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| <title>Boost Polygon Library: Polygon 45 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_rectangle_concept.htm">Rectangle Concept</a></li> |
| <li><a href="gtl_polygon_90_concept.htm">Polygon 90 Concept</a></li> |
| <li><a href="gtl_polygon_90_with_holes_concept.htm">Polygon 90 With Holes Concept</a></li> |
| <li><a href="gtl_polygon_45_concept.htm">Polygon 45 Concept</a></li> |
| <li><a href="gtl_polygon_45_with_holes_concept.htm">Polygon 45 With Holes Concept</a></li> |
| <li><a href="gtl_polygon_concept.htm">Polygon Concept</a></li> |
| <li><a href="gtl_polygon_with_holes_concept.htm">Polygon With Holes Concept</a></li> |
| <li><a href="gtl_polygon_90_set_concept.htm">Polygon 90 Set Concept</a></li> |
| <li>Polygon 45 Set Concept</li> |
| <li><a href="gtl_polygon_set_concept.htm">Polygon Set Concept</a></li> |
| <li><a href="gtl_connectivity_extraction_90.htm">Connectivity Extraction 90</a></li> |
| <li><a href="gtl_connectivity_extraction_45.htm">Connectivity Extraction 45</a></li> |
| <li><a href="gtl_connectivity_extraction.htm">Connectivity Extraction</a></li> |
| <li><a href="gtl_property_merge_90.htm">Property Merge 90</a></li> |
| <li><a href="gtl_property_merge_45.htm">Property Merge 45</a></li> |
| <li><a href="gtl_property_merge.htm">Property Merge</a></li> |
| </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> |
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| <br> |
| <p> |
| </p><h1>Polygon 45 Set Concept</h1> |
| |
| <p> |
| <p>The polygon_45_set concept tag is <font face="Courier New"> |
| polygon_45_set_concept</font></p> |
| <p> |
| <font face="Times New Roman">The semantic of a polygon_45_set is zero or more |
| geometry regions which have angles at the vertices that are multiples of |
| 45-degrees relative to the coordinate axis. A Polygon 45 Set Concept makes |
| no sense in floating point, but currently does not provide a static assert to |
| prevent it from being used with floating point coordinates. The result of |
| such use is undefined. When the intersection of two 45 degree edges |
| results in a vertex that is off the integer grid that case is handled by |
| inserting a unit length edge between the two 45 degree edges near the off grid |
| intersection point. In the case that data represented contains no |
| 45-degree angles and is Manhattan a runtime check will default to the Manhattan |
| algorithm. The results of which are identical to what the 45-degree |
| algorithm would do, but obtained more efficiently.</font><p> |
| <font face="Times New Roman">The motivation for providing the polygon_45_set is |
| to extend the special case of Manhattan geometry capability of the library to |
| encompass the slightly less common, but still important special case of geometry |
| that is described by angles that are multiples of 45-degress with respect to the |
| coordinate axis. This simplifies the implementation of geometry algorithms |
| and affords many opportunities for optimization. 45-degree algorithms can |
| be 50X faster than arbitrary angle algorithms and are required to provide a |
| complete feature set that meets the performance requirements of application |
| domains in which Manhattan and 45-degree geometry are a common special case.</font><p>Users are recommended to use std::vector and std::list of user defined polygons |
| or library provided polygon_45_set_data<coordinate_type> objects. Lists |
| and vectors of models of polygon_45_concept or polygon_45_with_holes_concept are automatically models of polygon_45_set_concept.</p> |
| <p>An object that is a model of <font face="Courier New"> |
| polygon_45_set_concept</font> can be viewed as a model of <font face="Courier New"> |
| polygon_90_set_concept</font> if it is determined at runtime to conform to the |
| restriction that all edges are axis-parallel. This concept casting is |
| accomplished through the <font face="Courier New">view_as<>()</font> function.</p> |
| <p><font face="Courier New">view_as<polygon_90_set_concept>(polygon_set_object)</font></p> |
| <p>The return value of <font face="Courier New">view_as<>()</font> can be passed |
| into any interface that expects an object of the conceptual type specified in |
| its template parameter. Polygon sets cannot be viewed as single polygons |
| or rectangles since it generally cannot be known whether a polygon set contains |
| only a single polygon without converting to polygons.</p> |
| <h2>Operators</h2> |
| <p>The return type of some operators is the <font face="Courier New">polygon_45_set_view</font> |
| operator template type. This type is itself a model of the polygon 90 set |
| concept, but furthermore can be used as an argument to the <font face="Courier New">polygon_45_set_data</font> |
| constructor and assignment operator. The operator template exists to |
| eliminate temp copies of intermediate results when Boolean operators are chained |
| together.</p> |
| <p>Operators are declared inside the namespace <font face="Courier New">boost::polygon::operators</font>.</p> |
| <table border="1" width="100%" id="table5"> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T1, typename |
| T2><br> |
| polygon_45_set_view <b>operator</b>|(const T1& l, const T2& r)</font></td> |
| <td>Boolean OR operation (polygon set union). Accepts two objects |
| that model polygon_45_set or one of its refinements. Returns an |
| operator template that performs the operation on demand when chained or |
| or nested in a library function call such as assign(). O( n log n) |
| runtime complexity and O(n) memory wrt vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T1, typename |
| T2><br> |
| polygon_45_set_view <b>operator</b>+(const T1& l, const T2& r)</font></td> |
| <td>Same as operator|. The plus sign is also used for OR |
| operations in Boolean logic expressions. O( n log n) runtime |
| complexity and O(n) memory wrt vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T1, typename |
| T2><br> |
| polygon_45_set_view <b>operator</b>&(const T1& l, const T2& r)</font></td> |
| <td>Boolean AND operation (polygon set intersection). Accepts two |
| objects that model polygon_45_set or one of its refinements. O( n |
| log n) runtime complexity and O(n) memory wrt vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T1, typename |
| T2><br> |
| polygon_45_set_view <b>operator</b>*(const T1& l, const T2& r)</font></td> |
| <td>Same as operator&. The multiplication symbol is also used for |
| AND operations in Boolean logic expressions. O( n log n) runtime |
| complexity and O(n) memory wrt vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T1, typename |
| T2><br> |
| polygon_45_set_view <b>operator</b>^(const T1& l, const T2& r)</font></td> |
| <td>Boolean XOR operation (polygon set disjoint-union). Accepts |
| two objects that model polygon_45_set or one of its refinements. |
| O( n log n) runtime complexity and O(n) memory wrt vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T1, typename |
| T2><br> |
| polygon_45_set_view <b>operator</b>-(const T1& l, const T2& r)</font></td> |
| <td>Boolean SUBTRACT operation (polygon set difference). Accepts |
| two objects that model polygon_45_set or one of its refinements. |
| O( n log n) runtime complexity and O(n) memory wrt vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T1, typename |
| T2><br> |
| T1& <b>operator</b>|=(const T1& l, const T2& r)</font></td> |
| <td>Same as operator|, but with self assignment, left operand must model |
| polygon_45_set and not one of it's refinements. O( n log n) |
| runtime complexity and O(n) memory wrt vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T1, typename |
| T2><br> |
| T1& <b>operator</b>+=(T1& l, const T2& r)</font></td> |
| <td>Same as operator+, but with self assignment, left operand must model |
| polygon_45_set and not one of it's refinements. O( n log n) |
| runtime complexity and O(n) memory wrt vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T1, typename |
| T2><br> |
| T1& <b>operator</b>&=(const T1& l, const T2& r)</font></td> |
| <td>Same as operator&, but with self assignment, left operand must model |
| polygon_45_set and not one of it's refinements. O( n log n) |
| runtime complexity and O(n) memory wrt vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T1, typename |
| T2><br> |
| T1& <b>operator</b>*=(T1& l, const T2& r)</font></td> |
| <td>Same as operator*, but with self assignment, left operand must model |
| polygon_45_set and not one of it's refinements. O( n log n) |
| runtime complexity and O(n) memory wrt vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T1, typename |
| T2><br> |
| T1& <b>operator</b>^=(const T1& l, const T2& r)</font></td> |
| <td>Same as operator^, but with self assignment, left operand must model |
| polygon_45_set and not one of it's refinements. O( n log n) |
| runtime complexity and O(n) memory wrt vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T1, typename |
| T2><br> |
| T1& <b>operator</b>-=(T1& l, const T2& r)</font></td> |
| <td>Same as operator-, but with self assignment, left operand must model |
| polygon_45_set and not one of it's refinements. O( n log n) |
| runtime complexity and O(n) memory wrt vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T1><br> |
| T1 <b>operator</b>+(const T1&, coordinate_type bloating)</font></td> |
| <td>Performs resize operation, inflating by bloating ammount. If |
| negative the result is a shrink instead of bloat. Note: returns |
| result by value. O( n log n) runtime complexity and O(n) memory |
| wrt vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T1, typename |
| T2><br> |
| T1 <b>operator</b>-(const T1&, coordinate_type shrinking)</font></td> |
| <td>Performs resize operation, deflating by bloating ammount. If |
| negative the result is a bloat instead of shrink. Note: returns |
| result by value. O( n log n) runtime complexity and O(n) memory |
| wrt vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T1, typename |
| T2><br> |
| T1& <b>operator</b>+=(const T1&, coordinate_type bloating)</font></td> |
| <td>Performs resize operation, inflating by bloating ammount. If |
| negative the result is a shrink instead of bloat. Returns |
| reference to modified argument. O( n log n) runtime complexity and |
| O(n) memory wrt vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T1, typename |
| T2><br> |
| T1& <b>operator</b>-=(const T1&, coordinate_type shrinking)</font></td> |
| <td>Performs resize operation, deflating by bloating ammount. If |
| negative the result is a bloat instead of shrink. Returns |
| reference to modified argument. O( n log n) runtime complexity and |
| O(n) memory wrt vertices + intersections.</td> |
| </tr> |
| </table> |
| <h2>Functions</h2> |
| <table border="1" width="100%" id="table3"> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T1, typename |
| T2><br> |
| T1& <b>assign</b>(T1& lvalue, const T2& rvalue)</font></td> |
| <td>Eliminates overlaps in geometry and copies from an object that |
| models polygon_45_set or any of its refinements into an object that |
| models polygon_45_set. O( n log n) runtime complexity and O(n) |
| memory wrt vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T1, typename |
| T2><br> |
| bool <b>equivalence</b>(const T1& lvalue, const T2& rvalue) </font></td> |
| <td>Returns true if an object that models polygon_45_set or one of its |
| refinements covers the exact same geometric regions as another object |
| that models polygon_45_set or one of its refinements. For example: |
| two of polygon_45 objects. O( n log n) runtime complexity and O(n) |
| memory wrt vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename |
| output_container_type, typename T><br> |
| void <b>get_trapezoids</b>(output_container_type& output, <br> |
| |
| const T& polygon_set)</font></td> |
| <td>Output container is expected to be a standard container. |
| Slices geometry of an object that models polygon_45_set or one of its |
| refinements into non overlapping trapezoids along a vertical slicing |
| orientation and appends them to the |
| output, which must have a value type that models polygon_45, |
| polygon_45_with_holes, polygon or polygon_with_holes. O( n |
| log n) runtime complexity and O(n) memory wrt vertices.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename |
| output_container_type, typename T><br> |
| void <b>get_trapezoids</b>(output_container_type& output, <br> |
| |
| const T& polygon_set,<br> orientation_2d orient)</font></td> |
| <td>Output container is expected to be a standard container. |
| Slices geometry of an object that models polygon_45_set or one of its |
| refinements into non overlapping trapezoids along a the specified slicing |
| orientation and appends them to the |
| output, which must have a value type that models polygon_45, |
| polygon_45_with_holes, polygon or polygon_with_holes. O( n |
| log n) runtime complexity and O(n) memory wrt vertices.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename |
| polygon_set_type><br> |
| void <b>clear</b>(polygon_set_type& polygon_set)</font></td> |
| <td>Makes the object empty of geometry.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename |
| polygon_set_type><br> |
| bool <b>empty</b>(const polygon_set_type& polygon_set)</font></td> |
| <td>Checks whether the object is empty of geometry. Polygons that |
| are completely covered by holes will result in empty returning true. |
| O( n log n) runtime complexity and O(n) memory wrt vertices.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T, typename |
| rectangle_type><br> |
| bool <b>extents</b>(rectangle_type& extents_rectangle, <br> |
| const |
| T& polygon_set)</font></td> |
| <td>Computes bounding box of an object that models polygon_45_set and |
| stores it in an object that models rectangle. If the polygon set |
| is empty returns false. If there are holes outside of shells they |
| do not contribute to the extents of the polygon set. O( n |
| log n) runtime complexity and O(n) memory wrt vertices.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T><br> |
| area_type <b>area</b>(const T& polygon_set)</font></td> |
| <td>Computes the area covered by geometry in an object that models |
| polygon_45_set. O( n log n) runtime complexity and O(n) |
| memory wrt vertices.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T1, typename |
| T2><br> |
| T1& <b>interact</b>(T1& a, const T2& b)</font></td> |
| <td>Given an object that models polygon_45_set and an object that models |
| polygon_45_set or one of its refinements, modifies a to retain only |
| regions that overlap or touch regions in b. O( n log n) |
| runtime complexity and O(n) memory wrt vertices plus intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T><br> |
| T& <b>self_intersect</b>(T& polygon_set)</font></td> |
| <td>Given an object that models polygon_45_set that has self overlapping |
| regions, modifies the argument to contain only the regions of overlap. |
| O( n log n) runtime complexity and O(n) memory wrt vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T><br> |
| T& <b>self_xor</b>(T& polygon_set)</font></td> |
| <td>Given an object that models polygon_45_set that has self overlapping |
| regions, modifies the argument to contain only the regions that do not |
| overlap. O( n log n) runtime complexity and O(n) memory wrt |
| vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T><br> |
| T& <b>bloat</b>(T& polygon_set, unsigned_area_type bloating)</font></td> |
| <td>Same as getting all the polygons, bloating them and putting them |
| back. O( n log n) runtime complexity and O(n) memory wrt vertices |
| + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T><br> |
| T& <b>shrink</b>(T& polygon_set, unsigned_area_type shrinking)</font></td> |
| <td>Same as getting all the polygons, shrinking them and overwriting |
| the polygon set with the resulting regions. O( n log n) runtime |
| complexity and O(n) memory wrt vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T, typename |
| coord_type><br> |
| T& <b>resize</b>(T& polygon_set, coord_type resizing,<br> |
| |
| RoundingOption rounding = CLOSEST, <br> CornerOption corner = INTERSECTION)</font></td> |
| <td>Same as bloat if resizing is positive, same as shrink if resizing is |
| negative. RoundingOption is an enum that controls snapping of |
| non-integer results of resizing 45 degree edges. CornerOption is |
| an enum that controls how corner filling is performed. |
| polygon_45_set_data.hpp defines these enums. O( n log n) runtime |
| complexity and O(n) memory wrt vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T><br> |
| T& <b>grow_and</b>(T& polygon_set, unsigned_area_type bloating)</font></td> |
| <td>Same as bloating non-overlapping regions and then applying self |
| intersect to retain only the overlaps introduced by the bloat. O( |
| n log n) runtime complexity and O(n) memory wrt vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T><br> |
| T& <b>scale_up</b>(T& polygon_set, unsigned_area_type factor)</font></td> |
| <td>Scales geometry up by unsigned factor. O( n log n) runtime |
| complexity and O(n) memory wrt vertices.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T><br> |
| T& <b>scale_down</b>(T& polygon_set, unsigned_area_type factor)</font></td> |
| <td>Scales geometry down by unsigned factor. Snaps 45 degree edges |
| back to 45 degrees after division truncation leads to small changes in |
| angle. O( n log n) runtime complexity and O(n) memory wrt |
| vertices.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T, typename scaling_type><br> |
| T& <b>scale</b>(polygon_set_type& polygon_set, double scaling)</font></td> |
| <td>Scales geometry by multiplying by floating point factor. |
| Snaps 45 degree edges back to 45 degrees after truncation of fractional |
| results of multiply leads to small changes in angle. O( n log n) |
| runtime complexity and O(n) memory wrt vertices.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T, typename transformation_type><br> |
| T& <b>transform</b>(T& polygon_set,<br> |
| const |
| transformation_type& transformation)</font></td> |
| <td>Applies transformation.transform() on all vertices. O( n log |
| n) runtime complexity and O(n) memory wrt vertices.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename T><br> |
| T& <b>keep</b>(T& polygon_set, <br> |
| unsigned_area_type min_area,<br> |
| unsigned_area_type max_area,<br> |
| unsigned_area_type min_width,<br> |
| unsigned_area_type max_width,<br> |
| unsigned_area_type min_height,<br> |
| unsigned_area_type max_height)</font></td> |
| <td>Retains only regions that satisfy the min/max criteria in the |
| argument list. Note: useful for visualization to cull too small |
| polygons. O( n log n) runtime complexity and O(n) memory wrt |
| vertices.</td> |
| </tr> |
| </table> |
| <h1>Polygon 45 Set Data Object</h1> |
| |
| <p> |
| <p>The polygon 45 set data type encapsulates the internal data format that |
| serves as the input to the sweep-line algorithm that implements polygon-clipping |
| Boolean operations. It also internally keeps track of whether that data |
| has been sorted or scanned and maintains the invariant that when its flags |
| indicate that the data is sorted or scanned the data has not been changed to |
| violate that assumption. Using the Polygon 45 Set Data type directly can |
| be more efficient than using lists and vectors of polygons in the functions |
| above because of the invariants it can enforce which provide the opportunity to |
| maintain the data is sorted form rather than going all the way out to polygons |
| then resorting those vertices for a subsequent operation.</p> |
| <p>The declaration of Polygon 45 Set Data is the following:</p> |
| <p><font face="Courier New">template <typename T><br> |
| class polygon_45_set_data;</font></p> |
| <p>The class is parameterized on the coordinate data type. Algorithms that |
| benefit from knowledge of the invariants enforced by the class are implemented |
| as member functions to provide them access to information about those |
| invariants. </p> |
| <h2>Member Functions</h2> |
| <table border="1" width="100%" id="table4"> |
| <tr> |
| <td width="586"><font face="Courier New"><b>polygon_45_set_data</b>()</font></td> |
| <td>Default constructor. </td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename iT><br> |
| <b>polygon_45_set_data</b>(iT input_begin, iT |
| input_end)</font></td> |
| <td>Construct from an iterator range of |
| insertable objects.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New"> |
| <b>polygon_45_set_data</b>(const polygon_45_set_data& that)</font></td> |
| <td>Copy construct.</td> |
| </tr> |
| <tr> |
| <td width="586"> |
| <font face="Courier New">template <typename l, typename r, typename op><br> |
| <b>polygon_45_set_data</b>(const polygon_45_set_view<l,r,op>& |
| t)</font></td> |
| <td>Copy construct from a Boolean operator template.</td> |
| </tr> |
| <tr> |
| <td width="586"> |
| <font face="Courier New">polygon_45_set_data& <br><b>operator=</b>(const polygon_45_set_data& that)</font></td> |
| <td>Assignment from another polygon set, may change scanning |
| orientation.</td> |
| </tr> |
| <tr> |
| <td width="586"> |
| <font face="Courier New">template <typename l, typename r, typename op><br> |
| polygon_45_set_data& <br><b>operator=</b>(const polygon_45_set_view<l, r, |
| op>& that)</font></td> |
| <td>Assignment from a Boolean operator template.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">template <typename geometry_object><br> |
| polygon_45_set_data& <b>operator=</b>(const geometry_object& geo)</font></td> |
| <td>Assignment from an insertable object.</td> |
| </tr> |
| <tr> |
| <td width="586"> |
| <font face="Courier New"> |
| template <typename iT><br> |
| void <b>insert</b>(iT input_begin, iT input_end, <br> bool is_hole = false)</font></td> |
| <td>Insert objects of an iterator range. If is_hole is true |
| inserts subtractive regions. Linear wrt the number of vertices |
| added.</td> |
| </tr> |
| <tr> |
| <td width="586"> |
| <font face="Courier New"> |
| void <b>insert</b>(const polygon_45_set_data& polygon_set, <br> bool is_hole |
| = false)</font></td> |
| <td>Insert a polygon set. Linear wrt the number of vertices added.</td> |
| </tr> |
| <tr> |
| <td width="586"> |
| <font face="Courier New"> |
| template <typename geometry_type><br> |
| void <b>insert</b>(const geometry_type& geometry_object, <br> bool is_hole |
| = false)</font></td> |
| <td>Insert a geometry object, if is_hole is true then the inserted |
| region is subtractive rather than additive. Linear wrt the number |
| of vertices added.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New"> |
| template <typename output_container><br> |
| void <b>get</b>(output_container& output) const</font></td> |
| <td>Expects a standard container of geometry objects. Will scan |
| and eliminate overlaps. Converts polygon set geometry to objects |
| of that type and appends them to the container. Polygons will be |
| output with counterclockwise winding, hole polygons will be output with |
| clockwise winding. The last vertex of an output polygon is not the |
| duplicate of the first, and the number of points is equal to the number |
| of edges. O(n log n) runtime and O(n) memory wrt. vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New"> |
| template <typename output_container><br> |
| void <b>get_polygons</b>(output_container& output) const</font></td> |
| <td>Expects a standard container of polygon objects. Will scan and |
| eliminate overlaps. Converts polygon set geometry to polygons and |
| appends them to the container. Polygons will have holes fractured |
| out to the outer boundary along the positive y direction. O(n log |
| n) runtime and O(n) memory wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New"> |
| template <typename output_container><br> |
| void <b>get_polygons_with_holes</b>(output_container& o) const</font></td> |
| <td>Expects a standard container of polygon with holes objects. Will scan and |
| eliminate overlaps. Converts polygon set geometry to polygons and |
| appends them to the container. O(n log n) runtime and O(n) memory |
| wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New"> |
| template <typename output_container><br> |
| void <b>get_trapezoids</b>(output_container& output) const</font></td> |
| <td>Expects a standard container of polygon objects. Will scan |
| and eliminate overlaps. Slices polygon set geometry to trapezoids |
| vertically and appends them to the container. O(n log n) runtime |
| and O(n) memory wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"> |
| <font face="Courier New"> |
| template <typename output_container><br> |
| void <b>get_trapezoids</b>(output_container& output, <br> orientation_2d |
| slicing_orientation) const </font> |
| </td> |
| <td>Expects a standard container of polygon objects. Will scan |
| and eliminate overlaps. Slices polygon set geometry to trapezoids |
| along the given orientation and appends them to the container. O(n |
| log n) runtime and O(n) memory wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"> |
| <font face="Courier New"> |
| bool <b>operator==</b>(const polygon_45_set_data& p) const</font></td> |
| <td>Once scanned the data representation of geometry within a polygon |
| set is in a mathematically canonical form. Comparison between two |
| sets is therefore a linear time operation once they are in the scanned |
| state. Will scan and eliminate overlaps in both polygon sets. O(n |
| log n) runtime and O(n) memory wrt. vertices + intersections the first |
| time and linear runtime and constant memory subsequently. </td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New"> |
| bool <b>operator!=</b>(const polygon_45_set_data& p) const</font></td> |
| <td>Inverse logic of equivalence operator.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">void <b>clear</b>()</font></td> |
| <td>Make the polygon set empty. Note: does not de-allocate memory. |
| Use shrink to fit idiom and assign default constructed polygon set to |
| de-allocate.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">bool <b>empty</b>() const </font> |
| </td> |
| <td>Check whether the polygon set contains no geometry. Will scan |
| and eliminate overlaps because subtractive regions might make the |
| polygon set empty. O(n log n) runtime and O(n) memory wrt. |
| vertices + intersections the first time and linear runtime and constant |
| memory subsequently. </td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">bool <b>is_manhattan</b>() |
| const</font></td> |
| <td>Returns in constant time the information about whether the geometry |
| contains only Manhattan (axis-parallel rectilinear) edges. |
| Constant time.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">void <b>clean</b>() const</font></td> |
| <td>Scan and eliminate overlaps. O(n log n) runtime and O(n) |
| memory wrt. vertices + intersections the first time and linear runtime |
| and constant memory subsequently. </td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New"> |
| template <typename input_iterator_type><br> |
| void <b>set</b>(input_iterator_type input_begin, <br> input_iterator_type input_end) </font> |
| </td> |
| <td>Overwrite geometry in polygon set with insertable objects in the |
| iterator range. </td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New"> |
| template <typename rectangle_type><br> |
| bool <b>extents</b>(rectangle_type& extents_rectangle) const</font></td> |
| <td>Given an object that models rectangle, scans and eliminates overlaps |
| in the polygon set because subtractive regions may alter its extents |
| then computes the bounding box and assigns it to extents_rectangle. |
| O(n log n) runtime and O(n) memory wrt. vertices the first time and |
| linear runtime and constant memory subsequently. </td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New"> |
| polygon_45_set_data&<br> |
| <b>resize</b>(coord_type resizing,<br> |
| RoundingOption rounding = CLOSEST, <br> CornerOption |
| corner = INTERSECTION)</font></td> |
| <td>Same as bloat if resizing is positive, same as shrink if resizing is |
| negative. RoundingOption is an enum that controls snapping of |
| non-integer results of resizing 45 degree edges. CornerOption is |
| an enum that controls how corner filling is performed. |
| polygon_45_set_data.hpp defines these enums. O(n log n) runtime |
| and O(n) memory wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New"> |
| template <typename transformation_type><br> |
| polygon_45_set_data& <br><b>transform</b>(const transformation_type& transformation) </font> |
| </td> |
| <td>Applies transformation.transform() on vertices stored within the |
| polygon set. O(n log n) runtime and O(n) memory wrt. vertices + |
| intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New"> |
| polygon_45_set_data& <b>scale_up</b>(unsigned_area_type factor)</font></td> |
| <td>Scales vertices stored within the polygon set up by factor. |
| Linear wrt vertices.</td> |
| </tr> |
| <tr> |
| <td width="586"> |
| <font face="Courier New">polygon_45_set_data& <b>scale_down</b>(unsigned_area_type |
| factor)</font> </td> |
| <td>Scales vertices stored within the polygon set down by factor. |
| Linear wrt vertices.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">polygon_45_set_data& <b>scale</b>(double factor) </font></td> |
| <td>Scales vertices stored within the polygon set by floating point |
| factor. Linear wrt vertices.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">polygon_45_set_data& <b>self_xor</b>()</font></td> |
| <td>Retain only non-overlapping regions of geometry within polygon set. |
| O(n log n) runtime and O(n) memory wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">polygon_45_set_data& <b>self_intersect</b>()</font></td> |
| <td>Retain only overlapping regions of geometry within a polygon set. |
| O(n log n) runtime and O(n) memory wrt. vertices + intersections.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">bool <b>has_error_data</b>() |
| const </font></td> |
| <td>Returns true if non-integer intersections resulted in small |
| artifacts in the output of a boolean. Constant time.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">std::size_t <b>error_count</b>() |
| const</font></td> |
| <td>Returns the number of artifacts that may potentially be present in |
| the output due to non-integer intersections. Constant time.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">void <b>get_error_data</b>(polygon_45_set_data& |
| p) const</font></td> |
| <td>Populates the input polygon set with 1x1 unit squares that bound the |
| error that may be present in the output due to non-integer |
| intersections. Linear wrt. vertices of error data.</td> |
| </tr> |
| <tr> |
| <td width="586"><font face="Courier New">polygon_45_set_data& <b>self_intersect</b>()</font></td> |
| <td>Retain only overlapping regions of geometry within a polygon set. |
| O(n log n) runtime and O(n) memory wrt. vertices + intersections.</td> |
| </tr> |
| </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="table6"> |
| <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> |
