| <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> |
| <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en" xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:(null)1="http://www.w3.org/TR/REC-html40"><head><!-- |
| 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"> |
| <table style="margin: 0pt; padding: 0pt; width: 100%;" border="0" cellpadding="0" cellspacing="0"><tbody><tr> |
| <td style="background-color: rgb(238, 238, 238);" nowrap="1" valign="top"> |
| <div style="padding: 5px;" align="center"> |
| <img border="0" src="images/boost.png" width="277" height="86"><a title="www.boost.org home page" href="http://www.boost.org/" tabindex="2" style="border: medium none ;"> |
| </a> |
| </div> |
| <div style="margin: 5px;"> |
| <h3 class="navbar">Contents</h3> |
| <ul> |
| <li><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_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> |
| </ul> |
| <h3 class="navbar">Other Resources</h3> |
| <ul> |
| <li><a href="GTL_boostcon2009.pdf">GTL Boostcon 2009 Paper</a></li> |
| <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009 |
| Presentation</a></li> |
| <li><a href="analysis.htm">Performance Analysis</a></li> |
| <li><a href="gtl_tutorial.htm">Layout Versus Schematic Tutorial</a></li> |
| <li><a href="gtl_minkowski_tutorial.htm">Minkowski Sum Tutorial</a></li> |
| </ul> |
| </div> |
| <h3 class="navbar">Polygon Sponsor</h3> |
| <div style="padding: 5px;" align="center"> |
| <img border="0" src="images/intlogo.gif" width="127" height="51"> |
| </div> |
| </td> |
| <td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%"> |
| |
| <!-- End Header --> |
| |
| <br> |
| <p> |
| </p><h1>Polygon Set Concept</h1> |
| |
| <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>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 border="1" width="100%" id="table5"> |
| <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> |
| </table> |
| <h2>Functions</h2> |
| <table border="1" width="100%" id="table6"> |
| <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> |
| </table> |
| <h1>Polygon Set Data Object</h1> |
| |
| <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 border="1" width="100%" id="table7"> |
| <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> |
| </table> |
| <tr> |
| <td style="background-color: rgb(238, 238, 238);" nowrap="1" valign="top"> |
| </td> |
| <td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%"> |
| |
| |
| <table class="docinfo" rules="none" frame="void" id="table8"> |
| <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> |
| </table> |
| |
| </html> |
