733 lines
35 KiB
HTML
733 lines
35 KiB
HTML
|
<!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>
|
|||
|
|
<!--
|
|||
|
|
Copyright 2009-2010 Intel Corporation
|
|||
|
|
license banner
|
|||
|
|
-->
|
|||
|
|
<title>Boost Polygon Library: Polygon Set Concept</title>
|
|||
|
|
<meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" />
|
|||
|
|
<!-- <link type="text/css" rel="stylesheet" href="adobe_source.css"> -->
|
|||
|
|
</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" href="http://www.boost.org/"
|
|||
|
|
tabindex="2" style="border: medium none ;"> </a> </div>
|
|||
|
|
<div style="margin: 5px;">
|
|||
|
|
<h3 class="navbar">Contents</h3>
|
|||
|
|
<ul>
|
|||
|
|
<li><a href="index.htm">Boost.Polygon Main Page</a></li>
|
|||
|
|
<li><a href="gtl_design_overview.htm">Design Overview</a></li>
|
|||
|
|
<li><a href="gtl_isotropy.htm">Isotropy</a></li>
|
|||
|
|
<li><a href="gtl_coordinate_concept.htm">Coordinate Concept</a></li>
|
|||
|
|
<li><a href="gtl_interval_concept.htm">Interval Concept</a></li>
|
|||
|
|
<li><a href="gtl_point_concept.htm">Point Concept</a></li>
|
|||
|
|
<li><a href="gtl_segment_concept.htm">Segment Concept</a></li>
|
|||
|
|
<li><a href="gtl_rectangle_concept.htm">Rectangle Concept</a></li>
|
|||
|
|
<li><a href="gtl_polygon_90_concept.htm">Polygon 90 Concept</a></li>
|
|||
|
|
<li><a href="gtl_polygon_90_with_holes_concept.htm">Polygon 90
|
|||
|
|
With Holes Concept</a></li>
|
|||
|
|
<li><a href="gtl_polygon_45_concept.htm">Polygon 45 Concept</a></li>
|
|||
|
|
<li><a href="gtl_polygon_45_with_holes_concept.htm">Polygon 45
|
|||
|
|
With Holes Concept</a></li>
|
|||
|
|
<li><a href="gtl_polygon_concept.htm">Polygon Concept</a></li>
|
|||
|
|
<li><a href="gtl_polygon_with_holes_concept.htm">Polygon With
|
|||
|
|
Holes Concept</a></li>
|
|||
|
|
<li><a href="gtl_polygon_90_set_concept.htm">Polygon 90 Set
|
|||
|
|
Concept</a></li>
|
|||
|
|
<li><a href="gtl_polygon_45_set_concept.htm">Polygon 45 Set
|
|||
|
|
Concept</a></li>
|
|||
|
|
<li>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><a href="gtl_property_merge_90.htm">Property Merge 90</a></li>
|
|||
|
|
<li><a href="gtl_property_merge_45.htm">Property Merge 45</a></li>
|
|||
|
|
<li><a href="gtl_property_merge.htm">Property Merge</a></li>
|
|||
|
|
<li><a href="voronoi_main.htm">Voronoi Main Page<br />
|
|||
|
|
</a></li>
|
|||
|
|
<li><a href="voronoi_benchmark.htm">Voronoi Benchmark</a><br />
|
|||
|
|
</li>
|
|||
|
|
<li><a href="voronoi_builder.htm">Voronoi Builder</a></li>
|
|||
|
|
<li><a href="voronoi_diagram.htm">Voronoi Diagram</a></li>
|
|||
|
|
</ul>
|
|||
|
|
<h3 class="navbar">Other Resources</h3>
|
|||
|
|
<ul>
|
|||
|
|
<li><a href="GTL_boostcon2009.pdf">GTL Boostcon 2009 Paper</a></li>
|
|||
|
|
<li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
|
|||
|
|
Presentation</a></li>
|
|||
|
|
<li><a href="analysis.htm">Performance Analysis</a></li>
|
|||
|
|
<li><a href="gtl_tutorial.htm">Layout Versus Schematic Tutorial</a></li>
|
|||
|
|
<li><a href="gtl_minkowski_tutorial.htm">Minkowski Sum Tutorial</a></li>
|
|||
|
|
<li><a href="voronoi_basic_tutorial.htm">Voronoi Basic Tutorial</a></li>
|
|||
|
|
<li><a href="voronoi_advanced_tutorial.htm">Voronoi Advanced
|
|||
|
|
Tutorial</a></li>
|
|||
|
|
</ul>
|
|||
|
|
</div>
|
|||
|
|
<h3 class="navbar">Polygon Sponsor</h3>
|
|||
|
|
<div style="padding: 5px;" align="center"> <img
|
|||
|
|
src="images/intlogo.gif" border="0" height="51" width="127" /><a
|
|||
|
|
title="www.adobe.com home page" href="http://www.adobe.com/"
|
|||
|
|
tabindex="2" style="border: medium none ;"> </a> </div>
|
|||
|
|
</td>
|
|||
|
|
<td
|
|||
|
|
style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;"
|
|||
|
|
valign="top" width="100%">
|
|||
|
|
<!-- End Header --><br />
|
|||
|
|
<p>
|
|||
|
|
</p>
|
|||
|
|
<h1>Polygon Set Concept</h1>
|
|||
|
|
<p> </p>
|
|||
|
|
<p>The polygon_set concept tag is <font face="Courier New">
|
|||
|
|
polygon_set_concept</font></p>
|
|||
|
|
<p> <font face="Times New Roman">The semantic of a polygon_set
|
|||
|
|
is zero or more geometry regions. A Polygon Set Concept may be
|
|||
|
|
defined with floating point 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 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.</font></p>
|
|||
|
|
<p>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.</p>
|
|||
|
|
<p>Example code <a href="gtl_custom_polygon_set.htm">custom_polygon_set.cpp</a>
|
|||
|
|
demonstrates mapping a user defined class to the library
|
|||
|
|
polygon_set_concept</p>
|
|||
|
|
<p>An object that is a model of <font face="Courier New">
|
|||
|
|
polygon_set_concept</font> can be viewed as a model of <font
|
|||
|
|
face="Courier New">
|
|||
|
|
polygon_90_set_concept</font> or <font face="Courier New">
|
|||
|
|
polygon_45_set_concept</font> if it is determined at runtime to conform
|
|||
|
|
to the restrictions of those concepts. This concept casting is
|
|||
|
|
accomplished through the <font face="Courier New">view_as<>()</font>
|
|||
|
|
function.</p>
|
|||
|
|
<p><font face="Courier New">view_as<polygon_90_set_concept>(polygon_set_object)<br />
|
|||
|
|
view_as<polygon_45_set_concept>(polygon_set_object)</font></p>
|
|||
|
|
<p>The return value of <font face="Courier New">view_as<>()</font>
|
|||
|
|
can be passed into any interface that expects an object of the
|
|||
|
|
conceptual type specified in its template parameter. Polygon sets
|
|||
|
|
cannot be viewed as single polygons or rectangles since it generally
|
|||
|
|
cannot be known whether a polygon set contains only a single polygon
|
|||
|
|
without converting to polygons.</p>
|
|||
|
|
<h2>Operators</h2>
|
|||
|
|
<p>The return type of some operators is the <font
|
|||
|
|
face="Courier New">polygon_set_view</font> operator template
|
|||
|
|
type. This type is itself a model of the polygon 90 set concept,
|
|||
|
|
but furthermore can be used as an argument to the <font
|
|||
|
|
face="Courier New">polygon_set_data</font> constructor and assignment
|
|||
|
|
operator. The operator template exists to eliminate temp copies
|
|||
|
|
of intermediate results when Boolean operators are chained together.</p>
|
|||
|
|
<p>Operators are declared inside the namespace <font
|
|||
|
|
face="Courier New">boost::polygon::operators</font>.</p>
|
|||
|
|
<table id="table5" border="1" width="100%">
|
|||
|
|
<tbody>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename T1, typename T2><br />
|
|||
|
|
polygon_set_view <b>operator</b>|(const T1& l, const T2& r)</font></td>
|
|||
|
|
<td>Boolean OR operation (polygon set union). Accepts
|
|||
|
|
two objects that model polygon_set or one of its refinements.
|
|||
|
|
Returns an operator template that performs the operation on demand when
|
|||
|
|
chained or or nested in a library function call such as assign().
|
|||
|
|
Expected n log n runtime, worst case quadratic runtime wrt. vertices +
|
|||
|
|
intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename T1, typename T2><br />
|
|||
|
|
polygon_set_view <b>operator</b>+(const T1& l, const T2& r)</font></td>
|
|||
|
|
<td>Same as operator|. The plus sign is also used for
|
|||
|
|
OR operations in Boolean logic expressions. Expected n log n
|
|||
|
|
runtime, worst case quadratic runtime wrt. vertices + intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename T1, typename T2><br />
|
|||
|
|
polygon_set_view <b>operator</b>&(const T1& l, const T2& r)</font></td>
|
|||
|
|
<td>Boolean AND operation (polygon set intersection).
|
|||
|
|
Accepts two objects that model polygon_set or one of its
|
|||
|
|
refinements. Expected n log n runtime, worst case quadratic
|
|||
|
|
runtime wrt. vertices + intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename T1, typename T2><br />
|
|||
|
|
polygon_set_view <b>operator</b>*(const T1& l, const T2& r)</font></td>
|
|||
|
|
<td>Same as operator&. The multiplication symbol
|
|||
|
|
is also used for AND operations in Boolean logic expressions.
|
|||
|
|
Expected n log n runtime, worst case quadratic runtime wrt. vertices +
|
|||
|
|
intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename T1, typename T2><br />
|
|||
|
|
polygon_set_view <b>operator</b>^(const T1& l, const T2& r)</font></td>
|
|||
|
|
<td>Boolean XOR operation (polygon set
|
|||
|
|
disjoint-union). Accepts two objects that model polygon_set or
|
|||
|
|
one of its refinements. Expected n log n runtime, worst case
|
|||
|
|
quadratic runtime wrt. vertices + intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename T1, typename T2><br />
|
|||
|
|
polygon_set_view <b>operator</b>-(const T1& l, const T2& r)</font></td>
|
|||
|
|
<td>Boolean SUBTRACT operation (polygon set
|
|||
|
|
difference). Accepts two objects that model polygon_set or one of
|
|||
|
|
its refinements. Expected n log n runtime, worst case quadratic
|
|||
|
|
runtime wrt. vertices + intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename T1, typename T2><br />
|
|||
|
|
T1& <b>operator</b>|=(const T1& l, const T2& r)</font></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"><font face="Courier New">template
|
|||
|
|
<typename T1, typename T2><br />
|
|||
|
|
T1& <b>operator</b>+=(T1& l, const T2& r)</font></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"><font face="Courier New">template
|
|||
|
|
<typename T1, typename T2><br />
|
|||
|
|
T1& <b>operator</b>&=(const T1& l, const T2& r)</font></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"><font face="Courier New">template
|
|||
|
|
<typename T1, typename T2><br />
|
|||
|
|
T1& <b>operator</b>*=(T1& l, const T2& r)</font></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"><font face="Courier New">template
|
|||
|
|
<typename T1, typename T2><br />
|
|||
|
|
T1& <b>operator</b>^=(const T1& l, const T2& r)</font></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"><font face="Courier New">template
|
|||
|
|
<typename T1, typename T2><br />
|
|||
|
|
T1& <b>operator</b>-=(T1& l, const T2& r)</font></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"><font face="Courier New">template
|
|||
|
|
<typename T1><br />
|
|||
|
|
T1 <b>operator</b>+(const T1&, coordinate_type bloating)</font></td>
|
|||
|
|
<td>Performs resize operation, inflating by bloating
|
|||
|
|
ammount. If negative the result is a shrink instead of
|
|||
|
|
bloat. Note: returns result by value. Expected n log n
|
|||
|
|
runtime, worst case quadratic runtime wrt. vertices + intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename T1, typename T2><br />
|
|||
|
|
T1 <b>operator</b>-(const T1&, coordinate_type shrinking)</font></td>
|
|||
|
|
<td>Performs resize operation, deflating by bloating
|
|||
|
|
ammount. If negative the result is a bloat instead of
|
|||
|
|
shrink. Note: returns result by value. Expected n log n
|
|||
|
|
runtime, worst case quadratic runtime wrt. vertices + intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename T1, typename T2><br />
|
|||
|
|
T1& <b>operator</b>+=(const T1&, coordinate_type bloating)</font></td>
|
|||
|
|
<td>Performs resize operation, inflating by bloating
|
|||
|
|
ammount. If negative the result is a shrink instead of
|
|||
|
|
bloat. Returns reference to modified argument. Expected n
|
|||
|
|
log n runtime, worst case quadratic runtime wrt. vertices +
|
|||
|
|
intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename T1, typename T2><br />
|
|||
|
|
T1& <b>operator</b>-=(const T1&, coordinate_type shrinking)</font></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>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
<h2>Functions</h2>
|
|||
|
|
<table id="table6" border="1" width="100%">
|
|||
|
|
<tbody>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename T1, typename T2><br />
|
|||
|
|
T1& <b>assign</b>(T1& lvalue, const T2& rvalue)</font></td>
|
|||
|
|
<td>Eliminates overlaps in geometry and copies from an
|
|||
|
|
object that models polygon_set or any of its refinements into an object
|
|||
|
|
that models polygon_set. Expected n log n runtime, worst case
|
|||
|
|
quadratic runtime wrt. vertices + intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename T1, typename T2><br />
|
|||
|
|
bool <b>equivalence</b>(const T1& lvalue, const T2& rvalue) </font></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 that models polygon_set or one of its refinements.
|
|||
|
|
For example: two of polygon objects. Expected n log n runtime,
|
|||
|
|
worst case quadratic runtime wrt. vertices + intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename output_container_type, typename T><br />
|
|||
|
|
void <b>get_trapezoids</b>(output_container_type& output, <br />
|
|||
|
|
|
|||
|
|
const T& polygon_set)</font></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
|
|||
|
|
vertical slicing orientation and appends them to the output, which must
|
|||
|
|
have a value type that models polygon or polygon_with_holes.
|
|||
|
|
Expected n log n runtime, worst case quadratic runtime wrt. vertices +
|
|||
|
|
intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename output_container_type, typename T><br />
|
|||
|
|
void <b>get_trapezoids</b>(output_container_type& output, <br />
|
|||
|
|
|
|||
|
|
const T& polygon_set,<br />
|
|||
|
|
|
|||
|
|
orientation_2d orient)</font></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 orientation and appends them to the output, which
|
|||
|
|
must have a value type that models polygon or polygon_with_holes.
|
|||
|
|
Expected n log n runtime, worst case quadratic runtime wrt. vertices +
|
|||
|
|
intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename polygon_set_type><br />
|
|||
|
|
void <b>clear</b>(polygon_set_type& polygon_set)</font></td>
|
|||
|
|
<td>Makes the object empty of geometry.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename polygon_set_type><br />
|
|||
|
|
bool <b>empty</b>(const polygon_set_type& polygon_set)</font></td>
|
|||
|
|
<td>Checks whether the object is empty of geometry.
|
|||
|
|
Polygons that are completely covered by holes will result in empty
|
|||
|
|
returning true. Expected n log n runtime, worst case quadratic
|
|||
|
|
runtime wrt. vertices + intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename T, typename rectangle_type><br />
|
|||
|
|
bool <b>extents</b>(rectangle_type& extents_rectangle, <br />
|
|||
|
|
|
|||
|
|
const T& polygon_set)</font></td>
|
|||
|
|
<td>Computes bounding box of an object that models
|
|||
|
|
polygon_set and stores it in an object that models rectangle. If
|
|||
|
|
the polygon set is empty returns false. If there are holes
|
|||
|
|
outside of shells they do not contribute to the extents of the polygon
|
|||
|
|
set. Expected n log n runtime, worst case quadratic runtime wrt.
|
|||
|
|
vertices + intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename T><br />
|
|||
|
|
area_type <b>area</b>(const T& polygon_set)</font></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"><font face="Courier New">template
|
|||
|
|
<typename T><br />
|
|||
|
|
T& <b>bloat</b>(T& polygon_set, unsigned_area_type bloating)</font></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"><font face="Courier New">template
|
|||
|
|
<typename T><br />
|
|||
|
|
T& <b>shrink</b>(T& polygon_set, unsigned_area_type shrinking)</font></td>
|
|||
|
|
<td>Same as getting all the polygons, shrinking them and
|
|||
|
|
overwriting the polygon set with the resulting regions. Expected
|
|||
|
|
n log n runtime, worst case quadratic runtime wrt. vertices +
|
|||
|
|
intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename T, typename coord_type><br />
|
|||
|
|
T& <b>resize</b>(T& polygon_set, coord_type resizing,<br />
|
|||
|
|
bool
|
|||
|
|
corner_fill_arc = false, <br />
|
|||
|
|
unsigned int
|
|||
|
|
num_circle_segments = 0)</font></td>
|
|||
|
|
<td>Same as bloat if resizing is positive, same as shrink
|
|||
|
|
if resizing is negative. Original topology at acute angle
|
|||
|
|
vertices is preserved by default, segmented circular arcs are inserted
|
|||
|
|
if corner_fill_arc is true. num_circle_segments specifies number
|
|||
|
|
of segments to introduce on a full circle when filling acute angle
|
|||
|
|
corners with circular arcs. Expected n log n runtime, worst case
|
|||
|
|
quadratic runtime wrt. vertices + intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename T><br />
|
|||
|
|
T& <b>scale_up</b>(T& polygon_set, unsigned_area_type factor)</font></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"><font face="Courier New">template
|
|||
|
|
<typename T><br />
|
|||
|
|
T& <b>scale_down</b>(T& polygon_set, unsigned_area_type factor)</font></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"><font face="Courier New">template
|
|||
|
|
<typename T, typename transformation_type><br />
|
|||
|
|
T& <b>transform</b>(T& polygon_set,<br />
|
|||
|
|
|
|||
|
|
const transformation_type& transformation)</font></td>
|
|||
|
|
<td>Applies transformation.transform() on all
|
|||
|
|
vertices. Expected n log n runtime, worst case quadratic runtime
|
|||
|
|
wrt. vertices + intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename T><br />
|
|||
|
|
T& <b>keep</b>(T& polygon_set, <br />
|
|||
|
|
unsigned_area_type min_area,<br />
|
|||
|
|
unsigned_area_type max_area,<br />
|
|||
|
|
unsigned_area_type min_width,<br />
|
|||
|
|
unsigned_area_type max_width,<br />
|
|||
|
|
unsigned_area_type
|
|||
|
|
min_height,<br />
|
|||
|
|
unsigned_area_type
|
|||
|
|
max_height)</font></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>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
<h1>Polygon Set Data Object</h1>
|
|||
|
|
<p> </p>
|
|||
|
|
<p>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 indicate that the data
|
|||
|
|
is sorted or scanned the data has not been changed to violate that
|
|||
|
|
assumption. Using the Polygon Set Data type directly can be more
|
|||
|
|
efficient than using lists and vectors of polygons in the functions
|
|||
|
|
above because of the invariants it can enforce which provide the
|
|||
|
|
opportunity to maintain the data is sorted form rather than going all
|
|||
|
|
the way out to polygons then resorting those vertices for a subsequent
|
|||
|
|
operation.</p>
|
|||
|
|
<p>The declaration of Polygon Set Data is the following:</p>
|
|||
|
|
<p><font face="Courier New">template <typename T><br />
|
|||
|
|
class polygon_set_data;</font></p>
|
|||
|
|
<p>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. </p>
|
|||
|
|
<p>Example code <a href="gtl_polygon_set_usage.htm">polygon_set_usage.cpp</a>
|
|||
|
|
demonstrates using the library provided polygon set data types and
|
|||
|
|
functions</p>
|
|||
|
|
<h2>Member Functions</h2>
|
|||
|
|
<table id="table7" border="1" width="100%">
|
|||
|
|
<tbody>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New"><b>polygon_set_data</b>()</font></td>
|
|||
|
|
<td>Default constructor. </td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename iT><br />
|
|||
|
|
<b>polygon_set_data</b>(iT input_begin, iT input_end)</font></td>
|
|||
|
|
<td>Construct with scanning orientation from an iterator
|
|||
|
|
range of insertable objects.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New"> <b>polygon_set_data</b>(const
|
|||
|
|
polygon_set_data& that)</font></td>
|
|||
|
|
<td>Copy construct.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename l, typename r, typename op><br />
|
|||
|
|
<b>polygon_set_data</b>(const
|
|||
|
|
polygon_set_view<l,r,op>& t)</font></td>
|
|||
|
|
<td>Copy construct from a Boolean operator template.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">polygon_set_data&
|
|||
|
|
<br />
|
|||
|
|
<b>operator=</b>(const polygon_set_data& that)</font></td>
|
|||
|
|
<td>Assignment from another polygon set, may change
|
|||
|
|
scanning orientation.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename l, typename r, typename op><br />
|
|||
|
|
polygon_set_data& <br />
|
|||
|
|
<b>operator=</b>(const polygon_set_view<l, r,
|
|||
|
|
op>& that)</font></td>
|
|||
|
|
<td>Assignment from a Boolean operator template.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename geometry_object><br />
|
|||
|
|
polygon_set_data& <b>operator=</b>(const geometry_object& geo)</font></td>
|
|||
|
|
<td>Assignment from an insertable object.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">
|
|||
|
|
template <typename iT><br />
|
|||
|
|
void <b>insert</b>(iT input_begin, iT input_end)</font></td>
|
|||
|
|
<td>Insert objects of an iterator range. Linear wrt
|
|||
|
|
vertices inserted.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">
|
|||
|
|
void <b>insert</b>(const polygon_set_data& polygon_set)</font></td>
|
|||
|
|
<td>Insert a polygon set. Linear wrt vertices
|
|||
|
|
inserted.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">
|
|||
|
|
template <typename geometry_type><br />
|
|||
|
|
void <b>insert</b>(const geometry_type& geometry_object, <br />
|
|||
|
|
bool
|
|||
|
|
is_hole = false)</font></td>
|
|||
|
|
<td>Insert a geometry object, if is_hole is true then the
|
|||
|
|
inserted region is subtractive rather than additive. Linear wrt
|
|||
|
|
vertices inserted.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename output_container><br />
|
|||
|
|
void <b>get</b>(output_container& output) const</font></td>
|
|||
|
|
<td>Expects a standard container of polygons objects.
|
|||
|
|
Will scan and eliminate overlaps. Converts polygon set geometry
|
|||
|
|
to objects of the polygon type and appends them to the container.
|
|||
|
|
Polygons will be output with counterclockwise winding, hole polygons
|
|||
|
|
will be output with clockwise winding. The last vertex of an
|
|||
|
|
output polygon is the duplicate of the first, and the number of points
|
|||
|
|
is equal to the number of edges plus 1. If required by the output
|
|||
|
|
data type, polygons will have holes fractured out to the outer boundary
|
|||
|
|
along the positive y direction and off grid intersections on the outer
|
|||
|
|
boundary introduced by this fracture will be truncated downward.
|
|||
|
|
Expected n log n runtime, worst case quadratic runtime wrt. vertices +
|
|||
|
|
intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename output_container><br />
|
|||
|
|
void <b>get_trapezoids</b>(output_container& output) const</font></td>
|
|||
|
|
<td>Expects a standard container of polygon objects.
|
|||
|
|
Will scan and eliminate overlaps. Slices polygon set geometry to
|
|||
|
|
trapezoids vertically and appends them to the container. Expected
|
|||
|
|
n log n runtime, worst case quadratic runtime wrt. vertices +
|
|||
|
|
intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">
|
|||
|
|
template <typename output_container><br />
|
|||
|
|
void <b>get_trapezoids</b>(output_container& output, <br />
|
|||
|
|
orientation_2d slicing_orientation) const </font> </td>
|
|||
|
|
<td>Expects a standard container of polygon objects.
|
|||
|
|
Will scan and eliminate overlaps. Slices polygon set geometry to
|
|||
|
|
trapezoids along the given orientation and appends them to the
|
|||
|
|
container. Expected n log n runtime, worst case quadratic runtime
|
|||
|
|
wrt. vertices + intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">
|
|||
|
|
bool <b>operator==</b>(const polygon_set_data& p) const</font></td>
|
|||
|
|
<td>Once scanned the data representation of geometry within
|
|||
|
|
a polygon set is in a mathematically canonical form. Comparison
|
|||
|
|
between two sets is therefore a linear time operation once they are in
|
|||
|
|
the scanned state. Will scan and eliminate overlaps in both polygon
|
|||
|
|
sets. Expected n log n runtime, worst case quadratic runtime wrt.
|
|||
|
|
vertices + intersections. </td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">bool <b>operator!=</b>(const
|
|||
|
|
polygon_set_data& p) const</font></td>
|
|||
|
|
<td>Inverse logic of equivalence operator.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">void <b>clear</b>()</font></td>
|
|||
|
|
<td>Make the polygon set empty. Note: does not
|
|||
|
|
de-allocate memory. Use shrink to fit idiom and assign default
|
|||
|
|
constructed polygon set to de-allocate.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">bool <b>empty</b>()
|
|||
|
|
const </font> </td>
|
|||
|
|
<td>Check whether the polygon set contains no
|
|||
|
|
geometry. Will scan and eliminate overlaps because subtractive
|
|||
|
|
regions might make the polygon set empty. Expected n log n
|
|||
|
|
runtime, worst case quadratic runtime wrt. vertices + intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">void <b>clean</b>()
|
|||
|
|
const</font></td>
|
|||
|
|
<td>Scan and eliminate overlaps. Expected n log n
|
|||
|
|
runtime, worst case quadratic runtime wrt. vertices + intersections the
|
|||
|
|
first time, constant time subsequently.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename input_iterator_type><br />
|
|||
|
|
void <b>set</b>(input_iterator_type input_begin, <br />
|
|||
|
|
input_iterator_type
|
|||
|
|
input_end) </font> </td>
|
|||
|
|
<td>Overwrite geometry in polygon set with insertable
|
|||
|
|
objects in the iterator range. </td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename rectangle_type><br />
|
|||
|
|
bool <b>extents</b>(rectangle_type& extents_rectangle) const</font></td>
|
|||
|
|
<td>Given an object that models rectangle, scans and
|
|||
|
|
eliminates overlaps in the polygon set because subtractive regions may
|
|||
|
|
alter its extents then computes the bounding box and assigns it to
|
|||
|
|
extents_rectangle. Expected n log n runtime, worst case quadratic
|
|||
|
|
runtime wrt. vertices + intersections the first time, linear
|
|||
|
|
subsequently.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">polygon_set_data&<br />
|
|||
|
|
<b>resize</b>(coord_type resizing,<br />
|
|||
|
|
bool corner_fill_arc = false, <br />
|
|||
|
|
unsigned int num_circle_segments =
|
|||
|
|
0)</font></td>
|
|||
|
|
<td>Inflates if resizing is positive, deflates if resizing
|
|||
|
|
is negative. Original topology at acute angle vertices is
|
|||
|
|
preserved by default, segmented circular arcs are inserted if
|
|||
|
|
corner_fill_arc is true. num_circle_segments specifies number of
|
|||
|
|
segments to introduce on a full circle when filling acute angle corners
|
|||
|
|
with circular arcs. Specifying zero for num_circle_segments
|
|||
|
|
results in only a single segment being inserted at acute corners.
|
|||
|
|
Expected n log n runtime, worst case quadratic runtime wrt. vertices +
|
|||
|
|
intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename transformation_type><br />
|
|||
|
|
polygon_set_data& <br />
|
|||
|
|
<b>transform</b>(const transformation_type&
|
|||
|
|
transformation) </font> </td>
|
|||
|
|
<td>Applies transformation.transform() on vertices stored
|
|||
|
|
within the polygon set. Expected n log n runtime, worst case
|
|||
|
|
quadratic runtime wrt. vertices + intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">polygon_set_data&
|
|||
|
|
<b>scale_up</b>(unsigned_area_type factor)</font></td>
|
|||
|
|
<td>Scales vertices stored within the polygon set up by
|
|||
|
|
factor. Expected n log n runtime, worst case quadratic runtime
|
|||
|
|
wrt. vertices + intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">polygon_set_data&
|
|||
|
|
<b>scale_down</b>(unsigned_area_type factor)</font> </td>
|
|||
|
|
<td>Scales vertices stored within the polygon set down by
|
|||
|
|
factor. Expected n log n runtime, worst case quadratic runtime
|
|||
|
|
wrt. vertices + intersections.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td width="586"><font face="Courier New">template
|
|||
|
|
<typename scaling_type><br />
|
|||
|
|
polygon_set_data&<br />
|
|||
|
|
<b>scale</b>(const scaling_type& f)</font></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>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr>
|
|||
|
|
<td style="background-color: rgb(238, 238, 238);" nowrap="1"
|
|||
|
|
valign="top"> </td>
|
|||
|
|
<td
|
|||
|
|
style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;"
|
|||
|
|
valign="top" width="100%">
|
|||
|
|
<table class="docinfo" id="table8" 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 <20> Intel Corporation 2008-2010.</td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="field">
|
|||
|
|
<th class="docinfo-name">License:</th>
|
|||
|
|
<td class="field-body">Distributed under the Boost Software
|
|||
|
|
License, Version 1.0. (See accompanying file <tt class="literal"> <span
|
|||
|
|
class="pre">LICENSE_1_0.txt</span></tt> or copy at <a
|
|||
|
|
class="reference" target="_top"
|
|||
|
|
href="http://www.boost.org/LICENSE_1_0.txt">
|
|||
|
|
http://www.boost.org/LICENSE_1_0.txt</a>)</td>
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
</td>
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
</body>
|
|||
|
|
</html>
|