool equivalence(const T1& lvalue, const T2& rvalue) </td>
 <td>Returns true if an object that models polygon_45_set or one of its
 refinements covers the exact same geometric regions as another object
@@ -266,8 +284,8 @@
 </tr>
 <tr>
 <td width="586">template <typename
- output_container_type, typename T> 
- void get_trapezoids(output_container_type& output, 
+ output_container_type, typename T> 
+ void get_trapezoids(output_container_type& output, 
                   
 const T& polygon_set)</td>
 <td>Output container is expected to be a standard container. 
@@ -280,10 +298,12 @@
 </tr>
 <tr>
 <td width="586">template <typename
- output_container_type, typename T> 
- void get_trapezoids(output_container_type& output, 
+ output_container_type, typename T> 
+ void get_trapezoids(output_container_type& output, 
                   
- const T& polygon_set,                     orientation_2d orient)</td>
+ const T& polygon_set, 
+                   
+orientation_2d orient)</td>
 <td>Output container is expected to be a standard container. 
 Slices geometry of an object that models polygon_45_set or one of its
 refinements into non overlapping trapezoids along a the specified slicing
@@ -294,13 +314,13 @@
 </tr>
 <tr>
 <td width="586">template <typename
- polygon_set_type> 
+ polygon_set_type> 
 void clear(polygon_set_type& polygon_set)</td>
 <td>Makes the object empty of geometry.</td>
 </tr>
 <tr>
 <td width="586">template <typename
- polygon_set_type> 
+ polygon_set_type> 
 bool empty(const polygon_set_type& polygon_set)</td>
 <td>Checks whether the object is empty of geometry.  Polygons that
 are completely covered by holes will result in empty returning true.  
@@ -308,8 +328,8 @@
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- rectangle_type> 
- bool extents(rectangle_type& extents_rectangle, 
+ rectangle_type> 
+ bool extents(rectangle_type& extents_rectangle, 
             const
 T& polygon_set)</td>
 <td>Computes bounding box of an object that models polygon_45_set and
@@ -319,7 +339,7 @@
 log n) runtime complexity and O(n) memory wrt vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 area_type area(const T& polygon_set)</td>
 <td>Computes the area covered by geometry in an object that models
 polygon_45_set.   O( n log n) runtime complexity and O(n)
@@ -327,7 +347,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& interact(T1& a, const T2& b)</td>
 <td>Given an object that models polygon_45_set and an object that models
 polygon_45_set or one of its refinements, modifies a to retain only
@@ -335,7 +355,7 @@
 runtime complexity and O(n) memory wrt vertices plus intersections.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& self_intersect(T& polygon_set)</td>
 <td>Given an object that models polygon_45_set that has self overlapping
 regions, modifies the argument to contain only the regions of overlap. 
@@ -343,7 +363,7 @@
 intersections.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& self_xor(T& polygon_set)</td>
 <td>Given an object that models polygon_45_set that has self overlapping
 regions, modifies the argument to contain only the regions that do not
@@ -351,14 +371,14 @@
 vertices + intersections.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& bloat(T& polygon_set, unsigned_area_type bloating)</td>
 <td>Same as getting all the polygons, bloating them and putting them
 back.  O( n log n) runtime complexity and O(n) memory wrt vertices
 + intersections.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& shrink(T& polygon_set, unsigned_area_type shrinking)</td>
 <td>Same as getting all the polygons, shrinking them and overwriting
 the polygon set with the resulting regions.  O( n log n) runtime
@@ -366,10 +386,10 @@
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- coord_type> 
- T& resize(T& polygon_set, coord_type resizing, 
+ coord_type> 
+ T& resize(T& polygon_set, coord_type resizing, 
          
- RoundingOption rounding = CLOSEST,           CornerOption corner = INTERSECTION)</td>
+ RoundingOption rounding = CLOSEST,           CornerOption corner = INTERSECTION)</td>
 <td>Same as bloat if resizing is positive, same as shrink if resizing is
 negative.  RoundingOption is an enum that controls snapping of
 non-integer results of resizing 45 degree edges.  CornerOption is
@@ -378,7 +398,7 @@
 complexity and O(n) memory wrt vertices + intersections.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
T& grow_and(T& polygon_set, unsigned_area_type bloating)</td>
 <td>Same as bloating non-overlapping regions and then applying self
 intersect to retain only the overlaps introduced by the bloat.  O(
@@ -386,13 +406,13 @@
 intersections.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
T& scale_up(T& polygon_set, unsigned_area_type factor)</td>
 <td>Scales geometry up by unsigned factor.  O( n log n) runtime
 complexity and O(n) memory wrt vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
T& scale_down(T& polygon_set, unsigned_area_type factor)</td>
 <td>Scales geometry down by unsigned factor.  Snaps 45 degree edges
 back to 45 degrees after division truncation leads to small changes in
@@ -400,7 +420,7 @@
 vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T, typename scaling_type> 
+ <td width="586">template <typename T, typename scaling_type> 
T& scale(polygon_set_type& polygon_set, double scaling)</td>
 <td>Scales geometry by multiplying by floating point factor.  
 Snaps 45 degree edges back to 45 degrees after truncation of fractional
@@ -408,32 +428,32 @@
 runtime complexity and O(n) memory wrt vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T, typename transformation_type> 
-T& transform(T& polygon_set, 
+ <td width="586">template <typename T, typename transformation_type> 
+T& transform(T& polygon_set, 
             const
transformation_type& transformation)</td>
 <td>Applies transformation.transform() on all vertices.  O( n log
 n) runtime complexity and O(n) memory wrt vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
-T& keep(T& polygon_set, 
-        unsigned_area_type min_area, 
-        unsigned_area_type max_area, 
-        unsigned_area_type min_width, 
-        unsigned_area_type max_width, 
-        unsigned_area_type min_height, 
+ <td width="586">template <typename T> 
+T& keep(T& polygon_set, 
+        unsigned_area_type min_area, 
+        unsigned_area_type max_area, 
+        unsigned_area_type min_width, 
+        unsigned_area_type max_width, 
+        unsigned_area_type min_height, 
        unsigned_area_type max_height)</td>
 <td>Retains only regions that satisfy the min/max criteria in the
 argument list.  Note: useful for visualization to cull too small
 polygons.  O( n log n) runtime complexity and O(n) memory wrt
 vertices.</td>
 </tr>
- </table>
+ </tbody></table>
 <h1>Polygon 45 Set Data Object</h1>


-The polygon 45 set data type encapsulates the internal data format that
+The polygon 45 set data type encapsulates the internal data format that
serves as the input to the sweep-line algorithm that implements polygon-clipping
Boolean operations.  It also internally keeps track of whether that data
has been sorted or scanned and maintains the invariant that when its flags
@@ -444,20 +464,20 @@
maintain the data is sorted form rather than going all the way out to polygons
then resorting those vertices for a subsequent operation.
The declaration of Polygon 45 Set Data is the following:
-template <typename T> 
+template <typename T> 
class polygon_45_set_data;
The class is parameterized on the coordinate data type.  Algorithms that
benefit from knowledge of the invariants enforced by the class are implemented
as member functions to provide them access to information about those
invariants.  
<h2>Member Functions</h2>
-<table border="1" width="100%" id="table4">
- <tr>
+<table id="table4" border="1" width="100%">
+ <tbody><tr>
 <td width="586">polygon_45_set_data()</td>
 <td>Default constructor. </td>
 </tr>
 <tr>
- <td width="586">template <typename iT> 
+ <td width="586">template <typename iT> 
 polygon_45_set_data(iT input_begin, iT
 input_end)</td>
 <td>Construct from an iterator range of
@@ -470,34 +490,34 @@
 </tr>
 <tr>
 <td width="586">
-template <typename l, typename r, typename op> 
+template <typename l, typename r, typename op> 
polygon_45_set_data(const polygon_45_set_view<l,r,op>&
t)</td>
 <td>Copy construct from a Boolean operator template.</td>
 </tr>
 <tr>
 <td width="586">
-polygon_45_set_data& operator=(const polygon_45_set_data& that)</td>
+polygon_45_set_data& operator=(const polygon_45_set_data& that)</td>
 <td>Assignment from another polygon set, may change scanning
 orientation.</td>
 </tr>
 <tr>
 <td width="586">
-template <typename l, typename r, typename op> 
-polygon_45_set_data& operator=(const polygon_45_set_view<l, r,
+template <typename l, typename r, typename op> 
+polygon_45_set_data& operator=(const polygon_45_set_view<l, r,
op>& that)</td>
 <td>Assignment from a Boolean operator template.</td>
 </tr>
 <tr>
- <td width="586">template <typename geometry_object> 
+ <td width="586">template <typename geometry_object> 
polygon_45_set_data& operator=(const geometry_object& geo)</td>
 <td>Assignment from an insertable object.</td>
 </tr>
 <tr>
 <td width="586">

-template <typename iT> 
-void insert(iT input_begin, iT input_end,             bool is_hole = false)</td>
+template <typename iT> 
+void insert(iT input_begin, iT input_end,             bool is_hole = false)</td>
 <td>Insert objects of an iterator range.  If is_hole is true
 inserts subtractive regions.  Linear wrt the number of vertices
 added.</td>
@@ -505,15 +525,15 @@
 <tr>
 <td width="586">

-void insert(const polygon_45_set_data& polygon_set,             bool is_hole
+void insert(const polygon_45_set_data& polygon_set,             bool is_hole
= false)</td>
 <td>Insert a polygon set.  Linear wrt the number of vertices added.</td>
 </tr>
 <tr>
 <td width="586">

-template <typename geometry_type> 
-void insert(const geometry_type& geometry_object,             bool is_hole
+template <typename geometry_type> 
+void insert(const geometry_type& geometry_object,             bool is_hole
= false)</td>
 <td>Insert a geometry object, if is_hole is true then the inserted
 region is subtractive rather than additive.  Linear wrt the number
@@ -521,7 +541,7 @@
 </tr>
 <tr>
 <td width="586">
-template <typename output_container> 
+template <typename output_container> 
void get(output_container& output) const</td>
 <td>Expects a standard container of geometry objects.  Will scan
 and eliminate overlaps.  Converts polygon set geometry to objects
@@ -534,7 +554,7 @@
 </tr>
 <tr>
 <td width="586">
-template <typename output_container> 
+template <typename output_container> 
void get_polygons(output_container& output) const</td>
 <td>Expects a standard container of polygon objects.  Will scan and
 eliminate overlaps.  Converts polygon set geometry to polygons and
@@ -544,7 +564,7 @@
 </tr>
 <tr>
 <td width="586">
-template <typename output_container> 
+template <typename output_container> 
void get_polygons_with_holes(output_container& o) const</td>
 <td>Expects a standard container of polygon with holes objects.  Will scan and
 eliminate overlaps.  Converts polygon set geometry to polygons and
@@ -553,7 +573,7 @@
 </tr>
 <tr>
 <td width="586">
-template <typename output_container> 
+template <typename output_container> 
void get_trapezoids(output_container& output) const</td>
 <td>Expects a standard container of polygon objects.  Will scan
 and eliminate overlaps.  Slices polygon set geometry to trapezoids
@@ -563,8 +583,8 @@
 <tr>
 <td width="586">

-template <typename output_container> 
-void get_trapezoids(output_container& output,   orientation_2d
+template <typename output_container> 
+void get_trapezoids(output_container& output,   orientation_2d
slicing_orientation) const 
 </td>
 <td>Expects a standard container of polygon objects.  Will scan
@@ -618,15 +638,15 @@
 </tr>
 <tr>
 <td width="586">
-template <typename input_iterator_type> 
-void set(input_iterator_type input_begin,          input_iterator_type input_end) 
+template <typename input_iterator_type> 
+void set(input_iterator_type input_begin,          input_iterator_type input_end) 
 </td>
 <td>Overwrite geometry in polygon set with insertable objects in the
 iterator range.  </td>
 </tr>
 <tr>
 <td width="586">
-template <typename rectangle_type> 
+template <typename rectangle_type> 
bool extents(rectangle_type& extents_rectangle) const</td>
 <td>Given an object that models rectangle, scans and eliminates overlaps
 in the polygon set because subtractive regions may alter its extents
@@ -636,9 +656,9 @@
 </tr>
 <tr>
 <td width="586">
-polygon_45_set_data& 
-resize(coord_type resizing, 
-        RoundingOption rounding = CLOSEST,        CornerOption
+polygon_45_set_data& 
+resize(coord_type resizing, 
+        RoundingOption rounding = CLOSEST,        CornerOption
 corner = INTERSECTION)</td>
 <td>Same as bloat if resizing is positive, same as shrink if resizing is
 negative.  RoundingOption is an enum that controls snapping of
@@ -649,8 +669,8 @@
 </tr>
 <tr>
 <td width="586">
-template <typename transformation_type> 
-polygon_45_set_data& transform(const transformation_type& transformation) 
+template <typename transformation_type> 
+polygon_45_set_data& transform(const transformation_type& transformation) 
 </td>
 <td>Applies transformation.transform() on vertices stored within the
 polygon set.  O(n log n) runtime and O(n) memory wrt. vertices +
@@ -708,18 +728,18 @@
 <td>Retain only overlapping regions of geometry within a polygon set. 
 O(n log n) runtime and O(n) memory wrt. vertices + intersections.</td>
 </tr>
- </table>
- <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" rules="none" frame="void" id="table6">
+<table class="docinfo" id="table6" frame="void" rules="none">
 <colgroup>
- <col class="docinfo-name"><col class="docinfo-content">
+ <col class="docinfo-name" /><col class="docinfo-content" />
 </colgroup>
- <tbody vAlign="top">
+ <tbody valign="top">
 <tr>
 <th class="docinfo-name">Copyright:</th>
 <td>Copyright © Intel Corporation 2008-2010.</td>
@@ -732,6 +752,6 @@
 <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt>)</td>
 </tr>
-</table>
+</tbody></table>

-</html>
\ No newline at end of file
+</td></tr></tbody></table></body></html>
\ No newline at end of file

Modified: trunk/libs/polygon/doc/gtl_polygon_45_with_holes_concept.htm
==============================================================================
--- trunk/libs/polygon/doc/gtl_polygon_45_with_holes_concept.htm (original)
+++ trunk/libs/polygon/doc/gtl_polygon_45_with_holes_concept.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -1,14 +1,15 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<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>
-<title>Boost Polygon Library: Polygon 45 With Holes Concept</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>
+--><title>Boost Polygon Library: Polygon 45 With Holes Concept</title>
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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;">
@@ -20,6 +21,8 @@
 <li>Coordinate Concept</li>
 <li>Interval Concept</li>
 <li>Point Concept</li>
+ <li>Segment Concept</li>
+
 <li>Rectangle Concept</li>
 <li>Polygon 90 Concept</li>
 <li>Polygon 90 With Holes Concept</li>
@@ -36,91 +39,106 @@
 <li>Property Merge 90</li>
 <li>Property Merge 45</li>
 <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+</a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+</a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+
 </ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
- <li>GTL Boostcon 2009 Paper</li>
- <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
 Presentation</a></li>
- <li>Performance Analysis</li>
- <li>Layout Versus Schematic Tutorial</li>
- <li>Minkowski Sum Tutorial</li>
- </ul>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</li>
+ <li>Voronoi Advanced Tutorial</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">
+ <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%">



- 
+ 

<h1>Polygon 45 With Holes Concept</h1>


-The polygon_45_with_holes concept tag is 
+The polygon_45_with_holes concept tag is 
polygon_45_with_holes_concept

To register a user defined type as a model of
polygon_45_with_holes concept, specialize
the geometry concept meta-function for that type.  In the example below
-CPolygon45WithHoles is registered as a model of polygon_45_with_holes  concept.
-template <> 
-struct geometry_concept<CPolygon45WithHoles> { typedef polygon_45_with_holes_concept type; };
+CPolygon45WithHoles is registered as a model of polygon_45_with_holes  concept.
+template <> 
+struct geometry_concept<CPolygon45WithHoles> { typedef polygon_45_with_holes_concept type; };
The semantic of a polygon_45_with_holes is a
polygon_45 that it can provide iterators over holes that are also polygon_45. 
A mutable polygon_45_with_holes must also be able to set its geometry based on
an interator range over polygon_45 holes.  There is no convention of
-winding of holes enforced within the library. 
+winding of holes enforced within the library. 
Below is shown the default polygon with holes
traits.  Specialization of these traits is required for types that don't
-conform to the default behavior.template <typename
-T, typename enable = void> 
-struct polygon_with_holes_traits { 
+conform to the default behavior.template <typename
+T, typename enable = void> 
+struct polygon_with_holes_traits { 
     typedef typename T::iterator_holes_type
-iterator_holes_type; 
-     typedef typename T::hole_type hole_type; 
+iterator_holes_type; 
+     typedef typename T::hole_type hole_type; 
     static inline iterator_holes_type begin_holes(const T&
-t) { 
-          return t.begin_holes(); 
-     } 
+t) { 
+          return t.begin_holes(); 
+     } 
     static inline iterator_holes_type end_holes(const T& t)
-{ 
-          return t.end_holes(); 
-     } 
-     static inline unsigned int size_holes(const T& t) { 
-          return t.size_holes(); 
-     } 
+{ 
+          return t.end_holes(); 
+     } 
+     static inline unsigned int size_holes(const T& t) { 
+          return t.size_holes(); 
+     } 
};
-template <typename T, typename enable = void> 
-struct polygon_with_holes_mutable_traits { 
-     template <typename iT> 
+template <typename T, typename enable = void> 
+struct polygon_with_holes_mutable_traits { 
+     template <typename iT> 
     static inline T& set_holes(T& t, iT inputBegin, iT
-inputEnd) { 
+inputEnd) { 
          t.set_holes(inputBegin,
-inputEnd); 
-          return t; 
-     } 
+inputEnd); 
+          return t; 
+     } 
};
An object that is a model of 
polygon_45_with_holes_concept can be viewed as a model of any of its
refinements if it is determined at runtime to conform to the restriction of
those concepts.  This concept casting is accomplished through the
view_as<>() function.
-view_as<rectangle_concept>(polygon_45_with_holes_object) 
-view_as<polygon_90_concept>(polygon_45_with_holes_object) 
-view_as<polygon_90_with_holes_concept>(polygon_45_with_holes_object) 
+view_as<rectangle_concept>(polygon_45_with_holes_object) 
+view_as<polygon_90_concept>(polygon_45_with_holes_object) 
+view_as<polygon_90_with_holes_concept>(polygon_45_with_holes_object) 
view_as<polygon_45_concept>(polygon_45_with_holes_object)
The return value of view_as<>() can be
passed into any interface that expects an object of the conceptual type
specified in its template parameter. 
<h2>Functions</h2>
-<table border="1" width="100%" id="table1">
- <tr>
- <td width="586">template <typename T> 
+<table id="table1" border="1" width="100%">
+ <tbody><tr>
+ <td width="586">template <typename T> 
 point_iterator_type begin_points(const T& polygon)</td>
 <td>Expects a model of
 polygon_45_with_holes. 
@@ -128,7 +146,7 @@
 vertices of the polygon.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 point_iterator_type end_points(const T& polygon)</td>
 <td>Expects a model of
 polygon_45_with_holes. 
@@ -136,7 +154,7 @@
 vertices of the polygon.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 hole_iterator_type begin_holes(const T& polygon)</td>
 <td>Expects a model of
 polygon_45_with_holes. 
@@ -144,7 +162,7 @@
 to horizontal and vertical edges.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 hole_iterator_type end_holes(const T& polygon)</td>
 <td>Expects a model of
 polygon_45_with_holes. 
@@ -153,7 +171,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- iterator> 
+ iterator> 
 void set_points(T& polygon, iterator b, iterator e)</td>
 <td>Expects a model of
 polygon_45_with_holes.  
@@ -162,14 +180,14 @@
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- iterator> 
+ iterator> 
 void set_holes(T& polygon, iterator b, iterator e)</td>
 <td>Expects a model of
 polygon_45_with_holes.  
 Sets the polygon holes to the hole data range [b,e)</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 unsigned int size(const T& polygon)</td>
 <td>Returns the number of edges in the
 outer shell of the polygon_45_with_holes.  Does not include sizes
@@ -177,7 +195,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& assign(T1& left, const T2& right)</td>
 <td>Copies data from right object that models polygon_45_with_holes or
 one of its refinements into left object
@@ -185,8 +203,8 @@
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename point_type> 
- bool contains(const T&, const point_type& point, 
+ typename point_type> 
+ bool contains(const T&, const point_type& point, 
             
 bool consider_touch=true)</td>
 <td>Given an object that models polygon_45_with_holes and an object that models
@@ -197,86 +215,85 @@
 the polygon or one of its holes.</td>
 </tr>
 <tr>
- <td width="586">// get the center coordinate 
- template <typename T, typename point_type> 
+ <td width="586">// get the center coordinate 
+ template <typename T, typename point_type> 
 void center(point_type& p, const T& polygon)</td>
 <td>Sets object that models point to the center point of the bounding
 box of an object that models polygon_45_with_holes.</td>
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename rectangle_type> 
+ typename rectangle_type> 
 bool extents(rectangle_type& bbox, const T& polygon)</td>
 <td>Sets object that models rectangle to the bounding box of an object
 that models polygon_45_with_holes and returns true.  Returns false
 and leaves bbox unchanged if polygon is empty.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 manhattan_area_type area(const T& polygon)</td>
 <td>Returns the area of an object
 that models polygon_45_with_holes including subtracting the area of its
 holes from the area of the outer shell polygon.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 direction_1d winding(const T& polygon)</td>
 <td>Returns the winding direction of an object
 that models polygon_45_with_holes, LOW == CLOCKWISE, HIGH =
 COUNTERCLOCKWISE.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 coordinate_difference perimeter(const T& polygon)</td>
 <td>Returns the perimeter length of an object
 that models polygon_45, including the perimeters of the holes.</td>
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename transform_type> 
+ typename transform_type> 
 T& transform(T& polygon, const transform_type&)</td>
 <td>Applies transform() on the vertices of polygon and sets the polygon to that described by the result of
 transforming its vertices.  Also applies transform() on the holes
 of the polygon.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& scale_up(T& polygon, unsigned_area_type factor)</td>
 <td>Scales up outer shell and holes of an object that models
 polygon_45 by unsigned factor.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& scale_down(T& polygon, unsigned_area_type factor)</td>
 <td>Scales down outer shell and holes of an object that models
 polygon_45 by unsigned factor.</td>
 </tr>
 <tr>
- <td width="586">template <typename T, scaling_type> 
+ <td width="586">template <typename T, scaling_type> 
 T& scale(T& rectangle, double scaling) </td>
 <td>Scales outer shell and holes of an object that models polygon_45 by
 floating point factor.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
- T& move(T& polygon, orientation_2d, 
+ <td width="586">template <typename T> 
+ T& move(T& polygon, orientation_2d, 
        coordinate_difference displacement)</td>
 <td>Adds displacement value to coordinate indicated by orientation_2d of
 vertices of an object that models polygon_45 .</td>
 </tr>
 <tr>
- <td width="586">template <typename polygon_type, typename point_type> 
- polygon_type& convolve(polygon_type& polygon, 
-                      
- const point_type& point)</td>
+ <td width="586">template <typename polygon_type, typename point_type> 
+ polygon_type& convolve(polygon_type& polygon,                       
+const point_type& point)</td>
 <td>Convolves coordinate values of point with the outer shell and holes of an
 object that models polygon_45_with_holes.</td>
 </tr>
- </table>
+ </tbody></table>
 <h1>Polygon 45 With Holes Data</h1>


-The library provides a model of polygon 45 with holes concept declared
+The library provides a model of polygon 45 with holes concept declared

template<typename T> polygon_45_with_holes_data where T is the
coordinate type.
@@ -285,8 +302,8 @@
library polygon data type instead of providing their own.  The data type is
implemented to be convenient to use with the library traits.
<h2>Members</h2>
-<table border="1" width="100%" id="table2">
- <tr>
+<table id="table2" border="1" width="100%">
+ <tbody><tr>
 <td width="586">geometry_type</td>
 <td>polygon_45_with_holes_concept</td>
 </tr>
@@ -314,13 +331,13 @@
 </tr>
 <tr>
 <td width="586">polygon_45_with_holes_data& 
- operator=(const polygon_45_with_holes_data& that)</td>
+ operator=(const polygon_45_with_holes_data& that)</td>
 <td>Assignment operator.</td>
 </tr>
 <tr>
 <td width="586">template <typename T2> 
 polygon_45_with_holes_data& 
- operator=(const T2& that) const</td>
+ operator=(const T2& that) const</td>
 <td>Assign from an object that is a model of polygon 45 with holes.</td>
 </tr>
 <tr>
@@ -356,30 +373,30 @@
 </tr>
 <tr>
 <td width="586">template <typename iT> 
- void set(iT begin_points, iT end_points)</td>
+ void set(iT begin_points, iT end_points)</td>
 <td>Sets the polygon to the iterator range of points.  No check is
 performed to ensure the points describe a 45 degree figure.</td>
 </tr>
 <tr>
 <td width="586">template <typename iT> 
- void set_holes(iT begin_holes, iT end_choless)</td>
+ void set_holes(iT begin_holes, iT end_choless)</td>
 <td>Sets the polygon holes the iterator range of hole polygons.  These
 polygons in the input range may be either polygon_45_data or
 polygon_45_with_holes_data or any type that provides begin and end
 member functions to iterate over point_data<T>.</td>
 </tr>
-</table>
- <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" rules="none" frame="void" id="table3">
+<table class="docinfo" id="table3" frame="void" rules="none">
 <colgroup>
- <col class="docinfo-name"><col class="docinfo-content">
+ <col class="docinfo-name" /><col class="docinfo-content" />
 </colgroup>
- <tbody vAlign="top">
+ <tbody valign="top">
 <tr>
 <th class="docinfo-name">Copyright:</th>
 <td>Copyright © Intel Corporation 2008-2010.</td>
@@ -392,6 +409,6 @@
 <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt>)</td>
 </tr>
-</table>
+</tbody></table>

-</html>
\ No newline at end of file
+</td></tr></tbody></table></body></html>
\ No newline at end of file

Modified: trunk/libs/polygon/doc/gtl_polygon_90_concept.htm
==============================================================================
--- trunk/libs/polygon/doc/gtl_polygon_90_concept.htm (original)
+++ trunk/libs/polygon/doc/gtl_polygon_90_concept.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -1,14 +1,15 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<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>
-<title>Boost Polygon Library: Polygon 90 Concept</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>
+--><title>Boost Polygon Library: Polygon 90 Concept</title>
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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;">
@@ -20,6 +21,8 @@
 <li>Coordinate Concept</li>
 <li>Interval Concept</li>
 <li>Point Concept</li>
+ <li>Segment Concept</li>
+
 <li>Rectangle Concept</li>
 <li>Polygon 90 Concept</li>
 <li>Polygon 90 With Holes Concept</li>
@@ -36,40 +39,55 @@
 <li>Property Merge 90</li>
 <li>Property Merge 45</li>
 <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+</a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+</a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+
 </ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
- <li>GTL Boostcon 2009 Paper</li>
- <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
 Presentation</a></li>
- <li>Performance Analysis</li>
- <li>Layout Versus Schematic Tutorial</li>
- <li>Minkowski Sum Tutorial</li>
- </ul>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</li>
+ <li>Voronoi Advanced Tutorial</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">
+ <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%">



- 
+ 

<h1>Polygon 90 Concept</h1>


-The polygon_90 concept tag is 
+The polygon_90 concept tag is 
polygon_90_concept

To register a user defined type as a model of
polygon_90 concept, specialize the
geometry concept meta-function for that type.  In the example below CPolygon90 is registered as a model of
-polygon_90  concept.
-template <> 
-struct geometry_concept<CPolygon90> { typedef polygon_90_concept type; };
+polygon_90  concept.
+template <> 
+struct geometry_concept<CPolygon90> { typedef polygon_90_concept type; };
The semantic of a polygon_90 is that it can provide
iterators over the x and y coordinates that correspond to its horizontal and
vertical sides, starting with an x coordinate.  A mutable polygon_90 must
@@ -80,40 +98,40 @@
specialization of polygon_90_traits.  A std::vector<int> or std::list<int>
could be made models of polygon_90_concept by simply providing access to their
iterators through traits.  Library functions that create polygon objects
-require that those objects provide a default constructor.
+require that those objects provide a default constructor.
Below is shown the default polygon traits. 
Specialization of these traits is required for types that don't conform to the
default behavior.  Note that these traits are also used by the
-polygon_90_with_holes concept.template <typename
-T> 
-struct polygon_90_traits { 
-     typedef typename T::coordinate_type coordinate_type; 
+polygon_90_with_holes concept.template <typename
+T> 
+struct polygon_90_traits { 
+     typedef typename T::coordinate_type coordinate_type; 
     typedef typename T::compact_iterator_type
-compact_iterator_type; 
+compact_iterator_type; 
     static inline compact_iterator_type begin_compact(const
-T& t) { 
-          return t.begin_compact(); 
-     } 
+T& t) { 
+          return t.begin_compact(); 
+     } 
     static inline compact_iterator_type end_compact(const
-T& t) { 
-          return t.end_compact(); 
-     } 
-     static inline unsigned int size(const T& t) { 
-          return t.size(); 
-     } 
-     static inline winding_direction winding(const T& t) { 
-          return unknown_winding; 
-     } 
+T& t) { 
+          return t.end_compact(); 
+     } 
+     static inline unsigned int size(const T& t) { 
+          return t.size(); 
+     } 
+     static inline winding_direction winding(const T& t) { 
+          return unknown_winding; 
+     } 
};
-template <typename T> 
-struct polygon_90_mutable_traits { 
-     template <typename iT> 
+template <typename T> 
+struct polygon_90_mutable_traits { 
+     template <typename iT> 
     static inline T& set_compact(T& t, iT input_begin, iT
-input_end) { 
+input_end) { 
          t.set_compact(input_begin,
-input_end); 
-          return t; 
-     } 
+input_end); 
+          return t; 
+     } 
};
An object that is a model of 
polygon_90_concept can be viewed as a model of any of its
@@ -125,30 +143,30 @@
passed into any interface that expects an object of the conceptual type
specified in its template parameter.
<h2>Functions</h2>
-<table border="1" width="100%" id="table1">
- <tr>
- <td width="586">template <typename T> 
+<table id="table1" border="1" width="100%">
+ <tbody><tr>
+ <td width="586">template <typename T> 
 compact_iterator_type begin_compact(const T& polygon)</td>
 <td>Expects a model of polygon_90. 
 Returns the begin iterator over the range of coordinates that correspond
 to horizontal and vertical edges.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 compact_iterator_type end_compact(const T& polygon)</td>
 <td>Expects a model of polygon_90. 
 Returns the end iterator over the range of coordinates that correspond
 to horizontal and vertical edges.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 point_iterator_type begin_points(const T& polygon)</td>
 <td>Expects a model of polygon_90. 
 Returns the begin iterator over the range of points that correspond to
 vertices of the polygon.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 point_iterator_type end_points(const T& polygon)</td>
 <td>Expects a model of polygon_90. 
 Returns the end iterator over the range of points that correspond to
@@ -156,7 +174,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- iterator> 
+ iterator> 
 void set_compact(T& polygon, iterator b, iterator e)</td>
 <td>Expects a model of polygon_90.  
 Sets the polygon to the coordinate data range [b,e) that corresponds to
@@ -164,7 +182,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- iterator> 
+ iterator> 
 void set_points(T& polygon, iterator b, iterator e)</td>
 <td>Expects a model of polygon_90.  
 Sets the polygon to the point data range [b,e) that corresponds to
@@ -172,22 +190,22 @@
 successive input points results in undefined behavior.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 unsigned int size(const T& polygon)</td>
 <td>Returns the number of edges in the
 polygon.</td>
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& assign(T1& left, const T2& right)</td>
 <td>Copies data from right object that models polygon_90 into left object
 that models polygon_90.</td>
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename point_type> 
- bool contains(const T&, const point_type& point, 
+ typename point_type> 
+ bool contains(const T&, const point_type& point, 
             
 bool consider_touch=true)</td>
 <td>Given an object that models polygon_90 and an object that models
@@ -197,85 +215,84 @@
 the polygon.  Linear wrt. vertices.</td>
 </tr>
 <tr>
- <td width="586">// get the center coordinate 
- template <typename T, typename point_type> 
+ <td width="586">// get the center coordinate 
+ template <typename T, typename point_type> 
 void center(point_type& p, const T& polygon)</td>
 <td>Sets object that models point to the center point of the bounding
 box of an object that models polygon_90.  Linear wrt. vertices.</td>
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename rectangle_type> 
+ typename rectangle_type> 
 bool extents(rectangle_type& bbox, const T& polygon)</td>
 <td>Sets object that models rectangle to the bounding box of an object
 that models polygon_90 and returns true.  Returns false and leaves
 bbox unchanged if polygon is empty.  Linear wrt. vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 manhattan_area_type area(const T& polygon)</td>
 <td>Returns the area of an object
 that models polygon_90.  Linear wrt. vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 direction_1d winding(const T& polygon)</td>
 <td>Returns the winding direction of an object
 that models polygon_90, LOW == CLOCKWISE, HIGH = COUNTERCLOCKWISE. 
 Complexity depends upon winding trait.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 coordinate_difference perimeter(const T& polygon)</td>
 <td>Returns the perimeter length of an object
 that models polygon_90.  Linear wrt. vertices.</td>
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename transform_type> 
+ typename transform_type> 
 T& transform(T& polygon, const transform_type&)</td>
 <td>Applies transform() on the vertices of polygon and sets the polygon to that described by the result of
 transforming its vertices.  Linear wrt. vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& scale_up(T& polygon, unsigned_area_type factor)</td>
 <td>Scales up coordinate of an object that models
 polygon_90 by unsigned factor.  Linear wrt. vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& scale_down(T& polygon, unsigned_area_type factor)</td>
 <td>Scales down coordinates of an object that models
 polygon_90 by unsigned factor.  Linear wrt. vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T, scaling_type> 
+ <td width="586">template <typename T, scaling_type> 
 T& scale(T& rectangle, double scaling) </td>
 <td>Scales coordinates of an object that models polygon_90 by floating
 point factor.  Linear wrt. vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
- T& move(T& polygon, orientation_2d, 
+ <td width="586">template <typename T> 
+ T& move(T& polygon, orientation_2d, 
        coordinate_difference displacement)</td>
 <td>Adds displacement value to coordinate indicated by orientation_2d of
 vertices of an object that models polygon_90 .  Linear wrt.
 vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename polygon_type, typename point_type> 
- polygon_type& convolve(polygon_type& polygon, 
-                      
- const point_type& point)</td>
+ <td width="586">template <typename polygon_type, typename point_type> 
+ polygon_type& convolve(polygon_type& polygon,                       
+const point_type& point)</td>
 <td>Convolves coordinate values of point with vertices of an
 object that models polygon_90.  Linear wrt. vertices.</td>
 </tr>
- </table>
+ </tbody></table>
 <h1>Polygon 90 Data</h1>


-The library provides a model of polygon 90 concept declared
+The library provides a model of polygon 90 concept declared

template<typename T> polygon_90_data where T is the coordinate type.
This data type is used internally when a Manhattan polygon is needed and is
@@ -283,8 +300,8 @@
data type instead of providing their own.  The data type is implemented to
be convenient to use with the library traits.
<h2>Members</h2>
-<table border="1" width="100%" id="table2">
- <tr>
+<table id="table2" border="1" width="100%">
+ <tbody><tr>
 <td width="586">geometry_type</td>
 <td>polygon_90_concept</td>
 </tr>
@@ -319,7 +336,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T2> 
- polygon_90_data& operator=(const T2& that) const</td>
+ polygon_90_data& operator=(const T2& that) const</td>
 <td>Assign from an object that is a model of polygon 90.</td>
 </tr>
 <tr>
@@ -351,31 +368,31 @@
 </tr>
 <tr>
 <td width="586">template <typename iT> 
- void set(iT begin_points, iT end_points)</td>
+ void set(iT begin_points, iT end_points)</td>
 <td>Sets the polygon to the iterator range of points.  No check is
 performed to ensure the points describe a Manhattan figure, every other
 x and y value of the points is used to initialize the polygon.</td>
 </tr>
 <tr>
 <td width="586">template <typename iT> 
- void set_compact(iT begin_coords, iT end_coords)</td>
+ void set_compact(iT begin_coords, iT end_coords)</td>
 <td>Sets the polygon to the iterator range of coordinates.  These
 coordinates correspond to the x values of vertical edges and y values of
 horizontal edges.  It is expected that the sequence start with an x
 value and proceed x then y then x then y.</td>
 </tr>
-</table>
- <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" rules="none" frame="void" id="table3">
+<table class="docinfo" id="table3" frame="void" rules="none">
 <colgroup>
- <col class="docinfo-name"><col class="docinfo-content">
+ <col class="docinfo-name" /><col class="docinfo-content" />
 </colgroup>
- <tbody vAlign="top">
+ <tbody valign="top">
 <tr>
 <th class="docinfo-name">Copyright:</th>
 <td>Copyright © Intel Corporation 2008-2010.</td>
@@ -388,6 +405,6 @@
 <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt>)</td>
 </tr>
-</table>
+</tbody></table>

-</html>
\ No newline at end of file
+</td></tr></tbody></table></body></html>
\ No newline at end of file

Modified: trunk/libs/polygon/doc/gtl_polygon_90_set_concept.htm
==============================================================================
--- trunk/libs/polygon/doc/gtl_polygon_90_set_concept.htm (original)
+++ trunk/libs/polygon/doc/gtl_polygon_90_set_concept.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -1,14 +1,15 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<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>
-<title>Boost Polygon Library: Polygon 90 Set Concept</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>
+--><title>Boost Polygon Library: Polygon 90 Set Concept</title>
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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;">
@@ -20,6 +21,8 @@
 <li>Coordinate Concept</li>
 <li>Interval Concept</li>
 <li>Point Concept</li>
+ <li>Segment Concept</li>
+
 <li>Rectangle Concept</li>
 <li>Polygon 90 Concept</li>
 <li>Polygon 90 With Holes Concept</li>
@@ -36,36 +39,51 @@
 <li>Property Merge 90</li>
 <li>Property Merge 45</li>
 <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+</a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+</a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+
 </ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
- <li>GTL Boostcon 2009 Paper</li>
- <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
 Presentation</a></li>
- <li>Performance Analysis</li>
- <li>Layout Versus Schematic Tutorial</li>
- <li>Minkowski Sum Tutorial</li>
- </ul>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</li>
+ <li>Voronoi Advanced Tutorial</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">
+ <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%">



- 
+ 

<h1>Polygon 90 Set Concept</h1>


-The polygon_90_set concept tag is 
+The polygon_90_set concept tag is 
polygon_90_set_concept

The semantic of a polygon_90_set is zero or more
-Manhattan geometry regions.
+Manhattan geometry regions.
The motivation for providing the
polygon_90_set_concept is that it is a very common special case of planar
geometry which afford the implementation of a variety of optimizations on the
@@ -73,7 +91,7 @@
polygon_90_set_concept can be 100X faster than arbitrary angle polygon
manipulation.  Because the performance benefits are so large and the
special case is important enough, the library provides these performance
-benefits for those application domains that require them.Users are recommended to use std::vector and std::list of user defined polygons
+benefits for those application domains that require them.Users are recommended to use std::vector and std::list of user defined polygons
or library provided polygon_90_set_data<coordinate_type> objects.  Lists
and vectors of models of polygon_90_concept or polygon_90_with_holes_concept or
rectangle_concept are automatically models of polygon_90_set_concept.
@@ -85,10 +103,10 @@
eliminate temp copies of intermediate results when Boolean operators are chained
together.
Operators are declared inside the namespace boost::polygon::operators.
-<table border="1" width="100%" id="table3">
- <tr>
+<table id="table3" border="1" width="100%">
+ <tbody><tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 polygon_90_set_view operator|(const T1& l, const T2& r)</td>
 <td>Boolean OR operation (polygon set union).  Accepts two objects
 that model polygon_90_set or one of its refinements.  Returns an
@@ -98,7 +116,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 polygon_90_set_view operator+(const T1& l, const T2& r)</td>
 <td>Same as operator|.  The plus sign is also used for OR
 operations in Boolean logic expressions.  O( n log n) runtime
@@ -106,7 +124,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 polygon_90_set_view operator&(const T1& l, const T2& r)</td>
 <td>Boolean AND operation (polygon set intersection).  Accepts two
 objects that model polygon_90_set or one of its refinements.  O( n
@@ -114,7 +132,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 polygon_90_set_view operator*(const T1& l, const T2& r)</td>
 <td>Same as operator&.  The multiplication symbol is also used for
 AND operations in Boolean logic expressions.  O( n log n) runtime
@@ -122,7 +140,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 polygon_90_set_view operator^(const T1& l, const T2& r)</td>
 <td>Boolean XOR operation (polygon set disjoint-union).  Accepts
 two objects that model polygon_90_set or one of its refinements. 
@@ -132,7 +150,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 polygon_90_set_view operator-(const T1& l, const T2& r)</td>
 <td>Boolean SUBTRACT operation (polygon set difference).  Accepts
 two objects that model polygon_90_set or one of its refinements. 
@@ -141,7 +159,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator|=(const T1& l, const T2& r)</td>
 <td>Same as operator|, but with self assignment, left operand must model
 polygon_90_set and not one of it's refinements.  O( n log n)
@@ -149,7 +167,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator+=(T1& l, const T2& r)</td>
 <td>Same as operator+, but with self assignment, left operand must model
 polygon_90_set and not one of it's refinements.  O( n log n)
@@ -157,7 +175,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator&=(const T1& l, const T2& r)</td>
 <td>Same as operator&, but with self assignment, left operand must model
 polygon_90_set and not one of it's refinements.  O( n log n)
@@ -165,7 +183,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator*=(T1& l, const T2& r)</td>
 <td>Same as operator*, but with self assignment, left operand must model
 polygon_90_set and not one of it's refinements.  O( n log n)
@@ -173,7 +191,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator^=(const T1& l, const T2& r)</td>
 <td>Same as operator^, but with self assignment, left operand must model
 polygon_90_set and not one of it's refinements.  O( n log n)
@@ -181,14 +199,14 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator-=(T1& l, const T2& r)</td>
 <td>Same as operator-, but with self assignment, left operand must model
 polygon_90_set and not one of it's refinements.  O( n log n)
 runtime complexity and O(n) memory wrt vertices + intersections.</td>
 </tr>
 <tr>
- <td width="586">template <typename T1> 
+ <td width="586">template <typename T1> 
 T1 operator+(const T1&, coordinate_type bloating)</td>
 <td>Performs resize operation, inflating by bloating ammount.  If
 negative the result is a shrink instead of bloat.  Note: returns
@@ -197,7 +215,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1 operator-(const T1&, coordinate_type shrinking)</td>
 <td>Performs resize operation, deflating by bloating ammount.  If
 negative the result is a bloat instead of shrink.  Note: returns
@@ -206,7 +224,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator+=(const T1&, coordinate_type bloating)</td>
 <td>Performs resize operation, inflating by bloating ammount.  If
 negative the result is a shrink instead of bloat.  Returns
@@ -215,19 +233,19 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator-=(const T1&, coordinate_type shrinking)</td>
 <td>Performs resize operation, deflating by bloating ammount.  If
 negative the result is a bloat instead of shrink.  Returns
 reference to modified argument.  O( n log n) runtime complexity and
 O(n) memory wrt vertices + intersections.</td>
 </tr>
- </table>
+ </tbody></table>
<h2>Functions</h2>
-<table border="1" width="100%" id="table1">
- <tr>
+<table id="table1" border="1" width="100%">
+ <tbody><tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& assign(T1& lvalue, const T2& rvalue)</td>
 <td>Eliminates overlaps in geometry and copies from an object that
 models polygon_90_set or any of its refinements into an object that
@@ -236,7 +254,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 bool equivalence(const T1& lvalue, const T2& rvalue) </td>
 <td>Returns true if an object that models polygon_90_set or one of its
 refinements covers the exact same geometric regions as another object
@@ -246,8 +264,8 @@
 </tr>
 <tr>
 <td width="586">template <typename
- output_container_type, typename T> 
- void get_rectangles(output_container_type& output, 
+ output_container_type, typename T> 
+ void get_rectangles(output_container_type& output, 
                   
 const T& polygon_set)</td>
 <td>Output container is expected to be a standard container. 
@@ -258,10 +276,9 @@
 </tr>
 <tr>
 <td width="586">template <typename
- output_container_type, typename T> 
- void get_max_rectangles(output_container_type& output, 
-                       
- const T& polygon_set)</td>
+ output_container_type, typename T> 
+ void get_max_rectangles(output_container_type& output,                        
+const T& polygon_set)</td>
 <td>Output container is expected to be a standard container.  Given
 an object that models polygon_90_set or one of its refinements finds all
 overlapping rectangles that are maximal in area and appends them to the
@@ -269,13 +286,13 @@
 </tr>
 <tr>
 <td width="586">template <typename
- polygon_set_type> 
+ polygon_set_type> 
 void clear(polygon_set_type& polygon_set)</td>
 <td>Makes the object empty of geometry.</td>
 </tr>
 <tr>
 <td width="586">template <typename
- polygon_set_type> 
+ polygon_set_type> 
 bool empty(const polygon_set_type& polygon_set)</td>
 <td>Checks whether the object is empty of geometry.  Polygons that
 are completely covered by holes will result in empty returning true. 
@@ -284,8 +301,8 @@
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- rectangle_type> 
- bool extents(rectangle_type& extents_rectangle, 
+ rectangle_type> 
+ bool extents(rectangle_type& extents_rectangle, 
             const
 T& polygon_set)</td>
 <td>Computes bounding box of an object that models polygon_90_set and
@@ -295,7 +312,7 @@
 runtime complexity and O(n) memory wrt vertices + intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 manhattan_area_type area(const T& polygon_set)</td>
 <td>Computes the area covered by geometry in an object that models
 polygon_90_set.  O( n log n) runtime complexity and O(n) memory wrt
@@ -303,7 +320,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& interact(T1& a, const T2& b)</td>
 <td>Given an object that models polygon_90_set and an object that models
 polygon_90_set or one of its refinements, modifies a to retain only
@@ -311,7 +328,7 @@
 complexity and O(n) memory wrt vertices + intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& self_intersect(T& polygon_set)</td>
 <td>Given an object that models polygon_90_set that has self overlapping
 regions, modifies the argument to contain only the regions of overlap. 
@@ -319,7 +336,7 @@
 intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& self_xor(T& polygon_set)</td>
 <td>Given an object that models polygon_90_set that has self overlapping
 regions, modifies the argument to contain only the regions that do not
@@ -327,24 +344,24 @@
 vertices + intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& bloat(T& polygon_set, unsigned_area_type bloating)</td>
 <td>Same as getting all the rectangles, bloating them and putting them
 back.  O( n log n) runtime complexity and O(n) memory wrt vertices
 + intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
- T& bloat(T& polygon_set, orientation_2d orient, 
+ <td width="586">template <typename T> 
+ T& bloat(T& polygon_set, orientation_2d orient, 
         unsigned_area_type bloating)</td>
 <td>Same as getting all the rectangles, bloating them and putting them
 back.  O( n log n) runtime complexity and O(n) memory wrt vertices
 + intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
- T& bloat(T& polygon_set, orientation_2d orient, 
-         unsigned_area_type low_bloating, 
+ <td width="586">template <typename T> 
+ T& bloat(T& polygon_set, orientation_2d orient, 
+         unsigned_area_type low_bloating, 
         unsigned_area_type
 high_bloating)</td>
 <td>Same as getting all the rectangles, bloating them and putting them
@@ -352,22 +369,22 @@
 + intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
- T& bloat(T& polygon_set, direction_2d dir, 
+ <td width="586">template <typename T> 
+ T& bloat(T& polygon_set, direction_2d dir, 
         unsigned_area_type bloating)</td>
 <td>Same as getting all the rectangles, bloating them and putting them
 back.  O( n log n) runtime complexity and O(n) memory wrt vertices
 + intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
- T& bloat(T& polygon_set, 
+ <td width="586">template <typename T> 
+ T& bloat(T& polygon_set, 
         unsigned_area_type
- west_bloating, 
+ west_bloating, 
         unsigned_area_type
- east_bloating, 
+ east_bloating, 
         unsigned_area_type
- south_bloating, 
+ south_bloating, 
         unsigned_area_type
 north_bloating)</td>
 <td>Same as getting all the rectangles, bloating them and putting them
@@ -375,15 +392,15 @@
 + intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& shrink(T& polygon_set, unsigned_area_type shrinking)</td>
 <td>Same as getting all the rectangles of the inverse, bloating them and overwriting
 the polygon set with the resulting regions then negating.  O( n log
 n) runtime complexity and O(n) memory wrt vertices + intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
- T& shrink(T& polygon_set, orientation_2d orient, 
+ <td width="586">template <typename T> 
+ T& shrink(T& polygon_set, orientation_2d orient, 
          unsigned_area_type
 shrinking)</td>
 <td>Same as getting all the rectangles of the inverse, bloating them and overwriting
@@ -391,10 +408,10 @@
 n) runtime complexity and O(n) memory wrt vertices + intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
- T& shrink(T& polygon_set, orientation_2d orient, 
+ <td width="586">template <typename T> 
+ T& shrink(T& polygon_set, orientation_2d orient, 
          unsigned_area_type
- low_shrinking, 
+ low_shrinking, 
          unsigned_area_type
 high_shrinking)</td>
 <td>Same as getting all the rectangles of the inverse, bloating them and overwriting
@@ -402,8 +419,8 @@
 n) runtime complexity and O(n) memory wrt vertices + intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
- T& shrink(T& polygon_set, direction_2d dir, 
+ <td width="586">template <typename T> 
+ T& shrink(T& polygon_set, direction_2d dir, 
          unsigned_area_type
 shrinking)</td>
 <td>Same as getting all the rectangles of the inverse, bloating them and overwriting
@@ -411,14 +428,14 @@
 n) runtime complexity and O(n) memory wrt vertices + intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
- T& shrink(T& polygon_set, 
+ <td width="586">template <typename T> 
+ T& shrink(T& polygon_set, 
          unsigned_area_type
- west_shrinking, 
+ west_shrinking, 
          unsigned_area_type
- east_shrinking, 
+ east_shrinking, 
          unsigned_area_type
- south_shrinking, 
+ south_shrinking, 
          unsigned_area_type
 north_shrinking)</td>
 <td>Same as getting all the rectangles of the inverse, bloating them and overwriting
@@ -427,23 +444,23 @@
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- coord_type> 
+ coord_type> 
 T& resize(T& polygon_set, coord_type resizing)</td>
 <td>Same as bloat if resizing is positive, same as shrink if resizing is
 negative.</td>
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- coord_type> 
- T& resize(polygon_set_type& polygon_set, 
+ coord_type> 
+ T& resize(polygon_set_type& polygon_set, 
          coord_type west, coord_type east,
-           coord_type south, coord_type north)</td>
+           coord_type south, coord_type north)</td>
 <td>Same as bloat if resizing is positive, same as shrink if resizing is
 negative.  O( n log n) runtime complexity and O(n) memory wrt
 vertices + intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
T& grow_and(T& polygon_set, unsigned_area_type bloating)</td>
 <td>Same as bloating non-overlapping regions and then applying self
 intersect to retain only the overlaps introduced by the bloat.  O(
@@ -451,8 +468,8 @@
 intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
-T& grow_and(T& polygon_set, orientation_2d orient, 
+ <td width="586">template <typename T> 
+T& grow_and(T& polygon_set, orientation_2d orient, 
           
unsigned_area_type bloating)</td>
 <td>Same as bloating non-overlapping regions and then applying self
@@ -461,10 +478,10 @@
 intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
-T& grow_and(T& polygon_set, orientation_2d orient, 
+ <td width="586">template <typename T> 
+T& grow_and(T& polygon_set, orientation_2d orient, 
           
-unsigned_area_type low_bloating, 
+unsigned_area_type low_bloating, 
           
unsigned_area_type high_bloating)</td>
 <td>Same as bloating non-overlapping regions and then applying self
@@ -473,8 +490,8 @@
 intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
-T& grow_and(T& polygon_set, direction_2d dir, 
+ <td width="586">template <typename T> 
+T& grow_and(T& polygon_set, direction_2d dir, 
           
unsigned_area_type bloating)</td>
 <td>Same as bloating non-overlapping regions and then applying self
@@ -483,14 +500,14 @@
 intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
-T& grow_and(T& polygon_set, 
+ <td width="586">template <typename T> 
+T& grow_and(T& polygon_set, 
           
-unsigned_area_type west_bloating, 
+unsigned_area_type west_bloating, 
           
-unsigned_area_type east_bloating, 
+unsigned_area_type east_bloating, 
           
-unsigned_area_type south_bloating, 
+unsigned_area_type south_bloating, 
           
unsigned_area_type north_bloating)</td>
 <td>Same as bloating non-overlapping regions and then applying self
@@ -499,28 +516,28 @@
 intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
T& scale_up(T& polygon_set, unsigned_area_type factor)</td>
 <td>Scales geometry up by unsigned factor.  O( n log n) runtime
 complexity and O(n) memory wrt vertices + intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
T& scale_down(T& polygon_set, unsigned_area_type factor)</td>
 <td>Scales geometry down by unsigned factor.  O( n log n) runtime
 complexity and O(n) memory wrt vertices + intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T, typename scaling_type> 
-T& scale(polygon_set_type& polygon_set, 
+ <td width="586">template <typename T, typename scaling_type> 
+T& scale(polygon_set_type& polygon_set, 
         const scaling_type& scaling)</td>
 <td>Scales geometry by applying scaling.scale() on all vertices. 
 O( n log n) runtime complexity and O(n) memory wrt vertices +
 intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T, typename coord_type> 
-T& move(T& polygon_set, 
+ <td width="586">template <typename T, typename coord_type> 
+T& move(T& polygon_set, 
        orientation_2d orient, coord_type
displacement)</td>
 <td>Moves geometry by displacement amount in the orientation.   
@@ -528,40 +545,40 @@
 intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T, typename coord_type> 
-T& move(T& polygon_set, coord_type x_displacement, 
+ <td width="586">template <typename T, typename coord_type> 
+T& move(T& polygon_set, coord_type x_displacement, 
        coord_type y_displacement)</td>
 <td>Moves the geometry by x_dispacement in x and y_displacement in y. 
 Note: for consistency should be convolve(polygon_set, point).  O( n
 log n) runtime complexity and O(n) memory wrt vertices + intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T, typename transformation_type> 
-T& transform(T& polygon_set, 
+ <td width="586">template <typename T, typename transformation_type> 
+T& transform(T& polygon_set, 
             const
transformation_type& transformation)</td>
 <td>Applies transformation.transform() on all vertices.  O( n log
 n) runtime complexity and O(n) memory wrt vertices + intersections. </td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
-T& keep(T& polygon_set, 
-        unsigned_area_type min_area, 
-        unsigned_area_type max_area, 
-        unsigned_area_type min_width, 
-        unsigned_area_type max_width, 
-        unsigned_area_type min_height, 
+ <td width="586">template <typename T> 
+T& keep(T& polygon_set, 
+        unsigned_area_type min_area, 
+        unsigned_area_type max_area, 
+        unsigned_area_type min_width, 
+        unsigned_area_type max_width, 
+        unsigned_area_type min_height, 
        unsigned_area_type max_height)</td>
 <td>Retains only regions that satisfy the min/max criteria in the
 argument list.  Note: useful for visualization to cull too small
 polygons.  O( n log n) runtime complexity and O(n) memory wrt
 vertices + intersections. </td>
 </tr>
- </table>
+ </tbody></table>
 <h1>Polygon 90 Set Data Object</h1>


-The polygon 90 set data type encapsulates the internal data format that
+The polygon 90 set data type encapsulates the internal data format that
serves as the input to the sweep-line algorithm that implements polygon-clipping
boolean operations.  It also internally keeps track of whether that data
has been sorted or scanned and maintains the invariant that when its flags
@@ -572,15 +589,15 @@
maintain the data is sorted form rather than going all the way out to polygons
then resorting those vertices for a subsequent operation.
The declaration of Polygon 90 Set Data is the following:
-template <typename T> 
+template <typename T> 
class polygon_90_set_data;
The class is parameterized on the coordinate data type.  Algorithms that
benefit from knowledge of the invariants enforced by the class are implemented
as member functions to provide them access to information about those
invariants.  
<h2>Member Functions</h2>
-<table border="1" width="100%" id="table2">
- <tr>
+<table id="table2" border="1" width="100%">
+ <tbody><tr>
 <td width="586">polygon_90_set_data()</td>
 <td>Default constructor.  Scanning orientation defaults to
 HORIZONTAL</td>
@@ -591,9 +608,9 @@
 <td>Construct with scanning orientation.</td>
 </tr>
 <tr>
- <td width="586">template <typename iT> 
- polygon_90_set_data(orientation_2d orient,                     iT input_begin, iT
- input_end)</td>
+ <td width="586">template <typename iT> 
+ polygon_90_set_data(orientation_2d orient,                    
+iT input_begin, iT input_end)</td>
 <td>Construct with scanning orientation from an iterator range of
 insertable objects.</td>
 </tr>
@@ -604,7 +621,7 @@
 </tr>
 <tr>
 <td width="586">
-template <typename l, typename r, typename op> 
+template <typename l, typename r, typename op> 
polygon_90_set_data(const polygon_90_set_view<l,r,op>&
t)</td>
 <td>Copy construct from a Boolean operator template.</td>
@@ -612,33 +629,33 @@
 <tr>
 <td width="586">

-polygon_90_set_data(orientation_2d orient,                     const polygon_90_set_data&
-that)</td>
+polygon_90_set_data(orientation_2d orient,                    
+const polygon_90_set_data& that)</td>
 <td>Construct with scanning orientation and copy from another polygon
 set.</td>
 </tr>
 <tr>
 <td width="586">
-polygon_90_set_data& operator=(const polygon_90_set_data& that)</td>
+polygon_90_set_data& operator=(const polygon_90_set_data& that)</td>
 <td>Assignment from another polygon set, may change scanning
 orientation.</td>
 </tr>
 <tr>
 <td width="586">
-template <typename l, typename r, typename op> 
-polygon_90_set_data& operator=(const polygon_90_set_view<l, r,
+template <typename l, typename r, typename op> 
+polygon_90_set_data& operator=(const polygon_90_set_view<l, r,
op>& that)</td>
 <td>Assignment from a Boolean operator template.</td>
 </tr>
 <tr>
- <td width="586">template <typename geometry_object> 
+ <td width="586">template <typename geometry_object> 
polygon_90_set_data& operator=(const geometry_object& geo)</td>
 <td>Assignment from an insertable object.</td>
 </tr>
 <tr>
 <td width="586">

-template <typename iT> 
+template <typename iT> 
void insert(iT input_begin, iT input_end)</td>
 <td>Insert objects of an iterator range.  Linear wrt. inserted
 vertices.</td>
@@ -652,8 +669,8 @@
 <tr>
 <td width="586">

-template <typename geometry_type> 
-void insert(const geometry_type& geometry_object,             bool is_hole
+template <typename geometry_type> 
+void insert(const geometry_type& geometry_object,             bool is_hole
= false)</td>
 <td>Insert a geometry object, if is_hole is true then the inserted
 region is subtractive rather than additive.  Linear wrt. inserted
@@ -661,7 +678,7 @@
 </tr>
 <tr>
 <td width="586">
-template <typename output_container> 
+template <typename output_container> 
void get(output_container& output) const</td>
 <td>Expects a standard container of geometry objects.  Will scan
 and eliminate overlaps.  Converts polygon set geometry to objects
@@ -674,7 +691,7 @@
 </tr>
 <tr>
 <td width="586">
-template <typename output_container> 
+template <typename output_container> 
void get_polygons(output_container& output) const</td>
 <td>Expects a standard container of polygon objects.  Will scan and
 eliminate overlaps.  Converts polygon set geometry to polygons and
@@ -685,7 +702,7 @@
 </tr>
 <tr>
 <td width="586">
-template <typename output_container> 
+template <typename output_container> 
void get_rectangles(output_container& output) const</td>
 <td>Expects a standard container of rectangle objects.  Will scan
 and eliminate overlaps.  Slices polygon set geometry to rectangles
@@ -696,8 +713,8 @@
 <tr>
 <td width="586">

-template <typename output_container> 
-void get_rectangles(output_container& output,   orientation_2d
+template <typename output_container> 
+void get_rectangles(output_container& output,   orientation_2d
slicing_orientation) const 
 </td>
 <td>Expects a standard container of rectangle objects.  Will scan
@@ -750,9 +767,9 @@
 </tr>
 <tr>
 <td width="586">
-template <typename input_iterator_type> 
-void set(input_iterator_type input_begin,          input_iterator_type input_end,
-          orientation_2d orient) 
+template <typename input_iterator_type> 
+void set(input_iterator_type input_begin,          input_iterator_type input_end,
+          orientation_2d orient) 
 </td>
 <td>Overwrite geometry in polygon set with insertable objects in the
 iterator range.  Also sets the scanning orientation to that
@@ -760,7 +777,7 @@
 </tr>
 <tr>
 <td width="586">
-template <typename rectangle_type> 
+template <typename rectangle_type> 
bool extents(rectangle_type& extents_rectangle) const</td>
 <td>Given an object that models rectangle, scans and eliminates overlaps
 in the polygon set because subtractive regions may alter its extents
@@ -770,12 +787,12 @@
 </tr>
 <tr>
 <td width="586">
-polygon_90_set_data& 
-bloat(unsigned_area_type west_bloating, 
+polygon_90_set_data& 
+bloat(unsigned_area_type west_bloating, 
     
-unsigned_area_type east_bloating, 
+unsigned_area_type east_bloating, 
     
-unsigned_area_type south_bloating, 
+unsigned_area_type south_bloating, 
     
unsigned_area_type north_bloating) </td>
 <td>Scans to eliminate overlaps and subtractive regions.  Inserts
@@ -786,12 +803,12 @@
 </tr>
 <tr>
 <td width="586">
-polygon_90_set_data& 
-shrink(unsigned_area_type west_shrinking, 
+polygon_90_set_data& 
+shrink(unsigned_area_type west_shrinking, 
      
-unsigned_area_type east_shrinking, 
+unsigned_area_type east_shrinking, 
      
-unsigned_area_type south_shrinking, 
+unsigned_area_type south_shrinking, 
      
unsigned_area_type north_shrinking)</td>
 <td>Scans to eliminate overlaps and subtractive regions.  Inserts
@@ -804,24 +821,24 @@
 </tr>
 <tr>
 <td width="586">
-polygon_90_set_data& 
-resize(coordinate_type west, coordinate_type east,        coordinate_type south, coordinate_type north)</td>
+polygon_90_set_data& 
+resize(coordinate_type west, coordinate_type east,        coordinate_type south, coordinate_type north)</td>
 <td>Call bloat or shrink or shrink then bloat depending on whether the
 resizing values are positive or negative.  O( n log n) runtime
 complexity and O(n) memory wrt vertices + intersections.</td>
 </tr>
 <tr>
 <td width="586">
-polygon_90_set_data& move(coordinate_type x_delta,                           coordinate_type
-y_delta) 
+polygon_90_set_data& move(coordinate_type x_delta,                          
+coordinate_type y_delta) 
 </td>
 <td>Add x_delta to x values and y_delta to y values of vertices stored
 within the polygon set.  Linear wrt. vertices.</td>
 </tr>
 <tr>
 <td width="586">
-template <typename transformation_type> 
-polygon_90_set_data& transform(const transformation_type& transformation) 
+template <typename transformation_type> 
+polygon_90_set_data& transform(const transformation_type& transformation) 
 </td>
 <td>Applies transformation.transform() on vertices stored within the
 polygon set.  Linear wrt. vertices.</td>
@@ -835,14 +852,14 @@
 <tr>
 <td width="586">
polygon_90_set_data& scale_down(unsigned_area_type
-factor) </td>
+factor) </td>
 <td>Scales vertices stored within the polygon set down by factor. 
 Linear wrt. vertices.</td>
 </tr>
 <tr>
 <td width="586">
-template <typename scaling_type> 
-polygon_90_set_data& scale(const anisotropic_scale_factor<scaling_type>&
+template <typename scaling_type> 
+polygon_90_set_data& scale(const anisotropic_scale_factor<scaling_type>&
 f)</td>
 <td>Scales vertices stored within the polygon set by applying f.scale(). 
 Linear wrt. vertices.</td>
@@ -865,23 +882,23 @@
 intersections.</td>
 </tr>
 <tr>
- <td width="586">polygon_90_set_data& interact(const polygon_90_set_data& that)</td>
+ <td width="586">polygon_90_set_data& interact(const polygon_90_set_data& that)</td>
 <td>Retain only regions that touch or overlap regions in argument. 
 O( n log n) runtime complexity and O(n) memory wrt vertices +
 intersections.</td>
 </tr>
- </table>
- <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" rules="none" frame="void" id="table4">
+<table class="docinfo" id="table4" frame="void" rules="none">
 <colgroup>
- <col class="docinfo-name"><col class="docinfo-content">
+ <col class="docinfo-name" /><col class="docinfo-content" />
 </colgroup>
- <tbody vAlign="top">
+ <tbody valign="top">
 <tr>
 <th class="docinfo-name">Copyright:</th>
 <td>Copyright © Intel Corporation 2008-2010.</td>
@@ -894,6 +911,6 @@
 <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt>)</td>
 </tr>
-</table>
+</tbody></table>

-</html>
\ No newline at end of file
+</td></tr></tbody></table></body></html>
\ No newline at end of file

Modified: trunk/libs/polygon/doc/gtl_polygon_90_with_holes_concept.htm
==============================================================================
--- trunk/libs/polygon/doc/gtl_polygon_90_with_holes_concept.htm (original)
+++ trunk/libs/polygon/doc/gtl_polygon_90_with_holes_concept.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -1,14 +1,15 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<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>
-<title>Boost Polygon Library: Polygon 90 With Holes Concept</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>
+--><title>Boost Polygon Library: Polygon 90 With Holes Concept</title>
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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;">
@@ -20,6 +21,8 @@
 <li>Coordinate Concept</li>
 <li>Interval Concept</li>
 <li>Point Concept</li>
+ <li>Segment Concept</li>
+
 <li>Rectangle Concept</li>
 <li>Polygon 90 Concept</li>
 <li>Polygon 90 With Holes Concept</li>
@@ -36,103 +39,118 @@
 <li>Property Merge 90</li>
 <li>Property Merge 45</li>
 <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+</a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+</a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+
 </ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
- <li>GTL Boostcon 2009 Paper</li>
- <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
 Presentation</a></li>
- <li>Performance Analysis</li>
- <li>Layout Versus Schematic Tutorial</li>
- <li>Minkowski Sum Tutorial</li>
- </ul>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</li>
+ <li>Voronoi Advanced Tutorial</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">
+ <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%">



- 
+ 

<h1>Polygon 90 With Holes Concept</h1>


-The polygon_90_with_holes concept tag is 
+The polygon_90_with_holes concept tag is 
polygon_90_with_holes_concept

To register a user defined type as a model of
polygon_90_with_holes concept, specialize the
geometry concept meta-function for that type.  In the example below CPolygon90WithHoles is registered as a model of
-polygon_90_with_holes  concept.
-template <> 
-struct geometry_concept<CPolygon90WithHoles> { typedef polygon_90_with_holes_concept type; };
+polygon_90_with_holes  concept.
+template <> 
+struct geometry_concept<CPolygon90WithHoles> { typedef polygon_90_with_holes_concept type; };
The semantic of a polygon_90_with_holes is a
polygon_90 that it can provide iterators over holes that are also polygon_90. 
A mutable polygon_90_with_holes must also be able to set its geometry based on
an interator range over polygon_90 holes.  There is no convention of
-winding of holes enforced within the library. 
+winding of holes enforced within the library. 
Below is shown the default polygon with holes
traits.  Specialization of these traits is required for types that don't
-conform to the default behavior.template <typename
-T, typename enable = void> 
-struct polygon_with_holes_traits { 
+conform to the default behavior.template <typename
+T, typename enable = void> 
+struct polygon_with_holes_traits { 
     typedef typename T::iterator_holes_type
-iterator_holes_type; 
-     typedef typename T::hole_type hole_type; 
+iterator_holes_type; 
+     typedef typename T::hole_type hole_type; 
     static inline iterator_holes_type begin_holes(const T&
-t) { 
-          return t.begin_holes(); 
-     } 
+t) { 
+          return t.begin_holes(); 
+     } 
     static inline iterator_holes_type end_holes(const T& t)
-{ 
-          return t.end_holes(); 
-     } 
-     static inline unsigned int size_holes(const T& t) { 
-          return t.size_holes(); 
-     } 
+{ 
+          return t.end_holes(); 
+     } 
+     static inline unsigned int size_holes(const T& t) { 
+          return t.size_holes(); 
+     } 
};
-template <typename T, typename enable = void> 
-struct polygon_with_holes_mutable_traits { 
-     template <typename iT> 
+template <typename T, typename enable = void> 
+struct polygon_with_holes_mutable_traits { 
+     template <typename iT> 
     static inline T& set_holes(T& t, iT inputBegin, iT
-inputEnd) { 
+inputEnd) { 
          t.set_holes(inputBegin,
-inputEnd); 
-          return t; 
-     } 
+inputEnd); 
+          return t; 
+     } 
};
An object that is a model of 
polygon_90_with_holes_concept can be viewed as a model of any of its
refinements if it is determined at runtime to conform to the restriction of
those concepts.  This concept casting is accomplished through the
view_as<>() function.
-view_as<rectangle_concept>(polygon_90_with_holes_object) 
+view_as<rectangle_concept>(polygon_90_with_holes_object) 
view_as<polygon_90_concept>(polygon_90_with_holes_object)
The return value of view_as<>() can be
passed into any interface that expects an object of the conceptual type
specified in its template parameter.
<h2>Functions</h2>
-<table border="1" width="100%" id="table1">
- <tr>
- <td width="586">template <typename T> 
+<table id="table1" border="1" width="100%">
+ <tbody><tr>
+ <td width="586">template <typename T> 
 compact_iterator_type begin_compact(const T& polygon)</td>
 <td>Expects a model of polygon_90. 
 Returns the begin iterator over the range of coordinates that correspond
 to horizontal and vertical edges.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 compact_iterator_type end_compact(const T& polygon)</td>
 <td>Expects a model of polygon_90. 
 Returns the end iterator over the range of coordinates that correspond
 to horizontal and vertical edges.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 point_iterator_type begin_points(const T& polygon)</td>
 <td>Expects a model of
 polygon_90_with_holes. 
@@ -140,7 +158,7 @@
 vertices of the polygon.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 point_iterator_type end_points(const T& polygon)</td>
 <td>Expects a model of
 polygon_90_with_holes. 
@@ -148,7 +166,7 @@
 vertices of the polygon.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 hole_iterator_type begin_holes(const T& polygon)</td>
 <td>Expects a model of
 polygon_90_with_holes. 
@@ -156,7 +174,7 @@
 to horizontal and vertical edges.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 hole_iterator_type end_holes(const T& polygon)</td>
 <td>Expects a model of
 polygon_90_with_holes. 
@@ -165,7 +183,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- iterator> 
+ iterator> 
 void set_compact(T& polygon, iterator b, iterator e)</td>
 <td>Expects a model of
 polygon_90_with_holes.  
@@ -174,7 +192,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- iterator> 
+ iterator> 
 void set_points(T& polygon, iterator b, iterator e)</td>
 <td>Expects a model of
 polygon_90_with_holes.  
@@ -184,14 +202,14 @@
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- iterator> 
+ iterator> 
 void set_holes(T& polygon, iterator b, iterator e)</td>
 <td>Expects a model of
 polygon_90_with_holes.  
 Sets the polygon holes to the hole data range [b,e)</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 unsigned int size(const T& polygon)</td>
 <td>Returns the number of edges in the
 outer shell of the polygon_90_with_holes.  Does not include sizes
@@ -199,7 +217,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& assign(T1& left, const T2& right)</td>
 <td>Copies data from right object that models polygon_90_with_holes or
 one of its refinements into left object
@@ -207,8 +225,8 @@
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename point_type> 
- bool contains(const T&, const point_type& point, 
+ typename point_type> 
+ bool contains(const T&, const point_type& point, 
             
 bool consider_touch=true)</td>
 <td>Given an object that models polygon_90_with_holes and an object that models
@@ -219,86 +237,85 @@
 the polygon or one of its holes.</td>
 </tr>
 <tr>
- <td width="586">// get the center coordinate 
- template <typename T, typename point_type> 
+ <td width="586">// get the center coordinate 
+ template <typename T, typename point_type> 
 void center(point_type& p, const T& polygon)</td>
 <td>Sets object that models point to the center point of the bounding
 box of an object that models polygon_90_with_holes.</td>
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename rectangle_type> 
+ typename rectangle_type> 
 bool extents(rectangle_type& bbox, const T& polygon)</td>
 <td>Sets object that models rectangle to the bounding box of an object
 that models polygon_90_with_holes and returns true.  Returns false
 and leaves bbox unchanged if polygon is empty.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 manhattan_area_type area(const T& polygon)</td>
 <td>Returns the area of an object
 that models polygon_90_with_holes including subtracting the area of its
 holes from the area of the outer shell polygon.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 direction_1d winding(const T& polygon)</td>
 <td>Returns the winding direction of an object
 that models polygon_90_with_holes, LOW == CLOCKWISE, HIGH =
 COUNTERCLOCKWISE.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 coordinate_difference perimeter(const T& polygon)</td>
 <td>Returns the perimeter length of an object
 that models polygon_90, including the perimeters of the holes.</td>
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename transform_type> 
+ typename transform_type> 
 T& transform(T& polygon, const transform_type&)</td>
 <td>Applies transform() on the vertices of polygon and sets the polygon to that described by the result of
 transforming its vertices.  Also applies transform() on the holes
 of the polygon.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& scale_up(T& polygon, unsigned_area_type factor)</td>
 <td>Scales up outer shell and holes of an object that models
 polygon_90 by unsigned factor.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& scale_down(T& polygon, unsigned_area_type factor)</td>
 <td>Scales down outer shell and holes of an object that models
 polygon_90 by unsigned factor.</td>
 </tr>
 <tr>
- <td width="586">template <typename T, scaling_type> 
+ <td width="586">template <typename T, scaling_type> 
 T& scale(T& rectangle, double scaling) </td>
 <td>Scales outer shell and holes of an object that models polygon_90 by
 floating point factor.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
- T& move(T& polygon, orientation_2d, 
+ <td width="586">template <typename T> 
+ T& move(T& polygon, orientation_2d, 
        coordinate_difference displacement)</td>
 <td>Adds displacement value to coordinate indicated by orientation_2d of
 vertices of an object that models polygon_90 .</td>
 </tr>
 <tr>
- <td width="586">template <typename polygon_type, typename point_type> 
- polygon_type& convolve(polygon_type& polygon, 
-                      
- const point_type& point)</td>
+ <td width="586">template <typename polygon_type, typename point_type> 
+ polygon_type& convolve(polygon_type& polygon,                       
+const point_type& point)</td>
 <td>Convolves coordinate values of point with the outer shell and holes of an
 object that models polygon_90_with_holes.</td>
 </tr>
- </table>
+ </tbody></table>
 <h1>Polygon 90 With Holes Data</h1>


-The library provides a model of polygon 90 with holes concept declared
+The library provides a model of polygon 90 with holes concept declared

template<typename T> polygon_90_with_holes_data where T is the
coordinate type.
@@ -307,8 +324,8 @@
library polygon data type instead of providing their own.  The data type is
implemented to be convenient to use with the library traits.
<h2>Members</h2>
-<table border="1" width="100%" id="table2">
- <tr>
+<table id="table2" border="1" width="100%">
+ <tbody><tr>
 <td width="586">geometry_type</td>
 <td>polygon_90_with_holes_concept</td>
 </tr>
@@ -343,12 +360,12 @@
 </tr>
 <tr>
 <td width="586">polygon_90_with_holes_data& 
- operator=(const polygon_90_with_holes_data& that)</td>
+ operator=(const polygon_90_with_holes_data& that)</td>
 <td>Assignment operator.</td>
 </tr>
 <tr>
 <td width="586">template <typename T2> polygon_90_with_holes_data& 
- operator=(const T2& that) const</td>
+ operator=(const T2& that) const</td>
 <td>Assign from an object that is a model of polygon 90 with holes.</td>
 </tr>
 <tr>
@@ -396,14 +413,14 @@
 </tr>
 <tr>
 <td width="586">template <typename iT> 
- void set(iT begin_points, iT end_points)</td>
+ void set(iT begin_points, iT end_points)</td>
 <td>Sets the polygon to the iterator range of points.  No check is
 performed to ensure the points describe a Manhattan figure, every other
 x and y value of the points is used to initialize the polygon.</td>
 </tr>
 <tr>
 <td width="586">template <typename iT> 
- void set_compact(iT begin_coords, iT end_coords)</td>
+ void set_compact(iT begin_coords, iT end_coords)</td>
 <td>Sets the polygon to the iterator range of coordinates.  These
 coordinates correspond to the x values of vertical edges and y values of
 horizontal edges.  It is expected that the sequence start with an x
@@ -411,24 +428,24 @@
 </tr>
 <tr>
 <td width="586">template <typename iT> 
- void set_holes(iT begin_holes, iT end_choless)</td>
+ void set_holes(iT begin_holes, iT end_choless)</td>
 <td>Sets the polygon holes the iterator range of hole polygons.  These
 polygons in the input range may be either polygon_90_data or
 polygon_90_with_holes_data or any type that provides begin_compact and
 end_compact member functions.</td>
 </tr>
-</table>
- <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" rules="none" frame="void" id="table3">
+<table class="docinfo" id="table3" frame="void" rules="none">
 <colgroup>
- <col class="docinfo-name"><col class="docinfo-content">
+ <col class="docinfo-name" /><col class="docinfo-content" />
 </colgroup>
- <tbody vAlign="top">
+ <tbody valign="top">
 <tr>
 <th class="docinfo-name">Copyright:</th>
 <td>Copyright © Intel Corporation 2008-2010.</td>
@@ -441,6 +458,6 @@
 <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt>)</td>
 </tr>
-</table>
+</tbody></table>

-</html>
\ No newline at end of file
+</td></tr></tbody></table></body></html>
\ No newline at end of file

Modified: trunk/libs/polygon/doc/gtl_polygon_concept.htm
==============================================================================
--- trunk/libs/polygon/doc/gtl_polygon_concept.htm (original)
+++ trunk/libs/polygon/doc/gtl_polygon_concept.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -1,14 +1,15 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<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>
-<title>Boost Polygon Library: Polygon Concept</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>
+--><title>Boost Polygon Library: Polygon Concept</title>
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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;">
@@ -20,6 +21,8 @@
 <li>Coordinate Concept</li>
 <li>Interval Concept</li>
 <li>Point Concept</li>
+ <li>Segment Concept</li>
+
 <li>Rectangle Concept</li>
 <li>Polygon 90 Concept</li>
 <li>Polygon 90 With Holes Concept</li>
@@ -36,40 +39,55 @@
 <li>Property Merge 90</li>
 <li>Property Merge 45</li>
 <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+</a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+</a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+
 </ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
- <li>GTL Boostcon 2009 Paper</li>
- <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
 Presentation</a></li>
- <li>Performance Analysis</li>
- <li>Layout Versus Schematic Tutorial</li>
- <li>Minkowski Sum Tutorial</li>
- </ul>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</li>
+ <li>Voronoi Advanced Tutorial</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">
+ <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%">



- 
+ 

<h1>Polygon Concept</h1>


-The polygon concept tag is 
+The polygon concept tag is 
polygon_concept

To register a user defined type as a model of
polygon concept, specialize the
geometry concept meta-function for that type.  In the example below CPolygon is registered as a model of
-polygon  concept.
-template <> 
-struct geometry_concept<CPolygon> { typedef polygon_concept type; };
+polygon  concept.
+template <> 
+struct geometry_concept<CPolygon> { typedef polygon_concept type; };
The semantic of a polygon is that it can provide
iterators over the points that represent its vertices.  It is acceptable to
have the last edge explict with the first and last point equal to each other or
@@ -79,53 +97,53 @@
>
could be made models of polygon_concept by simply providing access to their
iterators through traits.  Library functions that create polygon objects
-require that those objects provide a default constructor.
+require that those objects provide a default constructor.
Below is shown the default polygon traits. 
Specialization of these traits is required for types that don't conform to the
default behavior.  Note that these same traits are also used by several
other polygon concepts through SFINE enable template parameter.  The SFINE
enable parameter also allows the library to provide default specialization that
-work for any object that models the 90 degree polygon concepts.
-template <typename T, typename enable = gtl_yes> 
-struct polygon_traits {}; 
- 
-template <typename T> 
-struct polygon_traits<T, 
-  typename gtl_or_4< 
+work for any object that models the 90 degree polygon concepts.
+template <typename T, typename enable = gtl_yes> 
+struct polygon_traits {}; 
+ 
+template <typename T> 
+struct polygon_traits<T, 
+  typename gtl_or_4< 
    typename gtl_same_type<typename geometry_concept<T>::type,
-polygon_concept>::type, 
+polygon_concept>::type, 
    typename gtl_same_type<typename geometry_concept<T>::type,
-polygon_concept>::type, 
+polygon_concept>::type, 
    typename gtl_same_type<typename geometry_concept<T>::type,
-polygon_with_holes_concept>::type, 
+polygon_with_holes_concept>::type, 
    typename gtl_same_type<typename geometry_concept<T>::type,
-polygon_with_holes_concept>::type 
-  >::type> { 
-     typedef typename T::coordinate_type coordinate_type; 
-     typedef typename T::iterator_type iterator_type; 
-     typedef typename T::point_type point_type; 
-     static inline iterator_type begin_points(const T& t) { 
-          return t.begin(); 
-     } 
-     static inline iterator_type end_points(const T& t) { 
-          return t.end(); 
-     } 
-     static inline unsigned int size(const T& t) { 
-          return t.size(); 
-     } 
-     static inline winding_direction winding(const T& t) { 
-          return unknown_winding; 
-     } 
+polygon_with_holes_concept>::type 
+  >::type> { 
+     typedef typename T::coordinate_type coordinate_type; 
+     typedef typename T::iterator_type iterator_type; 
+     typedef typename T::point_type point_type; 
+     static inline iterator_type begin_points(const T& t) { 
+          return t.begin(); 
+     } 
+     static inline iterator_type end_points(const T& t) { 
+          return t.end(); 
+     } 
+     static inline unsigned int size(const T& t) { 
+          return t.size(); 
+     } 
+     static inline winding_direction winding(const T& t) { 
+          return unknown_winding; 
+     } 
};
-template <typename T, typename enable = void> 
-struct polygon_mutable_traits { 
-     template <typename iT> 
+template <typename T, typename enable = void> 
+struct polygon_mutable_traits { 
+     template <typename iT> 
     static inline T& set_points(T& t, iT input_begin, iT
-input_end) { 
+input_end) { 
          t.set(input_begin,
-input_end); 
-          return t; 
-     } 
+input_end); 
+          return t; 
+     } 
};
Example code custom_polygon.cpp
demonstrates mapping a
@@ -135,23 +153,23 @@
refinements if it is determined at runtime to conform to the restriction of
those concepts.  This concept casting is accomplished through the
view_as<>() function.
-view_as<rectangle_concept>(polygon_object) 
-view_as<polygon_90_concept>(polygon_object) 
+view_as<rectangle_concept>(polygon_object) 
+view_as<polygon_90_concept>(polygon_object) 
view_as<polygon_45_concept>(polygon_object)
The return value of view_as<>() can be
passed into any interface that expects an object of the conceptual type
specified in its template parameter. 
<h2>Functions</h2>
-<table border="1" width="100%" id="table1">
- <tr>
- <td width="586">template <typename T> 
+<table id="table1" border="1" width="100%">
+ <tbody><tr>
+ <td width="586">template <typename T> 
 point_iterator_type begin_points(const T& polygon)</td>
 <td>Expects a model of polygon. 
 Returns the begin iterator over the range of points that correspond to
 vertices of the polygon.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 point_iterator_type end_points(const T& polygon)</td>
 <td>Expects a model of polygon. 
 Returns the end iterator over the range of points that correspond to
@@ -159,29 +177,29 @@
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- iterator> 
+ iterator> 
 void set_points(T& polygon, iterator b, iterator e)</td>
 <td>Expects a model of polygon.  
 Sets the polygon to the point data range [b,e) that corresponds to
 vertices of a manhattan polygon.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 unsigned int size(const T& polygon)</td>
 <td>Returns the number of edges in the
 polygon.</td>
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& assign(T1& left, const T2& right)</td>
 <td>Copies data from right object that models polygon into left object
 that models polygon.</td>
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename point_type> 
- bool contains(const T&, const point_type& point, 
+ typename point_type> 
+ bool contains(const T&, const point_type& point, 
             
 bool consider_touch=true)</td>
 <td>Given an object that models polygon and an object that models
@@ -191,84 +209,83 @@
 the polygon.  Linear wrt. vertices.</td>
 </tr>
 <tr>
- <td width="586">// get the center coordinate 
- template <typename T, typename point_type> 
+ <td width="586">// get the center coordinate 
+ template <typename T, typename point_type> 
 void center(point_type& p, const T& polygon)</td>
 <td>Sets object that models point to the center point of the bounding
 box of an object that models polygon.  Linear wrt. vertices.</td>
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename rectangle_type> 
+ typename rectangle_type> 
 bool extents(rectangle_type& bbox, const T& polygon)</td>
 <td>Sets object that models rectangle to the bounding box of an object
 that models polygon and returns true.  Returns false and leaves
 bbox unchanged if polygon is empty.  Linear wrt. vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 area_type area(const T& polygon)</td>
 <td>Returns the area of an object
 that models polygon.  Linear wrt. vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 direction_1d winding(const T& polygon)</td>
 <td>Returns the winding direction of an object
 that models polygon, LOW == CLOCKWISE, HIGH = COUNTERCLOCKWISE. 
 Complexity depends upon winding trait.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 coordinate_distance perimeter(const T& polygon)</td>
 <td>Returns the perimeter length of an object
 that models polygon.  Linear wrt. vertices.</td>
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename transform_type> 
+ typename transform_type> 
 T& transform(T& polygon, const transform_type&)</td>
 <td>Applies transform() on the vertices of polygon and sets the polygon to that described by the result of
 transforming its vertices.  Linear wrt. vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& scale_up(T& polygon, unsigned_area_type factor)</td>
 <td>Scales up coordinate of an object that models
 polygon by unsigned factor.  Linear wrt. vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& scale_down(T& polygon, unsigned_area_type factor)</td>
 <td>Scales down coordinates of an object that models
 polygon by unsigned factor.  Linear wrt. vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T, scaling_type> 
+ <td width="586">template <typename T, scaling_type> 
 T& scale(T& rectangle, double scaling) </td>
 <td>Scales coordinates of an object that models polygon by floating
 point factor.  Linear wrt. vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
- T& move(T& polygon, orientation_2d, 
+ <td width="586">template <typename T> 
+ T& move(T& polygon, orientation_2d, 
        coordinate_difference displacement)</td>
 <td>Adds displacement value to coordinate indicated by orientation_2d of
 vertices of an object that models polygon .  Linear wrt. vertices.</td>
 </tr>
 <tr>
- <td width="586">template <typename polygon_type, typename point_type> 
- polygon_type& convolve(polygon_type& polygon, 
-                      
- const point_type& point)</td>
+ <td width="586">template <typename polygon_type, typename point_type> 
+ polygon_type& convolve(polygon_type& polygon,                       
+const point_type& point)</td>
 <td>Convolves coordinate values of point with vertices of an
 object that models polygon.  Linear wrt. vertices.</td>
 </tr>
- </table>
+ </tbody></table>
 <h1>Polygon Data</h1>


-The library provides a model of polygon concept declared
+The library provides a model of polygon concept declared

template<typename T> polygon_data where T is the coordinate type.
This data type is used internally when a polygon is needed and is available
@@ -279,8 +296,8 @@
demonstrates using
 the library provided polygon data types and functions
<h2>Members</h2>
-<table border="1" width="100%" id="table2">
- <tr>
+<table id="table2" border="1" width="100%">
+ <tbody><tr>
 <td width="586">geometry_type</td>
 <td>polygon_concept</td>
 </tr>
@@ -308,7 +325,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T2> 
- polygon_data& operator=(const T2& that) const</td>
+ polygon_data& operator=(const T2& that) const</td>
 <td>Assign from an object that is a model of polygon.</td>
 </tr>
 <tr>
@@ -328,21 +345,21 @@
 </tr>
 <tr>
 <td width="586">template <typename iT> 
- void set(iT begin_points, iT end_points)</td>
+ void set(iT begin_points, iT end_points)</td>
 <td>Sets the polygon to the iterator range of points.  </td>
 </tr>
-</table>
- <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" rules="none" frame="void" id="table3">
+<table class="docinfo" id="table3" frame="void" rules="none">
 <colgroup>
- <col class="docinfo-name"><col class="docinfo-content">
+ <col class="docinfo-name" /><col class="docinfo-content" />
 </colgroup>
- <tbody vAlign="top">
+ <tbody valign="top">
 <tr>
 <th class="docinfo-name">Copyright:</th>
 <td>Copyright © Intel Corporation 2008-2010.</td>
@@ -355,6 +372,6 @@
 <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt>)</td>
 </tr>
-</table>
+</tbody></table>

-</html>
\ No newline at end of file
+</td></tr></tbody></table></body></html>
\ No newline at end of file

Modified: trunk/libs/polygon/doc/gtl_polygon_set_concept.htm
==============================================================================
--- trunk/libs/polygon/doc/gtl_polygon_set_concept.htm (original)
+++ trunk/libs/polygon/doc/gtl_polygon_set_concept.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -1,14 +1,15 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<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>
-<title>Boost Polygon Library: Polygon Set Concept</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>
+--><title>Boost Polygon Library: Polygon Set Concept</title>
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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;">
@@ -20,6 +21,8 @@
 <li>Coordinate Concept</li>
 <li>Interval Concept</li>
 <li>Point Concept</li>
+ <li>Segment Concept</li>
+
 <li>Rectangle Concept</li>
 <li>Polygon 90 Concept</li>
 <li>Polygon 90 With Holes Concept</li>
@@ -36,32 +39,47 @@
 <li>Property Merge 90</li>
 <li>Property Merge 45</li>
 <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+</a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+</a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+
 </ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
- <li>GTL Boostcon 2009 Paper</li>
- <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
 Presentation</a></li>
- <li>Performance Analysis</li>
- <li>Layout Versus Schematic Tutorial</li>
- <li>Minkowski Sum Tutorial</li>
- </ul>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</li>
+ <li>Voronoi Advanced Tutorial</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">
+ <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%">



- 
+ 

<h1>Polygon Set Concept</h1>


-The polygon_set concept tag is 
+The polygon_set concept tag is 
polygon_set_concept

The semantic of a polygon_set is zero or more
@@ -69,9 +87,14 @@
coordinates, but a snap rounding distance of one integer unit will still be
applied, furthermore, geometry outside the domain where one integer unit is
sufficient to provide robustness may lead to undefined behavior in algorithms. 
-It is recommended to use 32-bit integer coordinates for robust operations.
-
-Users are recommended to use std::vector and std::list of user defined polygons
+It is recommended to use integer coordinates for robust operations.  In the
+case that data represented contains only Manhattan geometry a runtime check will
+default to the Manhattan algorithm.  The results of which are identical to
+what the general algorithm would do, but obtained more efficiently.  In the
+case that the data represented contains only Manhattan and 45-degree geometry a
+runtime check will default to the faster 45-degree algorithm.  The results
+of which may differ slight from what the general algorithm would do because
+non-integer intersections will be handled differently.Users are recommended to use std::vector and std::list of user defined polygons
or library provided polygon_set_data<coordinate_type> objects.  Lists
and vectors of models of polygon_concept or polygon_with_holes_concept are automatically models of polygon_set_concept.
Example code custom_polygon_set.cpp
@@ -82,7 +105,7 @@
polygon_45_set_concept if it is determined at runtime to conform to the
restrictions of those concepts.  This concept casting is accomplished
through the view_as<>() function.
-view_as<polygon_90_set_concept>(polygon_set_object) 
+view_as<polygon_90_set_concept>(polygon_set_object) 
view_as<polygon_45_set_concept>(polygon_set_object)
The return value of view_as<>() can be passed
into any interface that expects an object of the conceptual type specified in
@@ -97,10 +120,10 @@
eliminate temp copies of intermediate results when Boolean operators are chained
together.
Operators are declared inside the namespace boost::polygon::operators.
-<table border="1" width="100%" id="table5">
- <tr>
+<table id="table5" border="1" width="100%">
+ <tbody><tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 polygon_set_view operator|(const T1& l, const T2& r)</td>
 <td>Boolean OR operation (polygon set union).  Accepts two objects
 that model polygon_set or one of its refinements.  Returns an
@@ -111,7 +134,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 polygon_set_view operator+(const T1& l, const T2& r)</td>
 <td>Same as operator|.  The plus sign is also used for OR
 operations in Boolean logic expressions.  Expected n log n runtime,
@@ -119,7 +142,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 polygon_set_view operator&(const T1& l, const T2& r)</td>
 <td>Boolean AND operation (polygon set intersection).  Accepts two
 objects that model polygon_set or one of its refinements.  Expected
@@ -128,7 +151,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 polygon_set_view operator*(const T1& l, const T2& r)</td>
 <td>Same as operator&.  The multiplication symbol is also used for
 AND operations in Boolean logic expressions.  Expected n log n
@@ -136,7 +159,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 polygon_set_view operator^(const T1& l, const T2& r)</td>
 <td>Boolean XOR operation (polygon set disjoint-union).  Accepts
 two objects that model polygon_set or one of its refinements. 
@@ -145,7 +168,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 polygon_set_view operator-(const T1& l, const T2& r)</td>
 <td>Boolean SUBTRACT operation (polygon set difference).  Accepts
 two objects that model polygon_set or one of its refinements. 
@@ -154,7 +177,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator|=(const T1& l, const T2& r)</td>
 <td>Same as operator|, but with self assignment, left operand must model
 polygon_set and not one of it's refinements.  Expected n log n
@@ -162,7 +185,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator+=(T1& l, const T2& r)</td>
 <td>Same as operator+, but with self assignment, left operand must model
 polygon_set and not one of it's refinements.  Expected n log n
@@ -170,7 +193,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator&=(const T1& l, const T2& r)</td>
 <td>Same as operator&, but with self assignment, left operand must model
 polygon_set and not one of it's refinements.  Expected n log n
@@ -178,7 +201,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator*=(T1& l, const T2& r)</td>
 <td>Same as operator*, but with self assignment, left operand must model
 polygon_set and not one of it's refinements.  Expected n log n
@@ -186,7 +209,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator^=(const T1& l, const T2& r)</td>
 <td>Same as operator^, but with self assignment, left operand must model
 polygon_set and not one of it's refinements.  Expected n log n
@@ -194,14 +217,14 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator-=(T1& l, const T2& r)</td>
 <td>Same as operator-, but with self assignment, left operand must model
 polygon_set and not one of it's refinements.  Expected n log n
 runtime, worst case quadratic runtime wrt. vertices + intersections.</td>
 </tr>
 <tr>
- <td width="586">template <typename T1> 
+ <td width="586">template <typename T1> 
 T1 operator+(const T1&, coordinate_type bloating)</td>
 <td>Performs resize operation, inflating by bloating ammount.  If
 negative the result is a shrink instead of bloat.  Note: returns
@@ -210,7 +233,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1 operator-(const T1&, coordinate_type shrinking)</td>
 <td>Performs resize operation, deflating by bloating ammount.  If
 negative the result is a bloat instead of shrink.  Note: returns
@@ -219,7 +242,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator+=(const T1&, coordinate_type bloating)</td>
 <td>Performs resize operation, inflating by bloating ammount.  If
 negative the result is a shrink instead of bloat.  Returns
@@ -228,19 +251,19 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& operator-=(const T1&, coordinate_type shrinking)</td>
 <td>Performs resize operation, deflating by bloating ammount.  If
 negative the result is a bloat instead of shrink.  Returns
 reference to modified argument.  Expected n log n runtime, worst
 case quadratic runtime wrt. vertices + intersections.</td>
 </tr>
- </table>
+ </tbody></table>
<h2>Functions</h2>
-<table border="1" width="100%" id="table6">
- <tr>
+<table id="table6" border="1" width="100%">
+ <tbody><tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& assign(T1& lvalue, const T2& rvalue)</td>
 <td>Eliminates overlaps in geometry and copies from an object that
 models polygon_set or any of its refinements into an object that
@@ -249,7 +272,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 bool equivalence(const T1& lvalue, const T2& rvalue) </td>
 <td>Returns true if an object that models polygon_set or one of its
 refinements covers the exact same geometric regions as another object
@@ -259,8 +282,8 @@
 </tr>
 <tr>
 <td width="586">template <typename
- output_container_type, typename T> 
- void get_trapezoids(output_container_type& output, 
+ output_container_type, typename T> 
+ void get_trapezoids(output_container_type& output, 
                   
 const T& polygon_set)</td>
 <td>Output container is expected to be a standard container. 
@@ -273,10 +296,12 @@
 </tr>
 <tr>
 <td width="586">template <typename
- output_container_type, typename T> 
- void get_trapezoids(output_container_type& output, 
+ output_container_type, typename T> 
+ void get_trapezoids(output_container_type& output, 
                   
- const T& polygon_set,                     orientation_2d orient)</td>
+ const T& polygon_set, 
+                   
+orientation_2d orient)</td>
 <td>Output container is expected to be a standard container. 
 Slices geometry of an object that models polygon_set or one of its
 refinements into non overlapping trapezoids along a the specified slicing
@@ -287,13 +312,13 @@
 </tr>
 <tr>
 <td width="586">template <typename
- polygon_set_type> 
+ polygon_set_type> 
 void clear(polygon_set_type& polygon_set)</td>
 <td>Makes the object empty of geometry.</td>
 </tr>
 <tr>
 <td width="586">template <typename
- polygon_set_type> 
+ polygon_set_type> 
 bool empty(const polygon_set_type& polygon_set)</td>
 <td>Checks whether the object is empty of geometry.  Polygons that
 are completely covered by holes will result in empty returning true. 
@@ -302,8 +327,8 @@
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- rectangle_type> 
- bool extents(rectangle_type& extents_rectangle, 
+ rectangle_type> 
+ bool extents(rectangle_type& extents_rectangle, 
             const
 T& polygon_set)</td>
 <td>Computes bounding box of an object that models polygon_set and
@@ -314,21 +339,21 @@
 intersections.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 area_type area(const T& polygon_set)</td>
 <td>Computes the area covered by geometry in an object that models
 polygon_set.  Expected n log n runtime, worst case quadratic
 runtime wrt. vertices + intersections.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& bloat(T& polygon_set, unsigned_area_type bloating)</td>
 <td>Same as getting all the polygons, bloating them and putting them
 back.  Expected n log n runtime, worst case quadratic runtime wrt.
 vertices + intersections.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& shrink(T& polygon_set, unsigned_area_type shrinking)</td>
 <td>Same as getting all the polygons, shrinking them and overwriting
 the polygon set with the resulting regions.  Expected n log n
@@ -336,10 +361,10 @@
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- coord_type> 
- T& resize(T& polygon_set, coord_type resizing, 
+ coord_type> 
+ T& resize(T& polygon_set, coord_type resizing, 
          
- bool corner_fill_arc = false,          
+ bool corner_fill_arc = false,          
 unsigned int num_circle_segments = 0)</td>
 <td>Same as bloat if resizing is positive, same as shrink if resizing is
 negative.  Original topology at acute angle vertices is preserved
@@ -350,31 +375,20 @@
 runtime wrt. vertices + intersections.</td>
 </tr>
 <tr>
- <td width="586">template <typename T, typename
- coord_type> 
- T& simplify(T& polygon_set, distance_type
- threshold)</td>
- <td>Simplify the polygon set by removing vertices that lie
- within threshold distance of the line segment that
- connects the two adjacent points in the polygon. 
- Expected n log n runtime, worst case quadratic
- runtime wrt. vertices + intersections.</td>
- </tr>
- <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
T& scale_up(T& polygon_set, unsigned_area_type factor)</td>
 <td>Scales geometry up by unsigned factor.  Expected n log n
 runtime, worst case quadratic runtime wrt. vertices + intersections.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
T& scale_down(T& polygon_set, unsigned_area_type factor)</td>
 <td>Scales geometry down by unsigned factor.  Expected n log n
 runtime, worst case quadratic runtime wrt. vertices + intersections.</td>
 </tr>
 <tr>
- <td width="586">template <typename T, typename transformation_type> 
-T& transform(T& polygon_set, 
+ <td width="586">template <typename T, typename transformation_type> 
+T& transform(T& polygon_set, 
             const
transformation_type& transformation)</td>
 <td>Applies transformation.transform() on all vertices.  Expected n
@@ -382,24 +396,24 @@
 intersections.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
-T& keep(T& polygon_set, 
-        unsigned_area_type min_area, 
-        unsigned_area_type max_area, 
-        unsigned_area_type min_width, 
-        unsigned_area_type max_width, 
-        unsigned_area_type min_height, 
+ <td width="586">template <typename T> 
+T& keep(T& polygon_set, 
+        unsigned_area_type min_area, 
+        unsigned_area_type max_area, 
+        unsigned_area_type min_width, 
+        unsigned_area_type max_width, 
+        unsigned_area_type min_height, 
        unsigned_area_type max_height)</td>
 <td>Retains only regions that satisfy the min/max criteria in the
 argument list.  Note: useful for visualization to cull too small
 polygons.  Expected n log n runtime, worst case quadratic runtime
 wrt. vertices + intersections.</td>
 </tr>
- </table>
+ </tbody></table>
 <h1>Polygon Set Data Object</h1>


-The polygon set data type encapsulates the internal data format that
+The polygon set data type encapsulates the internal data format that
serves as the input to the sweep-line algorithm that implements polygon-clipping
Boolean operations.  It also internally keeps track of whether that data
has been sorted or scanned and maintains the invariant that when its flags
@@ -410,7 +424,7 @@
maintain the data is sorted form rather than going all the way out to polygons
then resorting those vertices for a subsequent operation.
The declaration of Polygon Set Data is the following:
-template <typename T> 
+template <typename T> 
class polygon_set_data;
The class is parameterized on the coordinate data type.  Algorithms that
benefit from knowledge of the invariants enforced by the class are implemented
@@ -420,13 +434,13 @@
demonstrates using
 the library provided polygon set data types and functions
<h2>Member Functions</h2>
-<table border="1" width="100%" id="table7">
- <tr>
+<table id="table7" border="1" width="100%">
+ <tbody><tr>
 <td width="586">polygon_set_data()</td>
 <td>Default constructor. </td>
 </tr>
 <tr>
- <td width="586">template <typename iT> 
+ <td width="586">template <typename iT> 
 polygon_set_data(iT input_begin, iT
 input_end)</td>
 <td>Construct with scanning orientation from an iterator range of
@@ -439,33 +453,33 @@
 </tr>
 <tr>
 <td width="586">
-template <typename l, typename r, typename op> 
+template <typename l, typename r, typename op> 
polygon_set_data(const polygon_set_view<l,r,op>&
t)</td>
 <td>Copy construct from a Boolean operator template.</td>
 </tr>
 <tr>
 <td width="586">
-polygon_set_data& operator=(const polygon_set_data& that)</td>
+polygon_set_data& operator=(const polygon_set_data& that)</td>
 <td>Assignment from another polygon set, may change scanning
 orientation.</td>
 </tr>
 <tr>
 <td width="586">
-template <typename l, typename r, typename op> 
-polygon_set_data& operator=(const polygon_set_view<l, r,
+template <typename l, typename r, typename op> 
+polygon_set_data& operator=(const polygon_set_view<l, r,
op>& that)</td>
 <td>Assignment from a Boolean operator template.</td>
 </tr>
 <tr>
- <td width="586">template <typename geometry_object> 
+ <td width="586">template <typename geometry_object> 
polygon_set_data& operator=(const geometry_object& geo)</td>
 <td>Assignment from an insertable object.</td>
 </tr>
 <tr>
 <td width="586">

-template <typename iT> 
+template <typename iT> 
void insert(iT input_begin, iT input_end)</td>
 <td>Insert objects of an iterator range.  Linear wrt vertices
 inserted.</td>
@@ -479,8 +493,8 @@
 <tr>
 <td width="586">

-template <typename geometry_type> 
-void insert(const geometry_type& geometry_object,             bool is_hole
+template <typename geometry_type> 
+void insert(const geometry_type& geometry_object,             bool is_hole
= false)</td>
 <td>Insert a geometry object, if is_hole is true then the inserted
 region is subtractive rather than additive.  Linear wrt vertices
@@ -488,7 +502,7 @@
 </tr>
 <tr>
 <td width="586">
-template <typename output_container> 
+template <typename output_container> 
void get(output_container& output) const</td>
 <td>Expects a standard container of polygons objects.  Will scan
 and eliminate overlaps.  Converts polygon set geometry to objects
@@ -505,7 +519,7 @@
 </tr>
 <tr>
 <td width="586">
-template <typename output_container> 
+template <typename output_container> 
void get_trapezoids(output_container& output) const</td>
 <td>Expects a standard container of polygon objects.  Will scan
 and eliminate overlaps.  Slices polygon set geometry to trapezoids
@@ -515,8 +529,8 @@
 <tr>
 <td width="586">

-template <typename output_container> 
-void get_trapezoids(output_container& output,   orientation_2d
+template <typename output_container> 
+void get_trapezoids(output_container& output,   orientation_2d
slicing_orientation) const 
 </td>
 <td>Expects a standard container of polygon objects.  Will scan
@@ -563,15 +577,15 @@
 </tr>
 <tr>
 <td width="586">
-template <typename input_iterator_type> 
-void set(input_iterator_type input_begin,          input_iterator_type input_end) 
+template <typename input_iterator_type> 
+void set(input_iterator_type input_begin,          input_iterator_type input_end) 
 </td>
 <td>Overwrite geometry in polygon set with insertable objects in the
 iterator range. </td>
 </tr>
 <tr>
 <td width="586">
-template <typename rectangle_type> 
+template <typename rectangle_type> 
bool extents(rectangle_type& extents_rectangle) const</td>
 <td>Given an object that models rectangle, scans and eliminates overlaps
 in the polygon set because subtractive regions may alter its extents
@@ -581,9 +595,9 @@
 </tr>
 <tr>
 <td width="586">
-polygon_set_data& 
-resize(coord_type resizing, 
-        bool corner_fill_arc = false,       
+polygon_set_data& 
+resize(coord_type resizing, 
+        bool corner_fill_arc = false,       
 unsigned int num_circle_segments = 0)</td>
 <td>Inflates if resizing is positive, deflates if resizing is
 negative.  Original topology at acute angle vertices is preserved
@@ -597,8 +611,8 @@
 </tr>
 <tr>
 <td width="586">
-template <typename transformation_type> 
-polygon_set_data& transform(const transformation_type& transformation) 
+template <typename transformation_type> 
+polygon_set_data& transform(const transformation_type& transformation) 
 </td>
 <td>Applies transformation.transform() on vertices stored within the
 polygon set.  Expected n log n runtime, worst case quadratic
@@ -621,25 +635,25 @@
 </tr>
 <tr>
 <td width="586">
-template <typename scaling_type> 
-polygon_set_data& scale(const scaling_type&
+template <typename scaling_type> 
+polygon_set_data& scale(const scaling_type&
 f)</td>
 <td>Scales vertices stored within the polygon set by applying f.scale(). 
 Expected n log n runtime, worst case quadratic runtime wrt. vertices +
 intersections.</td>
 </tr>
- </table>
- <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" rules="none" frame="void" id="table8">
+<table class="docinfo" id="table8" frame="void" rules="none">
 <colgroup>
- <col class="docinfo-name"><col class="docinfo-content">
+ <col class="docinfo-name" /><col class="docinfo-content" />
 </colgroup>
- <tbody vAlign="top">
+ <tbody valign="top">
 <tr>
 <th class="docinfo-name">Copyright:</th>
 <td>Copyright © Intel Corporation 2008-2010.</td>
@@ -652,6 +666,6 @@
 <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt>)</td>
 </tr>
-</table>
+</tbody></table>

-</html>
+</td></tr></tbody></table></body></html>
\ No newline at end of file

Modified: trunk/libs/polygon/doc/gtl_polygon_with_holes_concept.htm
==============================================================================
--- trunk/libs/polygon/doc/gtl_polygon_with_holes_concept.htm (original)
+++ trunk/libs/polygon/doc/gtl_polygon_with_holes_concept.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -1,14 +1,15 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<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>
-<title>Boost Polygon Library: Polygon With Holes Concept</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>
+--><title>Boost Polygon Library: Polygon With Holes Concept</title>
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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;">
@@ -20,6 +21,8 @@
 <li>Coordinate Concept</li>
 <li>Interval Concept</li>
 <li>Point Concept</li>
+ <li>Segment Concept</li>
+
 <li>Rectangle Concept</li>
 <li>Polygon 90 Concept</li>
 <li>Polygon 90 With Holes Concept</li>
@@ -36,115 +39,130 @@
 <li>Property Merge 90</li>
 <li>Property Merge 45</li>
 <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+</a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+</a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+
 </ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
- <li>GTL Boostcon 2009 Paper</li>
- <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
 Presentation</a></li>
- <li>Performance Analysis</li>
- <li>Layout Versus Schematic Tutorial</li>
- <li>Minkowski Sum Tutorial</li>
- </ul>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</li>
+ <li>Voronoi Advanced Tutorial</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">
+ <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%">



- 
+ 

<h1>Polygon With Holes Concept</h1>


-The polygon_with_holes concept tag is 
+The polygon_with_holes concept tag is 
polygon_with_holes_concept

To register a user defined type as a model of
polygon_with_holes concept, specialize the
geometry concept meta-function for that type.  In the example below
-CPolygonWithHoles is registered as a model of polygon_with_holes  concept.
-template <> 
-struct geometry_concept<CPolygonWithHoles> { typedef polygon_with_holes_concept type; };
+CPolygonWithHoles is registered as a model of polygon_with_holes  concept.
+template <> 
+struct geometry_concept<CPolygonWithHoles> { typedef polygon_with_holes_concept type; };
The semantic of a polygon_with_holes is a polygon
that it can provide iterators over holes that are also polygon.  A mutable
polygon_with_holes must also be able to set its geometry based on an interator
range over polygon holes.  There is no convention of winding of holes
-enforced within the library. 
+enforced within the library. 
Below is shown the default polygon with holes
traits.  Specialization of these traits is required for types that don't
conform to the default behavior.  Note, these traits are used by all
-polygon with holes concepts.template <typename
-T, typename enable = void> 
-struct polygon_with_holes_traits { 
+polygon with holes concepts.template <typename
+T, typename enable = void> 
+struct polygon_with_holes_traits { 
     typedef typename T::iterator_holes_type
-iterator_holes_type; 
-     typedef typename T::hole_type hole_type; 
+iterator_holes_type; 
+     typedef typename T::hole_type hole_type; 
     static inline iterator_holes_type begin_holes(const T&
-t) { 
-          return t.begin_holes(); 
-     } 
+t) { 
+          return t.begin_holes(); 
+     } 
     static inline iterator_holes_type end_holes(const T& t)
-{ 
-          return t.end_holes(); 
-     } 
-     static inline unsigned int size_holes(const T& t) { 
-          return t.size_holes(); 
-     } 
+{ 
+          return t.end_holes(); 
+     } 
+     static inline unsigned int size_holes(const T& t) { 
+          return t.size_holes(); 
+     } 
};
-template <typename T, typename enable = void> 
-struct polygon_with_holes_mutable_traits { 
-     template <typename iT> 
+template <typename T, typename enable = void> 
+struct polygon_with_holes_mutable_traits { 
+     template <typename iT> 
     static inline T& set_holes(T& t, iT inputBegin, iT
-inputEnd) { 
+inputEnd) { 
          t.set_holes(inputBegin,
-inputEnd); 
-          return t; 
-     } 
+inputEnd); 
+          return t; 
+     } 
};
An object that is a model of 
polygon_with_holes_concept can be viewed as a model of any of its
refinements if it is determined at runtime to conform to the restriction of
those concepts.  This concept casting is accomplished through the
view_as<>() function.
-view_as<rectangle_concept>(polygon_with_holes_object) 
-view_as<polygon_90_concept>(polygon_with_holes_object) 
-view_as<polygon_90_with_holes_concept>(polygon_with_holes_object) 
-view_as<polygon_45_concept>(polygon_with_holes_object) 
-view_as<polygon_45_with_holes_concept>(polygon_with_holes_object) 
+view_as<rectangle_concept>(polygon_with_holes_object) 
+view_as<polygon_90_concept>(polygon_with_holes_object) 
+view_as<polygon_90_with_holes_concept>(polygon_with_holes_object) 
+view_as<polygon_45_concept>(polygon_with_holes_object) 
+view_as<polygon_45_with_holes_concept>(polygon_with_holes_object) 
view_as<polygon_concept>(polygon_with_holes_object)
The return value of view_as<>() can be
passed into any interface that expects an object of the conceptual type
specified in its template parameter. 
<h2>Functions</h2>
-<table border="1" width="100%" id="table1">
- <tr>
- <td width="586">template <typename T> 
+<table id="table1" border="1" width="100%">
+ <tbody><tr>
+ <td width="586">template <typename T> 
 point_iterator_type begin_points(const T& polygon)</td>
 <td>Expects a model of polygon_with_holes. 
 Returns the begin iterator over the range of points that correspond to
 vertices of the polygon.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 point_iterator_type end_points(const T& polygon)</td>
 <td>Expects a model of polygon_with_holes. 
 Returns the end iterator over the range of points that correspond to
 vertices of the polygon.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 hole_iterator_type begin_holes(const T& polygon)</td>
 <td>Expects a model of polygon_with_holes. 
 Returns the begin iterator over the range of coordinates that correspond
 to horizontal and vertical edges.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 hole_iterator_type end_holes(const T& polygon)</td>
 <td>Expects a model of polygon_with_holes. 
 Returns the end iterator over the range of coordinates that correspond
@@ -152,7 +170,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- iterator> 
+ iterator> 
 void set_points(T& polygon, iterator b, iterator e)</td>
 <td>Expects a model of polygon_with_holes.  
 Sets the polygon to the point data range [b,e) that corresponds to
@@ -160,13 +178,13 @@
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- iterator> 
+ iterator> 
 void set_holes(T& polygon, iterator b, iterator e)</td>
 <td>Expects a model of polygon_with_holes.  
 Sets the polygon holes to the hole data range [b,e)</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 unsigned int size(const T& polygon)</td>
 <td>Returns the number of edges in the
 outer shell of the polygon_with_holes.  Does not include sizes of
@@ -174,7 +192,7 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& assign(T1& left, const T2& right)</td>
 <td>Copies data from right object that models polygon_with_holes or one
 of its refinements into left object
@@ -182,8 +200,8 @@
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename point_type> 
- bool contains(const T&, const point_type& point, 
+ typename point_type> 
+ bool contains(const T&, const point_type& point, 
             
 bool consider_touch=true)</td>
 <td>Given an object that models polygon_with_holes and an object that models
@@ -194,86 +212,85 @@
 the polygon or one of its holes.</td>
 </tr>
 <tr>
- <td width="586">// get the center coordinate 
- template <typename T, typename point_type> 
+ <td width="586">// get the center coordinate 
+ template <typename T, typename point_type> 
 void center(point_type& p, const T& polygon)</td>
 <td>Sets object that models point to the center point of the bounding
 box of an object that models polygon_with_holes.</td>
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename rectangle_type> 
+ typename rectangle_type> 
 bool extents(rectangle_type& bbox, const T& polygon)</td>
 <td>Sets object that models rectangle to the bounding box of an object
 that models polygon_with_holes and returns true.  Returns false and
 leaves bbox unchanged if polygon is empty.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 manhattan_area_type area(const T& polygon)</td>
 <td>Returns the area of an object
 that models polygon_with_holes including subtracting the area of its
 holes from the area of the outer shell polygon.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 direction_1d winding(const T& polygon)</td>
 <td>Returns the winding direction of an object
 that models polygon_with_holes, LOW == CLOCKWISE, HIGH =
 COUNTERCLOCKWISE.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 coordinate_difference perimeter(const T& polygon)</td>
 <td>Returns the perimeter length of an object
 that models polygon, including the perimeters of the holes.</td>
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename transform_type> 
+ typename transform_type> 
 T& transform(T& polygon, const transform_type&)</td>
 <td>Applies transform() on the vertices of polygon and sets the polygon to that described by the result of
 transforming its vertices.  Also applies transform() on the holes
 of the polygon.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& scale_up(T& polygon, unsigned_area_type factor)</td>
 <td>Scales up outer shell and holes of an object that models
 polygon by unsigned factor.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& scale_down(T& polygon, unsigned_area_type factor)</td>
 <td>Scales down outer shell and holes of an object that models
 polygon by unsigned factor.</td>
 </tr>
 <tr>
- <td width="586">template <typename T, scaling_type> 
+ <td width="586">template <typename T, scaling_type> 
 T& scale(T& rectangle, double scaling) </td>
 <td>Scales outer shell and holes of an object that models polygon by
 floating point factor.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
- T& move(T& polygon, orientation_2d, 
+ <td width="586">template <typename T> 
+ T& move(T& polygon, orientation_2d, 
        coordinate_difference displacement)</td>
 <td>Adds displacement value to coordinate indicated by orientation_2d of
 vertices of an object that models polygon .</td>
 </tr>
 <tr>
- <td width="586">template <typename polygon_type, typename point_type> 
- polygon_type& convolve(polygon_type& polygon, 
-                      
- const point_type& point)</td>
+ <td width="586">template <typename polygon_type, typename point_type> 
+ polygon_type& convolve(polygon_type& polygon,                       
+const point_type& point)</td>
 <td>Convolves coordinate values of point with the outer shell and holes of an
 object that models polygon_with_holes.</td>
 </tr>
- </table>
+ </tbody></table>
 <h1>Polygon With Holes Data</h1>


-The library provides a model of polygon with holes concept declared
+The library provides a model of polygon with holes concept declared

template<typename T> polygon_with_holes_data where T is the
coordinate type.
@@ -282,8 +299,8 @@
library polygon data type instead of providing their own.  The data type is
implemented to be convenient to use with the library traits.
<h2>Members</h2>
-<table border="1" width="100%" id="table2">
- <tr>
+<table id="table2" border="1" width="100%">
+ <tbody><tr>
 <td width="586">geometry_type</td>
 <td>polygon_with_holes_concept</td>
 </tr>
@@ -311,13 +328,13 @@
 </tr>
 <tr>
 <td width="586">polygon_with_holes_data& 
- operator=(const polygon_with_holes_data& that)</td>
+ operator=(const polygon_with_holes_data& that)</td>
 <td>Assignment operator.</td>
 </tr>
 <tr>
 <td width="586">template <typename T2> 
 polygon_with_holes_data& 
- operator=(const T2& that) const</td>
+ operator=(const T2& that) const</td>
 <td>Assign from an object that is a model of polygon with holes.</td>
 </tr>
 <tr>
@@ -353,29 +370,29 @@
 </tr>
 <tr>
 <td width="586">template <typename iT> 
- void set(iT begin_points, iT end_points)</td>
+ void set(iT begin_points, iT end_points)</td>
 <td>Sets the polygon to the iterator range of points. </td>
 </tr>
 <tr>
 <td width="586">template <typename iT> 
- void set_holes(iT begin_holes, iT end_choless)</td>
+ void set_holes(iT begin_holes, iT end_choless)</td>
 <td>Sets the polygon holes the iterator range of hole polygons.  These
 polygons in the input range may be either polygon_data or
 polygon_with_holes_data or any type that provides begin and end member
 functions to iterate over point_data<T>.</td>
 </tr>
-</table>
- <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" rules="none" frame="void" id="table3">
+<table class="docinfo" id="table3" frame="void" rules="none">
 <colgroup>
- <col class="docinfo-name"><col class="docinfo-content">
+ <col class="docinfo-name" /><col class="docinfo-content" />
 </colgroup>
- <tbody vAlign="top">
+ <tbody valign="top">
 <tr>
 <th class="docinfo-name">Copyright:</th>
 <td>Copyright © Intel Corporation 2008-2010.</td>
@@ -388,6 +405,6 @@
 <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt>)</td>
 </tr>
-</table>
+</tbody></table>

-</html>
\ No newline at end of file
+</td></tr></tbody></table></body></html>
\ No newline at end of file

Modified: trunk/libs/polygon/doc/gtl_property_merge.htm
==============================================================================
--- trunk/libs/polygon/doc/gtl_property_merge.htm (original)
+++ trunk/libs/polygon/doc/gtl_property_merge.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -1,14 +1,15 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<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>
-<title>Boost Polygon Library: Property Merge</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>
+--><title>Boost Polygon Library: Property Merge</title>
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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;">
@@ -20,6 +21,8 @@
 <li>Coordinate Concept</li>
 <li>Interval Concept</li>
 <li>Point Concept</li>
+ <li>Segment Concept</li>
+
 <li>Rectangle Concept</li>
 <li>Polygon 90 Concept</li>
 <li>Polygon 90 With Holes Concept</li>
@@ -36,35 +39,50 @@
 <li>Property Merge 90</li>
 <li>Property Merge 45</li>
 <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+</a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+</a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+
 </ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
- <li>GTL Boostcon 2009 Paper</li>
- <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
 Presentation</a></li>
- <li>Performance Analysis</li>
- <li>Layout Versus Schematic Tutorial</li>
- <li>Minkowski Sum Tutorial</li>
- </ul>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</li>
+ <li>Voronoi Advanced Tutorial</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">
+ <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%">



- 
+ 

<h1>Property Merge</h1>


-The following is the declaration of the property merge algorithm.
+The following is the declaration of the property merge algorithm.
template <typename coordinate_type, typename
-property_type> 
-class property_merge;The property algorithm computes the n-layer
+property_type> 
+class property_merge;The property algorithm computes the n-layer
map overlay of input polygon sets.  Each input geometry is inserted along
with a property value.  The property type can be anything suitable for use
as an element of a std::set.  Multiple geometry objects can be separately
@@ -72,13 +90,13 @@
operation a fairly complex container is required.  Resulting geometries are
associated with unique subsets of property values of the input geometry. 
Two suitable containers for storing the result of a property merge operation
-are:std::map<std::set<property_type>, polygon_set_data<coordinate_type>
-> 
-std::map<std::vector<property_type>, polygon_set_data<coordinate_type> >
+are:std::map<std::set<property_type>, polygon_set_data<coordinate_type>
+> 
+std::map<std::vector<property_type>, polygon_set_data<coordinate_type> >
Example code property_merge_usage.cpp
- demonstrates using the n-layer map-overlay algorithm on polygon data.<h2>Member Functions</h2>
-<table border="1" width="100%" id="table1">
- <tr>
+ demonstrates using the n-layer map-overlay algorithm on polygon data.<h2>Member Functions</h2>
+<table id="table1" border="1" width="100%">
+ <tbody><tr>
 <td width="586">property_merge()</td>
 <td>Default constructor. </td>
 </tr>
@@ -89,7 +107,7 @@
 </tr>
 <tr>
 <td width="586">
-void insert(const polygon_set_data<coordinate_type>& ps, 
+void insert(const polygon_set_data<coordinate_type>& ps, 
      
const property_type& property)</td>
 <td>Insert a polygon set with an associated
@@ -98,8 +116,8 @@
 <tr>
 <td width="586">

-template <class GeoObjT> 
-void insert(const GeoObjT& geoObj, 
+template <class GeoObjT> 
+void insert(const GeoObjT& geoObj, 
      
const property_type& property)</td>
 <td>Insert a geometry object that is a refinement of polygon set with an
@@ -108,25 +126,25 @@
 <tr>
 <td width="586">

-template <typename result_type> 
+template <typename result_type> 
void merge(result_type& result)</td>
 <td>Accepts a container object that conforms to the expectations defined
 above.  Performs property merge and populates the container
 object.  Expected n log n runtime, worst case quadratic runtime wrt.
 vertices + intersections.</td>
 </tr>
- </table>
- <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" rules="none" frame="void" id="table2">
+<table class="docinfo" id="table2" frame="void" rules="none">
 <colgroup>
- <col class="docinfo-name"><col class="docinfo-content">
+ <col class="docinfo-name" /><col class="docinfo-content" />
 </colgroup>
- <tbody vAlign="top">
+ <tbody valign="top">
 <tr>
 <th class="docinfo-name">Copyright:</th>
 <td>Copyright © Intel Corporation 2008-2010.</td>
@@ -139,6 +157,6 @@
 <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt>)</td>
 </tr>
-</table>
+</tbody></table>

-</html>
\ No newline at end of file
+</td></tr></tbody></table></body></html>
\ No newline at end of file

Modified: trunk/libs/polygon/doc/gtl_property_merge_45.htm
==============================================================================
--- trunk/libs/polygon/doc/gtl_property_merge_45.htm (original)
+++ trunk/libs/polygon/doc/gtl_property_merge_45.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -1,14 +1,15 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<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>
-<title>Boost Polygon Library: Property Merge 90</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>
+--><title>Boost Polygon Library: Property Merge 90</title>
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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;">
@@ -20,6 +21,8 @@
 <li>Coordinate Concept</li>
 <li>Interval Concept</li>
 <li>Point Concept</li>
+ <li>Segment Concept</li>
+
 <li>Rectangle Concept</li>
 <li>Polygon 90 Concept</li>
 <li>Polygon 90 With Holes Concept</li>
@@ -36,35 +39,50 @@
 <li>Property Merge 90</li>
 <li>Property Merge 45</li>
 <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+</a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+</a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+
 </ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
- <li>GTL Boostcon 2009 Paper</li>
- <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
 Presentation</a></li>
- <li>Performance Analysis</li>
- <li>Layout Versus Schematic Tutorial</li>
- <li>Minkowski Sum Tutorial</li>
- </ul>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</li>
+ <li>Voronoi Advanced Tutorial</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">
+ <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%">



- 
+ 

<h1>Property Merge 45</h1>


-The following is the declaration of the property merge algorithm.
+The following is the declaration of the property merge algorithm.
template <typename coordinate_type, typename
-property_type> 
-class property_merge_45;The property algorithm computes the n-layer
+property_type> 
+class property_merge_45;The property algorithm computes the n-layer
map overlay of input polygon sets.  Each input geometry is inserted along
with a property value.  The property type can be anything suitable for use
as an element of a std::set.  Multiple geometry objects can be separately
@@ -72,13 +90,13 @@
operation a fairly complex container is required.  Resulting geometries are
associated with unique subsets of property values of the input geometry. 
Two suitable containers for storing the result of a property merge operation
-are:std::map<std::set<property_type>, polygon_45_set_data<coordinate_type>
-> 
-std::map<std::vector<property_type>, polygon_45_set_data<coordinate_type> >
+are:std::map<std::set<property_type>, polygon_45_set_data<coordinate_type>
+> 
+std::map<std::vector<property_type>, polygon_45_set_data<coordinate_type> >
Example code property_merge_usage.cpp
- demonstrates using the n-layer map-overlay algorithm on polygon 90 data.<h2>Member Functions</h2>
-<table border="1" width="100%" id="table1">
- <tr>
+ demonstrates using the n-layer map-overlay algorithm on polygon 90 data.<h2>Member Functions</h2>
+<table id="table1" border="1" width="100%">
+ <tbody><tr>
 <td width="586">property_merge_45()</td>
 <td>Default constructor. </td>
 </tr>
@@ -89,7 +107,7 @@
 </tr>
 <tr>
 <td width="586">
-void insert(const polygon_45_set_data<coordinate_type>& ps, 
+void insert(const polygon_45_set_data<coordinate_type>& ps, 
      
const property_type& property)</td>
 <td>Insert a polygon set with an associated
@@ -98,8 +116,8 @@
 <tr>
 <td width="586">

-template <class GeoObjT> 
-void insert(const GeoObjT& geoObj, 
+template <class GeoObjT> 
+void insert(const GeoObjT& geoObj, 
      
const property_type& property)</td>
 <td>Insert a geometry object that is a refinement of polygon 45 set with
@@ -108,24 +126,24 @@
 <tr>
 <td width="586">

-template <typename result_type> 
+template <typename result_type> 
void merge(result_type& result)</td>
 <td>Accepts a container object that conforms to the expectations defined
 above.  Performs property merge and populates the container
 object.  O(n log n) runtime wrt. vertices + intersections.</td>
 </tr>
- </table>
- <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" rules="none" frame="void" id="table2">
+<table class="docinfo" id="table2" frame="void" rules="none">
 <colgroup>
- <col class="docinfo-name"><col class="docinfo-content">
+ <col class="docinfo-name" /><col class="docinfo-content" />
 </colgroup>
- <tbody vAlign="top">
+ <tbody valign="top">
 <tr>
 <th class="docinfo-name">Copyright:</th>
 <td>Copyright © Intel Corporation 2008-2010.</td>
@@ -138,6 +156,6 @@
 <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt>)</td>
 </tr>
-</table>
+</tbody></table>

-</html>
\ No newline at end of file
+</td></tr></tbody></table></body></html>
\ No newline at end of file

Modified: trunk/libs/polygon/doc/gtl_property_merge_90.htm
==============================================================================
--- trunk/libs/polygon/doc/gtl_property_merge_90.htm (original)
+++ trunk/libs/polygon/doc/gtl_property_merge_90.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -1,14 +1,15 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<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>
-<title>Boost Polygon Library: Property Merge 90</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>
+--><title>Boost Polygon Library: Property Merge 90</title>
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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;">
@@ -20,6 +21,8 @@
 <li>Coordinate Concept</li>
 <li>Interval Concept</li>
 <li>Point Concept</li>
+ <li>Segment Concept</li>
+
 <li>Rectangle Concept</li>
 <li>Polygon 90 Concept</li>
 <li>Polygon 90 With Holes Concept</li>
@@ -36,35 +39,50 @@
 <li>Property Merge 90</li>
 <li>Property Merge 45</li>
 <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+</a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+</a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+
 </ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
- <li>GTL Boostcon 2009 Paper</li>
- <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
 Presentation</a></li>
- <li>Performance Analysis</li>
- <li>Layout Versus Schematic Tutorial</li>
- <li>Minkowski Sum Tutorial</li>
- </ul>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</li>
+ <li>Voronoi Advanced Tutorial</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">
+ <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%">



- 
+ 

<h1>Property Merge 90</h1>


-The following is the declaration of the property merge algorithm.
+The following is the declaration of the property merge algorithm.
template <typename coordinate_type, typename
-property_type> 
-class property_merge_90;The property algorithm computes the n-layer
+property_type> 
+class property_merge_90;The property algorithm computes the n-layer
map overlay of input polygon sets.  Each input geometry is inserted along
with a property value.  The property type can be anything suitable for use
as an element of a std::set.  Multiple geometry objects can be separately
@@ -72,13 +90,13 @@
operation a fairly complex container is required.  Resulting geometries are
associated with unique subsets of property values of the input geometry. 
Two suitable containers for storing the result of a property merge operation
-are:std::map<std::set<property_type>, polygon_90_set_data<coordinate_type>
-> 
-std::map<std::vector<property_type>, polygon_90_set_data<coordinate_type> >
+are:std::map<std::set<property_type>, polygon_90_set_data<coordinate_type>
+> 
+std::map<std::vector<property_type>, polygon_90_set_data<coordinate_type> >
Example code property_merge_usage.cpp
- demonstrates using the n-layer map-overlay algorithm on polygon 90 data.<h2>Member Functions</h2>
-<table border="1" width="100%" id="table1">
- <tr>
+ demonstrates using the n-layer map-overlay algorithm on polygon 90 data.<h2>Member Functions</h2>
+<table id="table1" border="1" width="100%">
+ <tbody><tr>
 <td width="586">property_merge_90()</td>
 <td>Default constructor. </td>
 </tr>
@@ -89,7 +107,7 @@
 </tr>
 <tr>
 <td width="586">
-void insert(const polygon_90_set_data<coordinate_type>& ps, 
+void insert(const polygon_90_set_data<coordinate_type>& ps, 
      
const property_type& property)</td>
 <td>Insert a polygon set with an associated
@@ -98,8 +116,8 @@
 <tr>
 <td width="586">

-template <class GeoObjT> 
-void insert(const GeoObjT& geoObj, 
+template <class GeoObjT> 
+void insert(const GeoObjT& geoObj, 
      
const property_type& property)</td>
 <td>Insert a geometry object that is a refinement of polygon 90 set with
@@ -108,24 +126,24 @@
 <tr>
 <td width="586">

-template <typename result_type> 
+template <typename result_type> 
void merge(result_type& result)</td>
 <td>Accepts a container object that conforms to the expectations defined
 above.  Performs property merge and populates the container
 object.  O(n log n) runtime wrt. vertices + intersections.</td>
 </tr>
- </table>
- <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" rules="none" frame="void" id="table2">
+<table class="docinfo" id="table2" frame="void" rules="none">
 <colgroup>
- <col class="docinfo-name"><col class="docinfo-content">
+ <col class="docinfo-name" /><col class="docinfo-content" />
 </colgroup>
- <tbody vAlign="top">
+ <tbody valign="top">
 <tr>
 <th class="docinfo-name">Copyright:</th>
 <td>Copyright © Intel Corporation 2008-2010.</td>
@@ -138,6 +156,6 @@
 <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt>)</td>
 </tr>
-</table>
+</tbody></table>

-</html>
\ No newline at end of file
+</td></tr></tbody></table></body></html>
\ No newline at end of file

Modified: trunk/libs/polygon/doc/gtl_rectangle_concept.htm
==============================================================================
--- trunk/libs/polygon/doc/gtl_rectangle_concept.htm (original)
+++ trunk/libs/polygon/doc/gtl_rectangle_concept.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -1,14 +1,15 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
-<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>
-<title>Boost Polygon Library: Rectangle Concept</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>
+--><title>Boost Polygon Library: Rectangle Concept</title>
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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;">
@@ -20,6 +21,8 @@
 <li>Coordinate Concept</li>
 <li>Interval Concept</li>
 <li>Point Concept</li>
+ <li>Segment Concept</li>
+
 <li>Rectangle Concept</li>
 <li>Polygon 90 Concept</li>
 <li>Polygon 90 With Holes Concept</li>
@@ -36,6 +39,18 @@
 <li>Property Merge 90</li>
 <li>Property Merge 45</li>
 <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+</a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+</a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+
 </ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
@@ -45,31 +60,35 @@
 <li>Performance Analysis</li>
 <li>Layout Versus Schematic Tutorial</li>
 <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</li>
+ <li>Voronoi Advanced Tutorial</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">
+ <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%">



- 
+ 

<h1>Rectangle Concept</h1>


-The rectangle concept tag is 
+The rectangle concept tag is 
rectangle_concept

To register a user defined type as a model of
rectangle concept, specialize the
geometry concept meta-function for that type.  In the example below CRectangle is registered as a model of
-rectangle  concept.
-template <> 
-struct geometry_concept<CRectangle> { typedef rectangle_concept type; };
+rectangle  concept.
+template <> 
+struct geometry_concept<CRectangle> { typedef rectangle_concept type; };
The semantic of a rectangle is that it has an x and
a y interval and these intervals conform to the semantic of an interval
including its invariant.  This invariant on the intervals of a rectangle is enforced by the generic library functions that
@@ -77,7 +96,7 @@
mapping of that data type to the rectangle concept through its traits.  In
this way a boost::tuple<int, int, int, int> or boost::array<int, 4>
could be made models of rectangle by simply providing indirect access to their
-elements through traits.
+elements through traits.
Below is shown the default rectangle traits. 
Specialization of these traits is required for types that don't conform to the
default behavior.  The interested reader will note SFINAE is used on the
@@ -86,103 +105,104 @@
necessary when refinements of concepts are used and it is undesirable to attempt
to match default traits to non-rectangle types at compile time. 
Specializing rectangle_traits can be done easily by simply providing gtl_yes as
-the enable parameter.
-template <typename T, typename enable = gtl_yes> 
-struct rectangle_traits {};
-template <typename T> 
-struct rectangle_traits<T, gtl_no> {}; 
- 
-template <typename T> 
+the enable parameter.
+template <typename T, typename enable = gtl_yes> 
+struct rectangle_traits {};
+template <typename T> 
+struct rectangle_traits<T, gtl_no> {}; 
+ 
+template <typename T> 
struct rectangle_traits<T, typename gtl_same_type<typename T::interval_type,
-typename T::interval_type>::type> { 
-     typedef typename T::coordinate_type coordinate_type; 
-     typedef typename T::interval_type interval_type; 
+typename T::interval_type>::type> { 
+     typedef typename T::coordinate_type coordinate_type; 
+     typedef typename T::interval_type interval_type; 
     static inline interval_type get(const T& rectangle,
-orientation_2d orient) { 
+orientation_2d orient) { 
          return
-rectangle.get(orient); } 
-}; 
- 
-template <typename T> 
-struct rectangle_mutable_traits { 
-     template <typename T2> 
+rectangle.get(orient); } 
+}; 
+ 
+template <typename T> 
+struct rectangle_mutable_traits { 
+     template <typename T2> 
     static inline void set(T& rectangle, orientation_2d
-orient, const T2& interval) { 
+orient, const T2& interval) { 
          rectangle.set(orient,
-interval); } 
-     template <typename T2, typename T3> 
+interval); } 
+     template <typename T2, typename T3> 
     static inline T construct(const T2& interval_horizontal,
-const T3& interval_vertical) { 
+const T3& interval_vertical) { 
          return
-T(interval_horizontal, interval_vertical); } 
-};<h2>Functions</h2>
-<table border="1" width="100%" id="table1">
- <tr>
- <td width="586">template <typename T> 
+T(interval_horizontal, interval_vertical); } 
+};<h2>Functions</h2>
+<table id="table1" border="1" width="100%">
+ <tbody><tr>
+ <td width="586">template <typename T> 
 interval_type get(const T& rectangle, orientation_2d)</td>
 <td>Expects a model of rectangle. 
 Returns the x interval or y interval of the rectangle, depending on the
- orientation_2d value. 
+ orientation_2d value. 
 </td>
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- coordinate_type> 
+ coordinate_type> 
 void set(T& rectangle, orientation_2d, coordinate_type)</td>
 <td>Expects a model of rectangle.  
 Sets the x interval or y interval of the rectangle to the
 coordinate, depending on the orientation_2d value.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 interval_type get(const T& rectangle, orientation_2d,
-                   direction_1d)</td>
- <td>Expects a model of rectangle. 
- Returns the coordinate specificed by the direction_1d value of the x interval or y interval of the rectangle, depending on the
- orientation_2d value. 
+                   direction_1d)</td>
+ <td>Expects
+a model of rectangle.  Returns the coordinate specificed by the
+direction_1d value of the x interval or y interval of the rectangle,
+depending on the orientation_2d value. 
 </td>
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- coordinate_type> 
- void set(T& rectangle, orientation_2d, direction_1d,          coordinate_type)</td>
+ coordinate_type> 
+ void set(T& rectangle, orientation_2d, direction_1d,          coordinate_type)</td>
 <td>Expects a model of rectangle.  
 Sets the coordinate specified by the direction_1d value of the x interval or y interval of the rectangle to the
 coordinate, depending on the orientation_2d value.</td>
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- T2> 
+ T2> 
 T construct(const T2& h, const T2& v)</td>
 <td>Construct an object that is a model of rectangle given x interval
 and y intervals.</td>
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- T2> 
- T construct(coordinate_type xl, coordinate_type yl,             coordinate_type
+ T2> 
+ T construct(coordinate_type xl, coordinate_type yl,             coordinate_type
 xh, coordinate_type yh)</td>
 <td>Construct an object that is a model of rectangle given four coordinate values.</td>
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& assign(T1& left, const T2& right)</td>
 <td>Copies data from right object that models rectangle into left object
 that models rectangle.</td>
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- T2> 
+ T2> 
 bool equivalence(const T& rectangle1, 
-                  const T2& rectangle2)</td>
+                  const T2& rectangle2)</td>
 <td>Given two objects that model rectangle, compares and returns true if
 their x and y intervals are respectively equivalent.</td>
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename point_type> 
- bool contains(const T&, const point_type& point, 
+ typename point_type> 
+ bool contains(const T&, const point_type& point, 
             
 bool consider_touch=true)</td>
 <td>Given an object that models rectangle and an object that models
@@ -193,8 +213,8 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
- bool contains(const T1& a, const T2& b, 
+ T2> 
+ bool contains(const T1& a, const T2& b, 
             
 bool consider_touch = true) </td>
 <td>Returns true if model of rectangle a contains both intervals of
@@ -202,170 +222,174 @@
 consider rectangle b contained even if it touches the boundary of a.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 interval_type horizontal(const T& rectangle)</td>
 <td>Returns the x interval of an object that models rectangle.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 interval_type vertical(const T& rectangle)</td>
 <td>Returns the y interval of an object that models rectangle.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 coordinate_type xl(const T& rectangle)</td>
 <td>Returns the west coordinate of an object that models rectangle.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 coordinate_type xh(const T& rectangle)</td>
 <td>Returns the east coordinate of an object that models rectangle.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 coordinate_type yl(const T& rectangle)</td>
 <td>Returns the south coordinate of an object that models rectangle.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 coordinate_type yh(const T& rectangle)</td>
 <td>Returns the north coordinate of an object that models rectangle.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 point_type ll(const T& rectangle)</td>
 <td>Returns the lower left corner point of an object that models rectangle.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 point_type lr(const T& rectangle)</td>
 <td>Returns the lower right corner point of an object that models rectangle.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 point_type ul(const T& rectangle)</td>
 <td>Returns the upper left corner point of an object that models rectangle.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 point_type ur(const T& rectangle)</td>
 <td>Returns the upper right corner point of an object that models rectangle.</td>
 </tr>
 <tr>
- <td width="586">// get the center coordinate 
- template <typename T, typename point_type> 
+ <td width="586">// get the center coordinate 
+ template <typename T, typename point_type> 
 void center(point_type& p, const T& rectangle)</td>
 <td>Sets object that models point to the center point of an object that models rectangle.</td>
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename interval_type> 
+ typename interval_type> 
 void horizontal(T& rectangle, const interval_type& i)</td>
 <td>Sets the x interval of the object that models rectangle to be equal
 to the value of an object that models interval.</td>
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename interval_type> 
+ typename interval_type> 
 void vertical(T& rectangle, const interval_type& i )</td>
 <td>Sets the y interval of the object that models rectangle to be equal
 to the value of an object that models interval.</td>
 </tr>
 <tr>
 <td width="586">template <typename
- rectangle_type> 
+ rectangle_type> 
 void xl(rectangle_type& rectangle, coordinate_type )</td>
 <td>Sets the west coordinate of the object that models rectangle to be equal
 to the coordinate value.</td>
 </tr>
 <tr>
 <td width="586">template <typename
- rectangle_type> 
+ rectangle_type> 
 void xh(rectangle_type& rectangle, coordinate_type )</td>
 <td>Sets the east coordinate of the object that models rectangle to be equal
 to the coordinate value.</td>
 </tr>
 <tr>
 <td width="586">template <typename
- rectangle_type> 
+ rectangle_type> 
 void yl(rectangle_type& rectangle, coordinate_type )</td>
 <td>Sets the south coordinate of the object that models rectangle to be equal
 to the coordinate value.</td>
 </tr>
 <tr>
 <td width="586">template <typename
- rectangle_type> 
+ rectangle_type> 
 void yh(rectangle_type& rectangle, coordinate_type )</td>
 <td>Sets the north coordinate of the object that models rectangle to be equal
 to the coordinate value.</td>
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename T1, typename T2> 
+ typename T1, typename T2> 
 T& set_points(T& rectangle, const T1& p1, const T2& p2)</td>
 <td>Sets the rectangle to the rectangle fully described by the points p1
 and p2.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 coordinate_difference delta(const T& rectangle,
-                             orientation_2d)</td>
+                            
+orientation_2d)</td>
 <td>Returns the delta of the interval specified by orientation_2d of an object
 that models rectangle.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 manhattan_area_type area(const T& rectangle)</td>
 <td>Returns the area of an object
 that models rectangle.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 coordinate_difference half_perimeter(const T& rectangle)</td>
 <td>Returns the length plus width of an object
 that models rectangle.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 coordinate_difference perimeter(const T& rectangle)</td>
 <td>Returns the perimeter length of an object
 that models rectangle.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 orientation_2d quess_orientation(const T& rectangle)</td>
 <td>Returns the orientation in which the rectangle has a longer delta. 
 Returns HORIZONTAL if the rectangle is a square.</td>
 </tr>
 <tr>
 <td width="586">template <typename
- rectangle_type> 
- rectangle_type& transform(rectangle_type& rectangle, 
-                          coordinate_type axis = 0)</td>
+ rectangle_type> 
+ rectangle_type& transform(rectangle_type& rectangle, 
+                         
+coordinate_type axis = 0)</td>
 <td>Applies transform() on the two points that fully describe the
 rectangle and sets the rectangle to that described by the result of
 transforming those points.</td>
 </tr>
 <tr>
 <td width="586">template <typename
- rectangle_type> 
- rectangle_type& scale_up(rectangle_type& rectangle, 
-                         unsigned_area_type factor)</td>
+ rectangle_type> 
+ rectangle_type& scale_up(rectangle_type& rectangle, 
+                        
+unsigned_area_type factor)</td>
 <td>Scales up x interval and y interval  of an object that models
 rectangle by unsigned factor.</td>
 </tr>
 <tr>
 <td width="586">template <typename
- rectangle_type> 
- rectangle_type& scale_down(rectangle_type& rectangle, 
-                           unsigned_area_type factor)</td>
+ rectangle_type> 
+ rectangle_type& scale_down(rectangle_type& rectangle, 
+                          
+unsigned_area_type factor)</td>
 <td>Scales down x interval and y interval  of an object that models
 rectangle by unsigned factor.</td>
 </tr>
 <tr>
 <td width="586">template <typename
- rectangle_type, scaling_type> 
- rectangle_type& scale(rectangle_type& rectangle, 
+ rectangle_type, scaling_type> 
+ rectangle_type& scale(rectangle_type& rectangle, 
                     
 const scaling_type& scaling) </td>
 <td>Applies scale() on the two points that fully describe the rectangle
@@ -373,33 +397,33 @@
 those points.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
- T& move(T& rectangle, orientation_2d, 
+ <td width="586">template <typename T> 
+ T& move(T& rectangle, orientation_2d, 
        coordinate_difference displacement)</td>
 <td>Adds displacement value to interval indicated by orientation_2d of an
 object that models rectangle.</td>
 </tr>
 <tr>
 <td width="586">template <typename
- rectangle_type, typename point_type> 
- rectangle_type& convolve(rectangle_type& rectangle, 
-                        
- const point_type& point)</td>
+ rectangle_type, typename point_type> 
+ rectangle_type& convolve(rectangle_type& rectangle, 
+                        
+const point_type& point)</td>
 <td>Convolves coordinate values of point with x interval and y interval  of an
 object that models rectangle.</td>
 </tr>
 <tr>
 <td width="586">template <typename
- rectangle_type, typename point_type> 
- rectangle_type& deconvolve(rectangle_type& rectangle, 
-                          
- const point_type& point)</td>
+ rectangle_type, typename point_type> 
+ rectangle_type& deconvolve(rectangle_type& rectangle, 
+                          
+const point_type& point)</td>
 <td>Deconvolves coordinate values of point withx interval and y interval  of
 an object that models rectangle.</td>
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& convolve(T1& a, const T2& b)</td>
 <td>Convolves x interval  of b with x interval  of a and
 convolves y
@@ -407,14 +431,14 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& deconvolve(T1& a, const T2& b)</td>
 <td>Deconvolves x interval  of b with x interval  of a and
 deconvolves y interval  of b with y interval  of a. </td>
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& reflected_convolve(T1& a, const T2& b)</td>
 <td>Reflected convolves y interval  of b with x interval  of a and
 reflected convolves x
@@ -422,15 +446,15 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T1& reflected_deconvolve(T1& a, const T2& b)</td>
 <td>Reflected deconvolves y interval  of b with x interval  of a and
 reflected deconvolves x interval  of b with y interval  of a.</td>
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename point_type> 
- coordinate_difference euclidean_distance(const T&, 
+ typename point_type> 
+ coordinate_difference euclidean_distance(const T&, 
        const point_type& point,
 orienation_2d)</td>
 <td>Returns the distance from an object that models rectangle to an
@@ -439,8 +463,8 @@
 </tr>
 <tr>
 <td width="586">template <typename T1,
- typename T2> 
- coordinate_difference euclidean_distance(const T1& a, 
+ typename T2> 
+ coordinate_difference euclidean_distance(const T1& a, 
        const T2& b, orienation_2d)</td>
 <td>Returns the distance from an object that models rectangle to an
 object that models rectangle along the given orientation.  Returns
@@ -448,8 +472,8 @@
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename point_type> 
- coordinate_difference square_euclidean_distance(const T&, 
+ typename point_type> 
+ coordinate_difference square_euclidean_distance(const T&, 
        const point_type& point)</td>
 <td>Returns the square of the Euclidean distance between a point and a
 rectangle.  Returns zero if the point is contained within the
@@ -457,50 +481,50 @@
 </tr>
 <tr>
 <td width="586">template <typename T1,
- typename T2> 
- coordinate_difference square_euclidean_distance 
+ typename T2> 
+ coordinate_difference square_euclidean_distance 
        (const T1& a, const T2& b)</td>
 <td>Returns the square of the Euclidean distance between rectangles a
 and b.  Returns zero if the rectangles intersect.</td>
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename point_type> 
- coordinate_difference manhattan_distance(const T&, 
+ typename point_type> 
+ coordinate_difference manhattan_distance(const T&, 
        const point_type& point)</td>
 <td>Returns the Manhattan distance between a point and a rectangle. 
 Returns zero if the point is contained within the rectangle.</td>
 </tr>
 <tr>
 <td width="586">template <typename T1,
- typename T2> 
- coordinate_difference manhattan_distance(const T1& a, 
-                                         
- const T2& b)</td>
+ typename T2> 
+ coordinate_difference manhattan_distance(const T1& a, 
+                                        
+const T2& b)</td>
 <td>Returns the Manhattan distance between rectangles a and b. 
 Returns zero if the rectangles intersect.</td>
 </tr>
 <tr>
 <td width="586">template <typename T,
- typename point_type> 
- coordinate_distance euclidean_distance(const T&, 
+ typename point_type> 
+ coordinate_distance euclidean_distance(const T&, 
        const point_type& point)</td>
 <td>Returns the Euclidean distance between a point and a rectangle. 
 Returns zero if the point is contained within the rectangle.</td>
 </tr>
 <tr>
 <td width="586">template <typename T1,
- typename T2> 
- coordinate_distance euclidean_distance(const T1& a, 
-                                         
- const T2& b)</td>
+ typename T2> 
+ coordinate_distance euclidean_distance(const T1& a, 
+                                        
+const T2& b)</td>
 <td>Returns the Euclidean distance between rectangles a and b. 
 Returns zero if the rectangles intersect.</td>
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
- bool intersects(const T1& a, const T2& b, 
+ T2> 
+ bool intersects(const T1& a, const T2& b, 
               
 bool consider_touch = true)</td>
 <td>Returns true if two objects that model rectangle overlap.  If
@@ -509,10 +533,10 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
- bool boundaries_intersect(const T1& a, const T2& b, 
-                         
- bool consider_touch = true)</td>
+ T2> 
+ bool boundaries_intersect(const T1& a, const T2& b, 
+                         
+bool consider_touch = true)</td>
 <td>Returns true is two objects that model rectangle partially overlap
 such that one there is an intersection between the edges of the two
 rectangles  If the consider_touch flag is true a coordinate is
@@ -521,8 +545,8 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
- bool abuts(const T1& a, const T2& b, 
+ T2> 
+ bool abuts(const T1& a, const T2& b, 
           direction_2d dir)
 </td>
 <td>Returns true if rectangle b abuts but down not overlap rectangle a
@@ -530,8 +554,8 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
- bool abuts(const T1& a, const T2& b, 
+ T2> 
+ bool abuts(const T1& a, const T2& b, 
           orientation_2d)
 </td>
 <td>Returns true if rectangle b abuts but down not overlap rectangle a
@@ -539,15 +563,15 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 bool abuts(const T1& a, const T2& b)</td>
 <td>Returns true if rectangle b abuts but down not overlap rectangle a
 on any side.</td>
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
- bool intersect(T1& a, const T2& b, orientation_2d 
+ T2> 
+ bool intersect(T1& a, const T2& b, orientation_2d 
              
 bool consider_touch = true) </td>
 <td>Sets rectangle a to the intersection of rectangle a and interval b
@@ -558,8 +582,8 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
- bool intersect(T1& a, const T2& b, 
+ T2> 
+ bool intersect(T1& a, const T2& b, 
              
 bool consider_touch = true) </td>
 <td>Sets rectangle a to the intersection of rectangle a and rectangle b
@@ -569,84 +593,84 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 T& generalized_intersect(T1& a, const T2& b)</td>
 <td>Same as intersect, but if they do not intersect set a to the
 rectangle between a and b by applying generalized_intersect() on the
 intervals of the rectangles.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& bloat(T& rectangle, coordinate_type)</td>
 <td>Bloats x and y intervals of rectangle by coordinate value.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& bloat(T& rectangle, direction_2d, coordinate_type)</td>
 <td>Bloats side of rectangle specified by direction_2d by coordinate
 value.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& bloat(T& rectangle, orientation_2d, coordinate_type)</td>
 <td>Bloats interval of rectangle specified by orientation_2d by
 coordinate value.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& shrink(T& rectangle, coordinate_type)</td>
 <td>Shrinks x and y intervals of rectangle by coordinate value.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& shrink(T& rectangle, direction_2d, coordinate_type)</td>
 <td>Shrinks side of rectangle specified by direction_2d by coordinate
 value.</td>
 </tr>
 <tr>
- <td width="586">template <typename T> 
+ <td width="586">template <typename T> 
 T& shrink(T& rectangle, orientation_2d, coordinate_type)</td>
 <td>Shrinks interval of rectangle specified by orientation_2d by
 coordinate value.</td>
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
+ T2> 
 bool encompass(T1& a, const T2& b)</td>
 <td>The x and y intervals of a are set to encompass the x and y
 intervals of b respectively.</td>
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- point_type> 
+ point_type> 
 bool encompass(T& rectangle, const point_type& point)</td>
 <td>The x and y intervals of rectangle are set to encompass the x and y
 coordinates of point respectively.</td>
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- interval_type> 
+ interval_type> 
 bool encompass(T& rectangle, const interval_type& i,
-                orientation_2d)</td>
+                orientation_2d)</td>
 <td>The interval of rectangle specified by orientation_2d is set to encompass the
 interval i.</td>
 </tr>
 <tr>
 <td width="586">template <typename T, typename
- point_type> 
+ point_type> 
 bool get_corner(point_type& point, const T& rectangle, 
-                
+                
 direction_2d, direction_1d)</td>
 <td>Sets point to the corner of the rectangle you reach if you look at
 its side specified by direction_2d from within the rectangle and turn in
 the direction_1d direction (low == left, high = right).  Always
 returns true.</td>
 </tr>
-</table>
+</tbody></table>
 <h1>Rectangle Data</h1>


-The library provides a model of rectangle concept declared
+The library provides a model of rectangle concept declared

template<typename T> rectangle_data where T is the coordinate type.
This data type is used internally when a rectangle is needed and is available
@@ -654,8 +678,8 @@
instead of providing their own.  The data type is implemented to be
convenient to use with the library traits.
<h2>Members</h2>
-<table border="1" width="100%" id="table2">
- <tr>
+<table id="table2" border="1" width="100%">
+ <tbody><tr>
 <td width="586">geometry_type</td>
 <td>rectangle_concept</td>
 </tr>
@@ -675,8 +699,8 @@
 </tr>
 <tr>
 <td width="586">template <typename T1, typename
- T2> 
- rectangle_data(const T1& horizontal_interval, 
+ T2> 
+ rectangle_data(const T1& horizontal_interval, 
              
 const T2& vertical_interval)</td>
 <td>Constructs a rectangle with two objects
@@ -694,19 +718,19 @@
 </tr>
 <tr>
 <td width="586">template <typename T2>
- rectangle_data& 
+ rectangle_data& 
 operator=(const T2& that) const</td>
 <td>Assign from an object that is a model of rectangle.</td>
 </tr>
 <tr>
 <td width="586">template <typename T2>
- bool
+ bool
 operator==(const T2& that) const</td>
 <td>Compare equality to an object that is a model of rectangle.</td>
 </tr>
 <tr>
 <td width="586">template <typename T2>
- bool
+ bool
 operator!=(const T2& that) const</td>
 <td>Compare inequality to an object that is a model of rectangle.</td>
 </tr>
@@ -716,35 +740,15 @@
 <td>Get the interval in the given orientation.</td>
 </tr>
 <tr>
- <td width="586">template <typename T2> 
+ <td width="586">template <typename T2> 
 void set(orientation_2d orient, const T2& value)</td>
 <td>Sets the interval in the given orientation to the value of an object
 that models interval.</td>
 </tr>
- </table>
- <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" 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 © 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">
- LICENSE_1_0.txt</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>)</td>
- </tr>
-</table>
-
-</html>
\ No newline at end of file
+ </td></tr></tbody></table></body></html>
\ No newline at end of file

Added: trunk/libs/polygon/doc/gtl_segment_concept.htm
==============================================================================
--- (empty file)
+++ trunk/libs/polygon/doc/gtl_segment_concept.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -0,0 +1,492 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html xmlns="http://www.w3.org/1999/xhtml" xml: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" lang="en"><head>
+<title>Boost Polygon Library: Segment Concept</title>
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body>
+<table style="margin: 0pt; padding: 0pt; width: 100%;" border="0" cellpadding="0" cellspacing="0">
+
+ <tbody>
+ <tr>
+ <td style="background-color: rgb(238, 238, 238);" valign="top" nowrap="1">
+ <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>Boost.Polygon Main Page</li>
+ <li>Design Overview</li>
+ <li>Isotropy</li>
+ <li>Coordinate Concept</li>
+ <li>Interval Concept</li>
+ <li>Point Concept 
+ </li>
+ <li>Segment Concept</li>
+ <li>Rectangle Concept</li>
+ <li>Polygon 90 Concept</li>
+ <li><a href="gtl_polygon_90_with_holes_concept.htm">Polygon 90
+With Holes Concept</a></li>
+ <li>Polygon 45 Concept</li>
+ <li><a href="gtl_polygon_45_with_holes_concept.htm">Polygon 45
+With Holes Concept</a></li>
+ <li>Polygon Concept</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>Polygon Set Concept</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>Property Merge 90</li>
+ <li>Property Merge 45</li>
+ <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+ </a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+ </a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+ </ul>
+ <h3 class="navbar">Other Resources</h3>
+ <ul>
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+Presentation</a></li>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</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%"> 
+ 
+ <h1>Segment Concept</h1>
+ 
+ The segment concept tag is segment_concept
+ To register a user defined type as a model of the segment
+concept, specialize the geometry concept meta-function for that
+type.  In the example below CSegment is registered as a model of
+the segment concept.
+ template <> 
+struct geometry_concept<CSegment>
+{ typedef segment_concept type; };
+ The semantic of a segment is
+that it has a low and high point.  A
+std::pair<Point, Point>,
+boost::tuple<Point, Point> or boost::array<Point, 2> could all be made models of
+segment by simply providing indirect access to their elements through
+traits, however, these objects cannot be made a model of both segment
+and rectangle in the same compilation unit, for obvious reason that
+duplicate specialization of the geometry_concept struct is illegal, but
+also because it would make overloading generic function by concept
+ambiguous if a type modeled more than one concept.
+ Below is shown the default
+segment traits. Specialization of these traits is required for
+types that don't conform to the default behavior.
+
+
+ template <typename Segment> 
+ struct segment_traits { 
+   typedef typename Segment::coordinate_type coordinate_type; 
+   typedef typename Segment::point_type point_type; 
+ 
+   static inline point_type get(const Segment& segment, direction_1d dir) { 
+     return segment.get(dir); 
+   } 
+ }; 
+ template <typename Segment> 
+struct segment_mutable_traits { 
+  typedef typename segment_traits<Segment>::point_type point_type; 
+ 
+  static inline void set(Segment& segment, direction_1d dir, const point_type& point) { 
+    segment.set(dir, p); 
+  } 
+ 
+  static inline Segment construct(const point_type& low, const point_type& high) { 
+    return Segment(low, high); 
+  } 
+};<h2>Functions</h2>
+ <table style="width: 100%;" id="table1" border="1">
+ <tbody>
+ <tr>
+ <td width="586">template
+<typename Segment> point_type get(const Segment& segment, direction_1d dir)</td>
+ <td>Returns the low or high endpoint of an object that models a segment, depending on
+the direction_1d value. </td>
+ </tr>
+ <tr>
+ <td width="586">template
+<typename Segment, typename Point> 
+void set(Segment& segment, direction_1d dir, 
+         const Point& point)</td>
+ <td>Sets the low or high endpoint of an object that models a segment to an object that models a
+point, depending on the direction_1d value.</td>
+ </tr>
+ <tr>
+ <td width="586">template <typename Segment, typename Point1, typename Point2> 
+Segment construct(const Point1& low, const Point2& high)</td>
+ <td>Constructs an object that is a model of segment given the two objects that are models of point.</td>
+ </tr>
+ <tr>
+ <td>template <typename Segment1, typename Segment2> Segment1 copy_construct(const Segment2& segment)</td>
+ <td style="text-align: left;">Copy constructs an object that is a model of segment given another segment.</td>
+ </tr>
+<tr>
+ <td width="586">template
+<typename Segment1, typename Segment2> 
+ Segment1& assign(Segment1& segment1, 
+                 const Segment2& segment2)</td>
+ <td>Copies data from the second object that models a segment into
+the first object that models a segment.</td>
+ </tr>
+ <tr>
+ <td width="586">template
+<typename Segment1, typename Segment1> 
+bool equivalence(const Segment1& segment1, 
+                 const Segment1& segment2)</td>
+ <td>Given two objects that model a segment, compares and
+returns true if their low and high values are respectively equal.</td>
+ </tr>
+ <tr>
+ <td>template <typename Segment, typename Point> 
+ int orientation(const Segment& segment, 
+                 const Point& point) 
+ </td>
+ <td>Implements
+a robust orientation test for two objects that model segment and point.
+Returns 0, if the point is collinear to the segment. 
+Returns 1, if the point lies to the left of the segment. 
+Returns -1, if the point lies to the right of the segment. 
+
+ </td>
+ </tr>
+ <tr>
+ <td>template <typename Segment1, typename Segment2> 
+
+ int orientation(const Segment1& segment1, 
+
+                 const Segment2& segment2)</td>
+ <td>Implements a robust orientation test for two objects
+that are models of segment. Note: the segments are treated as math.
+vectors. 
+Returns 0, if the segments are collinear. 
+Returns 1, if the second segment is CCW oriented to the first segment. 
+Returns -1, if the second segment is CW oriented to the first segment. 
+ </td>
+ </tr>
+<tr>
+ <td>template <typename Segment, typename Point> 
+ bool contains(const Segment& segment, 
+     const Point& value, bool consider_touch) 
+ </td>
+ <td>Returns true if an object that is a model of segment contains an object that is a model of point, else false. 
+ </td>
+ </tr>
+ <tr>
+ <td>template <typename Segment1, typename Segment2> 
+
+ bool contains(const Segment1& segment1, 
+
+     const Segment2& segment2, bool consider_touch)</td>
+ <td>Returns true if the first object contains the second one, else false. Both objects model a segment. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">template <typename Segment> 
+point_type low(const Segment& segment) 
+ </td>
+ <td>Returns the low endpoint of an object that is a model of segment. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">template <typename Segment> 
+point_type high(const Segment& segment)</td>
+ <td>Returns the high endpoint of an object that is a model of segment. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">template <typename Segment> 
+point_type center(const Segment& segment)</td>
+ <td>Returns the central point of an object that is a model of segment. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">template <typename Segment, typename Point> void low(Segment& segment, const Point& point)</td>
+ <td>Sets the low endpoint of an object that is a model of segment. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">template <typename Segment, typename Point> 
+void high(Segment& segment, const Point& point)</td>
+ <td>Sets the high endpoint of an object that is a model of segment. 
+ </td>
+ </tr>
+ <tr>
+ <td>template <typename Segment> 
+ distance_type length(const Segment& segment) 
+ </td>
+ <td>Returns length of an object that is a model of segment. 
+ </td>
+ </tr>
+
+
+
+
+ <tr>
+ <td width="586">template
+<typename Segment> Segment& scale_up(Segment& segment,     unsigned_area_type factor)</td>
+ <td>Multiplies x and y coordinates of both endpoints of an object that is a model of segment by unsigned factor.</td>
+ </tr>
+ <tr>
+ <td width="586">template
+<typename Segment> 
+ Segment& scale_down(Segment& segment, 
+    unsigned_area_type factor)</td>
+ <td>Divides x and y coordinates of both endpoints of an object that is a model of segment by unsigned factor.</td>
+ </tr>
+ <tr>
+ <td width="586">template
+<typename Segment, typename Scale> 
+ Segment& scale(Segment& segment, const Scale& sc) </td>
+ <td>Calls
+the scale member function of the scaling type on the low and high endpoint of
+an object that is a model of segment and updates the segment with the
+scaled endpoints.</td>
+ </tr>
+ <tr>
+ <td width="586">template
+<typename Segment, typename Transform> Segment& transform(Segment& segment, const Transform& tr) </td>
+ <td>Calls the transform member function of transform type
+on the low and high endpoints of an object that is a model of segment and updates the segment with the transformed endpoints.</td>
+ </tr>
+ <tr>
+ <td width="586">template
+<typename Segment> 
+ Segment& move(Segment& segment, orientation_2d 
+    coordinate_difference displacement)</td>
+ <td>Adds displacement value to the x or y coordinates of both endpoints of an object
+that is a model of segment indicated by the orientation_2d.</td>
+ </tr>
+ <tr>
+ <td width="586">template
+<Segment, Point> 
+ Segment& convolve(Segment& segment, const Point& point)</td>
+ <td>Convolves both endpoints of an object that models a segment with an object that models a point. 
+</td>
+ </tr>
+ <tr>
+ <td width="586">template
+<Segment, Point> 
+ Segment& deconvolve(Segment& segment, const Point& point)</td>
+ <td>Deconvolves both endpoints of an object that models a segment with an object that models a point. </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">template <typename Segment1, typename Segment2> 
+
+
+bool abuts(const Segment1& segment1, 
+
+
+    const Segment2& segment2, direction_1d dir)</td>
+ <td>Returns true if two objects that model a segment abut, depending on the direction_1d value.</td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">template <typename Segment1, typename Segment2> 
+
+bool abuts(const Segment1& segment1, 
+
+           const Segment2& segment2)</td>
+ <td>Returns true if two objects that model a segment abut: either the first one to the second one or vice versa.</td>
+ </tr>
+
+
+ <tr>
+ <td>template <typename Segment1, typename Segment2> 
+ bool intersects(const Segment1& segment1, 
+                 const Segment2& segment2, 
+                bool consider_touch) 
+ </td>
+ <td>Returns true if two objects that model a segment intersect, else false. 
+ </td>
+ </tr>
+
+
+<tr>
+ <td style="font-family: Courier New,Courier,monospace;">template
+<typename Segment, typename Point> distance_type euclidean_distance( 
+    const Segment& segment, const Point& point)
+ </td>
+ <td>Returns distance from an object that is a model of segment
+to an object that is a model of point.
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">template
+<typename Segment1, typename Segment2> distance_type euclidean_distance( 
+    const Segment1& segment1, const Segment2& segment2)
+ </td>
+ <td>Returns distance between two objects that are models of segment.
+ </td>
+ </tr>
+
+
+
+
+ </tbody>
+ </table>
+ <h1>Segment Data</h1>
+ 
+ The library provides a model of the segment concept declared template<typename T> segment_data where
+T is the coordinate type.
+ This data type is used internally when a segment is needed and
+is available to the library user who finds it convenient to use a
+library segment data type instead of providing their own.  The data
+type is implemented to be convenient to use with the library traits.<h2>Members</h2>
+ <table style="width: 100%;" id="table2" border="1">
+ <tbody>
+ <tr>
+ <td width="586">geometry_type</td>
+ <td>segment_concept</td>
+ </tr>
+ <tr>
+ <td width="586">coordinate_type</td>
+ <td>T</td>
+ </tr>
+ <tr>
+ <td>point_type</td>
+ <td>point_data<T> 
+ </td>
+ </tr>
+<tr>
+ <td width="586">segment_data()</td>
+ <td>Default constructor.</td>
+ </tr>
+ <tr>
+ <td width="586">segment_data(const point_type& low, 
+             const point_type& high)</td>
+ <td>Constructs a segment from the given endpoints.</td>
+ </tr>
+ <tr>
+ <td width="586">segment_data(const segment_data& that)</td>
+ <td>Copy constructor.</td>
+ </tr>
+ <tr>
+ <td width="586">segment_data& operator=(const segment_data& that)</td>
+ <td>Assignment operator.</td>
+ </tr>
+ <tr>
+ <td width="586">template
+<typename Segment> 
+ segment_data& operator=(const Segment& that)
+const</td>
+ <td>Assign from an object that is a model of segment.</td>
+ </tr>
+ <tr>
+ <td width="586">bool operator==(const segment_data& that) const</td>
+ <td>Equality operator overload.</td>
+ </tr>
+ <tr>
+ <td width="586"> bool operator!=(const segment_data& that) const</td>
+ <td>Inequality operator overload.</td>
+ </tr>
+ <tr>
+ <td width="586"> bool operator<(const segment_data& that) const</td>
+ <td>Less operator overload. Compares low endpoints then high endpoints to break ties. 
+</td>
+ </tr>
+ <tr>
+ <td width="586"> bool operator<=(const segment_data& that) const</td>
+ <td>Less or equal operator overload. Compares low endpoints then high endpoints to break ties. 
+</td>
+ </tr>
+ <tr>
+ <td width="586"> bool operator>(const segment_data& that) const</td>
+ <td>Greater operator overload. Compares low endpoints then high endpoints to break ties. 
+</td>
+ </tr>
+ <tr>
+ <td width="586"> bool operator>=(const segment_data& that) const</td>
+ <td>Greater or equal operator overload. Compares low endpoints then high endpoints to break ties. 
+</td>
+ </tr>
+ <tr>
+ <td width="586">point_type get(direction_1d dir) const</td>
+ <td>Retrieves the low/high endpoint considering direction value.</td>
+ </tr>
+ <tr>
+ <td width="586">point_type low() const</td>
+ <td>Retrieves the low endpoint.</td>
+ </tr>
+ <tr>
+ <td width="586">point_type high() const</td>
+ <td>Retrieves the high endpoint.</td>
+ </tr>
+ <tr>
+ <td width="586">void set(direction_1d dir, const point_type& point)</td>
+ <td>Sets the endpoint in the given direction.</td>
+ </tr>
+ <tr>
+ <td width="586">segment_data& low(const point_type& point)</td>
+ <td>Sets the low endpoint.</td>
+ </tr>
+ <tr>
+ <td width="586">segment_data& high(const point_type& point)</td>
+ <td>Sets the high endpoint.</td>
+ </tr>
+ </tbody>
+ </table>
+ </td>
+ </tr>
+ <tr>
+ <td style="background-color: rgb(238, 238, 238);" valign="top" nowrap="1">  </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"> LICENSE_1_0.txt</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>)</td>
+ </tr>
+ </tbody>
+ </table>
+ </td>
+ </tr>
+ </tbody>
+</table>
+
+</body></html>
\ No newline at end of file

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Modified: trunk/libs/polygon/doc/index.htm
==============================================================================
--- trunk/libs/polygon/doc/index.htm (original)
+++ trunk/libs/polygon/doc/index.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -2,41 +2,71 @@
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"><head>
-<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>
+--><title>Boost Polygon Library: Main Page</title>
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /></head><body><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 ;">
+ <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>Boost.Polygon Main Page</li>
- <li>Design Overview</li>
- <li>Isotropy</li>
+ <li>Design Overview</li>
+ <li>Isotropy</li>
 <li>Coordinate Concept</li>
 <li>Interval Concept</li>
- <li>
- Point Concept</li>
- <li>Rectangle Concept</li>
- <li>Polygon 90 Concept</li>
- <li>Polygon 90 With Holes Concept</li>
- <li>Polygon 45 Concept</li>
- <li>Polygon 45 With Holes Concept</li>
- <li>Polygon Concept</li>
- <li>Polygon With Holes Concept</li>
- <li>Polygon 90 Set Concept</li>
- <li>Polygon 45 Set Concept</li>
- <li>Polygon Set Concept</li>
- <li>Connectivity Extraction 90</li>
- <li>Connectivity Extraction 45</li>
- <li>Connectivity Extraction</li>
- <li>Property Merge 90</li>
- <li>Property Merge 45</li>
- <li>Property Merge</li>
+ <li>Point Concept</li>
+ <li>Segment Concept</li>
+
+ <li>Rectangle Concept</li>
+ <li>Polygon 90 Concept</li>
+ <li>Polygon 90 With Holes Concept</li>
+ <li>Polygon 45 Concept</li>
+ <li>Polygon 45 With Holes Concept</li>
+ <li>Polygon Concept</li>
+ <li>Polygon With Holes Concept</li>
+ <li>Polygon 90 Set Concept</li>
+ <li>Polygon 45 Set Concept</li>
+ <li>Polygon Set Concept</li>
+ <li>Connectivity Extraction 90</li>
+ <li>Connectivity Extraction 45</li>
+ <li>Connectivity Extraction</li>
+ <li>Property Merge 90</li>
+ <li>Property Merge 45</li>
+ <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+</a></li>
+ <li>Voronoi Benchmark 
+ </li>
+
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+</a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils 
+ </li>
+
+
+
 </ul>
 <h3 class="navbar">Other Resources</h3>
 <ul>
@@ -46,18 +76,21 @@
 <li>Performance Analysis</li>
 <li>Layout Versus Schematic Tutorial</li>
 <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</li>
+ <li>Voronoi Advanced Tutorial</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">
+ <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%">



- 
+ 

<h1>THE BOOST.POLYGON LIBRARY</h1>
The Boost.Polygon library provides algorithms focused on manipulating planar
@@ -67,21 +100,38 @@
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
+Systems), VLSI CAD as well all 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.  <img border="0" src="images/hand.png" width="837" height="277">
-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 paper and
+implementing and interacting with polygon data structures and algorithms.  <img src="images/hand.png" border="0" height="277" width="837" />
+One of the important features of the library is the implementation of
+the generic sweepline algorithm to construct Voronoi diagrams of points and linear segments in 2D (developed
+as part of the GSoC 2010 program). Voronoi diagram data structure has
+applications in image segmentation, optical character recognition,
+nearest neighbor queries execution. It is closely related with the other
+computational geometry concepts: Delaunay triangulation, medial axis,
+straight skeleton, the largest empty circle. The Boost.Polygon library
+provides interface to construct Voronoi diagram of points figure a and
+line segments figure b (the last could be used to discretize any
+two-dimensional curve). Figure c contains the example of the medial axis of the
+non-convex polygon. The implementation outperforms most of the known
+commercial and non-commercial libraries in both efficiency and
+numerical robustness aspects. You may find more details on the topic at the Voronoi main page. 
+
+
+<img src="images/voronoi.png" border="0" height="300" width="900" />
+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 paper 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
@@ -95,40 +145,39 @@
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:colorscheme
- colors="#ffffff,#000000,#808080,#000000,#bbe0e3,#333399,#009999,#99cc00"/>
+<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">
+</p:colorscheme><div v:shape="_x0000_s1026" class="O">
+ <div style="text-align: justify;">
 
- 
- void foo(list<CPolygon>& result, const list<CPolygon>& a, 
-         
+ 
+ void foo(list<CPolygon>& result, const list<CPolygon>& a, 
+         
 
- 
+ 
 const list<CPolygon>&
 b, int deflateValue) { </div>
- <div style="text-align:justify;mso-char-wrap:1;mso-kinsoku-overflow:1">
+ <div style="text-align: justify;">
 
-    
+    
 CBoundingBox domainExtent; </div>
- <div style="text-align:justify;mso-char-wrap:1;mso-kinsoku-overflow:1">
+ <div style="text-align: justify;">
 
- 
-      using namespace boost::polygon::operators; </div>
- <div style="text-align:justify;mso-char-wrap:1;mso-kinsoku-overflow:1">
+ 
+      using namespace boost::polygon::operators; </div>
+ <div style="text-align: justify;">
 
- 
-     
+ 
+     
 boost::polygon::extents(domainExtent, a); </div>
- <div style="text-align:justify;mso-char-wrap:1;mso-kinsoku-overflow:1">
+ <div style="text-align: justify;">
 
- 
-      result += (b &
+ 
+      result += (b &
 domainExtent) ^ (a - deflateValue); </div>
- <div style="text-align:justify;mso-char-wrap:1;mso-kinsoku-overflow:1">
+ <div style="text-align: justify;">
 
- 
+ 
 }</div>
</div>
In the code snippet above the hypothetical polygon type CPolygon has been
@@ -139,10 +188,11 @@
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.
-<img border="0" src="images/foo.PNG" width="432" height="371">
-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 boost::polygon::operators
+<img src="images/foo.PNG" border="0" height="371" width="432" />
+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 boost::polygon::operators
so that they can be used outside the boost::polygon
namespace without bringing in the entire boost::polygon
namespace.  Following the
@@ -179,20 +229,27 @@
 <li>connectivity_extraction_usage.cpp
 Using the connectivity extraction algorithm to build a connectivity
 graph on polygons</li>
- <li>property_merge_usage.cpp
+
+ <li>property_merge_usage.cpp
 Using the n-layer map-overlay algorithm on polygon data</li>
+
 </ul>

-<li>Tutorials:
+</li><li>Tutorials:
<ul>
 <li>Layout Versus Schematic Learn how to
 apply Boost.Polygon capabilities to implement a simplified circuit
 extraction application</li>
 <li>Minkowski Sum Learn how to
 apply Boost.Polygon capabilities to implement Minkowski sum of polygon sets</li>
+ <li>Voronoi Basic Tutorial Learn how
+ to construct, traverse, visualize, associate data with Voronoi diagrams without digging into the library details.</li>
+ <li>Voronoi Advanced Tutorial
+ Learn how to configure the Voronoi builder and Voronoi diagram
+ data structure with the user provided coordinate types. </li>
</ul>

-</ul>
+</li></ul>

We would like to thank: Thomas Klimpel, Frank Mori Hess, Barend Gehrels,
@@ -206,17 +263,17 @@
process and Fernando Cacciola for graciously serving as review manager.

- <tr>
+ </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" rules="none" frame="void" id="table2">
+<table class="docinfo" id="table2" frame="void" rules="none">
 <colgroup>
- <col class="docinfo-name"><col class="docinfo-content">
+ <col class="docinfo-name" /><col class="docinfo-content" />
 </colgroup>
- <tbody vAlign="top">
+ <tbody valign="top">
 <tr>
 <th class="docinfo-name">Copyright:</th>
 <td>Copyright © Intel Corporation 2008-2010.</td>
@@ -229,6 +286,6 @@
 <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt>)</td>
 </tr>
-</table>
+</tbody></table>

-</html>
\ No newline at end of file
+</td></tr></tbody></table></body></html>
\ No newline at end of file

Added: trunk/libs/polygon/doc/voronoi_advanced_tutorial.htm
==============================================================================
--- (empty file)
+++ trunk/libs/polygon/doc/voronoi_advanced_tutorial.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -0,0 +1,481 @@
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html><head>
+
+
+ <meta http-equiv="Content-Type" content="text/html; charset=windows-1252"><title>Voronoi Advanced Tutorial</title></head><body>
+<h1>Voronoi Advanced Tutorial 
+</h1>
+
+This tutorial consists of two parts. The first one provides two
+examples of a real world problems that default configuration of Voronoi
+library is capable to solve. By default configuration we mean the one
+that accepts
+signed 32-bit integer and outputs floating-point (64-bit
+double) coordinates. We provide those examples to convince even the
+most skeptical users that they probably don't need to configure library
+for higher-precision input or output coordinate types. However if the
+posed problem really requires those, fully featured configuration of
+both input and output coordinate types is provided in the second part
+of this tutorial. 
+
+<h2>Red Planet</h2>
+
+<h3>Problem Statement</h3>
+
+<img style="width: 665px; height: 369px;" alt="" src="images/rover.jpg"> 
+
+ 
+
+Yes, we are going to talk about Mars. So lets imagine that NASA is
+planning to send a new robot to Mars. Each day center situated on Earth
+will send a destination point coordinates the robot needs to reach by
+the end of the day. Of course we'd like to save as much energy as
+possible thus choosing the shortest possible path. This would be a
+straight line in a perfect world (we don't consider curvature of
+surface), but situation becomes more complicated as there are some
+rocks and wells on Mars our robot can't go through. Behind of those our
+robot has some dimensions that might not allow it to pass narrow places. 
+
+<h3>Application of Voronoi diagram</h3>
+
+The problem above could be solved using Voronoi diagram. The first
+stage would be to discretize obstacles (rocks and wells) with
+polylines. Afterwards we will compute Voronoi diagram of the input set
+of segments. As each Voronoi edge is equidistant from the two closest
+sites we are able to filter edges the robot won't be able to pass due
+to it's dimensions. The last step would be to run a bit optimized A*
+algorithm to find
+the shortest or at least suboptimal path and we are done. 
+
+<h3>Discretization of input geometries</h3>
+
+To show how good is the default input coordinate type provided by the
+Voronoi library
+we will discretize the whole area of Mars. That will be approximately
+1.44 *  10^8  square kilometres that is equal to 1.44 * 
+10^18  square centimetres, which could be snapped to the integer
+grid with a side of 1.2 * 10^9 centimetres.  To make the Voronoi
+graph
+precise on the boundaries of that grid we will replicate input map 9
+times (3x3), thus Voronoi diagram within a central piece will
+provide us with a correct connectivity graph. This step will increase
+the size of our grid to 3.6 * 10^9 centimetres that is less than 2^32.
+So we are able to discretize the Red Planet's surface within a 1
+centimetre
+precision using the default input coordinate type (signed 32-bit
+integer). That would imply maximum absolute error to be
+equal up to 0.5 centimetres per coordinate. Considering the radius of
+our robot to be
+0.3 metres and for security reasons avoiding any large enough obstacles
+that are within 1 metre distance from it that error would be irrelevant. 
+
+<span style="color: rgb(0, 0, 0); font-family: sans-serif; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 13px; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; background-color: rgb(249, 249, 249); display: inline ! important; float: none;">
+<h3>Output analysis</h3>
+
+Estimates of the resulting Voronoi diagram precision were already
+explained here.
+So to avoid those computations again we will simply state that the
+maximum absolute error of the output geometries will be on the grid
+boundaries and will be equal to 2^-16 centimetres, which is
+approximately equal to 150 nanometres and is 100 times larger than
+a radius of a complex molecule. We would like to notice that the
+absolute error of the discretization step is much higher than the one
+produced by the Voronoi diagram construction algorithm.
+<h2>VLSI Design</h2>
+
+<h3>Problem Statement</h3>
+
+<img style="width: 400px; height: 283px;" alt="" src="images/vlsi.jpg"> 
+
+ 
+
+Very-large-scale integration (VLSI) is the
+process of creating
+integrated circuits by combining thousands of transistors into a single
+chip. Considering the fact that it may take weeks or months to get an
+integrated circuit manufactured, designers often spend large amounts of
+time analyzing their layouts to avoid costly mistakes. One of the
+common static analysis checks is minimum distance requirement between
+the components of an integrated circuit (distance should be not less
+than
+specified value). 
+
+<h3>Application of Voronoi diagram</h3>
+
+It appears that the minimum distance between components of the input
+set of points and segments corresponds to the one of the Voronoi
+diagram edges. This means that we can iterate through each edge of
+the Voronoi graph, extract the pair of input geometries that form it
+and find
+the distance between those. As the total amount of such edges is O(N)
+value
+(N - is the number of input geometries) the minimum distance could be
+efficiently find in a linear time once we construct the diagram. 
+
+<h3>Discretization of input geometries</h3>
+
+The average size of the modern CPUs is around 2.5 x 2.5 centimetres.
+Snapping this to the 32-bit integer grid will give discretization
+precision of 2.5 / 2^33 centimetres or 3 picometres that is 10 times
+smaller value than radius of an atom. That would be probably good
+enough precision even for a few next generations of processors. 
+
+<h3>Output analysis</h3>
+
+The maximum absolute error of the output geometries will be 2.5 / 2^47
+centimetres or 0.2 femtometres that is 10 times smaller value than
+the radius of an electron. However in this particular case we are not
+interested in the precision of the output, rather in its topology. As
+it was noticed on
+the Voronoi main page very small edges
+are removed from the Voronoi diagram. However user should not worry
+because the edge that correspond to the minimal distance won't be among
+those. That means that we would be able to 100% correctly identify a
+pair of closest objects within the discretization precision. 
+
+<h2>Conclusions</h2>
+
+The above two examples show usage of the default Voronoi coordinate
+types
+in the macro and micro world. The main point of those was to give user
+understanding of a scale the default coordinate types provides. There
+are
+two main points we didn't mention before, but that would be relevant to
+the most real world problems: 
+
+<ul>
+
+ <li>The absolute error of the coordinates of the output Voronoi
+diagram
+inside the 32-bit integer discretization grid is slightly smaller than
+the absolute error of discretization itself, thus could be neglected at
+all.</li>
+ <li>In both problems above we didn't consider error of measurement.
+For example: is it possible to construct a map of the Mars within the
+0.5
+centimetres precision, or to get coordinates of the circuit parts
+withing the subatomic precision? I guess the answer for both questions
+would be "No". And that actually means that the error of the
+discretization
+step could be neglected comparing to the error produced by the
+measuring
+devices. 
+ </li>
+</ul>
+
+The second statement means that there is actually no point to provide
+implementation that operates with floating-point input coordinates,
+because those always could be snapped to the integer grid. In case you
+are not satisfied with the precision that the 32-bit integer grid
+provides or would like to retrieve coordinates of the output geometries
+within a smaller
+relative error, follow the next paragraph. 
+
+<h2>Voronoi Coordinate Types Configuration</h2>
+
+In the following chapter we are going to extend input coordinate type
+to the 48-bit signed
+integer and output coordinate type to the 80-bit IEEE floating-point
+type
+(long double). The code for this chapter is available in voroni_advanced_tutorial.cpp.
+While it won't be possible to compile it using the MSVC compiler (it
+doesn't
+support 80-bit long double type; ieee754.h header is required), it
+should give a clear understanding of how the library supports the user
+provided coordinate types. 
+
+ 
+
+So the main step would be to declare the voronoi coordinate type traits
+that satisfy set of restrictions explained here: 
+
+ 
+
+struct
+my_voronoi_ctype_traits { 
+
+ 
+typedef boost::int64_t int_type; 
+
+ 
+typedef detail::extended_int<3> int_x2_type; 
+
+ 
+typedef detail::extended_int<3> uint_x2_type; 
+
+ 
+typedef detail::extended_int<128> big_int_type; 
+
+ 
+typedef fpt80 fpt_type; 
+
+ 
+typedef fpt80 efpt_type; 
+
+ 
+typedef my_ulp_comparison ulp_cmp_type; 
+
+ 
+typedef my_fpt_converter to_fpt_converter_type; 
+
+ 
+typedef my_fpt_converter to_efpt_converter_type; 
+
+}; 
+ 
+It is always better to use C++ built-in types wherever it's
+possible. That's why we use the 64-bit signed integer type to handle
+our
+input coordinates. int_x2_type
+and uint_x2_type
+is required to handle 96-bit signed/unsigned integers. As there is no
+such built-in type we use library provided efficient fixed integer
+type.
+The big integer type should be capable to handle 48 * 64 bit integers,
+that is
+less than 32 * 128, and so far we are good with extended_int<128>
+type. We use the same floating point type for both fpt_type
+and efpt_type
+as it has enough exponent bits to represent both 48 * 32 bit and 48 *
+64 bit integers (that is also the reason we don't need two
+floating-point converter structures). The ulp_cmp_type
+structure checks weather two IEEE floating-point values are within the
+given signed integer ulp range (we won't analyze corresponding code
+here as it requires deep understanding of the <a href="http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html">floating-point
+architecture</a> and its <a href="../boost/polygon/detail/voronoi_ctypes.hpp">usage to compare
+floating-point values</a>), but just to mention the declaration is
+following: 
+
+ 
+
+struct
+my_ulp_comparison { 
+
+  enum
+Result { 
+    LESS = -1, 
+
+   
+EQUAL = 0, 
+
+   
+MORE = 1 
+
+  }; 
+
+  Result
+operator()(fpt80 a, fpt80 b, unsigned int maxUlps) const; 
+
+}; 
+ 
+The last step would be to declare the my_fpt_converter
+structure (converts the integer types to the floating-point type): 
+
+ 
+
+struct
+my_fpt_converter { 
+
+ 
+template <typename T> 
+
+  fpt80
+operator()(const T& that) const { 
+
+   
+return static_cast<fpt80>(that); 
+
+  } 
+
+ 
+
+ 
+template <size_t N> 
+
+  fpt80
+operator()(const typename detail::extended_int<N> &that)
+const { 
+
+   
+fpt80 result = 0.0; 
+
+   
+for (size_t i = 1; i <= (std::min)((size_t)3, that.size()); ++i) { 
+
+     
+if (i != 1) 
+
+       
+result *= static_cast<fpt80>(0x100000000ULL); 
+
+     
+result += that.chunks()[that.size() - i]; 
+
+   
+} 
+
+   
+return (that.count() < 0) ? -result : result; 
+
+  } 
+
+}; 
+ 
+At this point we are done with declaration of the Voronoi
+coordinate type traits. The next step is to declare the Voronoi diagram
+traits: 
+
+ 
+
+struct
+my_voronoi_diagram_traits { 
+
+ 
+typedef fpt80 coordinate_type; 
+
+ 
+typedef struct { 
+
+   
+template <typename CT> 
+
+   
+fpt80 operator()(const CT& that) const { 
+
+     
+return static_cast<fpt80>(that); 
+
+   
+} 
+
+  }
+ctype_converter_type; 
+
+ 
+typedef detail::point_2d<coordinate_type> point_type; 
+
+ 
+typedef voronoi_cell<coordinate_type> cell_type; 
+
+ 
+typedef voronoi_vertex<coordinate_type> vertex_type; 
+
+ 
+typedef voronoi_edge<coordinate_type> edge_type; 
+
+ 
+typedef struct { 
+
+  public: 
+
+   
+enum { ULPS = 128 }; 
+
+   
+bool operator()(const point_type &v1, const point_type &v2)
+const { 
+
+     
+return (ulp_cmp(v1.x(), v2.x(), ULPS) == my_ulp_comparison::EQUAL
+&& 
+
+             
+ulp_cmp(v1.y(), v2.y(), ULPS) == my_ulp_comparison::EQUAL); 
+
+   
+} 
+
+ 
+private: 
+
+   
+my_ulp_comparison ulp_cmp; 
+
+  }
+vertex_equality_predicate_type; 
+
+}; 
+
+ 
+
+Above we simply declared the Voronoi primitive types, type converter
+and vertex
+equality predicate using the new coordinate type and corresponding ulp
+comparison structure. As we are done with the declaration of the
+coordinate
+type specific structures we are ready to proceed to the construction
+step itself. The first step would be to initialize voronoi_builder
+structure with a set of random points: 
+
+ 
+
+// Random
+generator and distribution. MAX is equal to 2^48. 
+
+boost::mt19937_64
+gen(std::time(0)); 
+
+boost::random::uniform_int_distribution<boost::int64_t>
+distr(-MAX, MAX-1); 
+// Declaring and configuring Voronoi builder with the new coordinate
+type traits. 
+voronoi_builder<boost::int64_t, my_voronoi_ctype_traits> vb; 
+
+// Voronoi
+builder initialization step. 
+for (size_t i = 0; i < GENERATED_POINTS; ++i) { 
+
+ 
+boost::int64_t x = distr(gen); 
+
+ 
+boost::int64_t y = distr(gen); 
+
+ 
+vb.insert_point(x, y); 
+
+} 
+ 
+The second step would be to generate the Voronoi diagram and
+this is done as before with the two lines of code: 
+
+ 
+
+// Declaring
+and configuring Voronoi diagram structure with the new coordinate type
+traits. 
+voronoi_diagram<fpt80, my_voronoi_diagram_traits> vd; 
+
+vb.construct(&vd); 
+ 
+From this point the user can operate with the Voronoi diagram
+data structure
+and in our tutorial we output some simple stats of the resulting
+Voronoi graph. Probably the hardest part of this tutorial is
+the declaration of the ulp comparison structure. The library provides
+efficient well-commented cross-platform implementation for 64-bit
+floating-point type (double). So the best advice would be to follow
+that implementation, but before doing that really consider if  the
+default
+coordinate types are not capable to solve your problem. 
+
+ 
+
+<table class="docinfo" id="table1" 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 © Andrii Sydorchuk 2010-2012.</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"> LICENSE_1_0.txt</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>)</td>
+ </tr>
+ </tbody>
+</table>
+
+</body></html>
\ No newline at end of file

Added: trunk/libs/polygon/doc/voronoi_basic_tutorial.htm
==============================================================================
--- (empty file)
+++ trunk/libs/polygon/doc/voronoi_basic_tutorial.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -0,0 +1,360 @@
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html><head>
+
+
+
+
+
+
+
+
+
+ <meta http-equiv="Content-Type" content="text/html; charset=windows-1252"><title>Voronoi Basic Tutorial</title><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body>
+<h1>Voronoi Basic Tutorial 
+</h1>
+
+In this tutorial we will cover the basic usage of the Boost.Polygon
+Voronoi library that should be enough for the 95% of cases. Below we will
+discuss the following topics: 
+
+
+<ul>
+
+ <li>preparing input geometries; 
+ </li>
+ <li>Voronoi diagram construction;</li>
+
+ <li>Voronoi graph traversal; 
+ </li>
+
+ <li>associating the user data with the Voronoi primitives;</li>
+ <li>Voronoi diagram discretization and rendering.</li>
+</ul>
+
+In the example that goes through this tutorial (voronoi_basic_tutorial.cpp)
+we
+are going to construct the Voronoi diagram of a few points and
+segments.
+On the image below one may see the corresponding rendered Voronoi
+graph. The primary Voronoi edges
+are marked with
+the black color, non-primary with green, input geometries have blue
+color. In
+case you forgot, we split each input segment onto three sites (segment
+itself and both endpoints), edges that go between those sites are
+considered to be non-primary. 
+
+ 
+
+<img style="border: 2px solid ; width: 300px; height: 300px;" alt="" src="images/voronoi4.png"> 
+
+ 
+
+And before you proceed don't forget to: 
+ 
+#include "boost/polygon/voronoi.hpp" 
+using boost::polygon; 
+
+<h2>Preparing Input Geometries</h2>Below is the example of how the user provided point and segment classes might look like: 
+ struct Point {   int a; 
+  int b; 
+  Point (int x, int y) : a(x), b(y) {} 
+
+}; 
+ struct Segment { 
+
+  Point p0; 
+  Point p1; 
+  Segment (int x1, int y1, int x2, int y2) : p0(x1, y1), p1(x2, y2) {} 
+
+
+}; 
+ 
+As we are going to use the default routines defined in the
+voronoi.hpp header to construct the Voronoi diagram, we are required to map
+our point and segment classes to the corresponding Boost.Polygon concepts: 
+ 
+<span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;">template <><span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;"> 
+struct geometry_concept<Point> { typedef point_concept type; };<br style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium;"><span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;"><span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! imp
ortant; float: none;">   <span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;"><br style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium;"><span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inli
ne ! important; float: none;">template <><br style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium;"><span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;">struct point_traits<Point<span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal;
widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;">> {<br style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium;"><span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;">  typedef int coordinate_type;<span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows:
2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;"> 
+    <br style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium;"><span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;">  static inline coordinate_type get(const Point<span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-tra
nsform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;">& point, <span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;">orientation_2d orient) { 
+    return <span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;">(orient == HORIZONTAL) ? point.a : point.b;<span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;"><br style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spaci
ng: 0px; font-size: medium;"><span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;">  } 
+}; 
+<span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;">
+ 
+template <> 
+<span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;">struct geometry_concept<Segment> { typedef segment_concept type; }; 
+ 
+<span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;">template <><br style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium;">
+<span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;">struct point_traits<Segment<span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;">> {<br style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: norm
al; widows: 2; word-spacing: 0px; font-size: medium;">
+<span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;">  typedef int coordinate_type; 
+  typedef Point point_type;<br style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium;">
+
+<span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;">    <br style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium;">
+<span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;">  static inline coordinate_type get(const Segment<span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;">& segment, direction_1d dir<span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: norm
al; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;">) { 
+    return <span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;">dir.to_int() ? segment.p1() : segment.p0();<span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;"><br style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spaci
ng: 0px; font-size: medium;">
+<span style="color: rgb(0, 0, 0); font-family: 'Courier New'; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; font-size: medium; display: inline ! important; float: none;">  } }; 
+ 
+It's also possible to use the native Boost.Polygon types as point_data and segment_data, that won't require the above mapping. 
+ 
+So once we are done we can create the sample input: 
+
+ 
+
+std::vector<Point>
+points; 
+points.push_back(Point(0, 0)); 
+points.push_back(Point(1, 6)); 
+std::vector<Segment> segments; 
+segments.push_back(Segment(-4, 5, 5, -1)); 
+segments.push_back(Segment(3, -11, 13, -1)); 
+
+<h2>Construction of the Voronoi Diagram 
+</h2>At this point we are ready to construct the Voronoi diagram: 
+ 
+
+voronoi_diagram<double> vd; 
+construct_voronoi(points.begin(), points.end(), segments.begin(), segments.end(), &vd); 
+ 
+So brief, isn't that awesome! 
+
+<h2>Traversing Voronoi Graph</h2>
+
+Voronoi graph traversal is the basic
+operation one would like to do once the Voronoi diagram is constructed.
+There are three ways to do that and we are going to cover all of them: 
+
+<ul>
+
+ <li>simply iterating over the Voronoi edges (counts each edge twice): 
+ 
+int iterate_primary_edges1(const voronoi_diagram<double> &vd)
+{ 
+  int result = 0; 
+  for (voronoi_diagram<double>::const_edge_iterator it =
+vd.edges().begin(); 
+       it != vd.edges().end(); ++it) { 
+    if (it->is_primary()) 
+      ++result; 
+  } 
+  return result; 
+} 
+   
+ </li>
+ <li>iterating over the Voronoi cells and then traversing edges around
+each cell (counts each edge twice): 
+ 
+ int
+iterate_primary_edges2(const voronoi_diagram<double> &vd) { 
+  int result = 0; 
+  for (voronoi_diagram<double>::const_cell_iterator it =
+vd.cells().begin(); 
+       it != vd.cells().end(); ++it) { 
+    const voronoi_diagram<double>::cell_type
+&cell = *it; 
+    const voronoi_diagram<double>::edge_type *edge
+= cell.incident_edge(); 
+    // This is convenient way to iterate edges around
+Voronoi cell. 
+    do { 
+      if (edge->is_primary()) 
+        ++result; 
+      edge = edge->next(); 
+    } while (edge != cell.incident_edge()); 
+  } 
+  return result; 
+} 
+ 
+ </li>
+ <li>iterating over the Voronoi
+vertices and then traversing edges around each vertex (the number of the
+iterations through each edge is equal to the number of finite endpoints
+of the edge): 
+ int
+iterate_primary_edges3(const voronoi_diagram<double> &vd) { 
+  int result = 0; 
+  for (voronoi_diagram<double>::const_vertex_iterator it =
+vd.vertices().begin(); 
+       it != vd.vertices().end(); ++it) { 
+    const voronoi_diagram<double>::vertex_type
+&vertex = *it; 
+    const voronoi_diagram<double>::edge_type *edge
+= vertex.incident_edge(); 
+    // This is convenient way to iterate edges around
+Voronoi vertex. 
+    do { 
+      if (edge->is_primary()) 
+        ++result; 
+      edge = edge->rot_next(); 
+    } while (edge != vertex.incident_edge()); 
+  } 
+  return result; 
+}</li>
+</ul>
+
+This should give a very nice idea on how to do the Voronoi
+diagram traversal. Notice that while the output from the first two methods should
+be the same, it wouldn't for the third one. The reason is that in the
+last case we will iterate only once through the edges with a single
+finite endpoint and will skip all the edges with no finite endpoints. 
+
+<h2>Associating User Data with Voronoi Primitives</h2>
+
+A few simple cases of associating the user data with the Voronoi primitives are
+following: 
+
+<ul>
+
+ <li>associating number of incident edges with each cell, vertex;</li>
+ <li>associating color information with each edge;</li>
+ <li>using DFS or BFS on the Voronoi graph requires to mark visited
+edges/vertices/cells.</li>
+</ul>
+
+We will consider the first example and will associate the total number
+of incident edges with each cell. 
+
+Note: Each Voronoi primitive contains mutable pointer to the void* type,
+that allows to associate any type of data with it. 
+
+ 
+
+std::vector<int>
+counts; 
+
+// This is
+required as reallocation of underlying vector will invalidate all the
+pointers. 
+counts.reserve(vd.num_cells()); 
+for (voronoi_diagram<double>::const_cell_iterator it =
+vd.cells().begin(); 
+     it != vd.cells().end(); ++it) { 
+  const voronoi_diagram<double>::cell_type &cell = *it; 
+  const voronoi_diagram<double>::edge_type *edge =
+cell.incident_edge(); 
+  int count = 0; 
+  do { 
+    ++count; 
+    edge = edge->next(); 
+  } while (edge != cell.incident_edge()); 
+  counts.push_back(count); 
+  cell.data(&counts.back()); 
+} 
+ 
+
+Note: In the example above we could not use count variable
+without the vector, because the pointer to it will become invalid as soon as
+we leave the scope of the enclosing for-loop. 
+
+<h2>Rendering Voronoi Diagram</h2>
+
+There are two main issues that don't allow to strictly render the resulting
+Voronoi diagram using such rendering tools as OpenGL or DirectX.
+Those are: 
+
+<ul>
+
+ <li>Some of the Voronoi edges are infinite, so should be clipped;</li>
+ <li>Some of the Voronoi edge are parabolic arcs, so should be
+discretized.</li>
+</ul>
+
+Note: This would be the issues not only for rendering tools.
+Basically every task that requires diagram to be represented as a set
+of finite segments will fall into this category. 
+
+ 
+
+All the above functionality is already implemented in the Voronoi
+utils.
+Before clipping an edge we are going to define the clipping rectangle.
+It is practical to choose it so that it wraps all the input geometries
+plus some offset. 
+
+ 
+bounding_rectangle<double> bbox; for (std::vector<Point>::iterator it = points.begin(); it != points.end(); ++it) 
+  bbox.update(it->a, it->b); 
+for (std::vector<Segment>::iterator it = segments.begin(); it != segments.end(); ++it) { 
+  bbox.update(it->p0.a, it->p0.b); 
+  bbox.update(it->p1.a, it->p1.b); 
+} 
+// Add 10% offset to the bounding rectangle. 
+bbox = voronoi_utils<double>::scale(bbox, 1.1); 
+ 
+
+Now lets consider that we have the 3rd party library function that
+draws segments using the following prototype: 
+ 
+void draw_segment(double x1, double y1, double x2, double y2); 
+ 
+Then the function that renders our diagram edges will have the
+following implementation: 
+
+ 
+
+void
+render_diagram(const voronoi_diagram<double> &vd, 
+                   
+const voronoi_utils<double>::brect_type &bbox) { 
+  int visited = 1; 
+  for (voronoi_diagram<double>::const_edge_iterator it =
+vd.edges().begin(); 
+       it != vd.edges().end(); ++it) { 
+    // We use data pointer to mark visited edges. 
+    it->data(&visited); 
+    // Don't render the same edge twice. 
+    if (it->twin()->data()) continue; 
+    voronoi_utils<double>::point_set_type polyline; 
+    if (it->is_linear()) 
+      voronoi_utils<double>::clip(*it,
+bbox, polyline); 
+    else 
+      // Parabolic edges are always finite. 
+     
+voronoi_utils<double>::discretize(*it, 1E-1, polyline); 
+    // Note: discretized edge segments may also lie
+outside of the bbox. 
+    for (int i = 1; i < polyline.size(); ++i) 
+      draw_segment(polyline[i-1].x(),
+polyline[i-1].y(), 
+                  
+polyline[i].x(), polyline[i].y()); 
+  } 
+} 
+ 
+voronoi_visualizer.cpp
+contains a simple fully featured implementation of the Voronoi diagram
+renderer using the Qt libraries. It was used to generate all the .png
+drawings under the ./libs/polygon/example directory. 
+
+ 
+I hope the reader managed to get to this point and found the
+basic tutorial to be useful (in the end it's not so basic). Worth
+to notice that construction of the Voronoi diagram takes only two lines
+of code, everything else is about initializing input data structures,
+traversing Voronoi graph, associating data with the diagram primitives and
+using the Voronoi utilities. In the
+default mode the Voronoi diagram operates with the signed int (32-bit) input
+coordinate type and double (64-bit) output coordinate type. In the advanced Voronoi tutorial we
+explain why this is enough for the 95% of cases and how to expand the
+algorithm coordinate types for the other 5%. 
+
+ 
+
+<table class="docinfo" id="table1" 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 © Andrii Sydorchuk 2010-2012.</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"> LICENSE_1_0.txt</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>)</td>
+ </tr>
+ </tbody>
+</table>
+
+</body></html>
\ No newline at end of file

Added: trunk/libs/polygon/doc/voronoi_benchmark.htm
==============================================================================
--- (empty file)
+++ trunk/libs/polygon/doc/voronoi_benchmark.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -0,0 +1,531 @@
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html><head>
+
+
+
+
+
+
+
+
+ <meta http-equiv="Content-Language" content="en-us">
+
+
+ <meta http-equiv="Content-Type" content="text/html; charset=windows-1252"><title>Voronoi Benchmark</title></head><body>
+<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 src="images/boost.png" border="0" height="86" width="277"><a title="www.boost.org home page" tabindex="2" style="border: medium none ;" href="http://www.boost.org/"> </a></div>
+ <div style="margin: 5px;">
+ <h3 class="navbar">Contents</h3>
+ <ul>
+ <li>Boost.Polygon Main Page</li>
+ <li>Design Overview</li>
+ <li>Isotropy</li>
+ <li>Coordinate Concept</li>
+ <li>Interval Concept</li>
+ <li>Point Concept</li>
+ <li>Segment Concept</li>
+
+ <li>Rectangle Concept</li>
+ <li>Polygon 90 Concept</li>
+ <li><a href="gtl_polygon_90_with_holes_concept.htm">Polygon 90
+With Holes Concept</a></li>
+ <li>Polygon 45 Concept</li>
+ <li><a href="gtl_polygon_45_with_holes_concept.htm">Polygon 45
+With Holes Concept</a></li>
+ <li>Polygon Concept</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>Polygon Set Concept</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>Property Merge 90</li>
+ <li>Property Merge 45</li>
+ <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+ </a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+ </a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+ </ul>
+ <h3 class="navbar">Other Resources</h3>
+ <ul>
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+Presentation</a></li>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</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" tabindex="2" style="border: medium none ;" href="http://www.adobe.com/"> </a></div>
+ </td>
+ <td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%"> 
+
+ <h1>Voronoi Benchmark</h1>
+There are not many known Voronoi libraries that are capable to satisfy the
+following set of conditions: 
+ <ul>
+ <li>could handle input data sets of points and segments 
+</li>
+ <li>give exact warranties about the algorithm robustness and
+output topology 
+ </li>
+ <li>compute coordinates of the output geometries within the fixed relative precision 
+</li>
+ </ul>Below is the list of libraries included in this benchmark sorted by the number of conditions each of them satisfies: 
+ <ul>
+ <li>Boost.Polygon Voronoi - satisfies all three items above, implements sweep-line algorithm. 
+ </li>
+ <li>CGAL - satisfies the first two items, implements incremental algorithm. CGAL is a well-known
+library in the computational geometry area, especially for its
+robustness. 
+</li>
+ <li>S-Hull
+- doesn't satisfy any of the above items. S-Hull is a non-robust
+implementation of the sweep-hull algorithm used to construct Delaunay
+triangulation of a set of points. 
+ </li>
+ </ul>At the moment this benchmark includes only two robust implementations:
+Boost.Polygon Voronoi and CGAL. Thus we are considering comparison of
+those two to be of the most interest. 
+ 
+Other libraries (OpenVoronoi, Triangle) would be added to this benchmark
+incrementally (we are open for suggestions). 
+ <h2>Important 
+ </h2>While results of this benchmark show complete dominance of
+the Boost.Polygon Voronoi over the CGAL Delaunay Graph implementation,
+we would like to make it clear
+that both libraries use different approach to construct Voronoi
+diagram. Thus there are problems where the CGAL's incremental approach would
+be still more vital than the sweep-line algorithm (e.g. input sites are
+inserted as a live stream
+data). 
+ <h2>Voronoi Benchmark Details 
+ </h2>
+The benchmark consists of the two parts: 
+ <ul>
+ <li>The first one constructs the Voronoi diagram of a set of random points (voronoi_benchmark_points.cpp)</li>
+ <li>The second one constructs the Voronoi diagram of a set of random
+segments (voronoi_benchmark_segments.cpp)</li>
+ </ul>
+Below we list important benchmark details that should be considered while reviewing its results: 
+ <ul>
+ <li>We ensure that input data sets are the same for all
+libraries by initializing random generator with the same seed</li>
+ <li>We ensure that input data sets that consist of segments
+don't contain intersections using Boost.Polygon functionality</li>
+ <li>S-Hull's implementation doesn't process duplicate points
+properly, thus those are eliminated before the algorithm execution
+explicitly (Boost.Polygon Voronoi and CGAL do that  implicitly) 
+ </li>
+
+ <li>There is no Voronoi diagram data structure in CGAL/S-Hull. That's why we use the segment Delaunay graph which is topologically
+dual to the Voronoi diagram</li>
+ <li>CGAL's and S-Hull's output Delaunay triangulation doesn't contain information
+about coordinates of the Voronoi vertices. We didn't include time to compute Voronoi vertices and memory
+storage required for those in this benchmark. 
+ </li>
+ <li>Both Boost.Polygon Voronoi and CGAL process each input
+segment
+as 3 input objects (segment itself and its endpoints), thus the running
+time and memory usage for Voronoi of segments would be at
+least 3 times
+slower than for Voronoi of points</li>
+
+
+ </ul>
+
+The benchmark was executed on the following two system configurations: 
+ 
+Hardware: Intel i5-7600 2.8 GHz, 4GiB RAM. 
+OS: Windows 7 Professional 32-bit. 
+Libraries: Boost 1.48.0, CGAL-4.0. 
+ 
+Hardware: Intel i5-7600 2.8 GHz, 4GiB RAM. 
+OS: Ubuntu 11.10 64-bit. 
+Libraries: Boost 1.48.0, CGAL-4.0, GMP 5.0.4, MPFR 3.1.0 + cumulative
+patch. 
+ <h2>Voronoi Benchmark Results</h2>
+ <h3>Random Points Benchmark</h3>
+ <table style="text-align: left; width: 100%; margin-left: auto; margin-right: auto;" border="1" cellpadding="2" cellspacing="2">
+ <tbody>
+ <tr>
+ <td colspan="2" rowspan="1" style="vertical-align: top; text-align: center;">Test specification 
+ </td>
+ <td colspan="6" rowspan="1" style="vertical-align: top; text-align: center;">Average construction
+time (in secs) 
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top; text-align: center;">Number
+of Points 
+ </td>
+ <td style="vertical-align: top; text-align: center;">Number
+of Runs 
+ </td>
+ <td style="vertical-align: top; text-align: center;">Boost
+Win-32 
+ </td>
+ <td style="vertical-align: top; text-align: center;">CGAL
+Win-32 
+ </td>
+ <td style="vertical-align: top; text-align: center;">S-Hull Win-32 
+ </td>
+<td style="vertical-align: top; text-align: center;">Boost
+Linux-64 
+ </td>
+ <td style="vertical-align: top; text-align: center;">CGAL
+Linux-64 
+ </td><td style="vertical-align: top; text-align: center;">S-Hull Linux-64 
+ </td>
+
+ </tr>
+ <tr>
+ <td style="vertical-align: top; text-align: right;">10 
+ </td>
+ <td style="vertical-align: top; text-align: right;">100000 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.000027 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.000116 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.000043 
+ </td>
+<td style="vertical-align: top; text-align: right;">0.000013 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.000052 
+ </td><td style="vertical-align: top; text-align: right;">0.000012 
+ </td>
+
+ </tr>
+ <tr>
+ <td style="vertical-align: top; text-align: right;">100 
+ </td>
+ <td style="vertical-align: top; text-align: right;">10000 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.000392 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.002649 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.000521 
+ </td>
+<td style="vertical-align: top; text-align: right;">0.000192 
+ </td>
+ <td style="vertical-align: top; text-align: right;"> 0.001150 
+ </td><td style="vertical-align: top; text-align: right;">0.000139 
+ </td>
+
+ </tr>
+ <tr>
+ <td style="vertical-align: top; text-align: right;">1000 
+ </td>
+ <td style="vertical-align: top; text-align: right;">1000 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.004541 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.039140 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.007125 
+ </td>
+<td style="vertical-align: top; text-align: right;">0.002130 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.016680 
+ </td><td style="vertical-align: top; text-align: right;">0.002010 
+ </td>
+
+ </tr>
+ <tr>
+ <td style="vertical-align: top; text-align: right;">10000 
+ </td>
+ <td style="vertical-align: top; text-align: right;">100 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.047540 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.684090 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.091640 
+ </td>
+<td style="vertical-align: top; text-align: right;">0.022900 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.297900 
+ </td><td style="vertical-align: top; text-align: right;">0.028300 
+ </td>
+
+ </tr>
+ <tr>
+ <td style="vertical-align: top; text-align: right;">100000 
+ </td>
+ <td style="vertical-align: top; text-align: right;">10 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.530200 
+ </td>
+ <td style="vertical-align: top; text-align: right;"> 16.904600 
+ </td>
+ <td style="vertical-align: top; text-align: right;">1.218000 
+ </td>
+<td style="vertical-align: top; text-align: right;">0.274000 
+ </td>
+ <td style="vertical-align: top; text-align: right;">8.047000 
+ </td><td style="vertical-align: top; text-align: right;">0.432000 
+ </td>
+
+ </tr>
+ <tr>
+ <td style="vertical-align: top; text-align: right;">1000000 
+ </td>
+ <td style="vertical-align: top; text-align: right;">1 
+ </td>
+ <td style="vertical-align: top; text-align: right;">5.882000 
+ </td>
+ <td style="vertical-align: top; text-align: right;">566.056000 
+ </td>
+ <td style="vertical-align: top; text-align: right;">15.394000 
+ </td>
+<td style="vertical-align: top; text-align: right;">3.290000 
+ </td>
+ <td style="vertical-align: top; text-align: right;">315.740000 
+ </td><td style="vertical-align: top; text-align: right;">6.350000 
+ </td>
+
+ </tr>
+ </tbody>
+ </table>
+ 
+ <table style="text-align: left;" border="1" cellpadding="2" cellspacing="2">
+ <tbody>
+ <tr>
+ <td style="vertical-align: top;"><img style="width: 500px; height: 300px;" alt="" src="../libs/polygon/benchmark/benchmark_results/plots/benchmark_points_10.png"></td>
+ <td style="vertical-align: top;"><img style="width: 500px; height: 300px;" alt="" src="../libs/polygon/benchmark/benchmark_results/plots/benchmark_points_100.png"></td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top;"><img style="width: 500px; height: 300px;" alt="" src="../libs/polygon/benchmark/benchmark_results/plots/benchmark_points_1000.png"></td>
+ <td style="vertical-align: top;"><img style="width: 500px; height: 300px;" alt="" src="../libs/polygon/benchmark/benchmark_results/plots/benchmark_points_10000.png"></td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top;"><img style="width: 500px; height: 300px;" alt="" src="../libs/polygon/benchmark/benchmark_results/plots/benchmark_points_100000.png"></td>
+ <td style="vertical-align: top;"><img style="width: 500px; height: 300px;" alt="" src="../libs/polygon/benchmark/benchmark_results/plots/benchmark_points_1000000.png"></td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top;"><img style="width: 500px; height: 300px;" alt="" src="../libs/polygon/benchmark/benchmark_results/plots/benchmark_points_memory.png"> 
+ </td>
+ <td style="vertical-align: top;"><img style="width: 500px; height: 300px;" alt="" src="../libs/polygon/benchmark/benchmark_results/plots/benchmark_points_all.png"> 
+ </td>
+ </tr>
+ </tbody>
+ </table>
+ <h3>Random Segments Benchmark</h3>
+ <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2">
+ <tbody>
+ <tr>
+ <td colspan="2" rowspan="1" style="vertical-align: top; text-align: center;">Test specification 
+ </td>
+ <td colspan="4" rowspan="1" style="vertical-align: top; text-align: center;">Average construction
+time (in secs)</td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top; text-align: center;">Number
+of Segments 
+ </td>
+ <td style="vertical-align: top; text-align: center;">Number
+of Runs 
+ </td>
+ <td style="vertical-align: top; text-align: center;">Boost
+Win-32 
+ </td>
+ <td style="vertical-align: top; text-align: center;">CGAL
+Win-32 
+ </td>
+ <td style="vertical-align: top; text-align: center;">Boost
+Linux-64 
+ </td>
+ <td style="vertical-align: top; text-align: center;">CGAL
+Linux-64 
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top; text-align: right;">10 
+ </td>
+ <td style="vertical-align: top; text-align: right;">100000 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.000290 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.001047 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.000165 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.000483 
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top; text-align: right;">100 
+ </td>
+ <td style="vertical-align: top; text-align: right;">10000 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.003655 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.014812 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.002006 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.007006 
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top; text-align: right;">1000 
+ </td>
+ <td style="vertical-align: top; text-align: right;">1000 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.038158 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.177315 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.020440 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.084000 
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top; text-align: right;">10000 
+ </td>
+ <td style="vertical-align: top; text-align: right;">100 
+ </td>
+ <td style="vertical-align: top; text-align: right;">0.389470 
+ </td>
+ <td style="vertical-align: top; text-align: right;">2.561340 
+ </td>
+ <td style="vertical-align: top; text-align: right;"> 0.209700 
+ </td>
+ <td style="vertical-align: top; text-align: right;">1.191900 
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top; text-align: right;">100000 
+ </td>
+ <td style="vertical-align: top; text-align: right;">10 
+ </td>
+ <td style="vertical-align: top; text-align: right;">4.031300 
+ </td>
+ <td style="vertical-align: top; text-align: right;">49.314600 
+ </td>
+ <td style="vertical-align: top; text-align: right;">2.228000 
+ </td>
+ <td style="vertical-align: top; text-align: right;">23.538000 
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top; text-align: right;">1000000 
+ </td>
+ <td style="vertical-align: top; text-align: right;">1 
+ </td>
+ <td style="vertical-align: top; text-align: right;">40.912000 
+ </td>
+ <td style="vertical-align: top; text-align: right;">1640.830000 
+ </td>
+ <td style="vertical-align: top; text-align: right;">22.250000 
+ </td>
+ <td style="vertical-align: top; text-align: right;">856.650000 
+ </td>
+ </tr>
+ </tbody>
+ </table>
+ 
+ <table style="text-align: left;" border="1" cellpadding="2" cellspacing="2">
+ <tbody>
+ <tr>
+ <td style="vertical-align: top;"><img style="width: 500px; height: 300px;" alt="" src="../libs/polygon/benchmark/benchmark_results/plots/benchmark_segments_10.png"></td>
+ <td style="vertical-align: top;"><img style="width: 500px; height: 300px;" alt="" src="../libs/polygon/benchmark/benchmark_results/plots/benchmark_segments_100.png"></td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top;"><img style="width: 500px; height: 300px;" alt="" src="../libs/polygon/benchmark/benchmark_results/plots/benchmark_segments_1000.png"></td>
+ <td style="vertical-align: top;"><img style="width: 500px; height: 300px;" alt="" src="../libs/polygon/benchmark/benchmark_results/plots/benchmark_segments_10000.png"></td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top;"><img style="width: 500px; height: 300px;" alt="" src="../libs/polygon/benchmark/benchmark_results/plots/benchmark_segments_100000.png"></td>
+ <td style="vertical-align: top;"><img style="width: 500px; height: 300px;" alt="" src="../libs/polygon/benchmark/benchmark_results/plots/benchmark_segments_1000000.png"></td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top;"><img style="width: 500px; height: 300px;" alt="" src="../libs/polygon/benchmark/benchmark_results/plots/benchmark_segments_memory.png"> 
+ </td>
+ <td style="vertical-align: top;"><img style="width: 500px; height: 300px;" alt="" src="../libs/polygon/benchmark/benchmark_results/plots/benchmark_segments_all.png"> 
+ </td>
+ </tr>
+ </tbody>
+ </table>
+ 
+ <h2>Voronoi Benchmark Conclusions</h2>
+The main conclusions for the benchmark results above are following: 
+ <ul>
+ <li>There is no input size range were CGAL would outperform
+Boost.Polygon Voronoi. Even considering the fact that we didn't include
+time it would take CGAL to compute coordinates of the Voronoi vertices.</li>
+ <li>The more interesting fact is that robust implementation of
+the Boost.Polygon Voronoi is faster than non-robust of
+S-Hull (except small input sets of around 100 points on Linux-64). 
+ </li>
+
+ <li>Logarithmic execution time shows that Boost.Polygon Voronoi and S-Hull
+have clear N*log(N) complexity, while this doesn't seem to be true for
+CGAL (at least for large input data sets). 
+ </li>
+ <li>Boost.Polygon Voronoi computes coordinates of the output
+Voronoi vertices within 64 machine epsilon precision. There are no such
+warranties for the CGAL library. 
+ </li>
+ <li>Boost.Polygon Voronoi of points is 4 times faster for small
+input data sets (10 points) and this factor grows up to 100 for large
+input data sets (1000000 points).</li>
+ <li>Boost.Polygon Voronoi of segments is 3 times faster for
+small input data sets (10 segments) and this factor grows up to 40 for
+large input data sets (1000000 segments).</li>
+ <li>Boost.Polygon
+Voronoi is capable to construct Voronoi of 10000 points or 1000
+segments in 0.02 seconds. This allows to produce real time frame rate
+for those quantities.</li>
+ </ul>
+ </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="table2" 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 © Andrii Sydorchuk 2010-2012.</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">LICENSE_1_0.txt</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>)</td>
+ </tr>
+ </tbody>
+ </table>
+ </td>
+ </tr>
+ </tbody>
+</table>
+
+</body></html>
\ No newline at end of file

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==============================================================================
--- (empty file)
+++ trunk/libs/polygon/doc/voronoi_builder.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -0,0 +1,385 @@
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html><head>
+
+
+
+
+
+
+
+
+
+ <meta http-equiv="Content-Language" content="en-us">
+
+
+ <meta http-equiv="Content-Type" content="text/html; charset=windows-1252"><title>Voronoi Builder</title></head><body>
+<table style="margin: 0pt; padding: 0pt; width: 100%;" border="0" cellpadding="0" cellspacing="0">
+
+ <tbody>
+ <tr>
+ <td style="background-color: rgb(238, 238, 238);" valign="top" nowrap="1">
+ <div style="padding: 5px;" align="center"> <img src="images/boost.png" border="0" height="86" width="277"><a title="www.boost.org home page" tabindex="2" style="border: medium none ;" href="http://www.boost.org/"> </a></div>
+ <div style="margin: 5px;">
+ <h3 class="navbar">Contents</h3>
+ <ul>
+ <li>Boost.Polygon Main Page</li>
+ <li>Design Overview</li>
+ <li>Isotropy</li>
+ <li>Coordinate Concept</li>
+ <li>Interval Concept</li>
+ <li>Point Concept</li>
+ <li>Segment Concept</li>
+
+ <li>Rectangle Concept</li>
+ <li>Polygon 90 Concept</li>
+ <li><a href="gtl_polygon_90_with_holes_concept.htm">Polygon 90
+With Holes Concept</a></li>
+ <li>Polygon 45 Concept</li>
+ <li><a href="gtl_polygon_45_with_holes_concept.htm">Polygon 45
+With Holes Concept</a></li>
+ <li>Polygon Concept</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>Polygon Set Concept</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>Property Merge 90</li>
+ <li>Property Merge 45</li>
+ <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+ </a></li>
+ <li>Voronoi Benchmark 
+ </li>
+ <li>Voronoi Builder</li>
+ <li><a href="voronoi_diagram.htm">Voronoi Diagram 
+ </a></li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils</li>
+ </ul>
+ <h3 class="navbar">Other Resources</h3>
+ <ul>
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+Presentation</a></li>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</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" tabindex="2" style="border: medium none ;" href="http://www.adobe.com/"> </a></div>
+ </td>
+ <td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%"> 
+ <h1>Voronoi Builder 
+ </h1>
+
+Voronoi builder is the event generator structure. It implements the <a href="http://www.ams.org/samplings/feature-column/fcarc-voronoi">sweepline
+algorithm</a>
+that scans a 2D space and generates two types of events:
+site events and circle events (we won't go into details what those are
+exactly). Each event is reported to the output data structure builder.
+The structure shares Voronoi name as the events generated by it
+correspond to the Voronoi diagram edges and vertices, thus giving
+enough information to construct the Voronoi diagram of a set of points
+and linear segments. The requirements for the input/output
+coordinate type of
+the builder geometries are not the same as for the rest of the
+Boost.Polygon library. The main differences are in the following: 
+ <ul>
+ <li>The input coordinate type is not required to be integral (while it
+still should be integer type)</li>
+ <li>The output coordinate type (for
+Voronoi vertices) is required to be IEEE-754 floating point type</li>
+ </ul>
+ <h2>Important</h2>
+
+
+We encourage users to use default static methods defined in the voronoi.hpp
+header to construct Voronoi diagram, however it's always possible to
+use Voronoi builder explicitly, especially if the user wants to drop
+the external dependencies such as MPL (metaprogramming library). So the
+following include set woudn't depend on any heavy external headers (except STL and boost/cstdint.hpp), even
+Boost.Polygon itself: 
+
+ 
+
+ #include <voronoi_builder.hpp> 
+
+ #include <voronoi_diagram.hpp> 
+
+ #include <voronoi_utils.hpp> 
+ 
+ This
+also gives a way to build Voronoi construction API on top of the
+Voronoi builder data strcture for the other Boost libraries. 
+ <h2>Declaration 
+ </h2>
+
+
+
+
+ template
+<typename T, 
+          
+typename CTT = detail::voronoi_ctype_traits<T>, 
+          
+typename VP = detail::voronoi_predicates<CTT> > 
+ class
+voronoi_builder; 
+ 
+ T
+- specifies coordinate type of the input geometries (points and
+segments). 
+
+ CTT
+- defines input/output coordinate type used by VP. 
+
+ VP
+- predicate kernel, that provides builder with robust and
+efficient predicates and functors. 
+
+The Voronoi builder data structure is ready to use from the box with
+32-bit signed integer input coordinate type. The user may extend the
+input coordinate range to the other integer types (e.g. 64-bit
+integer), however this will also require manual set up of the
+coordinate type traits. Default voronoi_predicates<CTT>
+structure provides correct and efficient predicates as soon as types defined by CTT
+satisfy the requirements explained at the end of this page. In case those
+requirements are not satisfied for the user provided CTT,
+proper VP
+implementation is required. 
+<h2>Member Functions</h2>
+ <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2">
+ <tbody>
+ <tr>
+ <td style="font-family: 'Courier New',Courier,monospace;">
+voronoi_builder()</td>
+ <td width="693">Default
+constructor.</td>
+ </tr>
+ <tr>
+ <td>void insert_point(const int_type& x, 
+                  const int_type& y) 
+ </td>
+ <td>Inserts a point object with
+the specified coordinates into the Voronoi builder.
+ </td>
+ </tr>
+
+
+ <tr>
+ <td>void
+insert_segment(const int_type& x1, 
+                    const int_type& y1,                    
+const int_type& x2, 
+                    const int_type& y2) 
+ </td>
+ <td>Inserts a segment object
+with the specified coordinates into the Voronoi builder.
+ </td>
+ </tr>
+
+
+
+
+ <tr>
+ <td style="font-family: 'Courier New',Courier,monospace;">
+template <typename OUTPUT> 
+void construct(OUTPUT *output) 
+ </td>
+ <td width="693">Runs sweepline
+algorithm over the set of the inserted geometries, outputs site and
+circle events to the OUTPUT data structure. It's responsibility of the
+output structure builder object to process them. For example both
+Voronoi diagram and Delaunay triangulation could be constructed from
+the Voronoi builder events, however internally they are different data
+structures, so it's up to them to process properly events produced by
+the builder object. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: 'Courier New',Courier,monospace;">
+void clear() 
+ </td>
+ <td width="693">Clears the
+list of the inserted geometries. 
+ </td>
+ </tr>
+ </tbody>
+ </table>
+ <h1>Voronoi Coordinate Type Traits</h1>
+
+
+ The library provides the default coordinate type traits for the
+32-bit signed integer type:
+
+ 
+ template <typename T> 
+struct voronoi_ctype_traits; 
+ 
+template <> 
+struct voronoi_ctype_traits<int32> { 
+    typedef int32 int_type; 
+    typedef int64 int_x2_type; 
+    typedef uint64 uint_x2_type; 
+    typedef extended_int<128> big_int_type; 
+    typedef fpt64 fpt_type; 
+    typedef extended_exponent_fpt<fpt_type>
+efpt_type; 
+    typedef ulp_comparison<fpt_type> ulp_cmp_type; 
+    typedef type_converter_fpt to_fpt_converter_type; 
+    typedef type_converter_efpt to_efpt_converter_type; 
+};
+ 
+ One
+of the most important features of the library is that Voronoi builder
+output geometries are constructed within defined relative error (64
+machine epsilons). That means the more mantissa bits the user provided
+fpt_type has the better precision of the output geometries will be. In
+order for the user defined traits to be consistent with the default
+Voronoi builder predicates user should define following set of
+coordinate types (the assumption is made that input geometries have
+X-bit signed integer coordinate type): 
+ 
+<table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2">
+ <tbody>
+ <tr>
+ <td style="font-family: 'Courier New',Courier,monospace;">int_type 
+ </td>
+ <td style="vertical-align: top;">At least X-bit signed
+integer type. 
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top; font-family: 'Courier New',Courier,monospace;">
+int_x2_type 
+ </td>
+ <td style="vertical-align: top;">At least 2X-bit signed
+integer type. 
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top; font-family: 'Courier New',Courier,monospace;">
+uint_x2_type 
+ </td>
+ <td style="vertical-align: top;">At least 2X-bit unsigned
+integer type. 
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top; font-family: 'Courier New',Courier,monospace;">
+big_int_type 
+ </td>
+ <td style="vertical-align: top;">At least 8X-bit signed
+integer type for voronoi of points. 
+At least 64X-bit signed integer type for voronoi of segments. 
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top; font-family: 'Courier New',Courier,monospace;">
+fpt_type 
+ </td>
+ <td style="vertical-align: top;">IEEE-754 floating point
+type, with mantissa at least (X+16) bits and exponent able to handle
+32X-bit unsigned integer type. 
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top; font-family: 'Courier New',Courier,monospace;">
+efpt_type 
+ </td>
+ <td style="vertical-align: top;">IEEE-754 floating point
+type, with mantissa at least (X+16) bits and exponent able to handle
+64X-bit unsigned integer type. 
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top; font-family: 'Courier New',Courier,monospace;">
+ulp_cmp_type 
+ </td>
+ <td style="vertical-align: top;">Ulp comparison structure
+that checks if two fpt_type values are withing the given ulp range
+(relative error range). 
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top; font-family: 'Courier New',Courier,monospace;">
+to_fpt_converter_type 
+ </td>
+ <td style="vertical-align: top;">Type converter structure
+that converts any of the integer types above plus efpt_type to the
+fpt_type using operator(). 
+ </td>
+ </tr>
+ <tr>
+ <td style="vertical-align: top; font-family: 'Courier New',Courier,monospace;">
+to_efpt_converter_type 
+ </td>
+ <td style="vertical-align: top;">Type converter structure
+that converts any of the integer types above to the efpt_type using
+operator(). 
+ </td>
+ </tr>
+ </tbody>
+ </table>
+ Notes: 
+ <ul>
+ <li>
+Four different integer types are used (instead of a single
+big_int_type) to slightly improve algorithm performance and memory
+usage.</li>
+ <li>As the maximum required size of the big_int_type is known in advance
+(based on the size of the integer type), library provided
+implementation of a fixed integer could be used (it is much faster than
+heap-allocated big integers).</li>
+ <li>
+Two separate floating-point types are defined because for the input
+with
+32-bit signed integer coordinates double won't be able to handle
+2048-bit (64 * 32) integers as they will overflow its exponent. On the
+gcc compiler it's possible to use 80-bit long doubles for both fpt
+types, however this is not supported by MSVC compiler.</li>
+ <li>efpt_type and to_efpt_converter_type are not used to construct Voronoi diagram of points (mocks will work fine).</li>
+ <li>
+For an example of the user defined coordinate type traits
+see advanced Voronoi tutorial.</li>
+ </ul>
+
+ </td>
+ </tr>
+ <tr>
+ <td style="background-color: rgb(238, 238, 238);" valign="top" nowrap="1"> </td>
+ <td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%">
+ <table class="docinfo" id="table2" 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 © Andrii Sydorchuk 2010-2012.</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">LICENSE_1_0.txt</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>)</td>
+ </tr>
+ </tbody>
+ </table>
+ </td>
+ </tr>
+ </tbody>
+</table>
+
+</body></html>
\ No newline at end of file

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+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html><head>
+
+
+
+
+
+
+
+ <meta http-equiv="Content-Language" content="en-us">
+
+
+ <meta http-equiv="Content-Type" content="text/html; charset=windows-1252"><title>Voronoi Diagram</title>
+
+
+
+
+ <meta http-equiv="content-type" content="text/html; charset=utf-8">
+
+
+ <meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body>
+<table style="margin: 0pt; padding: 0pt; width: 100%;" border="0" cellpadding="0" cellspacing="0">
+
+ <tbody>
+ <tr>
+ <td style="background-color: rgb(238, 238, 238);" valign="top" nowrap="1">
+ <div style="padding: 5px;" align="center"> <img src="images/boost.png" border="0" height="86" width="277"><a title="www.boost.org home page" tabindex="2" style="border: medium none ;" href="http://www.boost.org/"> </a></div>
+ <div style="margin: 5px;">
+ <h3 class="navbar">Contents</h3>
+ <ul>
+ <li>Boost.Polygon Main Page</li>
+ <li>Design Overview</li>
+ <li>Isotropy</li>
+ <li>Coordinate Concept</li>
+ <li>Interval Concept</li>
+ <li>Point Concept</li>
+ <li>Segment Concept</li>
+
+ <li>Rectangle Concept</li>
+ <li>Polygon 90 Concept</li>
+ <li><a href="gtl_polygon_90_with_holes_concept.htm">Polygon 90
+With Holes Concept</a></li>
+ <li>Polygon 45 Concept</li>
+ <li><a href="gtl_polygon_45_with_holes_concept.htm">Polygon 45
+With Holes Concept</a></li>
+ <li>Polygon Concept</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>Polygon Set Concept</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>Property Merge 90</li>
+ <li>Property Merge 45</li>
+ <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+ </a></li>
+ <li>Voronoi Benchmark</li>
+ <li>Voronoi Builder 
+ </li>
+ <li>Voronoi Diagram</li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils 
+ </li>
+ </ul>
+ <h3 class="navbar">Other Resources</h3>
+ <ul>
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+Presentation</a></li>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</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" tabindex="2" style="border: medium none ;" href="http://www.adobe.com/"> </a></div>
+ </td>
+ <td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%"> 
+
+ <h1>Voronoi Diagram</h1>
+A Voronoi
+diagram is the computational geometry concept that represents partition
+of the given space onto regions, with bounds determined by distances to a
+specified family of objects. The application area of this concept vary <a href="http://www.ics.uci.edu/%7Eeppstein/gina/scot.drysdale.html">from
+Archaeology to Zoology</a>. The Boost.Polygon library provides implementation of
+the Voronoi diagram data structure in 2D space. The internal representation
+consists of the three arrays, that respectively contain: Voronoi cells
+(represents the area around input site bounded by the Voronoi edges), Voronoi vertices
+(points where three or more Voronoi edges intersect), Voronoi edges
+(the one dimensional curves containing points equidistant from the two
+closest input sites). Each of the primitives (cell, vertex, edge)
+contains pointers to the other linked primitives, so that it's always
+possible to efficiently traverse Voronoi graph. The picture below shows
+the Voronoi vertices in red, Voronoi edges in black, input sites that
+correspond to the Voronoi cells in blue. It is considered that each
+input segment consists of the three sites: segment itself and its
+endpoints. As the result two additional
+Voronoi edges are constructed per each input segment. This is made to
+simplify the representation of the Voronoi diagram. 
+ 
+ <img style="border: 1px solid ; width: 300px; height: 300px;" alt="" src="images/voronoi2.png"> 
+ <h2>Declaration 
+ </h2>
+
+
+
+ template
+<typename T, typename TRAITS = voronoi_diagram_traits<T> > 
+ class
+voronoi_diagram; 
+ 
+T
+- specifies the coordinate type of the output geometries: input sites (points / segments), Voronoi vertices. 
+ TRAITS
+- Voronoi diagram traits (explained in the end of this chapter). 
+ <h2>Member Functions</h2>
+
+ 
+
+ 
+ <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2">
+ <tbody>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">voronoi_diagram() 
+ </td>
+ <td>Default constructor. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">void
+clear() 
+ </td>
+ <td>Clears diagram. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">const
+cell_container_type &cells() const 
+ </td>
+ <td>Returns the const
+reference to the cell container. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">const
+vertex_container_type &vertices() const 
+ </td>
+ <td>Returns the const
+reference to the vertex container. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">const
+edge_container_type &edges() const 
+ </td>
+ <td>Returns the const
+reference to the edge container. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">unsigned
+int num_cells() const 
+ </td>
+ <td>Returns the number of the
+cells in the Voronoi diagram. 
+This value should be the same as the size of the cell container. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">unsigned
+int num_edges() const 
+ </td>
+ <td>Returns the number of the
+edges in the Voronoi diagram. 
+This value should be twice smaller than the size of the edge container. 
+The reason is that two half-edges are present for each Voronoi edge. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">unsigned
+int num_vertices() const 
+ </td>
+ <td>Returns the number of the
+vertices in the Voronoi diagram. 
+This value should be the same as the size of the vertex container. 
+ </td>
+ </tr>
+ </tbody>
+ </table>
+
+ <h2>Member Types</h2>
+ <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2">
+ <tbody>
+ <tr>
+ <td>coordinate_type 
+ </td>
+ <td>Coordinate type. 
+ </td>
+ </tr>
+ <tr>
+ <td>point_type 
+ </td>
+ <td>2D point. 
+ </td>
+ </tr>
+ <tr>
+ <td>cell_type 
+ </td>
+ <td>Voronoi cell. 
+ </td>
+ </tr>
+ <tr>
+ <td>vertex_type 
+ </td>
+ <td>Voronoi vertex. 
+ </td>
+ </tr>
+ <tr>
+ <td>edge_type 
+ </td>
+ <td>Voronoi edge. 
+ </td>
+ </tr>
+ <tr>
+ <td>cell_container_type 
+ </td>
+ <td>Container of Voronoi cells. 
+ </td>
+ </tr>
+ <tr>
+ <td>cell_iterator 
+ </td>
+ <td>Cell container iterator. 
+ </td>
+ </tr>
+ <tr>
+ <td>const_cell_iterator 
+ </td>
+ <td>Const cell container iterator. 
+ </td>
+ </tr>
+ <tr>
+ <td>vertex_container_type 
+ </td>
+ <td>Container of Voronoi vertices. 
+ </td>
+ </tr>
+ <tr>
+ <td>vertex_iterator 
+ </td>
+ <td>Vertex container iterator. 
+ </td>
+ </tr>
+ <tr>
+ <td>const_vertex_iterator 
+ </td>
+ <td>Const vertex container iterator. 
+ </td>
+ </tr>
+ <tr>
+ <td>edge_container_type 
+ </td>
+ <td>Container of Voronoi edges. 
+ </td>
+ </tr>
+ <tr>
+ <td>edge_iterator 
+ </td>
+ <td>Edge container iterator. 
+ </td>
+ </tr>
+ <tr>
+ <td>const_edge_iterator 
+ </td>
+ <td>Const edge container iterator. 
+ </td>
+ </tr>
+ </tbody>
+ </table>
+
+
+ <h1>Voronoi Edge</h1>
+
+Voronoi edge is represented as a bit improved classical half-edge
+data structure. 
+ <h2>Declaration</h2>
+
+
+
+ template
+<typename T> 
+ class
+voronoi_edge; 
+ 
+T - coordinate type. While Voronoi edge doesn't contain coordinates itself, it stores pointers to the Voronoi cell and vertex. 
+ <h2>Member Functions</h2>
+
+ 
+
+ 
+ <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2">
+ <tbody>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">voronoi_edge() 
+ </td>
+ <td>Default constructor. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">voronoi_cell_type
+*cell() 
+ </td>
+ <td>Returns the pointer to the
+Voronoi cell
+that edge belongs to. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">const
+voronoi_cell_type *cell() const 
+ </td>
+ <td>Returns the const pointer
+to the Voronoi cell that edge belongs to. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">void
+cell(voronoi_cell_type *c) 
+ </td>
+ <td>Sets the Voronoi cell
+pointer for the cell current edge belongs to. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">voronoi_vertex_type
+*vertex0() 
+ </td>
+ <td>Returns the pointer to the
+start point of the edge. 
+If the edge is infinite in that direction returns NULL. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">const
+voronoi_vertex_type *vertex0() const 
+ </td>
+ <td>Returns the const pointer
+to the point vertex of the edge. 
+If the edge is infinite in that direction returns NULL. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">void
+vertex0(voronoi_vertex_type *v) 
+ </td>
+ <td>Sets the start point
+pointer of the edge. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">voronoi_vertex_type
+*vertex1() 
+ </td>
+ <td>Returns the pointer to the
+end point of the edge. 
+If the edge is infinite in that direction returns NULL. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">const
+voronoi_vertex_type *vertex1() const 
+ </td>
+ <td>Returns the const pointer
+to the end point of the edge. 
+If the edge is infinite in that direction returns NULL. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">void
+vertex1(voronoi_vertex_type *v) 
+ </td>
+ <td>Sets the end point pointer
+of the edge. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">voronoi_edge_type
+*twin() 
+ </td>
+ <td>Returns the pointer to the
+twin edge. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">const
+voronoi_edge_type *twin() const 
+ </td>
+ <td>Returns the const pointer
+to the twin edge. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">void
+twin(voronoi_edge_type *e) 
+ </td>
+ <td>Sets the twin edge pointer
+of the edge. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">voronoi_edge_type
+*next() 
+ </td>
+ <td>Returns the pointer to the
+CCW next edge within the corresponding Voronoi cell. 
+Edges not necessarily share a common vertex (e.g. infinite edges). 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">const
+voronoi_edge_type *next() const 
+ </td>
+ <td>Returns the const pointer
+to the CCW next edge within the corresponding Voronoi cell. 
+Edges not necessarily share a common vertex (e.g. infinite edges). 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">void
+next(voronoi_edge_type *e) 
+ </td>
+ <td>Sets the CCW next edge
+pointer of the edge. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">voronoi_edge_type
+*prev() 
+ </td>
+ <td>Returns the pointer to the
+CCW prev edge within the corresponding Voronoi cell. 
+Edges not necessarily share a common vertex (e.g. infinite edges). 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">const
+voronoi_edge_type *prev() const 
+ </td>
+ <td>Returns the const pointer
+to the CCW prev edge within the corresponding Voronoi cell. 
+Edges not necessarily share a common vertex (e.g. infinite edges). 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">void
+prev(voronoi_edge_type *e) 
+ </td>
+ <td>Sets the CCW prev edge
+pointer of the edge. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">void
+*data() const 
+ </td>
+ <td>Returns the pointer to the
+data associated with the edge. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">void
+data(void *d) const 
+ </td>
+ <td>Sets the data pointer of
+the edge. 
+This allows the user to associate any data type with the edge. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">voronoi_edge_type
+*rot_next() 
+ </td>
+ <td>Returns the pointer to the
+CCW next edge rotated around the edge start point. 
+If the edge is infinite in that direction returns NULL. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">const
+voronoi_edge_type *rot_next() const 
+ </td>
+ <td>Returns the const pointer
+to the CCW next edge rotated around the edge start point. 
+If the edge is infinite in that direction returns NULL.</td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">voronoi_edge_type
+*rot_prev() 
+ </td>
+ <td>Returns the pointer to the
+CCW prev edge rotated around the edge start point. 
+If the edge is infinite in that direction returns NULL. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">const
+voronoi_edge_type *rot_prev() const 
+ </td>
+ <td>Returns the const pointer
+to the CCW prev edge rotated around the edge start point. 
+If the edge is infinite in that direction returns NULL.</td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">bool
+is_finite() const 
+ </td>
+ <td>Returns true if the both
+end points of the edge are finite, else false. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">bool
+is_linear() const 
+ </td>
+ <td>Returns true if the edge
+is linear (segment, ray, line), else false. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">bool
+is_curved() const 
+ </td>
+ <td>Returns true if the edge
+is curved (parabolic arc), else false. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">bool
+is_primary() const 
+ </td>
+ <td>Returns false if the edge
+goes through the endpoint of the segment site, else true. 
+ </td>
+ </tr>
+ </tbody>
+ </table>
+ 
+ All
+the above methods have O(1) complexity. The size of
+the Voronoi edge structure is equal to: 6 * sizeof(void *). It is
+possible to disable the data member of the Voronoi edge data structure
+during the compile time using the following directive: 
+ 
+ #define NO_VORONOI_EDGE_DATA 
+ <h2>Member Types</h2>
+
+ <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2">
+ <tbody>
+ <tr>
+ <td>coordinate_type 
+ </td>
+ <td>Coordinate type. 
+ </td>
+ </tr>
+ <tr>
+ <td>voronoi_cell_type 
+ </td>
+ <td>Voronoi cell type. 
+ </td>
+ </tr>
+ <tr>
+ <td>voronoi_vertex_type 
+ </td>
+ <td>Voronoi vertex type. 
+ </td>
+ </tr>
+ <tr>
+ <td>voronoi_edge_type 
+ </td>
+ <td>Voronoi edge type. 
+ </td>
+ </tr>
+ </tbody>
+ </table>
+ <h1>Voronoi Cell</h1>
+
+Voronoi cell is represented by a site the cell contains and a pointer
+to the incident edge. 
+ <h2>Declaration</h2>
+
+
+
+ template
+<typename T> 
+class voronoi_cell; 
+ 
+T - coordinate type. 
+ <h2>Member Functions</h2>
+
+ 
+
+ 
+ <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2">
+ <tbody>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">voronoi_cell(const
+point_type &p1, 
+            
+voronoi_edge_type *edge) 
+ </td>
+ <td>Constructs the Voronoi
+cell from the given point site and pointer to the one of the boundary
+edges. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">voronoi_cell(const
+point_type &p1, 
+            
+const point_type &p2, 
+            
+voronoi_edge_type *edge) 
+ </td>
+ <td>Constructs the Voronoi
+cell from the given segment site and pointer to the one of the boundary
+edges. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">const
+point_type &point0() const 
+ </td>
+ <td>If the cell contains point
+site returns it. 
+If the cell contains segment site returns its first endpoint. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">const
+point_type &point1() const 
+ </td>
+ <td>If the cell contains point
+site returns it. 
+If the cell contains segment site returns its second endpoint. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">voronoi_edge_type
+*incident_edge() 
+ </td>
+ <td>Returns the pointer to the
+one of the boundary edges. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">const
+voronoi_edge_type *incident_edge() const 
+ </td>
+ <td>Returns the const pointer
+to the one of the boundary edges. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">void
+incident_edge(voronoi_edge_type *e) 
+ </td>
+ <td>Sets the incident boundary
+edge pointer of the cell. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">void
+*data() const 
+ </td>
+ <td>Returns the pointer to the
+data associated with the cell.</td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">void
+data(void *d) const 
+ </td>
+ <td>Sets the data pointer of
+the cell. 
+This allows the user to associate any data type with the cell.</td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">bool
+contains_point() const</td>
+ <td>Returns true if the cell
+contains a point site, else false.</td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">bool
+contains_segment() const</td>
+ <td>Returns true if the cell
+contains a segment site, else false.</td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">bool
+is_degenerate() const </td>
+ <td>Returns true if the cell
+doesn't have an incident edge. 
+Could happen if a few input segments share a common endpoint.</td>
+ </tr>
+ </tbody>
+ </table>
+ 
+ All the above methods have O(1) complexity. The size of
+the Voronoi cell structure is equal to: 2 * sizeof(void *) + 4 *
+sizeof(coordinate_type). It is possible to disable the data member of the Voronoi cell data
+structure during the compile time using the following directive: 
+
+ 
+
+ #define NO_VORONOI_CELL_DATA
+ <h2>Member Types</h2>
+
+
+
+ <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2">
+ <tbody>
+ <tr>
+ <td>coordinate_type 
+ </td>
+ <td>Coordinate type. 
+ </td>
+ </tr>
+ <tr>
+ <td>point_type</td>
+ <td>Point type. 
+ </td>
+ </tr>
+ <tr>
+ <td>voronoi_edge_type 
+ </td>
+ <td>Voronoi edge type. 
+ </td>
+ </tr>
+ </tbody>
+ </table>
+ <h2>Miscellaneous</h2>
+
+The following code snippet effectively traverses the Voronoi edges around the
+Voronoi cell: 
+ 
+ const
+voronoi_edge<double> *edge = cell->incident_edge(); 
+ do { 
+  
+edge = edge->next(); 
+  
+// Do smth. with edge. 
+ } while
+(edge != cell->incident_edge()); 
+ <h1>Voronoi Vertex</h1>
+Voronoi vertex is represented by a point that corresponds to the vertex
+and a pointer to the incident edge. 
+ <h2>Declaration</h2>
+
+
+
+ template
+<typename T> 
+ class
+voronoi_vertex; 
+ 
+T - coordinate type. 
+ <h2>Member Functions</h2>
+
+ 
+
+ 
+ <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2">
+ <tbody>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">voronoi_vertex(const
+point_type &vertex, 
+               voronoi_edge_type *edge) 
+ </td>
+ <td>Constructs the Voronoi
+vertex that corresponds to the give point and incident edge. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">const
+point_type &vertex() const 
+ </td>
+ <td>Returns the point that
+represents vertex. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">voronoi_edge_type
+*incident_edge() 
+ </td>
+ <td>Returns the incident edge
+pointer. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">const
+voronoi_edge_type *incident_edge() const 
+ </td>
+ <td>Returns the const pointer
+to the incident edge. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">void
+incident_edge(voronoi_edge_type *e) 
+ </td>
+ <td>Sets the incident edge
+pointer. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">void
+*data() const 
+ </td>
+ <td>Returns the pointer to the
+data associated with the vertex.</td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">void
+data(void *d) const 
+ </td>
+ <td>Sets the data pointer of
+the cell. 
+This allows the user to associate any data type with the vertex.</td>
+ </tr>
+ </tbody>
+ </table>
+ 
+ All the above methods have O(1) complexity. The size of
+the Voronoi vertex structure is equal to: 2 * sizeof(void *) + 2 *
+sizeof(coordinate_type). It is possible to disable the data member of the Voronoi vertex data
+structure during the compile time using the following directive: 
+
+ 
+
+ #define NO_VORONOI_VERTEX_DATA
+ <h2>Member Types</h2>
+ <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2">
+ <tbody>
+ <tr>
+ <td>coordinate_type 
+ </td>
+ <td>Coordainte type. 
+ </td>
+ </tr>
+ <tr>
+ <td>point_type 
+ </td>
+ <td>Point type. 
+ </td>
+ </tr>
+ <tr>
+ <td>voronoi_edge_type 
+ </td>
+ <td>Voronoi edge type. 
+ </td>
+ </tr>
+ </tbody>
+ </table>
+
+ <h2>Miscellaneous</h2>The following code snippet effectively traverses the Voronoi edges around the
+Voronoi vertex: 
+ 
+ const
+voronoi_edge<double> *edge = vertex->incident_edge(); 
+ do { 
+  
+edge = edge->next(); 
+  
+// Do smth. with edge. 
+ } while
+(edge != vertex->incident_edge()); 
+
+ <h1>Voronoi Diagram Traits 
+ </h1>
+Voronoi diagram traits are used to configure Voronoi diagram data
+structure. 
+ <h2>Declaration</h2>
+
+
+
+ template
+<typename T> 
+ struct
+voronoi_diagram_traits; 
+ 
+T - coordinate type. 
+ <h2>Member Types</h2>
+
+ 
+
+ 
+ <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2">
+ <tbody>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">coordinate_type 
+ </td>
+ <td>The main coordinate type
+of the Voronoi diagram primitives. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">ctype_converter_type 
+ </td>
+ <td>Coordinate type converter
+structure. 
+Converts coordinates provided by the Voronoi builder to the
+internal coordinate type. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">point_type 
+ </td>
+ <td>2D point data structure. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">cell_type 
+ </td>
+ <td>Voronoi cell type. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">vertex_type 
+ </td>
+ <td>Voronoi vertex_type. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">edge_type 
+ </td>
+ <td>Voronoi edge_type. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">vertex_equality_predicate_type 
+ </td>
+ <td>Predicate that returns
+true if two points are considered to be equal. 
+This is used to unite nearby Voronoi vertices. 
+ </td>
+ </tr>
+ </tbody>
+ </table>
+ </td>
+ </tr>
+ <tr>
+ <td style="background-color: rgb(238, 238, 238);" valign="top" nowrap="1"> </td>
+ <td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%">
+ <table class="docinfo" id="table2" 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 © Andrii Sydorchuk 2010-2012.</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">LICENSE_1_0.txt</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>)</td>
+ </tr>
+ </tbody>
+ </table>
+ </td>
+ </tr>
+ </tbody>
+</table>
+
+</body></html>
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+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html><head>
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ <meta http-equiv="Content-Language" content="en-us">
+
+
+ <meta http-equiv="Content-Type" content="text/html; charset=windows-1252"><title>Voronoi Main</title>
+
+
+
+
+ <meta http-equiv="content-type" content="text/html; charset=utf-8">
+
+
+ <meta http-equiv="content-type" content="text/html; charset=utf-8">
+
+
+ <meta http-equiv="content-type" content="text/html; charset=utf-8"><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body>
+<table style="margin: 0pt; padding: 0pt; width: 100%;" border="0" cellpadding="0" cellspacing="0">
+
+ <tbody>
+ <tr>
+ <td style="background-color: rgb(238, 238, 238);" valign="top" nowrap="1">
+ <div style="padding: 5px;" align="center"> <img src="images/boost.png" border="0" height="86" width="277"><a title="www.boost.org home page" tabindex="2" style="border: medium none ;" href="http://www.boost.org/"> </a></div>
+ <div style="margin: 5px;">
+ <h3 class="navbar">Contents</h3>
+ <ul>
+ <li>Boost.Polygon Main Page</li>
+ <li>Design Overview</li>
+ <li>Isotropy</li>
+ <li>Coordinate Concept</li>
+ <li>Interval Concept</li>
+ <li>Point Concept</li>
+ <li>Segment Concept</li>
+
+ <li>Rectangle Concept</li>
+ <li>Polygon 90 Concept</li>
+ <li><a href="gtl_polygon_90_with_holes_concept.htm">Polygon 90
+With Holes Concept</a></li>
+ <li>Polygon 45 Concept</li>
+ <li><a href="gtl_polygon_45_with_holes_concept.htm">Polygon 45
+With Holes Concept</a></li>
+ <li>Polygon Concept</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>Polygon Set Concept</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>Property Merge 90</li>
+ <li>Property Merge 45</li>
+ <li>Property Merge</li>
+ <li>Voronoi Main Page 
+ </li>
+ <li>Voronoi Benchmark</li>
+ <li>Voronoi Builder 
+ </li>
+ <li>Voronoi Diagram</li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils 
+ </li>
+ </ul>
+ <h3 class="navbar">Other Resources</h3>
+ <ul>
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+Presentation</a></li>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</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" tabindex="2" style="border: medium none ;" href="http://www.adobe.com/"> </a></div>
+ </td>
+ <td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%"> 
+
+ <h1>THE BOOST.POLYGON VORONOI LIBRARY 
+ </h1>
+ <img style="width: 900px; height: 300px;" alt="" src="images/voronoi3.png"> 
+The Boost.Polygon Voronoi library provides functionality to construct the Voronoi diagram
+of a set of points and linear segments in 2D space with the following
+set of
+limitations: 
+ <ul>
+ <li>coordinates of the input points and endpoints of the
+segments
+should be of the integer type;</li>
+ <li>input segments should not overlap
+except their endpoints.</li>
+ </ul>
+While the first restriction is permanent (it
+allows to give the exact warranties about the output precision and
+algorithm execution),
+the second one may be resolved using the Boost.Polygon functionality.
+The strong sides of the
+library and main benefits comparing to the other implementations are
+discussed in the following paragraphs. 
+ <h2>Robustness and Efficiency</h2>
+Lets explain a bit those terms. The efficiency is simply measured by
+the time it takes the algorithm to execute. The robustness is a bit
+more harder to explain. But those of you who had the experience with
+the following situations would understand what it doesn't mean: application segfaults randomly, algorithm output contains
+degeneracies or is completely invalid (e.g. a point is considered to be outside of the polygon,
+while should be inside). In other words robust implementation doesn't
+fail and produces expected output in 100% of cases, thus user can rely
+on
+it. Robustness is a weak place of the most non-commercial
+implementations of any complex geometric algorithm. The main issues of
+that could be divided onto two main categories: memory management
+issues, numeric stability issues. Our implementation avoids the
+first type of issues using pure STL data structures, thus you won't find
+any operator new in the code. The second category of problems is
+resolved using multiprecision <a href="voronoi_predicates.htm">geometric
+predicates</a>.
+Even for commercial implementations usage of such predicates usually
+results in a huge performance slowdown. Here is another strong side of
+the Boost.Polygon
+Voronoi library: we avoid multiprecision computations in 95% of cases
+using
+extremely fast floating-point predicates. Yes, those are not always
+exact, but we developed the <a href="voronoi_robust_fpt.htm">relative
+error arithmetic apparatus</a> to identify them and switch to the
+higher precision predicates when required. 
+ <h2>Precision of the Output Structures 
+ </h2>
+One of the extremely important results of using two types of predicates
+is that library efficiently computes relatively precise coordinates of
+the output geometries. Here we will explain a bit what exactly
+"relatively precise" means and how the received output may differ from
+the theoretically correct one (here and after we assume that output
+coordinate type is the IEEE-754 floating-point type). 
+ 
+Voronoi implementation guaranties that the relative error of the
+coordinates of the output
+geometries is always not higher than 64 machine epsilons (6
+bits of mantissa), while in many cases it is slightly less. That also
+means that using floating-point type with the larger mantissa will
+produce more precise output. Let's consider
+the following example: the output Voronoi
+vertex has double (53-bit mantissa) x-coordinate equal to 1.0, then the
+absolute error is at most 2^-53 * 2^6 = 2^-47 and the exact value of
+x-coordinate lies in the range [1.0 - 2^-47, 1.0 + 2^-47]. For
+x-coordinate equal to 2^31, the absolute error will be at most 2^-53 *
+2^31 * 2^6 = 2^-16 and the exact value of x-coordinate lies in the
+range
+[2^31 - 2^-16, 2^31 + 2^16]. For the output Voronoi vertex with long
+double
+(64-bit mantissa) x-coordinate equal to 2^31, the absolute error will
+be at most 2^-64 * 2 ^31 * 2^6 = 2^-27 and the exact value of
+x-coordinate
+lies in the range [2^31-2^-27, 2^31+2^-27]. If you'd like to become
+master of the absolute and relative error try this article. 
+ 
+During the finalization step the implementation unites Voronoi vertices whose both
+coordinates are situated within the relative error range equal to 128
+machine epsilons and removes any Voronoi edges between them. That is
+the only case that might cause differences between the algorithm output
+topology and theoretically precise one.  Now let's see what is the practical
+impact of this. Consider the following example: we are going to construct the
+Voronoi diagram of our Solar System. The radius of our Solar System is
+approximately 2^42 metres, and we are going to snap it to the integer
+grid of [-2^42; 2^42] x [-2^42; 2^42].  Let's choose the long double
+(64 bit mantissa) output coordinate type, then the maximum absolute error
+for the output geometries within our Solar System will be on its boundaries
+and equal to 2^-64 * 2^42 * 2^6 = 2^-18 metres. In the output we are going to
+consider vertices with both coordinates that are within 2^-17 metres (8
+micrometres) distance to be equal. Come on, that distance is equal to
+the size of a bacteria. Can you even see those? 
+ <h2>Fully Functional with Segments</h2>
+There are not many implementations of the Voronoi diagram construction
+algorithm that could
+handle linear segment inputs, even considering the commercial libraries.
+Support of the
+segments allows to discretize any input geometry (circle, ellipse,
+parabola). Of course as the result those might have floating-point
+coordinates, but that is resolved using scaling and snapping to the
+integer grid. This functionality is very handy as allows to compute
+the medial axis transform of the arbitrary set of input geometries. So
+one may start
+using it for the next generation pattern recognition or computer vision
+project. 
+ <h2>Basic and Advanced Usage Cases</h2>
+The main library header voronoi.hpp
+defines the following static functions to integrate the Voronoi library functionality with the Boost.Polygon interfaces: 
+ 
+ <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2">
+ <tbody>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">template <typename Point, typename VB> 
+void insert(const Point &point, VB *vb) 
+ </td>
+ <td>Inserts a point into the Voronoi builder data structure. 
+Point type should model the point concept. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">template <typename PointIterator, typename VB> 
+void insert(PointIterator first, 
+            PointIterator last, 
+            VB *vb) 
+ </td>
+ <td>Inserts an iterator range of points into the Voronoi builder data structure. 
+Corresponding point type should model the point concept. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">template <typename Segment, typename VB> 
+void insert(const Segment &segment, VB *vb) 
+ </td>
+ <td>Inserts a segment into the Voronoi builder data structure. 
+Segment type should model the segment concept. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">template <typename SegmentIterator, typename VB> 
+void insert(SegmentIterator first, 
+            SegmentIterator last, 
+            VB *vb) 
+ </td>
+ <td>Inserts an iterator range of segments into the Voronoi builder data structure. 
+Corresponding segment type should model the segment concept. 
+ </td>
+ </tr>
+<tr>
+ <td style="font-family: Courier New,Courier,monospace;">template <typename PointIterator, typename VD> 
+void construct_voronoi(PointIterator first, 
+                      
+PointIterator last, 
+                      
+VD *vd) 
+ </td>
+ <td>Constructs Voronoi diagram of a set of points. Corresponding point type should model the point concept. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">template <typename SegmentIterator, typename VD> 
+void construct_voronoi(SegmentIterator first, 
+                      
+SegmentIterator last, 
+                      
+VD *vd) 
+ </td>
+ <td>Constructs Voronoi diagram of a set of segments. Corresponding segment type should model the segment concept. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">template <typename PointIterator, 
+          typename SegmentIterator, 
+          typename VD> void construct_voronoi(PointIterator p_first, 
+                      
+PointIterator p_last,                       
+SegmentIterator s_first, 
+                      
+SegmentIterator s_last,                       
+VD *vd) 
+ </td>
+ <td>Constructs Voronoi
+diagram of a set of points and segments. Corresponding point type should model the point concept. 
+Corresponding segment type should model the segment concept. 
+ </td>
+ </tr>
+ </tbody>
+ </table>
+ This
+means that it's possible to construct the Voronoi diagram with the
+following two lines of code (if corresponding input types satisfy the Boost.Polygon concept model): 
+ 
+ voronoi_diagram<double>
+vd; 
+ construct_voronoi(points.begin(), points.end(), &vd); 
+ 
+Isn't that simple? The library also provides the clear interfaces to
+ associate user data with the output geometries, efficiently traverse Voronoi graph and utilities to
+ visualize output primitives (e.g.
+discretization of the parabolic edges, clipping of the linear edges).
+More details on those are covered in the basic Voronoi tutorial. Advanced usage of the library with the configuration of the coordinate
+types is explained in the <a href="voronoi_advanced_tutorial.htm">advanced
+Voronoi tutorial</a>.
+The library also allows users to implement their own Voronoi diagram /
+Delaunay triangulation construction routines based on the Voronoi builder API. 
+ <h2>No Third Party Dependencies 
+ </h2>Yes,
+the library doesn't depend on any 3rd party code. Even more than that
+there is only one dependency on the Boost libraries: boost/cstdint.hpp.
+All the required multiprecision types functionality is implemented as
+part of the library and is not exposed to the user. Considering the
+fact that Voronoi implementation consists of just 7 headers (3 public
+and 4 private) it is easy to compile it within a minute after download.
+On the other hand voronoi.hpp header provides integration routines with
+the Boost.Polygon concepts and models with a drawback of additional
+dependencies. <h2>Extensible for the User Provided Coordinate Types</h2>
+Our implementation is coordinate type agnostic. That means that as soon
+as user provides types satisfy the set of restrictions of the Voronoi builder coordinate type traits
+and implement methods required by the library no changes are required
+neither
+from the algorithm, nor from the implementation of the predicates. So it's
+possible to
+construct Voronoi diagram for the 256-bit integer input coordinate type
+and
+512-bit output floating-point type without making any changes to the
+internal code. 
+ <h2>Bright Future 
+ </h2>
+Below one may find the list of the main directions for the future
+development of the library. 
+High-priority tasks that already have approximate implementation plan
+are following (some of those may be proposed as future GSoC projects): 
+ <ul>
+ <li>Implementing Delaunay triangulation data structure. 
+Note: only data structure needs to be implemented that properly
+processes events provided by the Voronoi builder.</li>
+ <li>Implementing medial axis transform data structure. 
+Note: in general case the Voronoi diagram has completely the same
+geometry
+as the medial axis (they are 100% equal), however for many applications
+user is not interested in the Voronoi edges inside the hole regions.
+The main point
+of this data structure is to automatically filter Voronoi edges that
+belong to those areas.</li>
+ <li>Voronoi
+diagram data structure could be used to find K nearest neighbors of N
+sites in O(N*K*log(K) + N*log(N)) time. The return value would be a
+list of the k nearest neighbors for each site. 
+</li>
+ <li>Using the r-tree data structure built on top of the
+bounding rectangles around the Voronoi cells to answer the nearest
+neighbor queries in log(N) time, where N is the number of the Voronoi cells. 
+Note: there should be r-tree data structure available soon as part of
+the Boost libraries.</li>
+
+ <li>Providing interface to retrieve the convex hull of a set of
+points and segments from the Voronoi builder once the Voronoi diagram is
+constructed in O(N) time.</li>
+ <li>Providing serialization utilities for the Voronoi diagram data structure. 
+ </li>
+
+
+ </ul>
+High-priority tasks to be considered: 
+ <ul>
+ <li>Dropping the restriction on the non-intersecting input
+geometries.</li>
+ <li>Integration of the Voronoi diagram data structure with the BGL (Boost
+Graph Library).</li>
+ <li>Support of the other types of distance metrics.</li>
+ <li>Construction of the constrained Delaunay triangulation.</li>
+ <li>Support of the circular input geometries.</li>
+ </ul>
+Based on the community suggestions priorities may be changed. 
+ <h2>Theoretical Research 
+ </h2>Voronoi
+was developed as part of the Google Summer of Code 2010. The
+library was actively maintained for the last two years and involved
+strong mathematical research in the field of algorithms, data
+structures,
+relative error arithmetic and numerical robustness. Nowadays one can
+often read a scientific article that contains non-practical theoretical
+results or implementation with
+benchmarks nobody else can reproduce. The opposite story is with
+the Boost.Polygon Voronoi library. We provide pure implementation and
+benchmarks one may run on
+his PC. In case community finds it useful we will incrementally
+add more documentation on the theoretical side of our realization. The
+authors would like to acknowledge the Steven Fortune's article "<a href="http://dl.acm.org/citation.cfm?id=10549">A Sweepline algorithm
+for Voronoi diagrams</a>", that contains the fundamental ideas of the
+current implementation. 
+ </td>
+ </tr>
+ <tr>
+ <td style="background-color: rgb(238, 238, 238);" valign="top" nowrap="1"> </td>
+ <td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%">
+ <table class="docinfo" id="table2" 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 © Andrii Sydorchuk 2010-2012.</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">LICENSE_1_0.txt</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>)</td>
+ </tr>
+ </tbody>
+ </table>
+ </td>
+ </tr>
+ </tbody>
+</table>
+
+
+</body></html>
\ No newline at end of file

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==============================================================================
--- (empty file)
+++ trunk/libs/polygon/doc/voronoi_predicates.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -0,0 +1,250 @@
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html><head>
+
+
+
+
+
+ <meta http-equiv="Content-Language" content="en-us">
+
+
+ <meta http-equiv="Content-Type" content="text/html; charset=windows-1252"><title>Voronoi Predicates</title>
+
+
+
+
+ <meta http-equiv="content-type" content="text/html; charset=utf-8">
+
+
+ <meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body>
+<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 src="images/boost.png" border="0" height="86" width="277"><a title="www.boost.org home page" tabindex="2" style="border: medium none ;" href="http://www.boost.org/"> </a></div>
+ <div style="margin: 5px;">
+ <h3 class="navbar">Contents</h3>
+ <ul>
+ <li>Boost.Polygon Main Page</li>
+ <li>Design Overview</li>
+ <li>Isotropy</li>
+ <li>Coordinate Concept</li>
+ <li>Interval Concept</li>
+ <li>Point Concept</li>
+ <li>Segment Concept</li>
+
+ <li>Rectangle Concept</li>
+ <li>Polygon 90 Concept</li>
+ <li><a href="gtl_polygon_90_with_holes_concept.htm">Polygon 90
+With Holes Concept</a></li>
+ <li>Polygon 45 Concept</li>
+ <li><a href="gtl_polygon_45_with_holes_concept.htm">Polygon 45
+With Holes Concept</a></li>
+ <li>Polygon Concept</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>Polygon Set Concept</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>Property Merge 90</li>
+ <li>Property Merge 45</li>
+ <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+ </a></li>
+ <li>Voronoi Benchmark</li>
+ <li>Voronoi Builder 
+ </li>
+ <li>Voronoi Diagram</li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils 
+ </li>
+ </ul>
+ <h3 class="navbar">Other Resources</h3>
+ <ul>
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+Presentation</a></li>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</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" tabindex="2" style="border: medium none ;" href="http://www.adobe.com/"> </a></div>
+ </td>
+ <td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%"> 
+
+
+ <h1>Voronoi Predicates 
+ </h1>
+
+In mathematical theory predicate is an operator which returns true
+or false (e.g. it may answer a question: "is it sunny today?"). 
+
+Voronoi predicates contain implementation of a set of the geometric
+predicates used by the Voronoi builder.
+Except of those it also provides
+functors that allow to compute coordinates of the centers of the
+inscribed
+circles (those correspond to the Voronoi vertices) within the given
+relative error precision range (64 machine epsilons). This means that
+the more mantissa bits
+your floating point type has the better precision of the output
+geometries you'll get. This
+is a very handy functionality as it allows to improve output precision
+simply providing 3rd party IEEE-754 like floating-point types. 
+
+
+ <h2>Geometric Predicates</h2>
+
+The main issues with the implementation of any complex geometric
+algorithm arise when dealing with the robustness of the geometric
+predicates.
+Usually this
+is also the point where the commercial projects stand strong against
+noncommercial implementations (it's not the case with our
+implementation).
+For the short example let's consider the following code snippet, that
+could
+be used to compute orientation of the three points: 
+
+ 
+
+ double
+cross_product(double dx1, double dy1, double dx2, double dy2) { 
+
+  
+return dx1 * dy2 - dx2 * dy1; 
+
+ } 
+ 
+int main() { 
+  int v = 1 << 30;  // 2 ^ 30 
+  double result = cross_product(v, v - 1, v + 1,
+v); 
+  printf("%.3f", result); 
+  return 0; 
+} 
+ 
+ The
+output of this simple program will be "0.000", while
+the correct one is "1.000". In terms of the orientation test this means
+that points are collinear instead of being CCW oriented. This is one of
+the basic predicates used in any geometric algorithm and taking wrong
+output from it may influence the further algorithm execution:
+corrupting algorithm underlying structures or producing completely
+invalid output. Voronoi uses
+slightly more complex predicates. To insure that they are robust and
+efficient the approach that combines two known techniques (lazy
+arithmetic and multiple
+precision computations) is used. 
+
+
+ <h2>Lazy Arithmetic</h2>
+
+Lazy
+arithmetic is based on the usage of IEEE-754 floating-point types to
+quickly evaluate the result of the expression. While this approach has
+a good speed
+performance it doesn't produce reliable results all the time (as in the
+example above). The way to solve the issue is apart from computing
+result of the expression compute the relative error of it also. This
+will
+give us the range of values the evaluated result belongs to and based
+on that we can
+come up with two decisions: 1) output the value; 2) recompute the
+expression using multiprecision type. The way relative errors are
+evaluated is explained in the <a href="voronoi_robust_fpt.htm">Voronoi
+Robust FPT</a> section. 
+
+
+ <h2>Multiple Precision Arithmetic</h2>
+
+In the vast majority of cases
+the lazy arithmetic approach produces correct result thus further
+processing is not required. In other cases the Voronoi library defined
+or user
+provided multiple precision types are used to produce correct result.
+However even that doesn't solve all the cases. Multiprecision geometric
+predicates could be divided onto two categories: 
+
+ 
+
+1) mathematical transformation of the predicate exists that evaluates
+exact result: 
+ 
+Predicate: A/B + C/D ?< 0; 
+After math. transform: (A*D + B*C) / (B * D) ?< 0; 
+ 
+Predicate: sqrt(A) ?< 1.2; 
+After math. transform: A ?< 1.44; 
+ 
+ 2) the correct result could be produced only by increasing
+precision of the multiprecision type and with defined relative error
+for the output type: 
+
+ 
+
+ Predicate:
+sqrt(A) + sqrt(B) + sqrt(C) + sqrt(D) + sqrt(E) ?< 1.2; 
+Imagine that value of the expression to the left is very close to 1.2; 
+ 
+
+ Predicate:
+sin(x) ?< 0.57; 
+Relative error of sin function should be known; 
+ 
+ The Voronoi of points could be completely
+implemented using predicates of the first type, however the Voronoi of
+segments could not.
+The predicate that doesn't fall into the first category is responsible
+for comparison of the Voronoi circle events. However it appears that
+properly used
+this predicate can't corrupt algorithm internal structures and produces
+output technically the same as produced in case this predicate fell in
+the first category.  The main reasons for this are: 1) algorithm
+operates with integer coordinate type of the input geometries; 2)
+closely
+situated Voronoi vertices are considered to be the same in the output
+data structure (this won't influence main targets algorithm is used
+for). 
+</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="table2" 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 © Andrii Sydorchuk 2010-2012.</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">LICENSE_1_0.txt</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>)</td>
+ </tr>
+ </tbody>
+ </table>
+ </td>
+ </tr>
+ </tbody>
+</table>
+
+
+</body></html>
\ No newline at end of file

Added: trunk/libs/polygon/doc/voronoi_robust_fpt.htm
==============================================================================
--- (empty file)
+++ trunk/libs/polygon/doc/voronoi_robust_fpt.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -0,0 +1,211 @@
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html><head>
+
+
+
+
+ <meta http-equiv="Content-Language" content="en-us">
+
+
+ <meta http-equiv="Content-Type" content="text/html; charset=windows-1252"><title>Voronoi Robust FPT</title></head><body>
+<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 src="images/boost.png" border="0" height="86" width="277"><a title="www.boost.org home page" tabindex="2" style="border: medium none ;" href="http://www.boost.org/"> </a></div>
+ <div style="margin: 5px;">
+ <h3 class="navbar">Contents</h3>
+ <ul>
+ <li>Boost.Polygon Main Page</li>
+ <li>Design Overview</li>
+ <li>Isotropy</li>
+ <li>Coordinate Concept</li>
+ <li>Interval Concept</li>
+ <li>Point Concept</li>
+ <li>Segment Concept</li>
+
+ <li>Rectangle Concept</li>
+ <li>Polygon 90 Concept</li>
+ <li><a href="gtl_polygon_90_with_holes_concept.htm">Polygon 90
+With Holes Concept</a></li>
+ <li>Polygon 45 Concept</li>
+ <li><a href="gtl_polygon_45_with_holes_concept.htm">Polygon 45
+With Holes Concept</a></li>
+ <li>Polygon Concept</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>Polygon Set Concept</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>Property Merge 90</li>
+ <li>Property Merge 45</li>
+ <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+ </a></li>
+ <li>Voronoi Benchmark</li>
+ <li>Voronoi Builder 
+ </li>
+ <li>Voronoi Diagram</li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils 
+ </li>
+ </ul>
+ <h3 class="navbar">Other Resources</h3>
+ <ul>
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+Presentation</a></li>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</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" tabindex="2" style="border: medium none ;" href="http://www.adobe.com/"> </a></div>
+ </td>
+ <td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%"> 
+
+ <h1>Voronoi Robust FPT</h1>
+The Voronoi
+robust floating-point types are the set of classes and tools that
+allow to estimate relative error of the arithmetic expressions. It is
+assumed that the other Boost libraries may find this unit functionality
+extremely useful, as it can be used to implement robust and efficient
+arithmetic predicates or functors that compute values within known
+relative error. 
+ <h2>Robust Fpt Type</h2>
+The robust
+fpt type (robust floating-point type)
+- represents the IEEE-754 floating-point type wrapper that also
+contains
+information about the relative error of the underlying value. The
+implementation overloads 5 standard operations: +, -, *, /, sqrt and
+apart from the evaluating value of the expression also computes its
+relative
+error. Let's consider two values A and B; C - rounding error, re(X)
+- relative error of the X expression, then following rules apply: 
+ 
+ re(A+B)
+<= max(re(A), re(B)) + C, if A * B >= 0; 
+ re(A-B)
+<= (B * re(A) + A * re(B)) / |A - B| + C, if A * B < 0; 
+ re(A*B)
+<= re(A) + re(B) + C; 
+ re(A/B)
+<= re(A) + re(B) + C; 
+ re(sqrt(A))
+<= re(A) * 0.5 + C; 
+ 
+ The constant C is equal to the rounding error,
+which for the above set of arithmetic operations in the IEEE-754
+floating-point implementation should be equal to 1 machine epsilon. 
+ <h2>Robust Difference Type</h2>
+The robust
+difference type -
+represents expression wrapper that holds the positive and negative
+partial
+sums of the expression in a separate values in order to avoid
+the cancellation errors before evaluating the final difference.
+Following
+arithmetic operators are overloaded for the robust difference type: +,
+-, *, / (division operator is not overloaded for the case were both
+arguments have robust difference type). 
+Looking at the relative error formulas above one may notice a few facts: 
+1) all of the formulas evaluate upper bound of the relative error, the
+actual value could be a lot smaller; 
+2) relative error estimate for the expression depends on the order
+operations are evaluated; 
+3) relative error of  the difference of two positive numbers may
+be
+extremely large in case their values are close to each other (this is
+also known as the cancellation error). 
+To explain this a bit consider the following expression (~ - stands for
+almost equal, << - many times larger than): 
+ 
+ A - B +
+C, where A ~ B and C << B; 
+ 
+Computing the relative error of this expression from left to right will
+produce extremely large relative error: 
+ 
+ re(A-B+C)
+= max(re(A-B), re(C)) = re(A-B) = (B * re(A) + A * re(B)) / 0 = INF; 
+ 
+ While doing this from right to left will keep the relative
+error value small: 
+ 
+ re(A-B+C)
+= re(C-B+A) = max(re(C-B), re(A)) = max(re(A), re(B)); 
+ 
+ While both estimates are valid (they define upper bound of
+the relative error), of course the second one is preferable. 
+Here is the place where robust difference type comes useful. Basically
+it splits expression onto positive and negative partial sums and
+evaluates the
+difference only when the result is required. And did I mention that
+positive and negative values might be of the robust fpt type, that's
+why
+the relative error is always known for the expression result. 
+ <h2>Robust Sqrt Expression Structure</h2>
+The robust square root expression structure allows to compute the
+result of
+the expression that contains square roots within defined relative
+error.
+As an example consider the following expression: 
+ 
+ A *
+sqrt(a) - B * sqrt(b), A * B > 0, a >= 0, b >= 0; 
+ 
+Computing this expressions directly may apply huge cancellation error,
+however it may be transformed to the next equivalent expression: 
+ 
+(A * A * a - B * B * b) / (A * sqrt(a) + B * sqrt(b)); 
+ 
+The numerator and denominator of this expression could be computed
+directly as those won't lead to the cancellation errors. 
+ 
+In general case the robust sqrt expression structure allows to evaluate
+the following set of expressions: 
+ 
+sum(A[i] * sqrt(a[i]), i = 1 .. N), N <= 4; 
+ 
+This appears to be enough for the Boost.Polygon Voronoi. 
+ </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="table2" 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 © Andrii Sydorchuk 2010-2012</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">LICENSE_1_0.txt</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>)</td>
+ </tr>
+ </tbody>
+ </table>
+ </td>
+ </tr>
+ </tbody>
+</table>
+
+</body></html>
\ No newline at end of file

Added: trunk/libs/polygon/doc/voronoi_utils.htm
==============================================================================
--- (empty file)
+++ trunk/libs/polygon/doc/voronoi_utils.htm 2012-05-10 17:45:11 EDT (Thu, 10 May 2012)
@@ -0,0 +1,380 @@
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html><head>
+
+
+
+
+
+
+ <meta http-equiv="Content-Language" content="en-us">
+
+
+ <meta http-equiv="Content-Type" content="text/html; charset=windows-1252"><title>Voronoi Utils</title>
+
+
+
+
+ <meta http-equiv="content-type" content="text/html; charset=utf-8">
+
+
+ <meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body>
+<table style="margin: 0pt; padding: 0pt; width: 100%;" border="0" cellpadding="0" cellspacing="0">
+
+ <tbody>
+ <tr>
+ <td style="background-color: rgb(238, 238, 238);" valign="top" nowrap="1">
+ <div style="padding: 5px;" align="center"> <img src="images/boost.png" border="0" height="86" width="277"><a title="www.boost.org home page" tabindex="2" style="border: medium none ;" href="http://www.boost.org/"> </a></div>
+ <div style="margin: 5px;">
+ <h3 class="navbar">Contents</h3>
+ <ul>
+ <li>Boost.Polygon Main Page</li>
+ <li>Design Overview</li>
+ <li>Isotropy</li>
+ <li>Coordinate Concept</li>
+ <li>Interval Concept</li>
+ <li>Point Concept</li>
+ <li>Segment Concept</li>
+
+ <li>Rectangle Concept</li>
+ <li>Polygon 90 Concept</li>
+ <li><a href="gtl_polygon_90_with_holes_concept.htm">Polygon 90
+With Holes Concept</a></li>
+ <li>Polygon 45 Concept</li>
+ <li><a href="gtl_polygon_45_with_holes_concept.htm">Polygon 45
+With Holes Concept</a></li>
+ <li>Polygon Concept</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>Polygon Set Concept</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>Property Merge 90</li>
+ <li>Property Merge 45</li>
+ <li>Property Merge</li>
+ <li><a href="voronoi_main.htm">Voronoi Main Page 
+ </a></li>
+ <li>Voronoi Benchmark</li>
+ <li>Voronoi Builder 
+ </li>
+ <li>Voronoi Diagram</li>
+ <li>Voronoi Predicates</li>
+ <li>Voronoi Robust FPT 
+ </li>
+ <li>Voronoi Utils 
+ </li>
+ </ul>
+ <h3 class="navbar">Other Resources</h3>
+ <ul>
+ <li>GTL Boostcon 2009 Paper</li>
+ <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
+Presentation</a></li>
+ <li>Performance Analysis</li>
+ <li>Layout Versus Schematic Tutorial</li>
+ <li>Minkowski Sum Tutorial</li>
+ <li>Voronoi Basic Tutorial</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" tabindex="2" style="border: medium none ;" href="http://www.adobe.com/"> </a></div>
+ </td>
+ <td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%"> 
+
+ <h1>Voronoi Utils</h1>
+Voronoi
+utilities implements a set of tools that users may find useful
+especially for
+the visualization of the Voronoi diagrams or discretization of the
+parabolic
+edges. 
+ <h2>Important 
+ </h2>
+
+There are no warranties about precision of the
+output structures produced by the utilities class. This is mostly
+because input
+coordinate type the utilities operate with
+is supposed to be double. Any degeneracies may be reported, however those are of low
+priority to be fixed. 
+ <h2>Declaration</h2>
+
+
+ template
+<typename T, typename TRAITS = voronoi_utils_traits<T> > 
+ class
+voronoi_utils; 
+ 
+ T
+- output coordinate type used by the utilities. 
+ TRAITS
+- output geometries type traits (see definition below). 
+ <h2 style="color: rgb(0, 0, 0); font-family: 'Times New Roman'; font-style: normal; font-variant: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">Member
+Functions</h2>
+ <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2">
+ <tbody>
+ <tr>
+ <td>template
+<typename CT> 
+ static
+brect_type scale_bounding_rectangle( 
+  const bounding_rectangle<CT> &brect,   fpt_type factor = 1.0) 
+ </td>
+ <td>Returns the scaled
+bounding rectangle. 
+The center of the transformation corresponds to the center of the input
+rectangle. 
+ </td>
+ </tr>
+ <tr>
+ <td>template
+<typename CT> 
+static void discretize_finite_edge( 
+  const voronoi_edge<CT> &edge,   coordinate_type max_error,   point_set_type &discretization) 
+ </td>
+ <td>Provides the point
+discretization of the input voronoi edge. 
+If the edge is infinite (ray, line) returns empty output set. 
+Max error specifies the maximum distance between approximation and original parabolic arc. 
+ </td>
+ </tr>
+ <tr>
+ <td>template
+<typename CT> 
+static void clip_linear_edge( 
+  const voronoi_edge<CT> &edge,   const brect_type &brect,   point_set_type &clipped_edge) 
+ </td>
+ <td>Clips the input Voronoi
+edges with the specified rectangle. 
+If the edge is a parabolic arc returns empty output set. 
+ </td>
+ </tr>
+ <tr>
+ <td>template
+<typename PointType> 
+ static
+void clip_linear_edge( 
+  const PointType &p1,   const PointType &p2,   const brect_type &brect,   point_set_type &clipped_edge) 
+ </td>
+ <td>Clips the input linear
+edge with the specified rectangle. 
+The edge is defined by its endpoints. 
+ </td>
+ </tr>
+ </tbody>
+ </table>
+
+ <h2 style="color: rgb(0, 0, 0); font-family: 'Times New Roman'; font-style: normal; font-variant: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">Member Types</h2>
+
+
+ <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2">
+ <tbody>
+ <tr>
+ <td>coordinate_type</td>
+ <td>Coordinate type.</td>
+ </tr>
+ <tr>
+ <td>point_type</td>
+ <td>2D Point</td>
+ </tr>
+ <tr>
+ <td>point_set_type</td>
+ <td>2D Point set.</td>
+ </tr>
+ <tr>
+ <td>brect_type</td>
+ <td>Bounding rectangle.</td>
+ </tr>
+ </tbody>
+ </table>
+ <h1>Bounding Rectangle</h1>
+
+The module provides implementation of a simple bounding rectangle data structure. 
+ <h2>Declaration</h2>
+
+
+
+ template
+<typename T> 
+ class
+bounding_rectangle; 
+ 
+T - coordinate type the rectangle operates with. 
+ <h2 style="color: rgb(0, 0, 0); font-family: 'Times New Roman'; font-style: normal; font-variant: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">Member
+Functions</h2>
+ <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2">
+ <tbody>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">bounding_rectangle() 
+ </td>
+ <td>Default constructor.
+Initializes the empty bounding rectangle. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">bounding_rectangle( 
+    coordinate_type x1, 
+    coordinate_type y1, 
+    coordinate_type x2, 
+    coordinate_type y2) 
+ </td>
+ <td>Constructs the bounding
+rectangle with the given coordinates. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">void
+update( 
+    coordinate_type x, 
+    coordinate_type y) 
+ </td>
+ <td>Extends the bounding
+rectangle with the specified point defined by its coordinates. 
+If the rectangle is not initialized, initializes it with the specifed
+point. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">bool
+is_empty() const 
+ </td>
+ <td>Returns true if the
+rectangle is empty (uninitialized), else false. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">void
+clear() 
+ </td>
+ <td>Sets rectangle to an empty
+state. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">bool
+contains( 
+   coordinate_type x, 
+   coordinate_type y) const 
+ </td>
+ <td>Returns true if the
+rectangle contains the given point defined by its coordinates, else
+false. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">coordinate_type
+x_min() const 
+ </td>
+ <td>Returns the x coordinate
+of the bottom left corner of the rectangle. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">coordinate_type
+y_min() const 
+ </td>
+ <td>Returns the y coordinate
+of the bottom left corner of the rectangle. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">coordinate_type
+x_max() const 
+ </td>
+ <td>Returns the x coordinate
+of the top right corner of the rectangle. 
+ </td>
+ </tr>
+ <tr>
+ <td style="font-family: Courier New,Courier,monospace;">coordinate_type
+y_max() const 
+ </td>
+ <td>Returns the y coordinate
+of the top right corner of the rectangle. 
+ </td>
+ </tr>
+ </tbody>
+ </table>
+
+ <h1>Voronoi Utils Traits</h1>
+Voronoi utils traits supply Voronoi utilities with appropriate input/output types and type converter structure. 
+ <h2>Declaration</h2>
+
+
+
+ template
+<typename fpt> 
+ struct
+voronoi_utils_traits; 
+
+
+ <h2 style="color: rgb(0, 0, 0); font-family: 'Times New Roman'; font-style: normal; font-variant: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;">Member Types 
+ </h2>
+ <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2">
+ <tbody>
+ <tr>
+ <td>coordinate_type 
+ </td>
+ <td>Coordinate type. 
+ </td>
+ </tr>
+ <tr>
+ <td>point_type 
+ </td>
+ <td>2D Point . 
+ </td>
+ </tr>
+ <tr>
+ <td>point_set_type 
+ </td>
+ <td>2D Point set. 
+ </td>
+ </tr>
+ <tr>
+ <td>brect_type 
+ </td>
+ <td>Bounding rectangle. 
+ </td>
+ </tr>
+ <tr>
+ <td>ctype_converter_type 
+ </td>
+ <td>Coordinate type converter structure. 
+ </td>
+ </tr>
+ </tbody>
+ </table>
+
+ </td>
+ </tr>
+ <tr>
+ <td style="background-color: rgb(238, 238, 238);" valign="top" nowrap="1"> </td>
+ <td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%">
+ <table class="docinfo" id="table2" 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 © Andrii Sydorchuk 2010-2012.</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">LICENSE_1_0.txt</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>)</td>
+ </tr>
+ </tbody>
+ </table>
+ </td>
+ </tr>
+ </tbody>
+</table>
+
+</body></html>
\ No newline at end of file

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