843 lines
40 KiB
HTML
843 lines
40 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 45 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>Polygon 45 Set Concept</li>
|
||
<li><a href="gtl_polygon_set_concept.htm">Polygon Set Concept</a></li>
|
||
<li><a href="gtl_connectivity_extraction_90.htm">Connectivity
|
||
Extraction 90</a></li>
|
||
<li><a href="gtl_connectivity_extraction_45.htm">Connectivity
|
||
Extraction 45</a></li>
|
||
<li><a href="gtl_connectivity_extraction.htm">Connectivity
|
||
Extraction</a></li>
|
||
<li><a href="gtl_property_merge_90.htm">Property Merge 90</a></li>
|
||
<li><a href="gtl_property_merge_45.htm">Property Merge 45</a></li>
|
||
<li><a href="gtl_property_merge.htm">Property Merge</a></li>
|
||
<li><a href="voronoi_main.htm">Voronoi Main Page<br />
|
||
</a></li>
|
||
<li><a href="voronoi_benchmark.htm">Voronoi Benchmark</a><br />
|
||
</li>
|
||
<li><a href="voronoi_builder.htm">Voronoi Builder</a></li>
|
||
<li><a href="voronoi_diagram.htm">Voronoi Diagram</a></li>
|
||
</ul>
|
||
<h3 class="navbar">Other Resources</h3>
|
||
<ul>
|
||
<li><a href="GTL_boostcon2009.pdf">GTL Boostcon 2009 Paper</a></li>
|
||
<li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
|
||
Presentation</a></li>
|
||
<li><a href="analysis.htm">Performance Analysis</a></li>
|
||
<li><a href="gtl_tutorial.htm">Layout Versus Schematic Tutorial</a></li>
|
||
<li><a href="gtl_minkowski_tutorial.htm">Minkowski Sum Tutorial</a></li>
|
||
<li><a href="voronoi_basic_tutorial.htm">Voronoi Basic Tutorial</a></li>
|
||
<li><a href="voronoi_advanced_tutorial.htm">Voronoi Advanced
|
||
Tutorial</a></li>
|
||
</ul>
|
||
</div>
|
||
<h3 class="navbar">Polygon Sponsor</h3>
|
||
<div style="padding: 5px;" align="center"> <img
|
||
src="images/intlogo.gif" border="0" height="51" width="127" /><a
|
||
title="www.adobe.com home page" href="http://www.adobe.com/"
|
||
tabindex="2" style="border: medium none ;"> </a> </div>
|
||
</td>
|
||
<td
|
||
style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;"
|
||
valign="top" width="100%">
|
||
<!-- End Header --><br />
|
||
<p>
|
||
</p>
|
||
<h1>Polygon 45 Set Concept</h1>
|
||
<p> </p>
|
||
<p>The polygon_45_set concept tag is <font face="Courier New">
|
||
polygon_45_set_concept</font></p>
|
||
<p> <font face="Times New Roman">The semantic of a
|
||
polygon_45_set is zero or more geometry regions which have angles at
|
||
the vertices that are multiples of 45-degrees relative to the
|
||
coordinate axis. A Polygon 45 Set Concept makes no sense in
|
||
floating point, but currently does not provide a static assert to
|
||
prevent it from being used with floating point coordinates. The
|
||
result of such use is undefined. When the intersection of two 45
|
||
degree edges results in a vertex that is off the integer grid that case
|
||
is handled by inserting a unit length edge between the two 45 degree
|
||
edges near the off grid 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.</font></p>
|
||
<p> <font face="Times New Roman">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 that is described by angles
|
||
that are multiples of 45-degress with respect to the coordinate
|
||
axis. This simplifies the implementation of geometry algorithms
|
||
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.</font></p>
|
||
<p>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.</p>
|
||
<p>An object that is a model of <font face="Courier New">
|
||
polygon_45_set_concept</font> can be viewed as a model of <font
|
||
face="Courier New">
|
||
polygon_90_set_concept</font> if it is determined at runtime to conform
|
||
to the restriction that all edges are axis-parallel. 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)</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_45_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_45_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_45_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_45_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().
|
||
O( n log n) runtime complexity and O(n) memory wrt vertices +
|
||
intersections.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">template
|
||
<typename T1, typename T2><br />
|
||
polygon_45_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. O( n log n) runtime
|
||
complexity and O(n) memory wrt vertices + intersections.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">template
|
||
<typename T1, typename T2><br />
|
||
polygon_45_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_45_set or one of its
|
||
refinements. O( n log n) runtime complexity and O(n) memory wrt
|
||
vertices + intersections.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">template
|
||
<typename T1, typename T2><br />
|
||
polygon_45_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. O(
|
||
n log n) runtime complexity and O(n) memory wrt vertices +
|
||
intersections.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">template
|
||
<typename T1, typename T2><br />
|
||
polygon_45_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_45_set or
|
||
one of its refinements. O( n log n) runtime complexity and O(n)
|
||
memory wrt vertices + intersections.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">template
|
||
<typename T1, typename T2><br />
|
||
polygon_45_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_45_set or one
|
||
of its refinements. O( n log n) runtime complexity and O(n)
|
||
memory 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_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"><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_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"><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_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"><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_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"><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_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"><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_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"><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. O( n log n) runtime
|
||
complexity and O(n) memory 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. O( n log n) runtime
|
||
complexity and O(n) memory 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. O( n log n)
|
||
runtime complexity and O(n) memory 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. O( n log n)
|
||
runtime complexity and O(n) memory wrt vertices + intersections.</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<h2>Functions</h2>
|
||
<table id="table3" 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_45_set or any of its refinements into an
|
||
object that models polygon_45_set. O( n log n) runtime complexity
|
||
and O(n) memory 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_45_set or
|
||
one of its refinements covers the exact same geometric regions as
|
||
another object that models polygon_45_set or one of its
|
||
refinements. For example: two of polygon_45 objects. O( n
|
||
log n) runtime complexity and O(n) memory 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_45_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_45,
|
||
polygon_45_with_holes, polygon or polygon_with_holes. O( n
|
||
log n) runtime complexity and O(n) memory wrt vertices.</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_45_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_45,
|
||
polygon_45_with_holes, polygon or polygon_with_holes. O( n
|
||
log n) runtime complexity and O(n) memory wrt vertices.</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. O( n log n) runtime complexity and O(n)
|
||
memory wrt vertices.</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_45_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. O( n log n) runtime complexity and O(n) memory wrt
|
||
vertices.</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_45_set. O( n log n) runtime complexity and
|
||
O(n) memory wrt vertices.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">template
|
||
<typename T1, typename T2><br />
|
||
T1& <b>interact</b>(T1& a, const T2& b)</font></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 regions that overlap or touch regions in b.
|
||
O( n log n) runtime complexity and O(n) memory wrt vertices plus
|
||
intersections.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">template
|
||
<typename T><br />
|
||
T& <b>self_intersect</b>(T& polygon_set)</font></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. O( n log n) runtime complexity and O(n)
|
||
memory wrt vertices + intersections.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">template
|
||
<typename T><br />
|
||
T& <b>self_xor</b>(T& polygon_set)</font></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 overlap. O( n log n) runtime complexity and
|
||
O(n) memory 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. O( n log n) runtime complexity and O(n) memory
|
||
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. O( n log
|
||
n) runtime complexity and O(n) memory 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 />
|
||
RoundingOption
|
||
rounding = CLOSEST, <br />
|
||
CornerOption
|
||
corner = INTERSECTION)</font></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 an enum that controls how corner filling is
|
||
performed. polygon_45_set_data.hpp defines these enums. O(
|
||
n log n) runtime complexity and O(n) memory wrt vertices +
|
||
intersections.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">template
|
||
<typename T><br />
|
||
T& <b>grow_and</b>(T& polygon_set, unsigned_area_type bloating)</font></td>
|
||
<td>Same as bloating non-overlapping regions and then
|
||
applying self intersect to retain only the overlaps introduced by the
|
||
bloat. O( n log n) runtime complexity and O(n) memory 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. O( n log
|
||
n) runtime complexity and O(n) memory wrt vertices.</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. Snaps 45
|
||
degree edges back to 45 degrees after division truncation leads to
|
||
small changes in angle. O( n log n) runtime complexity and O(n)
|
||
memory wrt vertices.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">template
|
||
<typename T, typename scaling_type><br />
|
||
T& <b>scale</b>(polygon_set_type& polygon_set, double scaling)</font></td>
|
||
<td>Scales geometry by multiplying by floating point
|
||
factor. Snaps 45 degree edges back to 45 degrees after
|
||
truncation of fractional results of multiply leads to small changes in
|
||
angle. O( n log n) runtime complexity and O(n) memory wrt
|
||
vertices.</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. O( n log n) runtime complexity and O(n) memory wrt
|
||
vertices.</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. O( n log n) runtime complexity and O(n) memory
|
||
wrt vertices.</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<h1>Polygon 45 Set Data Object</h1>
|
||
<p> </p>
|
||
<p>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 indicate that the data
|
||
is sorted or scanned the data has not been changed to violate that
|
||
assumption. Using the Polygon 45 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 45 Set Data is the following:</p>
|
||
<p><font face="Courier New">template <typename T><br />
|
||
class polygon_45_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>
|
||
<h2>Member Functions</h2>
|
||
<table id="table4" border="1" width="100%">
|
||
<tbody>
|
||
<tr>
|
||
<td width="586"><font face="Courier New"><b>polygon_45_set_data</b>()</font></td>
|
||
<td>Default constructor. </td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">template
|
||
<typename iT><br />
|
||
<b>polygon_45_set_data</b>(iT input_begin, iT input_end)</font></td>
|
||
<td>Construct from an iterator range of insertable objects.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New"> <b>polygon_45_set_data</b>(const
|
||
polygon_45_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_45_set_data</b>(const
|
||
polygon_45_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_45_set_data&
|
||
<br />
|
||
<b>operator=</b>(const polygon_45_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_45_set_data& <br />
|
||
<b>operator=</b>(const polygon_45_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_45_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, <br />
|
||
bool
|
||
is_hole = false)</font></td>
|
||
<td>Insert objects of an iterator range. If is_hole
|
||
is true inserts subtractive regions. Linear wrt the number of
|
||
vertices added.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">
|
||
void <b>insert</b>(const polygon_45_set_data& polygon_set, <br />
|
||
bool
|
||
is_hole = false)</font></td>
|
||
<td>Insert a polygon set. Linear wrt the number of
|
||
vertices added.</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
|
||
the number of vertices added.</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 geometry objects.
|
||
Will scan and eliminate overlaps. Converts polygon set geometry
|
||
to objects of that 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 not the duplicate of the first, and the number of
|
||
points is equal to the number of edges. O(n log n) runtime and
|
||
O(n) memory wrt. vertices + intersections.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">template
|
||
<typename output_container><br />
|
||
void <b>get_polygons</b>(output_container& output) const</font></td>
|
||
<td>Expects a standard container of polygon objects.
|
||
Will scan and eliminate overlaps. Converts polygon set geometry
|
||
to polygons and appends them to the container. Polygons will have
|
||
holes fractured out to the outer boundary along the positive y
|
||
direction. O(n log n) runtime and O(n) memory wrt. vertices +
|
||
intersections.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">template
|
||
<typename output_container><br />
|
||
void <b>get_polygons_with_holes</b>(output_container& o) const</font></td>
|
||
<td>Expects a standard container of polygon with holes
|
||
objects. Will scan and eliminate overlaps. Converts polygon
|
||
set geometry to polygons and appends them to the container. O(n
|
||
log n) runtime and O(n) memory 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. O(n log
|
||
n) runtime and O(n) memory 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. O(n log n) runtime and O(n) memory wrt. vertices +
|
||
intersections.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">
|
||
bool <b>operator==</b>(const polygon_45_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. O(n log n) runtime and O(n) memory wrt. vertices +
|
||
intersections the first time and linear runtime and constant memory
|
||
subsequently. </td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">bool <b>operator!=</b>(const
|
||
polygon_45_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. O(n log n) runtime and
|
||
O(n) memory wrt. vertices + intersections the first time and linear
|
||
runtime and constant memory subsequently. </td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">bool <b>is_manhattan</b>()
|
||
const</font></td>
|
||
<td>Returns in constant time the information about whether
|
||
the geometry contains only Manhattan (axis-parallel rectilinear)
|
||
edges. Constant time.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">void <b>clean</b>()
|
||
const</font></td>
|
||
<td>Scan and eliminate overlaps. O(n log n) runtime
|
||
and O(n) memory wrt. vertices + intersections the first time and linear
|
||
runtime and constant memory 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. O(n log n) runtime and O(n) memory wrt.
|
||
vertices the first time and linear runtime and constant memory
|
||
subsequently. </td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">polygon_45_set_data&<br />
|
||
<b>resize</b>(coord_type resizing,<br />
|
||
RoundingOption rounding = CLOSEST,
|
||
<br />
|
||
CornerOption corner = INTERSECTION)</font></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 an enum that controls how corner filling is
|
||
performed. polygon_45_set_data.hpp defines these enums. O(n
|
||
log n) runtime and O(n) memory wrt. vertices + intersections.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">template
|
||
<typename transformation_type><br />
|
||
polygon_45_set_data& <br />
|
||
<b>transform</b>(const transformation_type&
|
||
transformation) </font> </td>
|
||
<td>Applies transformation.transform() on vertices stored
|
||
within the polygon set. O(n log n) runtime and O(n) memory wrt.
|
||
vertices + intersections.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">polygon_45_set_data&
|
||
<b>scale_up</b>(unsigned_area_type factor)</font></td>
|
||
<td>Scales vertices stored within the polygon set up by
|
||
factor. Linear wrt vertices.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">polygon_45_set_data&
|
||
<b>scale_down</b>(unsigned_area_type factor)</font> </td>
|
||
<td>Scales vertices stored within the polygon set down by
|
||
factor. Linear wrt vertices.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">polygon_45_set_data&
|
||
<b>scale</b>(double factor) </font></td>
|
||
<td>Scales vertices stored within the polygon set by
|
||
floating point factor. Linear wrt vertices.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">polygon_45_set_data&
|
||
<b>self_xor</b>()</font></td>
|
||
<td>Retain only non-overlapping regions of geometry within
|
||
polygon set. O(n log n) runtime and O(n) memory wrt. vertices +
|
||
intersections.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">polygon_45_set_data&
|
||
<b>self_intersect</b>()</font></td>
|
||
<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>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">bool <b>has_error_data</b>()
|
||
const </font></td>
|
||
<td>Returns true if non-integer intersections resulted in
|
||
small artifacts in the output of a boolean. Constant time.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">std::size_t <b>error_count</b>()
|
||
const</font></td>
|
||
<td>Returns the number of artifacts that may potentially be
|
||
present in the output due to non-integer intersections. Constant
|
||
time.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">void <b>get_error_data</b>(polygon_45_set_data&
|
||
p) const</font></td>
|
||
<td>Populates the input polygon set with 1x1 unit squares
|
||
that bound the error that may be present in the output due to
|
||
non-integer intersections. Linear wrt. vertices of error data.</td>
|
||
</tr>
|
||
<tr>
|
||
<td width="586"><font face="Courier New">polygon_45_set_data&
|
||
<b>self_intersect</b>()</font></td>
|
||
<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>
|
||
</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="table6" 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>
|