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| <title>Boost Polygon Library: Polygon Set Concept</title> |
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| <h3 class="navbar">Contents</h3> |
| <ul> |
| <li><a href="index.htm">Boost.Polygon Main Page</a></li> |
| <li><a href="gtl_design_overview.htm">Design Overview</a></li> |
| <li><a href="gtl_isotropy.htm">Isotropy</a></li> |
| <li><a href="gtl_coordinate_concept.htm">Coordinate Concept</a></li> |
| <li><a href="gtl_interval_concept.htm">Interval Concept</a></li> |
| <li><a href="gtl_point_concept.htm">Point Concept</a></li> |
| <li><a href="gtl_segment_concept.htm">Segment Concept</a></li> |
| <li><a href="gtl_rectangle_concept.htm">Rectangle Concept</a></li> |
| <li><a href="gtl_polygon_90_concept.htm">Polygon 90 Concept</a></li> |
| <li><a href="gtl_polygon_90_with_holes_concept.htm">Polygon 90 |
| With Holes Concept</a></li> |
| <li><a href="gtl_polygon_45_concept.htm">Polygon 45 Concept</a></li> |
| <li><a href="gtl_polygon_45_with_holes_concept.htm">Polygon 45 |
| With Holes Concept</a></li> |
| <li><a href="gtl_polygon_concept.htm">Polygon Concept</a></li> |
| <li><a href="gtl_polygon_with_holes_concept.htm">Polygon With |
| Holes Concept</a></li> |
| <li><a href="gtl_polygon_90_set_concept.htm">Polygon 90 Set |
| Concept</a></li> |
| <li><a href="gtl_polygon_45_set_concept.htm">Polygon 45 Set |
| Concept</a></li> |
| <li>Polygon Set Concept</li> |
| <li><a href="gtl_connectivity_extraction_90.htm">Connectivity |
| Extraction 90</a></li> |
| <li><a href="gtl_connectivity_extraction_45.htm">Connectivity |
| Extraction 45</a></li> |
| <li><a href="gtl_connectivity_extraction.htm">Connectivity |
| Extraction</a></li> |
| <li><a href="gtl_property_merge_90.htm">Property Merge 90</a></li> |
| <li><a href="gtl_property_merge_45.htm">Property Merge 45</a></li> |
| <li><a href="gtl_property_merge.htm">Property Merge</a></li> |
| <li><a href="voronoi_main.htm">Voronoi Main Page<br /> |
| </a></li> |
| <li><a href="voronoi_benchmark.htm">Voronoi Benchmark</a><br /> |
| </li> |
| <li><a href="voronoi_builder.htm">Voronoi Builder</a></li> |
| <li><a href="voronoi_diagram.htm">Voronoi Diagram</a></li> |
| </ul> |
| <h3 class="navbar">Other Resources</h3> |
| <ul> |
| <li><a href="GTL_boostcon2009.pdf">GTL Boostcon 2009 Paper</a></li> |
| <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009 |
| Presentation</a></li> |
| <li><a href="analysis.htm">Performance Analysis</a></li> |
| <li><a href="gtl_tutorial.htm">Layout Versus Schematic Tutorial</a></li> |
| <li><a href="gtl_minkowski_tutorial.htm">Minkowski Sum Tutorial</a></li> |
| <li><a href="voronoi_basic_tutorial.htm">Voronoi Basic Tutorial</a></li> |
| <li><a href="voronoi_advanced_tutorial.htm">Voronoi Advanced |
| Tutorial</a></li> |
| </ul> |
| </div> |
| <h3 class="navbar">Polygon Sponsor</h3> |
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| </p> |
| <h1>Polygon Set Concept</h1> |
| <p> </p> |
| <p>The polygon_set concept tag is <font face="Courier New"> |
| polygon_set_concept</font></p> |
| <p> <font face="Times New Roman">The semantic of a polygon_set |
| is zero or more geometry regions. A Polygon Set Concept may be |
| defined with floating point coordinates, but a snap rounding distance |
| of one integer unit will still be applied, furthermore, geometry |
| outside the domain where one integer unit is sufficient to provide |
| robustness may lead to undefined behavior in algorithms. It is |
| recommended to use integer coordinates for robust operations. In |
| the case that data represented contains only Manhattan geometry a |
| runtime check will default to the Manhattan algorithm. The |
| results of which are identical to what the general algorithm would do, |
| but obtained more efficiently. In the case that the data |
| represented contains only Manhattan and 45-degree geometry a runtime |
| check will default to the faster 45-degree algorithm. The results |
| of which may differ slight from what the general algorithm would do |
| because non-integer intersections will be handled differently.</font></p> |
| <p>Users are recommended to use std::vector and std::list of user |
| defined polygons or library provided |
| polygon_set_data<coordinate_type> objects. Lists and |
| vectors of models of polygon_concept or polygon_with_holes_concept are |
| automatically models of polygon_set_concept.</p> |
| <p>Example code <a href="gtl_custom_polygon_set.htm">custom_polygon_set.cpp</a> |
| demonstrates mapping a user defined class to the library |
| polygon_set_concept</p> |
| <p>An object that is a model of <font face="Courier New"> |
| polygon_set_concept</font> can be viewed as a model of <font |
| face="Courier New"> |
| polygon_90_set_concept</font> or <font face="Courier New"> |
| polygon_45_set_concept</font> if it is determined at runtime to conform |
| to the restrictions of those concepts. This concept casting is |
| accomplished through the <font face="Courier New">view_as<>()</font> |
| function.</p> |
| <p><font face="Courier New">view_as<polygon_90_set_concept>(polygon_set_object)<br /> |
| view_as<polygon_45_set_concept>(polygon_set_object)</font></p> |
| <p>The return value of <font face="Courier New">view_as<>()</font> |
| can be passed into any interface that expects an object of the |
| conceptual type specified in its template parameter. Polygon sets |
| cannot be viewed as single polygons or rectangles since it generally |
| cannot be known whether a polygon set contains only a single polygon |
| without converting to polygons.</p> |
| <h2>Operators</h2> |
| <p>The return type of some operators is the <font |
| face="Courier New">polygon_set_view</font> operator template |
| type. This type is itself a model of the polygon 90 set concept, |
| but furthermore can be used as an argument to the <font |
| face="Courier New">polygon_set_data</font> constructor and assignment |
| operator. The operator template exists to eliminate temp copies |
| of intermediate results when Boolean operators are chained together.</p> |
| <p>Operators are declared inside the namespace <font |
| face="Courier New">boost::polygon::operators</font>.</p> |
| <table id="table5" border="1" width="100%"> |
| <tbody> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T1, typename T2><br /> |
| polygon_set_view <b>operator</b>|(const T1& l, const T2& r)</font></td> |
| <td>Boolean OR operation (polygon set union). Accepts |
| two objects that model polygon_set or one of its refinements. |
| Returns an operator template that performs the operation on demand when |
| chained or or nested in a library function call such as assign(). |
| Expected n log n runtime, worst case quadratic runtime wrt. vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T1, typename T2><br /> |
| polygon_set_view <b>operator</b>+(const T1& l, const T2& r)</font></td> |
| <td>Same as operator|. The plus sign is also used for |
| OR operations in Boolean logic expressions. Expected n log n |
| runtime, worst case quadratic runtime wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T1, typename T2><br /> |
| polygon_set_view <b>operator</b>&(const T1& l, const T2& r)</font></td> |
| <td>Boolean AND operation (polygon set intersection). |
| Accepts two objects that model polygon_set or one of its |
| refinements. Expected n log n runtime, worst case quadratic |
| runtime wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T1, typename T2><br /> |
| polygon_set_view <b>operator</b>*(const T1& l, const T2& r)</font></td> |
| <td>Same as operator&. The multiplication symbol |
| is also used for AND operations in Boolean logic expressions. |
| Expected n log n runtime, worst case quadratic runtime wrt. vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T1, typename T2><br /> |
| polygon_set_view <b>operator</b>^(const T1& l, const T2& r)</font></td> |
| <td>Boolean XOR operation (polygon set |
| disjoint-union). Accepts two objects that model polygon_set or |
| one of its refinements. Expected n log n runtime, worst case |
| quadratic runtime wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T1, typename T2><br /> |
| polygon_set_view <b>operator</b>-(const T1& l, const T2& r)</font></td> |
| <td>Boolean SUBTRACT operation (polygon set |
| difference). Accepts two objects that model polygon_set or one of |
| its refinements. Expected n log n runtime, worst case quadratic |
| runtime wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T1, typename T2><br /> |
| T1& <b>operator</b>|=(const T1& l, const T2& r)</font></td> |
| <td>Same as operator|, but with self assignment, left |
| operand must model polygon_set and not one of it's refinements. |
| Expected n log n runtime, worst case quadratic runtime wrt. vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T1, typename T2><br /> |
| T1& <b>operator</b>+=(T1& l, const T2& r)</font></td> |
| <td>Same as operator+, but with self assignment, left |
| operand must model polygon_set and not one of it's refinements. |
| Expected n log n runtime, worst case quadratic runtime wrt. vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T1, typename T2><br /> |
| T1& <b>operator</b>&=(const T1& l, const T2& r)</font></td> |
| <td>Same as operator&, but with self assignment, left |
| operand must model polygon_set and not one of it's refinements. |
| Expected n log n runtime, worst case quadratic runtime wrt. vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T1, typename T2><br /> |
| T1& <b>operator</b>*=(T1& l, const T2& r)</font></td> |
| <td>Same as operator*, but with self assignment, left |
| operand must model polygon_set and not one of it's refinements. |
| Expected n log n runtime, worst case quadratic runtime wrt. vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T1, typename T2><br /> |
| T1& <b>operator</b>^=(const T1& l, const T2& r)</font></td> |
| <td>Same as operator^, but with self assignment, left |
| operand must model polygon_set and not one of it's refinements. |
| Expected n log n runtime, worst case quadratic runtime wrt. vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T1, typename T2><br /> |
| T1& <b>operator</b>-=(T1& l, const T2& r)</font></td> |
| <td>Same as operator-, but with self assignment, left |
| operand must model polygon_set and not one of it's refinements. |
| Expected n log n runtime, worst case quadratic runtime wrt. vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T1><br /> |
| T1 <b>operator</b>+(const T1&, coordinate_type bloating)</font></td> |
| <td>Performs resize operation, inflating by bloating |
| ammount. If negative the result is a shrink instead of |
| bloat. Note: returns result by value. Expected n log n |
| runtime, worst case quadratic runtime wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T1, typename T2><br /> |
| T1 <b>operator</b>-(const T1&, coordinate_type shrinking)</font></td> |
| <td>Performs resize operation, deflating by bloating |
| ammount. If negative the result is a bloat instead of |
| shrink. Note: returns result by value. Expected n log n |
| runtime, worst case quadratic runtime wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T1, typename T2><br /> |
| T1& <b>operator</b>+=(const T1&, coordinate_type bloating)</font></td> |
| <td>Performs resize operation, inflating by bloating |
| ammount. If negative the result is a shrink instead of |
| bloat. Returns reference to modified argument. Expected n |
| log n runtime, worst case quadratic runtime wrt. vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T1, typename T2><br /> |
| T1& <b>operator</b>-=(const T1&, coordinate_type shrinking)</font></td> |
| <td>Performs resize operation, deflating by bloating |
| ammount. If negative the result is a bloat instead of |
| shrink. Returns reference to modified argument. Expected n |
| log n runtime, worst case quadratic runtime wrt. vertices + |
| intersections.</td> |
| </tr> |
| </tbody> |
| </table> |
| <h2>Functions</h2> |
| <table id="table6" border="1" width="100%"> |
| <tbody> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T1, typename T2><br /> |
| T1& <b>assign</b>(T1& lvalue, const T2& rvalue)</font></td> |
| <td>Eliminates overlaps in geometry and copies from an |
| object that models polygon_set or any of its refinements into an object |
| that models polygon_set. Expected n log n runtime, worst case |
| quadratic runtime wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T1, typename T2><br /> |
| bool <b>equivalence</b>(const T1& lvalue, const T2& rvalue) </font></td> |
| <td>Returns true if an object that models polygon_set or |
| one of its refinements covers the exact same geometric regions as |
| another object that models polygon_set or one of its refinements. |
| For example: two of polygon objects. Expected n log n runtime, |
| worst case quadratic runtime wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename output_container_type, typename T><br /> |
| void <b>get_trapezoids</b>(output_container_type& output, <br /> |
| |
| const T& polygon_set)</font></td> |
| <td>Output container is expected to be a standard |
| container. Slices geometry of an object that models polygon_set |
| or one of its refinements into non overlapping trapezoids along a |
| vertical slicing orientation and appends them to the output, which must |
| have a value type that models polygon or polygon_with_holes. |
| Expected n log n runtime, worst case quadratic runtime wrt. vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename output_container_type, typename T><br /> |
| void <b>get_trapezoids</b>(output_container_type& output, <br /> |
| |
| const T& polygon_set,<br /> |
| |
| orientation_2d orient)</font></td> |
| <td>Output container is expected to be a standard |
| container. Slices geometry of an object that models polygon_set |
| or one of its refinements into non overlapping trapezoids along a the |
| specified slicing orientation and appends them to the output, which |
| must have a value type that models polygon or polygon_with_holes. |
| Expected n log n runtime, worst case quadratic runtime wrt. vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename polygon_set_type><br /> |
| void <b>clear</b>(polygon_set_type& polygon_set)</font></td> |
| <td>Makes the object empty of geometry.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename polygon_set_type><br /> |
| bool <b>empty</b>(const polygon_set_type& polygon_set)</font></td> |
| <td>Checks whether the object is empty of geometry. |
| Polygons that are completely covered by holes will result in empty |
| returning true. Expected n log n runtime, worst case quadratic |
| runtime wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T, typename rectangle_type><br /> |
| bool <b>extents</b>(rectangle_type& extents_rectangle, <br /> |
| |
| const T& polygon_set)</font></td> |
| <td>Computes bounding box of an object that models |
| polygon_set and stores it in an object that models rectangle. If |
| the polygon set is empty returns false. If there are holes |
| outside of shells they do not contribute to the extents of the polygon |
| set. Expected n log n runtime, worst case quadratic runtime wrt. |
| vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T><br /> |
| area_type <b>area</b>(const T& polygon_set)</font></td> |
| <td>Computes the area covered by geometry in an object that |
| models polygon_set. Expected n log n runtime, worst case |
| quadratic runtime wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T><br /> |
| T& <b>bloat</b>(T& polygon_set, unsigned_area_type bloating)</font></td> |
| <td>Same as getting all the polygons, bloating them and |
| putting them back. Expected n log n runtime, worst case quadratic |
| runtime wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T><br /> |
| T& <b>shrink</b>(T& polygon_set, unsigned_area_type shrinking)</font></td> |
| <td>Same as getting all the polygons, shrinking them and |
| overwriting the polygon set with the resulting regions. Expected |
| n log n runtime, worst case quadratic runtime wrt. vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T, typename coord_type><br /> |
| T& <b>resize</b>(T& polygon_set, coord_type resizing,<br /> |
| bool |
| corner_fill_arc = false, <br /> |
| unsigned int |
| num_circle_segments = 0)</font></td> |
| <td>Same as bloat if resizing is positive, same as shrink |
| if resizing is negative. Original topology at acute angle |
| vertices is preserved by default, segmented circular arcs are inserted |
| if corner_fill_arc is true. num_circle_segments specifies number |
| of segments to introduce on a full circle when filling acute angle |
| corners with circular arcs. Expected n log n runtime, worst case |
| quadratic runtime wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T><br /> |
| T& <b>scale_up</b>(T& polygon_set, unsigned_area_type factor)</font></td> |
| <td>Scales geometry up by unsigned factor. Expected n |
| log n runtime, worst case quadratic runtime wrt. vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T><br /> |
| T& <b>scale_down</b>(T& polygon_set, unsigned_area_type factor)</font></td> |
| <td>Scales geometry down by unsigned factor. Expected |
| n log n runtime, worst case quadratic runtime wrt. vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T, typename transformation_type><br /> |
| T& <b>transform</b>(T& polygon_set,<br /> |
| |
| const transformation_type& transformation)</font></td> |
| <td>Applies transformation.transform() on all |
| vertices. Expected n log n runtime, worst case quadratic runtime |
| wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename T><br /> |
| T& <b>keep</b>(T& polygon_set, <br /> |
| unsigned_area_type min_area,<br /> |
| unsigned_area_type max_area,<br /> |
| unsigned_area_type min_width,<br /> |
| unsigned_area_type max_width,<br /> |
| unsigned_area_type |
| min_height,<br /> |
| unsigned_area_type |
| max_height)</font></td> |
| <td>Retains only regions that satisfy the min/max criteria |
| in the argument list. Note: useful for visualization to cull too |
| small polygons. Expected n log n runtime, worst case quadratic |
| runtime wrt. vertices + intersections.</td> |
| </tr> |
| </tbody> |
| </table> |
| <h1>Polygon Set Data Object</h1> |
| <p> </p> |
| <p>The polygon set data type encapsulates the internal data |
| format that serves as the input to the sweep-line algorithm that |
| implements polygon-clipping Boolean operations. It also |
| internally keeps track of whether that data has been sorted or scanned |
| and maintains the invariant that when its flags indicate that the data |
| is sorted or scanned the data has not been changed to violate that |
| assumption. Using the Polygon Set Data type directly can be more |
| efficient than using lists and vectors of polygons in the functions |
| above because of the invariants it can enforce which provide the |
| opportunity to maintain the data is sorted form rather than going all |
| the way out to polygons then resorting those vertices for a subsequent |
| operation.</p> |
| <p>The declaration of Polygon Set Data is the following:</p> |
| <p><font face="Courier New">template <typename T><br /> |
| class polygon_set_data;</font></p> |
| <p>The class is parameterized on the coordinate data type. |
| Algorithms that benefit from knowledge of the invariants enforced by |
| the class are implemented as member functions to provide them access to |
| information about those invariants. </p> |
| <p>Example code <a href="gtl_polygon_set_usage.htm">polygon_set_usage.cpp</a> |
| demonstrates using the library provided polygon set data types and |
| functions</p> |
| <h2>Member Functions</h2> |
| <table id="table7" border="1" width="100%"> |
| <tbody> |
| <tr> |
| <td width="586"><font face="Courier New"><b>polygon_set_data</b>()</font></td> |
| <td>Default constructor. </td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename iT><br /> |
| <b>polygon_set_data</b>(iT input_begin, iT input_end)</font></td> |
| <td>Construct with scanning orientation from an iterator |
| range of insertable objects.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New"> <b>polygon_set_data</b>(const |
| polygon_set_data& that)</font></td> |
| <td>Copy construct.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename l, typename r, typename op><br /> |
| <b>polygon_set_data</b>(const |
| polygon_set_view<l,r,op>& t)</font></td> |
| <td>Copy construct from a Boolean operator template.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">polygon_set_data& |
| <br /> |
| <b>operator=</b>(const polygon_set_data& that)</font></td> |
| <td>Assignment from another polygon set, may change |
| scanning orientation.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename l, typename r, typename op><br /> |
| polygon_set_data& <br /> |
| <b>operator=</b>(const polygon_set_view<l, r, |
| op>& that)</font></td> |
| <td>Assignment from a Boolean operator template.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename geometry_object><br /> |
| polygon_set_data& <b>operator=</b>(const geometry_object& geo)</font></td> |
| <td>Assignment from an insertable object.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New"> |
| template <typename iT><br /> |
| void <b>insert</b>(iT input_begin, iT input_end)</font></td> |
| <td>Insert objects of an iterator range. Linear wrt |
| vertices inserted.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New"> |
| void <b>insert</b>(const polygon_set_data& polygon_set)</font></td> |
| <td>Insert a polygon set. Linear wrt vertices |
| inserted.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New"> |
| template <typename geometry_type><br /> |
| void <b>insert</b>(const geometry_type& geometry_object, <br /> |
| bool |
| is_hole = false)</font></td> |
| <td>Insert a geometry object, if is_hole is true then the |
| inserted region is subtractive rather than additive. Linear wrt |
| vertices inserted.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename output_container><br /> |
| void <b>get</b>(output_container& output) const</font></td> |
| <td>Expects a standard container of polygons objects. |
| Will scan and eliminate overlaps. Converts polygon set geometry |
| to objects of the polygon type and appends them to the container. |
| Polygons will be output with counterclockwise winding, hole polygons |
| will be output with clockwise winding. The last vertex of an |
| output polygon is the duplicate of the first, and the number of points |
| is equal to the number of edges plus 1. If required by the output |
| data type, polygons will have holes fractured out to the outer boundary |
| along the positive y direction and off grid intersections on the outer |
| boundary introduced by this fracture will be truncated downward. |
| Expected n log n runtime, worst case quadratic runtime wrt. vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename output_container><br /> |
| void <b>get_trapezoids</b>(output_container& output) const</font></td> |
| <td>Expects a standard container of polygon objects. |
| Will scan and eliminate overlaps. Slices polygon set geometry to |
| trapezoids vertically and appends them to the container. Expected |
| n log n runtime, worst case quadratic runtime wrt. vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New"> |
| template <typename output_container><br /> |
| void <b>get_trapezoids</b>(output_container& output, <br /> |
| orientation_2d slicing_orientation) const </font> </td> |
| <td>Expects a standard container of polygon objects. |
| Will scan and eliminate overlaps. Slices polygon set geometry to |
| trapezoids along the given orientation and appends them to the |
| container. Expected n log n runtime, worst case quadratic runtime |
| wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New"> |
| bool <b>operator==</b>(const polygon_set_data& p) const</font></td> |
| <td>Once scanned the data representation of geometry within |
| a polygon set is in a mathematically canonical form. Comparison |
| between two sets is therefore a linear time operation once they are in |
| the scanned state. Will scan and eliminate overlaps in both polygon |
| sets. Expected n log n runtime, worst case quadratic runtime wrt. |
| vertices + intersections. </td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">bool <b>operator!=</b>(const |
| polygon_set_data& p) const</font></td> |
| <td>Inverse logic of equivalence operator.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">void <b>clear</b>()</font></td> |
| <td>Make the polygon set empty. Note: does not |
| de-allocate memory. Use shrink to fit idiom and assign default |
| constructed polygon set to de-allocate.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">bool <b>empty</b>() |
| const </font> </td> |
| <td>Check whether the polygon set contains no |
| geometry. Will scan and eliminate overlaps because subtractive |
| regions might make the polygon set empty. Expected n log n |
| runtime, worst case quadratic runtime wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">void <b>clean</b>() |
| const</font></td> |
| <td>Scan and eliminate overlaps. Expected n log n |
| runtime, worst case quadratic runtime wrt. vertices + intersections the |
| first time, constant time subsequently.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename input_iterator_type><br /> |
| void <b>set</b>(input_iterator_type input_begin, <br /> |
| input_iterator_type |
| input_end) </font> </td> |
| <td>Overwrite geometry in polygon set with insertable |
| objects in the iterator range. </td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename rectangle_type><br /> |
| bool <b>extents</b>(rectangle_type& extents_rectangle) const</font></td> |
| <td>Given an object that models rectangle, scans and |
| eliminates overlaps in the polygon set because subtractive regions may |
| alter its extents then computes the bounding box and assigns it to |
| extents_rectangle. Expected n log n runtime, worst case quadratic |
| runtime wrt. vertices + intersections the first time, linear |
| subsequently.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">polygon_set_data&<br /> |
| <b>resize</b>(coord_type resizing,<br /> |
| bool corner_fill_arc = false, <br /> |
| unsigned int num_circle_segments = |
| 0)</font></td> |
| <td>Inflates if resizing is positive, deflates if resizing |
| is negative. Original topology at acute angle vertices is |
| preserved by default, segmented circular arcs are inserted if |
| corner_fill_arc is true. num_circle_segments specifies number of |
| segments to introduce on a full circle when filling acute angle corners |
| with circular arcs. Specifying zero for num_circle_segments |
| results in only a single segment being inserted at acute corners. |
| Expected n log n runtime, worst case quadratic runtime wrt. vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename transformation_type><br /> |
| polygon_set_data& <br /> |
| <b>transform</b>(const transformation_type& |
| transformation) </font> </td> |
| <td>Applies transformation.transform() on vertices stored |
| within the polygon set. Expected n log n runtime, worst case |
| quadratic runtime wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">polygon_set_data& |
| <b>scale_up</b>(unsigned_area_type factor)</font></td> |
| <td>Scales vertices stored within the polygon set up by |
| factor. Expected n log n runtime, worst case quadratic runtime |
| wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">polygon_set_data& |
| <b>scale_down</b>(unsigned_area_type factor)</font> </td> |
| <td>Scales vertices stored within the polygon set down by |
| factor. Expected n log n runtime, worst case quadratic runtime |
| wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template |
| <typename scaling_type><br /> |
| polygon_set_data&<br /> |
| <b>scale</b>(const scaling_type& f)</font></td> |
| <td>Scales vertices stored within the polygon set by |
| applying f.scale(). Expected n log n runtime, worst case |
| quadratic runtime wrt. vertices + intersections.</td> |
| </tr> |
| </tbody> |
| </table> |
| </td> |
| </tr> |
| <tr> |
| <td style="background-color: rgb(238, 238, 238);" nowrap="1" |
| valign="top"> </td> |
| <td |
| style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" |
| valign="top" width="100%"> |
| <table class="docinfo" id="table8" frame="void" rules="none"> |
| <colgroup> <col class="docinfo-name" /><col |
| class="docinfo-content" /> </colgroup> <tbody valign="top"> |
| <tr> |
| <th class="docinfo-name">Copyright:</th> |
| <td>Copyright © 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> |
