boost-react-native-bundle

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> <meta http-equiv="Content-Language" content="en-us"> <meta http-equiv="Content-Type" content="text/html; charset=windows-1252"> <title>Voronoi Diagram</title> <meta http-equiv="content-type" content="text/html; charset=utf-8"> <meta http-equiv="content-type" content="text/html; charset=utf-8"> </head> <body> <table style="margin: 0pt; padding: 0pt; width: 100%;" border="0" cellpadding="0" cellspacing="0"> <tbody> <tr> <td style="background-color: rgb(238, 238, 238);" nowrap="1" valign="top"> <div style="padding: 5px;" align="center"> <img src="images/boost.png" border="0" height="86" width="277"><a title="www.boost.org home page" tabindex="2" style="border: medium none ;" href="http://www.boost.org/"> </a></div> <div style="margin: 5px;"> <h3 class="navbar">Contents</h3> <ul> <li><a href="index.htm">Boost.Polygon Main Page</a></li> <li><a href="gtl_design_overview.htm">Design Overview</a></li> <li><a href="gtl_isotropy.htm">Isotropy</a></li> <li><a href="gtl_coordinate_concept.htm">Coordinate Concept</a></li> <li><a href="gtl_interval_concept.htm">Interval Concept</a></li> <li><a href="gtl_point_concept.htm">Point Concept</a></li> <li><a href="gtl_segment_concept.htm">Segment Concept</a></li> <li><a href="gtl_rectangle_concept.htm">Rectangle Concept</a></li> <li><a href="gtl_polygon_90_concept.htm">Polygon 90 Concept</a></li> <li><a href="gtl_polygon_90_with_holes_concept.htm">Polygon 90 With Holes Concept</a></li> <li><a href="gtl_polygon_45_concept.htm">Polygon 45 Concept</a></li> <li><a href="gtl_polygon_45_with_holes_concept.htm">Polygon 45 With Holes Concept</a></li> <li><a href="gtl_polygon_concept.htm">Polygon Concept</a></li> <li><a href="gtl_polygon_with_holes_concept.htm">Polygon With Holes Concept</a></li> <li><a href="gtl_polygon_90_set_concept.htm">Polygon 90 Set Concept</a></li> <li><a href="gtl_polygon_45_set_concept.htm">Polygon 45 Set Concept</a></li> <li><a href="gtl_polygon_set_concept.htm">Polygon Set Concept</a></li> <li><a href="gtl_connectivity_extraction_90.htm">Connectivity Extraction 90</a></li> <li><a href="gtl_connectivity_extraction_45.htm">Connectivity Extraction 45</a></li> <li><a href="gtl_connectivity_extraction.htm">Connectivity Extraction</a></li> <li><a href="gtl_property_merge_90.htm">Property Merge 90</a></li> <li><a href="gtl_property_merge_45.htm">Property Merge 45</a></li> <li><a href="gtl_property_merge.htm">Property Merge</a></li> <li><a href="voronoi_main.htm">Voronoi Main Page </a></li> <li><a href="voronoi_benchmark.htm">Voronoi Benchmark</a></li> <li><a href="voronoi_builder.htm">Voronoi Builder</a> </li> <li>Voronoi Diagram</li> </ul> <h3 class="navbar">Other Resources</h3> <ul> <li><a href="GTL_boostcon2009.pdf">GTL Boostcon 2009 Paper</a></li> <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009 Presentation</a></li> <li><a href="analysis.htm">Performance Analysis</a></li> <li><a href="gtl_tutorial.htm">Layout Versus Schematic Tutorial</a></li> <li><a href="gtl_minkowski_tutorial.htm">Minkowski Sum Tutorial</a></li> <li><a href="voronoi_basic_tutorial.htm">Voronoi Basic Tutorial</a></li> <li><a href="voronoi_advanced_tutorial.htm">Voronoi Advanced Tutorial</a></li> </ul> </div> <h3 class="navbar">Polygon Sponsor</h3> <div style="padding: 5px;" align="center"> <img src="images/intlogo.gif" border="0" height="51" width="127"><a title="www.adobe.com home page" tabindex="2" style="border: medium none ;" href="http://www.adobe.com/"> </a></div> </td> <td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%"> <br> <h1>Voronoi Diagram</h1> A Voronoi diagram is the computational geometry concept that represents partition of the given space onto regions, with bounds determined by distances to a specified family of objects. The application area of this concept varies <a href="http://www.ics.uci.edu/%7Eeppstein/gina/scot.drysdale.html">from Archaeology to Zoology</a>. The Boost.Polygon Voronoi extension provides implementation of the Voronoi diagram data structure in the 2D space. The internal representation consists of the three arrays, that respectively contain: Voronoi cells (represent the area around the input sites bounded by the Voronoi edges), Voronoi vertices (points where three or more Voronoi edges intersect), Voronoi edges (one dimensional curves containing points equidistant from the two closest input sites). Each of the primitives (cell, vertex, edge) contains pointers to the other linked primitives, so that it's always possible to efficiently traverse the Voronoi graph. The picture below shows the Voronoi vertices in red, Voronoi edges in black, input sites that correspond to the Voronoi cells in blue. It is considered, that each input segment consists of the three sites: segment itself and its endpoints. As the result, two additional Voronoi edges are constructed per each input segment. This is made to simplify the representation of the Voronoi diagram and Voronoi edges in particular.<br> <br> <img src="images/voronoi2.png" alt="" style="width: 600px; height: 600px;"><br> <h2>Important</h2> All the Voronoi primitive data structures (edge, vertex, cell) contain mutable color member. Color type is equivalent to the std::size_t type, except that the upper five bits are reserved for the internal usage. That means, that the maximum supported value by the color member is 32 times less than the one supported by std::size_t.<br> <h2>Declaration</h2> Header: <a href="../../../boost/polygon/voronoi_diagram.hpp">boost/polygon/voronoi_diagram.hpp</a><br> <br> <span style="font-family: Courier New,Courier,monospace;">template <typename T, typename TRAITS = voronoi_diagram_traits<T> ></span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">class voronoi_diagram;<br> </span><font face="Courier New"><span style="font-family: 'Courier New',Courier,monospace;"><br> T</span></font> - the coordinate type of the Voronoi vertices.<br> <span style="font-family: Courier New,Courier,monospace;">TRAITS</span><font face="Courier New"><span style="font-family: 'Courier New',Courier,monospace;"></span></font> - the Voronoi diagram traits.<br> <h2>Member Functions</h2> <span style="font-family: Courier New,Courier,monospace;"> </span> <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2"> <tbody> <tr> <td style="font-family: Courier New,Courier,monospace;"><span style="font-weight: bold;">voronoi_diagram</span>() </td> <td>Default constructor. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">void <span style="font-weight: bold;">clear</span>() </td> <td>Removes all primitives from the Voronoi diagram. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">const cell_container_type& <span style="font-weight: bold;">cells</span>() const </td> <td>Returns the const reference to the cell container. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">const vertex_container_type& <span style="font-weight: bold;">vertices</span>() const </td> <td>Returns the const reference to the vertex container. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">const edge_container_type& <span style="font-weight: bold;">edges</span>() const </td> <td>Returns the const reference to the edge container. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">size_t <span style="font-weight: bold;">num_cells</span>() const </td> <td>Returns the number of the Voronoi cells in the Voronoi diagram. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">size_t <span style="font-weight: bold;">num_edges</span>() const </td> <td>Returns the number of the Voronoi edges (half-edges) in the Voronoi diagram. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">size_t <span style="font-weight: bold;">num_vertices</span>() const </td> <td>Returns the number of the Voronoi vertices in the Voronoi diagram. </td> </tr> </tbody> </table> <h2>Member Types</h2> <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2"> <tbody> <tr> <td style="font-weight: bold;">coordinate_type </td> <td>Coordinate type. </td> </tr> <tr> <td style="font-weight: bold;">cell_type </td> <td>Voronoi cell. </td> </tr> <tr> <td style="font-weight: bold;">vertex_type </td> <td>Voronoi vertex. </td> </tr> <tr> <td style="font-weight: bold;">edge_type </td> <td>Voronoi edge. </td> </tr> <tr> <td style="font-weight: bold;">cell_container_type </td> <td>Container of the Voronoi cells. </td> </tr> <tr> <td style="font-weight: bold;">const_cell_iterator </td> <td>Const cell container iterator. </td> </tr> <tr> <td style="font-weight: bold;">vertex_container_type </td> <td>Container of the Voronoi vertices. </td> </tr> <tr> <td style="font-weight: bold;">const_vertex_iterator </td> <td>Const vertex container iterator. </td> </tr> <tr> <td style="font-weight: bold;">edge_container_type </td> <td>Container of the Voronoi edges. </td> </tr> <tr> <td style="font-weight: bold;">const_edge_iterator </td> <td>Const edge container iterator. </td> </tr> </tbody> </table> <h1>Voronoi Geometry Type</h1> The Voronoi diagram data structure doesn't embed coordinates of the input geometries. Instead it links with those via source index and source category methods of the Voronoi cell primitive. Source index is incrementally given (starting from zero) to each input site inserted into the <a href="voronoi_builder.htm">Voronoi builder</a>. Considering the fact, that each input segment is splitted onto three separate sites with the same index, we distinguish between those using source category. For more examples check the <a href="voronoi_basic_tutorial.htm">Voronoi basic tutorial</a>.<br> <h2>GeometryCategory </h2> Defines geometric category of the input object.<br> Header: <a href="../../../boost/polygon/voronoi_geometry_type.hpp">boost/polygon/</a><a href="../../../boost/polygon/voronoi_geometry_type.hpp">voronoi_geometry_type.hpp</a><br> <br> <span style="font-family: Courier New,Courier,monospace;">enum GeometryCategory {</span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">  GEOMETRY_CATEGORY_POINT = 0x0,</span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">  GEOMETRY_CATEGORY_SEGMENT = 0x1</span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">};</span><br> <h2>SourceCategory</h2> Defines semantic category of the input site.<br> Header: <a href="../../../boost/polygon/voronoi_geometry_type.hpp">boost/polygon/</a><a href="../../../boost/polygon/voronoi_geometry_type.hpp">voronoi_geometry_type.hpp</a><br> <br> <span style="font-family: Courier New,Courier,monospace;">enum SourceCategory {</span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">  // Point subtypes.</span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">  SOURCE_CATEGORY_SINGLE_POINT = 0x0,</span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">  SOURCE_CATEGORY_SEGMENT_START_POINT = 0x1,</span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">  SOURCE_CATEGORY_SEGMENT_END_POINT = 0x2,</span><br style="font-family: Courier New,Courier,monospace;"> <br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">  // Segment subtypes.</span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">  SOURCE_CATEGORY_INITIAL_SEGMENT = 0x8,</span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">  SOURCE_CATEGORY_REVERSE_SEGMENT = 0x9,</span><br style="font-family: Courier New,Courier,monospace;"> <br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">  SOURCE_CATEGORY_GEOMETRY_SHIFT = 0x3,</span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">  SOURCE_CATEGORY_BITMASK = 0x1F</span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">};</span><br> <h2>Member Functions</h2> <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2"> <tbody> <tr> <td style="vertical-align: top;"><span style="font-family: Courier New,Courier,monospace;">bool <span style="font-weight: bold;">belongs</span>(</span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">    SourceCategory source_category,</span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">    GeometryCategory geometry_category)</span> </td> <td style="vertical-align: middle;">Returns true if the given source category belongs to the given geometry category.<br> Returns false otherwise. </td> </tr> </tbody> </table> <h1>Voronoi Edge</h1> A Voronoi edge is a one-dimenstion curve, that contains points equidistant from the two closest input geometries. The Voronoi edge data structure is implemented as the enhanced classical <a href="http://www.flipcode.com/archives/The_Half-Edge_Data_Structure.shtml">half-edge</a> data structure. On the image below, the Voronoi edges are drawn as directed linear (e.g. AE) or curved (e.g. DE) dashed lines of either green (e.g. AE) or black (e.g DE) color. The green edges are considered to be secondary, as they are generated by an input segment and its endpoint (e.g. edge EA, made by segment MN and its endpoint M). All the other edges are considered to be primary (e.g. curved edge CD, made by segment KL and point N). Apart from that, each edge can be finite (e.g. ED) or infinite (e.g. edge starting at point B and going in the east direction).<br> <img src="images/voronoi1.png" alt="" style="width: 600px; height: 600px;"><br> Each Voronoi edge (consider directed edge BA) provides efficient access to the following primitives:<br> <ul> <li>Cell the edge belongs to (Voronoi cell P, with source segment MN)</li> <li>Start point of the edge (Voronoi vertex B, that is equidistant from the following input sites: O, L, MN)</li> <li>End point of the edge (Voronoi vertex A, that is equidistant from the following input sites: O, M, MN)</li> <li>Twin edge (Voronoi edge AB)</li> <li>CCW next edge inside the Voronoi cell, that the edge belongs to (green Voronoi edge AE)</li> <li>CCW previous edge inside the Voronoi cell, that the edge belongs to (Voronoi edge CB)</li> <li>CCW rotated next edge around the start point of the edge (Voronoi edge BC)</li> <li>CCW rotated previous edge around the start point of the edge (infinite Voronoi edge starting at the Voronoi vertex B and going in the east direction) </li> </ul> <h2>Declaration</h2> Header: <a href="../../../boost/polygon/voronoi_diagram.hpp">boost/polygon/voronoi_diagram.hpp</a><br> <br> <span style="font-family: Courier New,Courier,monospace;">template <typename T></span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">class voronoi_edge;<br> <br> T</span> - coordinate type.<br> <h2>Member Functions</h2> <span style="font-family: Courier New,Courier,monospace;"> </span> <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2"> <tbody> <tr> <td><span style="font-family: Courier New,Courier,monospace;"><span style="font-weight: bold;">voronoi_edge</span>(bool is_linear, bool is_primary)</span> </td> <td>Voronoi edge constructor. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">voronoi_cell_type* <span style="font-weight: bold;">cell</span>() </td> <td>Returns the pointer to the Voronoi <span style="font-family: Courier New,Courier,monospace;"></span>cell that the edge belongs to. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">const voronoi_cell_type* <span style="font-weight: bold;">cell</span>() const </td> <td>Returns the const pointer to the Voronoi cell that the edge belongs to. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">void <span style="font-weight: bold;">cell</span>(voronoi_cell_type* c) </td> <td>Sets the Voronoi cell pointer to the cell the current edge belongs to. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">voronoi_vertex_type* <span style="font-weight: bold;">vertex0</span>() </td> <td>Returns the pointer to the start point of the edge.<br> If the edge is infinite in that direction returns NULL. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">const voronoi_vertex_type* <span style="font-weight: bold;">vertex0</span>() const </td> <td>Returns the const pointer to the start point vertex of the edge.<br> If the edge is infinite in that direction returns NULL. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">void <span style="font-weight: bold;">vertex0</span>(voronoi_vertex_type* v) </td> <td>Sets the start point pointer of the edge. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">voronoi_vertex_type* <span style="font-weight: bold;">vertex1</span>() </td> <td>Returns the pointer to the end point of the edge.<br> If the edge is infinite in that direction returns NULL. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">const voronoi_vertex_type* <span style="font-weight: bold;">vertex1</span>() const </td> <td>Returns the const pointer to the end point of the edge.<br> If the edge is infinite in that direction returns NULL. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">voronoi_edge_type* <span style="font-weight: bold;">twin</span>() </td> <td>Returns the pointer to the twin edge. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">const voronoi_edge_type* <span style="font-weight: bold;">twin</span>() const </td> <td>Returns the const pointer to the twin edge. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">void <span style="font-weight: bold;">twin</span>(voronoi_edge_type* e) </td> <td>Sets the twin edge pointer of the edge. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">voronoi_edge_type* <span style="font-weight: bold;">next</span>() </td> <td>Returns the pointer to the CCW next edge within the corresponding Voronoi cell.<br> Edges not necessarily share a common vertex (e.g. infinite edges). </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">const voronoi_edge_type* <span style="font-weight: bold;">next</span>() const </td> <td>Returns the const pointer to the CCW next edge within the corresponding Voronoi cell.<br> Edges not necessarily share a common vertex (e.g. infinite edges). </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">void <span style="font-weight: bold;">next</span>(voronoi_edge_type* e) </td> <td>Sets the CCW next edge pointer of the edge. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">voronoi_edge_type* <span style="font-weight: bold;">prev</span>() </td> <td>Returns the pointer to the CCW prev edge within the corresponding Voronoi cell.<br> Edges not necessarily share a common vertex (e.g. infinite edges). </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">const voronoi_edge_type* <span style="font-weight: bold;">prev</span>() const </td> <td>Returns the const pointer to the CCW prev edge within the corresponding Voronoi cell.<br> Edges not necessarily share a common vertex (e.g. infinite edges). </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">void <span style="font-weight: bold;">prev</span>(voronoi_edge_type* e) </td> <td>Sets the CCW prev edge pointer of the edge. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">color_type <span style="font-weight: bold;">color</span>() const </td> <td>Returns the color value. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">void <span style="font-weight: bold;">color</span>(color_type color) const </td> <td>Sets the color of the edge.<br> Allows to associate the user provided data with the primitive. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">voronoi_edge_type* <span style="font-weight: bold;">rot_next</span>() </td> <td>Returns the pointer to the CCW next edge rotated around the edge start point.<br> Works for infinite edges as well. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">const voronoi_edge_type* <span style="font-weight: bold;">rot_next</span>() const </td> <td>Returns the const pointer to the CCW next edge rotated around the edge start point.<br> Works for infinite edges as well.</td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">voronoi_edge_type* <span style="font-weight: bold;">rot_prev</span>() </td> <td>Returns the pointer to the CCW prev edge rotated around the edge start point.<br> Works for infinite edges as well. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">const voronoi_edge_type* <span style="font-weight: bold;">rot_prev</span>() const </td> <td>Returns the const pointer to the CCW prev edge rotated around the edge start point.<br> Works for infinite edges as well.</td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">bool <span style="font-weight: bold;">is_finite</span>() const </td> <td>Returns true if the both end points of the edge are finite, else false. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">bool <span style="font-weight: bold;">is_infinite</span>() const</td> <td>Returns true if one of the end points of the edge is infinite, else false.</td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">bool <span style="font-weight: bold;">is_linear</span>() const </td> <td>Returns true if the edge is linear (segment, ray, line), else false. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">bool <span style="font-weight: bold;">is_curved</span>() const </td> <td>Returns true if the edge is curved (parabolic arc), else false. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">bool <span style="font-weight: bold;">is_primary</span>() const </td> <td>Returns false if the edge goes through the endpoint of the segment site, else true. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">bool <span style="font-weight: bold;">is_secondary</span>() const</td> <td>Returns true if the edge goes through the endpoint of the segment site, else false.</td> </tr> </tbody> </table> <span style="font-family: Courier New,Courier,monospace;"> </span>All the above methods have O(1) complexity. The size of the Voronoi edge structure is equal to: 5 * sizeof(void *) + sizeof(size_t).<span style="font-family: Courier New,Courier,monospace;"></span><br> <h2>Member Types</h2> <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2"> <tbody> <tr> <td style="font-weight: bold;">coordinate_type </td> <td>Coordinate type. </td> </tr> <tr> <td style="font-weight: bold;">voronoi_cell_type </td> <td>Voronoi cell type. </td> </tr> <tr> <td style="font-weight: bold;">voronoi_vertex_type </td> <td>Voronoi vertex type. </td> </tr> <tr> <td style="font-weight: bold;">voronoi_edge_type </td> <td>Voronoi edge type. </td> </tr> <tr> <td style="vertical-align: top; font-weight: bold;">color_type </td> <td style="vertical-align: top;">Color type (check the Important section). </td> </tr> </tbody> </table> <h1>Voronoi Cell</h1> A Voronoi cell represents a region of the Voronoi diagram bounded by the Voronoi edges. On the image below, there are 7 such regions: P, Q, R, S, T, U, V. Each Voronoi cell can contain a point (e.g. cells Q, S, T, U, V with corresponding input sources N, K, L, O, M respectively) or a segment (e.g. cells P and R with corresponding input sources MN and KL respectively) as its source. The Voronoi cell primitive doesn't contain coordinates of the source geometry, instead it stores the index and category of the source geometry. Source index corresponds to the unique id, issued to each input geometry (e.g. incremental counter, used by the Voronoi builder). Such an index uniquely identifies any input point (e.g. O), however doesn't make any distinction between segment (e.g. MN) and both its end points (e.g. M, N). In order to resolve possible ambiguity, the source category is used, that specifies the semantic topology of the input object (e.g. segment's startpoint, segment's endpoint or segment itself). The Voronoi cell data structure also provides access to a random Voronoi edge, located on the boundary of the cell (e.g. edge AE for the cell P).<br> <img style="width: 600px; height: 600px;" alt="" src="images/voronoi1.png"><br> <h2>Declaration</h2> Header: <a href="../../../boost/polygon/voronoi_diagram.hpp">boost/polygon/voronoi_diagram.hpp</a><br> <br> <span style="font-family: Courier New,Courier,monospace;">template <typename T><br> class voronoi_cell;<br> <br> </span><span style="font-family: Courier New,Courier,monospace;">T</span> - coordinate type.<br> <h2>Member Functions</h2> <span style="font-family: Courier New,Courier,monospace;"> </span> <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2"> <tbody> <tr> <td><span style="font-family: Courier New,Courier,monospace;"><span style="font-weight: bold;">voronoi_cell</span>(source_index_type source_index,</span><span style="font-family: Courier New,Courier,monospace;"><br>              source_category_type source_category)</span> </td> <td>Voronoi cell constructor. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">source_index_type <span style="font-weight: bold;">source_index</span>() const </td> <td>Returns input site index among the other sites.<br> Both segment and its end points will have the same index. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">source_category_type <span style="font-weight: bold;">source_category</span>() const </td> <td>Returns input site category among the other sites.<br> Allows to distinguish between segment site and its endpoints. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">voronoi_edge_type* <span style="font-weight: bold;">incident_edge</span>() </td> <td>Returns the pointer to the one of the boundary edges. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">const voronoi_edge_type* <span style="font-weight: bold;">incident_edge</span>() const </td> <td>Returns the const pointer to the one of the boundary edges. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">void <span style="font-weight: bold;">incident_edge</span>(voronoi_edge_type* e) </td> <td>Sets the incident boundary edge pointer of the cell. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">color_type <span style="font-weight: bold;">color</span>() const </td> <td>Returns the color associated with the cell.</td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">void <span style="font-weight: bold;">color</span>(color_type color) const </td> <td>Sets the color of the cell.<br> Allows to associate the user provided data with the primitive. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">bool <span style="font-weight: bold;">contains_point</span>() const</td> <td>Returns true if the cell contains a point site, else false.</td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">bool <span style="font-weight: bold;">contains_segment</span>() const</td> <td>Returns true if the cell contains a segment site, else false.</td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">bool <span style="font-weight: bold;">is_degenerate</span>() const </td> <td>Returns true if the cell doesn't have an incident edge.<br> Can happen if a few input segments share a common endpoint.</td> </tr> </tbody> </table> <span style="font-family: Courier New,Courier,monospace;"> </span>All the above methods have O(1) complexity. The size of the Voronoi cell structure is equal to: sizeof(void *) + 2 * sizeof(size_t).<span style="font-family: Courier New,Courier,monospace;"></span> <h2>Member Types</h2> <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2"> <tbody> <tr> <td style="font-weight: bold;">coordinate_type </td> <td>Coordinate type. </td> </tr> <tr> <td style="font-weight: bold;">source_index_type</td> <td>Source index type. </td> </tr> <tr> <td style="vertical-align: top; font-weight: bold;">source_category_type </td> <td style="vertical-align: top;">Source category type. </td> </tr> <tr> <td style="vertical-align: top; font-weight: bold;">voronoi_edge_type </td> <td style="vertical-align: top;">Voronoi edge type. </td> </tr> <tr> <td style="font-weight: bold;">color_type </td> <td>Color type (check the Important section). </td> </tr> </tbody> </table> <h2>Miscellaneous</h2> The following code snippet effectively traverses the Voronoi edges around the Voronoi cell:<br> <br> <span style="font-family: Courier New,Courier,monospace;">const voronoi_edge<double>* edge = cell->incident_edge();</span><br> <span style="font-family: Courier New,Courier,monospace;">do {</span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">  edge = edge->next();</span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">  // Do smth. with edge.</span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">} while (edge != cell->incident_edge());</span><br> <h1>Voronoi Vertex</h1> A Voronoi vertex represents a point, that is equidistant from the three or more input geometries. As a consequence, it corresponds to the point of the intersection of the three or more Voronoi edges. On the image below, there are 5 such vertices: A, B, C, D, E. The Voronoi vertex data structure embeds the coordinates of the underlying point and provides access to a random Voronoi edge originating from the vertex (e.g. edge BC for the vertex B).<br> <img style="width: 600px; height: 600px;" alt="" src="images/voronoi1.png"><br> <h2>Declaration</h2> Header: <a href="../../../boost/polygon/voronoi_diagram.hpp">boost/polygon/voronoi_diagram.hpp</a><br> <br> <span style="font-family: Courier New,Courier,monospace;">template <typename T></span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">class voronoi_vertex;<br> <br> </span><span style="font-family: Courier New,Courier,monospace;">T</span> - coordinate type.<br> <h2>Member Functions</h2> <span style="font-family: Courier New,Courier,monospace;"> </span> <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2"> <tbody> <tr> <td><span style="font-family: Courier New,Courier,monospace;"><span style="font-weight: bold;">voronoi_vertex</span>(const coordinate_type& x,<br>                const coordinate_type& y)</span><span style="font-family: Courier New,Courier,monospace;"></span> </td> <td>Voronoi vertex constructor. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">const point_type& <span style="font-weight: bold;">x</span>() const </td> <td>Returns the x-coordinate of the point that represents the vertex. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">const point_type& <span style="font-weight: bold;">y</span>() const</td> <td>Returns the y-coordinate of the point that represents the vertex. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">voronoi_edge_type* <span style="font-weight: bold;">incident_edge</span>() </td> <td>Returns the incident edge pointer. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">const voronoi_edge_type* <span style="font-weight: bold;">incident_edge</span>() const </td> <td>Returns the const pointer to the incident edge. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">void <span style="font-weight: bold;">incident_edge</span>(voronoi_edge_type* e) </td> <td>Sets the incident edge pointer. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">color_type <span style="font-weight: bold;">color</span>() const </td> <td>Returns the color associated with the vertex.</td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace;">void <span style="font-weight: bold;">color</span>(color_type color) const </td> <td>Sets the color of the vertex.<br> Allows to associate the user provided data with the primitive.</td> </tr> </tbody> </table> <span style="font-family: Courier New,Courier,monospace;"> </span>All the above methods have O(1) complexity. The size of the Voronoi vertex structure is equal to: sizeof(void *) + sizeof(size_t) + 2 * sizeof(coordinate_type).<span style="font-family: Courier New,Courier,monospace;"></span> <h2>Member Types</h2> <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2"> <tbody> <tr> <td style="font-weight: bold;">coordinate_type </td> <td>Coordainte type. </td> </tr> <tr> <td style="vertical-align: top; font-weight: bold;">voronoi_edge_type </td> <td style="vertical-align: top;">Voronoi edge type. </td> </tr> <tr> <td style="font-weight: bold;">color_type </td> <td>Color type (check the Important section). </td> </tr> </tbody> </table> <h2>Miscellaneous</h2> The following code snippet effectively traverses the Voronoi edges around the Voronoi vertex:<br> <br> <span style="font-family: Courier New,Courier,monospace;">const voronoi_edge<double>* edge = vertex->incident_edge();</span><br> <span style="font-family: Courier New,Courier,monospace;">do {</span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">  edge = edge->next();</span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">  // Do smth. with edge.</span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">} while (edge != vertex->incident_edge()); </span> <h1>Voronoi Diagram Traits </h1> The Voronoi diagram traits are used to configure the Voronoi primitive types and predicates, used by the Voronoi diagram data structure.<br> The implementation includes default traits specialization for the double output coordinate type.<br> <h2>Declaration</h2> Header: <a href="../../../boost/polygon/voronoi_diagram.hpp">boost/polygon/voronoi_diagram.hpp</a><br> <br> <span style="font-family: Courier New,Courier,monospace;">template <typename T></span><br style="font-family: Courier New,Courier,monospace;"> <span style="font-family: Courier New,Courier,monospace;">struct voronoi_diagram_traits;<br> <br> </span><span style="font-family: Courier New,Courier,monospace;">T</span> - coordinate type.<br> <h2>Member Types</h2> <span style="font-family: Courier New,Courier,monospace;"> </span> <table style="text-align: left; width: 100%;" border="1" cellpadding="2" cellspacing="2"> <tbody> <tr> <td style="font-family: Courier New,Courier,monospace; font-weight: bold;">coordinate_type </td> <td>Coordinate type of the Voronoi diagram primitives. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace; font-weight: bold;">cell_type </td> <td>Voronoi cell type. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace; font-weight: bold;">vertex_type </td> <td>Voronoi vertex type. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace; font-weight: bold;">edge_type </td> <td>Voronoi edge type. </td> </tr> <tr> <td style="font-family: Courier New,Courier,monospace; font-weight: bold;">vertex_equality_predicate_type </td> <td>Predicate that returns true if the two points are considered to be equal.<br> False otherwise. It is used to unite nearby Voronoi vertices. </td> </tr> </tbody> </table> </td> </tr> <tr> <td style="background-color: rgb(238, 238, 238);" nowrap="1"> </td> <td style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" valign="top" width="100%"> <table class="docinfo" id="table2" 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 � Andrii Sydorchuk 2010-2013.</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>