| <!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 90 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>Polygon 90 Set Concept</li> |
| <li><a href="gtl_polygon_45_set_concept.htm">Polygon 45 Set |
| Concept</a></li> |
| <li><a href="gtl_polygon_set_concept.htm">Polygon Set Concept</a></li> |
| <li><a href="gtl_connectivity_extraction_90.htm">Connectivity |
| Extraction 90</a></li> |
| <li><a href="gtl_connectivity_extraction_45.htm">Connectivity |
| Extraction 45</a></li> |
| <li><a href="gtl_connectivity_extraction.htm">Connectivity |
| Extraction</a></li> |
| <li><a href="gtl_property_merge_90.htm">Property Merge 90</a></li> |
| <li><a href="gtl_property_merge_45.htm">Property Merge 45</a></li> |
| <li><a href="gtl_property_merge.htm">Property Merge</a></li> |
| <li><a href="voronoi_main.htm">Voronoi Main Page<br /> |
| </a></li> |
| <li><a href="voronoi_benchmark.htm">Voronoi Benchmark</a><br /> |
| </li> |
| <li><a href="voronoi_builder.htm">Voronoi Builder</a></li> |
| <li><a href="voronoi_diagram.htm">Voronoi Diagram</a></li> |
| </ul> |
| <h3 class="navbar">Other Resources</h3> |
| <ul> |
| <li><a href="GTL_boostcon2009.pdf">GTL Boostcon 2009 Paper</a></li> |
| <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009 |
| Presentation</a></li> |
| <li><a href="analysis.htm">Performance Analysis</a></li> |
| <li><a href="gtl_tutorial.htm">Layout Versus Schematic Tutorial</a></li> |
| <li><a href="gtl_minkowski_tutorial.htm">Minkowski Sum Tutorial</a></li> |
| <li><a href="voronoi_basic_tutorial.htm">Voronoi Basic Tutorial</a></li> |
| <li><a href="voronoi_advanced_tutorial.htm">Voronoi Advanced |
| Tutorial</a></li> |
| </ul> |
| </div> |
| <h3 class="navbar">Polygon Sponsor</h3> |
| <div style="padding: 5px;" align="center"> <img src="images/intlogo.gif" border="0" height="51" width="127" /><a title="www.adobe.com home page" href="http://www.adobe.com/" tabindex="2" style="border: medium none ;"> </a> </div> |
| </td> |
| <td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%"> |
| <!-- End Header --><br /> |
| <p> |
| </p> |
| <h1>Polygon 90 Set Concept</h1> |
| <p> </p> |
| <p>The polygon_90_set concept tag is <font face="Courier New"> |
| polygon_90_set_concept</font></p> |
| <p> <font face="Times New Roman">The semantic of a |
| polygon_90_set is zero or more Manhattan geometry regions.</font></p> |
| <p> <font face="Times New Roman">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 general planar geometry algorithms. |
| Manhattan geometry processing by the 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.</font></p> |
| <p>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.</p> |
| <h2>Operators</h2> |
| <p>The return type of some operators is the <font face="Courier New">polygon_90_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_90_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="table3" border="1" width="100%"> |
| <tbody> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T1, typename T2><br /> |
| polygon_90_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_90_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_90_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_90_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_90_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_90_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_90_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_90_set or |
| one of its refinements. O( n log n) runtime complexity and O(n) |
| memory wrt vertices + intersections. 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_90_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_90_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_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"><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_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"><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_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"><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_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"><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_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"><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_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"><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="table1" 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_90_set or any of its refinements into an |
| object that models polygon_90_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_90_set or |
| one of its refinements covers the exact same geometric regions as |
| another object that models polygon_90_set or one of its |
| refinements. For example: two of polygon_90 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_rectangles</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_90_set or one of its refinements into non overlapping |
| rectangles and appends them to the output. 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_max_rectangles</b>(output_container_type& output, <br /> |
| |
| const T& polygon_set)</font></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 output. Expected n log n runtime, |
| worst case quadratic rutnime.</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 + 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_90_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 |
| + intersections. </td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T><br /> |
| manhattan_area_type <b>area</b>(const T& polygon_set)</font></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 vertices + intersections. </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_90_set and an |
| object that models polygon_90_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 + 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_90_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_90_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 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"><font face="Courier New">template |
| <typename T><br /> |
| T& <b>bloat</b>(T& polygon_set, orientation_2d orient,<br /> |
| unsigned_area_type |
| bloating)</font></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"><font face="Courier New">template |
| <typename T><br /> |
| T& <b>bloat</b>(T& polygon_set, orientation_2d orient,<br /> |
| unsigned_area_type |
| low_bloating,<br /> |
| unsigned_area_type |
| high_bloating)</font></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"><font face="Courier New">template |
| <typename T><br /> |
| T& <b>bloat</b>(T& polygon_set, direction_2d dir,<br /> |
| unsigned_area_type |
| bloating)</font></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"><font face="Courier New">template |
| <typename T><br /> |
| T& <b>bloat</b>(T& polygon_set, <br /> |
| unsigned_area_type |
| west_bloating,<br /> |
| unsigned_area_type |
| east_bloating,<br /> |
| unsigned_area_type |
| south_bloating,<br /> |
| unsigned_area_type |
| north_bloating)</font></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"><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 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"><font face="Courier New">template |
| <typename T><br /> |
| T& <b>shrink</b>(T& polygon_set, orientation_2d orient,<br /> |
| |
| unsigned_area_type shrinking)</font></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"><font face="Courier New">template |
| <typename T><br /> |
| T& <b>shrink</b>(T& polygon_set, orientation_2d orient,<br /> |
| |
| unsigned_area_type low_shrinking,<br /> |
| |
| unsigned_area_type high_shrinking)</font></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"><font face="Courier New">template |
| <typename T><br /> |
| T& <b>shrink</b>(T& polygon_set, direction_2d dir,<br /> |
| |
| unsigned_area_type shrinking)</font></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"><font face="Courier New">template |
| <typename T><br /> |
| T& <b>shrink</b>(T& polygon_set, <br /> |
| |
| unsigned_area_type west_shrinking,<br /> |
| |
| unsigned_area_type east_shrinking,<br /> |
| |
| unsigned_area_type south_shrinking,<br /> |
| |
| unsigned_area_type north_shrinking)</font></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"><font face="Courier New">template |
| <typename T, typename coord_type><br /> |
| T& <b>resize</b>(T& polygon_set, coord_type resizing)</font></td> |
| <td>Same as bloat if resizing is positive, same as shrink |
| if resizing is negative.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T, typename coord_type><br /> |
| T& <b>resize</b>(polygon_set_type& polygon_set, <br /> |
| coord_type west, |
| coord_type east, <br /> |
| coord_type |
| south, coord_type north)</font></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"><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>grow_and</b>(T& polygon_set, orientation_2d orient,<br /> |
| |
| 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>grow_and</b>(T& polygon_set, orientation_2d orient,<br /> |
| |
| unsigned_area_type low_bloating,<br /> |
| |
| unsigned_area_type high_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>grow_and</b>(T& polygon_set, direction_2d dir,<br /> |
| |
| 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>grow_and</b>(T& polygon_set, <br /> |
| |
| unsigned_area_type west_bloating,<br /> |
| |
| unsigned_area_type east_bloating,<br /> |
| |
| unsigned_area_type south_bloating,<br /> |
| |
| unsigned_area_type north_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 + 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. 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 scaling_type><br /> |
| T& <b>scale</b>(polygon_set_type& polygon_set, <br /> |
| const |
| scaling_type& scaling)</font></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"><font face="Courier New">template |
| <typename T, typename coord_type><br /> |
| T& <b>move</b>(T& polygon_set,<br /> |
| orientation_2d orient, |
| coord_type displacement)</font></td> |
| <td>Moves geometry by displacement amount in the |
| orientation. 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>move</b>(T& polygon_set, coord_type x_displacement, <br /> |
| coord_type y_displacement)</font></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"><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 + 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. O( n log n) runtime complexity and O(n) memory |
| wrt vertices + intersections. </td> |
| </tr> |
| </tbody> |
| </table> |
| <h1>Polygon 90 Set Data Object</h1> |
| <p> </p> |
| <p>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 indicate that the data |
| is sorted or scanned the data has not been changed to violate that |
| assumption. Using the Polygon 90 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 90 Set Data is the following:</p> |
| <p><font face="Courier New">template <typename T><br /> |
| class polygon_90_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="table2" border="1" width="100%"> |
| <tbody> |
| <tr> |
| <td width="586"><font face="Courier New"><b>polygon_90_set_data</b>()</font></td> |
| <td>Default constructor. Scanning orientation |
| defaults to HORIZONTAL</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New"><b>polygon_90_set_data</b>(orientation_2d |
| orient)</font></td> |
| <td>Construct with scanning orientation.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename iT><br /> |
| <b>polygon_90_set_data</b>(orientation_2d orient, <br /> |
| |
| 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_90_set_data</b>(const |
| polygon_90_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_90_set_data</b>(const |
| polygon_90_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"> |
| <b>polygon_90_set_data</b>(orientation_2d orient, <br /> |
| |
| const polygon_90_set_data& that)</font></td> |
| <td>Construct with scanning orientation and copy from |
| another polygon set.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">polygon_90_set_data& |
| <br /> |
| <b>operator=</b>(const polygon_90_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_90_set_data& <br /> |
| <b>operator=</b>(const polygon_90_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_90_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. |
| inserted vertices.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New"> |
| void <b>insert</b>(const polygon_90_set_data& polygon_set)</font></td> |
| <td>Insert a polygon set. Linear wrt. inserted |
| vertices.</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. |
| inserted vertices.</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 |
| complexity and O(n) memory wrt vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td style="vertical-align: top;"><font face="Courier New">template |
| <typename output_container><br /> |
| void <b>get</b>(output_container& output, size_t k) const</font></td> |
| <td style="vertical-align: top;">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. The resulting polygons will |
| have at most k vertices. For Manhattan data k should be at least 4 . |
| 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 |
| complexity and O(n) memory wrt vertices + intersections.<br /> |
| </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 direction |
| of the scanline orientation of the polygon 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 output_container><br /> |
| void <b>get_rectangles</b>(output_container& output) const</font></td> |
| <td>Expects a standard container of rectangle |
| objects. Will scan and eliminate overlaps. Slices polygon |
| set geometry to rectangles along the scanning orientation and appends |
| them to the container. 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><br /> |
| void <b>get_rectangles</b>(output_container& output, <br /> |
| orientation_2d slicing_orientation) const </font> </td> |
| <td>Expects a standard container of rectangle |
| objects. Will scan and eliminate overlaps. Slices polygon |
| set geometry to rectangles along the given orientation and appends them |
| to the container. O( n log n) runtime complexity and O(n) memory |
| wrt vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New"> |
| bool <b>operator==</b>(const polygon_90_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 complexity and O(n) memory wrt vertices |
| + intersections the first time, linear subsequently.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">bool <b>operator!=</b>(const |
| polygon_90_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 |
| complexity and O(n) memory wrt vertices + intersections the first time, |
| linear subsequently.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">orientation_2d <b>orient</b>() |
| const</font></td> |
| <td>Get the scanning orientation. Depending on the |
| data it is sometimes more efficient to scan in a specific |
| orientation. This is particularly true of Manhattan geometry |
| data. 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 |
| complexity and O(n) memory 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, <br /> |
| orientation_2d orient) |
| </font> </td> |
| <td>Overwrite geometry in polygon set with insertable |
| objects in the iterator range. Also sets the scanning orientation |
| to that specified.</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 complexity and O(n) memory |
| wrt vertices + intersections the first time, linear subsequently.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">polygon_90_set_data&<br /> |
| <b>bloat</b>(unsigned_area_type west_bloating,<br /> |
| |
| unsigned_area_type east_bloating,<br /> |
| |
| unsigned_area_type south_bloating,<br /> |
| |
| unsigned_area_type north_bloating) </font></td> |
| <td>Scans to eliminate overlaps and subtractive |
| regions. Inserts rectangles of width specified by bloating values |
| to the indicated side of geometry within the polygon set and fills |
| corners with rectangles of the length and width specified for the |
| adjacent sides. O( n log n) runtime complexity and O(n) memory |
| wrt vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">polygon_90_set_data&<br /> |
| <b>shrink</b>(unsigned_area_type west_shrinking,<br /> |
| |
| unsigned_area_type east_shrinking,<br /> |
| |
| unsigned_area_type south_shrinking,<br /> |
| |
| unsigned_area_type north_shrinking)</font></td> |
| <td>Scans to eliminate overlaps and subtractive |
| regions. Inserts subtractiive rectangles of width specified by |
| bloating values to the indicated side of geometry within the polygon |
| set and subtractive rectangle at convex corners of the length and width |
| specified for the adjacent sides. Scans to eliminate overlapping |
| subtractive regions. O( n log n) runtime complexity and O(n) |
| memory wrt vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">polygon_90_set_data&<br /> |
| <b>resize</b>(coordinate_type west, coordinate_type east, <br /> |
| coordinate_type south, |
| coordinate_type north)</font></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"><font face="Courier New">polygon_90_set_data& |
| <b>move</b>(coordinate_type x_delta, <br /> |
| coordinate_type y_delta) </font> </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"><font face="Courier New">template |
| <typename transformation_type><br /> |
| polygon_90_set_data& <br /> |
| <b>transform</b>(const transformation_type& |
| transformation) </font> </td> |
| <td>Applies transformation.transform() on vertices stored |
| within the polygon set. Linear wrt. vertices.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">polygon_90_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"> |
| <p><font face="Courier New">polygon_90_set_data& <b>scale_down</b>(unsigned_area_type |
| factor)</font> </p> |
| </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">template |
| <typename scaling_type><br /> |
| polygon_90_set_data&<br /> |
| <b>scale</b>(const |
| anisotropic_scale_factor<scaling_type>& f)</font></td> |
| <td>Scales vertices stored within the polygon set by |
| applying f.scale(). Linear wrt. vertices.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">polygon_90_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_90_set_data& |
| <b>self_xor</b>()</font></td> |
| <td>Retain only non-overlapping regions of geometry within |
| polygon set. O( n log n) runtime complexity and O(n) memory wrt |
| vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">polygon_90_set_data& |
| <b>self_intersect</b>()</font></td> |
| <td>Retain only overlapping regions of geometry within a |
| polygon set. O( n log n) runtime complexity and O(n) memory wrt |
| vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">polygon_90_set_data&<br /> |
| <b>interact</b>(const polygon_90_set_data& that)</font></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> |
| </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="table4" frame="void" rules="none"> |
| <colgroup> <col class="docinfo-name" /><col class="docinfo-content" /> </colgroup> <tbody valign="top"> |
| <tr> |
| <th class="docinfo-name">Copyright:</th> |
| <td>Copyright © Intel Corporation 2008-2010.</td> |
| </tr> |
| <tr class="field"> |
| <th class="docinfo-name">License:</th> |
| <td class="field-body">Distributed under the Boost Software |
| License, Version 1.0. (See accompanying file <tt class="literal"> <span class="pre">LICENSE_1_0.txt</span></tt> or copy at <a class="reference" target="_top" href="http://www.boost.org/LICENSE_1_0.txt"> |
| http://www.boost.org/LICENSE_1_0.txt</a>)</td> |
| </tr> |
| </tbody> |
| </table> |
| </td> |
| </tr> |
| </tbody> |
| </table> |
| |
| </body></html> |
