ceph/src/boost/libs/polygon/doc/gtl_polygon_90_concept.htm

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  11   <title>Boost Polygon Library: Polygon 90 Concept</title>
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  27       <h3 class="navbar">Contents</h3>
  28       <ul>
  29         <li><a href="index.htm">Boost.Polygon Main Page</a></li>
  30         <li><a href="gtl_design_overview.htm">Design Overview</a></li>
  31         <li><a href="gtl_isotropy.htm">Isotropy</a></li>
  32         <li><a href="gtl_coordinate_concept.htm">Coordinate Concept</a></li>
  33         <li><a href="gtl_interval_concept.htm">Interval Concept</a></li>
  34         <li><a href="gtl_point_concept.htm">Point Concept</a></li>
  35         <li><a href="gtl_segment_concept.htm">Segment Concept</a></li>
  36         <li><a href="gtl_rectangle_concept.htm">Rectangle Concept</a></li>
  37         <li>Polygon 90 Concept</li>
  38         <li><a href="gtl_polygon_90_with_holes_concept.htm">Polygon 90
  39 With Holes Concept</a></li>
  40         <li><a href="gtl_polygon_45_concept.htm">Polygon 45 Concept</a></li>
  41         <li><a href="gtl_polygon_45_with_holes_concept.htm">Polygon 45
  42 With Holes Concept</a></li>
  43         <li><a href="gtl_polygon_concept.htm">Polygon Concept</a></li>
  44         <li><a href="gtl_polygon_with_holes_concept.htm">Polygon With
  45 Holes Concept</a></li>
  46         <li><a href="gtl_polygon_90_set_concept.htm">Polygon 90 Set
  47 Concept</a></li>
  48         <li><a href="gtl_polygon_45_set_concept.htm">Polygon 45 Set
  49 Concept</a></li>
  50         <li><a href="gtl_polygon_set_concept.htm">Polygon Set Concept</a></li>
  51         <li><a href="gtl_connectivity_extraction_90.htm">Connectivity
  52 Extraction 90</a></li>
  53         <li><a href="gtl_connectivity_extraction_45.htm">Connectivity
  54 Extraction 45</a></li>
  55         <li><a href="gtl_connectivity_extraction.htm">Connectivity
  56 Extraction</a></li>
  57         <li><a href="gtl_property_merge_90.htm">Property Merge 90</a></li>
  58         <li><a href="gtl_property_merge_45.htm">Property Merge 45</a></li>
  59         <li><a href="gtl_property_merge.htm">Property Merge</a></li>
  60         <li><a href="voronoi_main.htm">Voronoi Main Page<br />
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  66       </ul>
  67       <h3 class="navbar">Other Resources</h3>
  68       <ul>
  69         <li><a href="GTL_boostcon2009.pdf">GTL Boostcon 2009 Paper</a></li>
  70         <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009
  71 Presentation</a></li>
  72         <li><a href="analysis.htm">Performance Analysis</a></li>
  73         <li><a href="gtl_tutorial.htm">Layout Versus Schematic Tutorial</a></li>
  74         <li><a href="gtl_minkowski_tutorial.htm">Minkowski Sum Tutorial</a></li>
  75         <li><a href="voronoi_basic_tutorial.htm">Voronoi Basic Tutorial</a></li>
  76         <li><a href="voronoi_advanced_tutorial.htm">Voronoi Advanced
  77 Tutorial</a></li>
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  80       <h3 class="navbar">Polygon Sponsor</h3>
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  90       <p>
  91       </p>
  92       <h1>Polygon 90 Concept</h1>
  93       <p> </p>
  94       <p>The polygon_90 concept tag is <font face="Courier New">
  95 polygon_90_concept</font></p>
  96       <p> To register a user defined type as a model of <font
  97  face="Times New Roman">polygon_90 </font>concept, specialize the
  98 geometry concept meta-function for that type.&nbsp; In the example
  99 below CPolygon90 is registered as a model of polygon_90&nbsp; concept.</p>
 100       <p> <font face="Courier New">template &lt;&gt;<br />
 101 struct geometry_concept&lt;CPolygon90&gt; { typedef polygon_90_concept
 102 type; };</font></p>
 103       <p> <font face="Times New Roman">The semantic of a polygon_90 is
 104 that it can provide iterators over the x and y coordinates that
 105 correspond to its horizontal and vertical sides, starting with an x
 106 coordinate.&nbsp; A mutable polygon_90 must also be able to set its
 107 geometry based on an interator range over such coordinates.&nbsp; Since
 108 most polygons use vertex points in internal storage iterator adaptors
 109 for converting to and from point sequences are provided in
 110 iterator_points_to_compact.hpp and iterator_compact_to_points.hpp to
 111 aid in the specialization of polygon_90_traits.&nbsp; A
 112 std::vector&lt;int&gt; or std::list&lt;int&gt; could be made models of
 113 polygon_90_concept by simply providing access to their iterators
 114 through traits.&nbsp; Library functions that create polygon objects
 115 require that those objects provide a default constructor.</font></p>
 116       <p> <font face="Times New Roman">Below is shown the default
 117 polygon traits.&nbsp; Specialization of these traits is required for
 118 types that don't conform to the default behavior.&nbsp; Note that these
 119 traits are also used by the polygon_90_with_holes concept.</font></p>
 120       <p><font face="Courier New">template &lt;typename T&gt;<br />
 121 struct polygon_90_traits {<br />
 122 &nbsp;&nbsp;&nbsp;&nbsp; typedef typename T::coordinate_type
 123 coordinate_type;<br />
 124 &nbsp;&nbsp;&nbsp;&nbsp; typedef typename T::compact_iterator_type
 125 compact_iterator_type;<br />
 126 &nbsp;&nbsp;&nbsp;&nbsp; static inline compact_iterator_type
 127 begin_compact(const T&amp; t) {<br />
 128 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return
 129 t.begin_compact();<br />
 130 &nbsp;&nbsp;&nbsp;&nbsp; }<br />
 131 &nbsp;&nbsp;&nbsp;&nbsp; static inline compact_iterator_type
 132 end_compact(const T&amp; t) {<br />
 133 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return
 134 t.end_compact();<br />
 135 &nbsp;&nbsp;&nbsp;&nbsp; }<br />
 136 &nbsp;&nbsp;&nbsp;&nbsp; static inline unsigned int size(const T&amp;
 137 t) {<br />
 138 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return t.size();<br />
 139 &nbsp;&nbsp;&nbsp;&nbsp; }<br />
 140 &nbsp;&nbsp;&nbsp;&nbsp; static inline winding_direction winding(const
 141 T&amp; t) {<br />
 142 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return
 143 unknown_winding;<br />
 144 &nbsp;&nbsp;&nbsp;&nbsp; }<br />
 145 };</font></p>
 146       <p><font face="Courier New">template &lt;typename T&gt;<br />
 147 struct polygon_90_mutable_traits { <br />
 148 &nbsp;&nbsp;&nbsp;&nbsp; template &lt;typename iT&gt;<br />
 149 &nbsp;&nbsp;&nbsp;&nbsp; static inline T&amp; set_compact(T&amp; t, iT
 150 input_begin, iT input_end) {<br />
 151 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 152 t.set_compact(input_begin, input_end);<br />
 153 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return t;<br />
 154 &nbsp;&nbsp;&nbsp;&nbsp; }</font><br />
 155       <font face="Courier New">};</font></p>
 156       <p>An object that is a model of <font face="Courier New">
 157 polygon_90_concept</font> can be viewed as a model of any of its
 158 refinements if it is determined at runtime to conform to the
 159 restriction of those concepts.&nbsp; This concept casting is
 160 accomplished through the
 161       <font face="Courier New">view_as&lt;&gt;()</font> function.</p>
 162       <p><font face="Courier New">view_as&lt;rectangle_concept&gt;(polygon_90_object)</font></p>
 163       <p>The return value of <font face="Courier New">view_as&lt;&gt;()</font>
 164 can be passed into any interface that expects an object of the
 165 conceptual type specified in its template parameter.</p>
 166       <h2>Functions</h2>
 167       <table id="table1" border="1" width="100%">
 168         <tbody>
 169           <tr>
 170             <td width="586"><font face="Courier New">template
 171 &lt;typename T&gt;<br />
 172 compact_iterator_type <b>begin_compact</b>(const T&amp; polygon)</font></td>
 173             <td><font face="Times New Roman">Expects a model of
 174 polygon_90.&nbsp; Returns the begin iterator over the range of
 175 coordinates that correspond to horizontal and vertical edges.</font></td>
 176           </tr>
 177           <tr>
 178             <td width="586"><font face="Courier New">template
 179 &lt;typename T&gt;<br />
 180 compact_iterator_type <b>end_compact</b>(const T&amp; polygon)</font></td>
 181             <td><font face="Times New Roman">Expects a model of
 182 polygon_90.&nbsp; Returns the end iterator over the range of
 183 coordinates that correspond to horizontal and vertical edges.</font></td>
 184           </tr>
 185           <tr>
 186             <td width="586"><font face="Courier New">template
 187 &lt;typename T&gt;<br />
 188 point_iterator_type <b>begin_points</b>(const T&amp; polygon)</font></td>
 189             <td><font face="Times New Roman">Expects a model of
 190 polygon_90.&nbsp; Returns the begin iterator over the range of points
 191 that correspond to vertices of the polygon.</font></td>
 192           </tr>
 193           <tr>
 194             <td width="586"><font face="Courier New">template
 195 &lt;typename T&gt;<br />
 196 point_iterator_type <b>end_points</b>(const T&amp; polygon)</font></td>
 197             <td><font face="Times New Roman">Expects a model of
 198 polygon_90.&nbsp; Returns the end iterator over the range of points
 199 that correspond to vertices of the polygon.</font></td>
 200           </tr>
 201           <tr>
 202             <td width="586"><font face="Courier New">template
 203 &lt;typename T, typename iterator&gt;<br />
 204 void <b>set_compact</b>(T&amp; polygon, iterator b, iterator e)</font></td>
 205             <td><font face="Times New Roman">Expects a model of
 206 polygon_90.&nbsp;&nbsp; Sets the polygon to the coordinate data range
 207 [b,e) that corresponds to .horizontal and vertical edges.</font></td>
 208           </tr>
 209           <tr>
 210             <td width="586"><font face="Courier New">template
 211 &lt;typename T, typename iterator&gt;<br />
 212 void <b>set_points</b>(T&amp; polygon, iterator b, iterator e)</font></td>
 213             <td><font face="Times New Roman">Expects a model of
 214 polygon_90.&nbsp;&nbsp; Sets the polygon to the point data range [b,e)
 215 that corresponds to vertices of a manhattan polygon.&nbsp;
 216 Non-manhattan edges between successive input points results in
 217 undefined behavior.</font></td>
 218           </tr>
 219           <tr>
 220             <td width="586"><font face="Courier New">template
 221 &lt;typename T&gt;<br />
 222 unsigned int <b>size</b>(const T&amp; polygon)</font></td>
 223             <td><font face="Times New Roman">Returns the number of
 224 edges in the polygon.</font></td>
 225           </tr>
 226           <tr>
 227             <td width="586"><font face="Courier New">template
 228 &lt;typename T1, typename T2&gt;<br />
 229 T1&amp; <b>assign</b>(T1&amp; left, const T2&amp; right)</font></td>
 230             <td>Copies data from right object that models polygon_90
 231 into left object that models polygon_90.</td>
 232           </tr>
 233           <tr>
 234             <td width="586"><font face="Courier New">template
 235 &lt;typename T, typename point_type&gt;<br />
 236 bool <b>contains</b>(const T&amp;, const point_type&amp; point, <br />
 237 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 238 bool consider_touch=true)</font></td>
 239             <td>Given an object that models polygon_90 and an object
 240 that models point, returns true if the polygon contains the
 241 point.&nbsp; If the consider_touch flag is true will return true if the
 242 point lies along the boundary of the polygon.&nbsp; Linear wrt.
 243 vertices.</td>
 244           </tr>
 245           <tr>
 246             <td width="586"><font face="Courier New">// get the center
 247 coordinate<br />
 248 template &lt;typename T, typename point_type&gt;<br />
 249 void <b>center</b>(point_type&amp; p, const T&amp; polygon)</font></td>
 250             <td>Sets object that models point to the center point of
 251 the bounding box of an object that models polygon_90.&nbsp; Linear wrt.
 252 vertices.</td>
 253           </tr>
 254           <tr>
 255             <td width="586"><font face="Courier New">template
 256 &lt;typename T, typename rectangle_type&gt;<br />
 257 bool <b>extents</b>(rectangle_type&amp; bbox, const T&amp; polygon)</font></td>
 258             <td>Sets object that models rectangle to the bounding box
 259 of an object that models polygon_90 and returns true.&nbsp; Returns
 260 false and leaves bbox unchanged if polygon is empty.&nbsp; Linear wrt.
 261 vertices.</td>
 262           </tr>
 263           <tr>
 264             <td width="586"><font face="Courier New">template
 265 &lt;typename T&gt;<br />
 266 manhattan_area_type <b>area</b>(const T&amp; polygon)</font></td>
 267             <td>Returns the area of an object that models
 268 polygon_90.&nbsp; Linear wrt. vertices.</td>
 269           </tr>
 270           <tr>
 271             <td width="586"><font face="Courier New">template
 272 &lt;typename T&gt;<br />
 273 direction_1d <b>winding</b>(const T&amp; polygon)</font></td>
 274             <td>Returns the winding direction of an object that models
 275 polygon_90, LOW == CLOCKWISE, HIGH = COUNTERCLOCKWISE.&nbsp; Complexity
 276 depends upon winding trait.</td>
 277           </tr>
 278           <tr>
 279             <td width="586"><font face="Courier New">template
 280 &lt;typename T&gt;<br />
 281 coordinate_difference <b>perimeter</b>(const T&amp; polygon)</font></td>
 282             <td>Returns the perimeter length of an object that models
 283 polygon_90.&nbsp; Linear wrt. vertices.</td>
 284           </tr>
 285           <tr>
 286             <td width="586"><font face="Courier New">template
 287 &lt;typename T, typename transform_type&gt;<br />
 288 T&amp; <b>transform</b>(T&amp; polygon, const transform_type&amp;)</font></td>
 289             <td>Applies transform() on the vertices of polygon and sets
 290 the polygon to that described by the result of transforming its
 291 vertices.&nbsp; Linear wrt. vertices.</td>
 292           </tr>
 293           <tr>
 294             <td width="586"><font face="Courier New">template
 295 &lt;typename T&gt;<br />
 296 T&amp; <b>scale_up</b>(T&amp; polygon, unsigned_area_type factor)</font></td>
 297             <td>Scales up coordinate of an object that models
 298 polygon_90 by unsigned factor.&nbsp; Linear wrt. vertices.</td>
 299           </tr>
 300           <tr>
 301             <td width="586"><font face="Courier New">template
 302 &lt;typename T&gt;<br />
 303 T&amp; <b>scale_down</b>(T&amp; polygon, unsigned_area_type factor)</font></td>
 304             <td>Scales down coordinates of an object that models
 305 polygon_90 by unsigned factor.&nbsp; Linear wrt. vertices.</td>
 306           </tr>
 307           <tr>
 308             <td width="586"><font face="Courier New">template
 309 &lt;typename T, scaling_type&gt;<br />
 310 T&amp; <b>scale</b>(T&amp; rectangle, double scaling) </font></td>
 311             <td>Scales coordinates of an object that models polygon_90
 312 by floating point factor.&nbsp; Linear wrt. vertices.</td>
 313           </tr>
 314           <tr>
 315             <td width="586"><font face="Courier New">template
 316 &lt;typename T&gt;<br />
 317 T&amp; <b>move</b>(T&amp; polygon, orientation_2d,<br />
 318 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; coordinate_difference
 319 displacement)</font></td>
 320             <td>Adds displacement value to coordinate indicated by
 321 orientation_2d of vertices of an object that models polygon_90 .&nbsp;
 322 Linear wrt. vertices.</td>
 323           </tr>
 324           <tr>
 325             <td width="586"><font face="Courier New">template
 326 &lt;typename polygon_type, typename point_type&gt;<br />
 327 polygon_type&amp; <b>convolve</b>(polygon_type&amp; polygon,<br />
 328 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 329 const point_type&amp; point)</font></td>
 330             <td>Convolves coordinate values of point with vertices of
 331 an object that models polygon_90.&nbsp; Linear wrt. vertices.</td>
 332           </tr>
 333         </tbody>
 334       </table>
 335       <h1>Polygon 90 Data</h1>
 336       <p> </p>
 337       <p>The library provides a model of polygon 90 concept declared
 338       <font face="Courier New">template&lt;typename T&gt;
 339 polygon_90_data </font>where T is the coordinate type.</p>
 340       <p>This data type is used internally when a Manhattan polygon is
 341 needed and is available to the library user who finds it convenient to
 342 use a library polygon data type instead of providing their own.&nbsp;
 343 The data type is implemented to be convenient to use with the library
 344 traits.</p>
 345       <h2>Members</h2>
 346       <table id="table2" border="1" width="100%">
 347         <tbody>
 348           <tr>
 349             <td width="586"><b><font face="Courier New">geometry_type</font></b></td>
 350             <td><font face="Times New Roman">polygon_90_concept</font></td>
 351           </tr>
 352           <tr>
 353             <td width="586"><b><font face="Courier New">coordinate_type</font></b></td>
 354             <td><font face="Times New Roman">T</font></td>
 355           </tr>
 356           <tr>
 357             <td width="586"><b><font face="Courier New">iterator_type</font></b></td>
 358             <td>Iterator over vertices point_data&lt;T&gt; vertices of
 359 polygon</td>
 360           </tr>
 361           <tr>
 362             <td width="586"><b><font face="Courier New">compact_iterator_type</font></b></td>
 363             <td><font face="Times New Roman">Iterator over
 364 non-redundant coordinates of the polygon, alternating x, y, x, y
 365 starting with an x, where each x corresponds to a vertical edge and
 366 each y corresponds to a horizontal edge.</font></td>
 367           </tr>
 368           <tr>
 369             <td width="586"><font face="Courier New"><b>polygon_90_data</b>()</font></td>
 370             <td><font face="Times New Roman">Default constructs the </font>polygon.</td>
 371           </tr>
 372           <tr>
 373             <td width="586"><font face="Courier New"><b>polygon_90_data</b>(const
 374 polygon_90_data&amp; that)</font></td>
 375             <td><font face="Times New Roman">Copy construct</font></td>
 376           </tr>
 377           <tr>
 378             <td width="586"><font face="Courier New">polygon_90_data&amp;
 379             <b>operator=</b>(const polygon_90_data&amp; that)</font></td>
 380             <td>Assignment operator.</td>
 381           </tr>
 382           <tr>
 383             <td width="586"><font face="Courier New">template
 384 &lt;typename T2&gt;<b>&nbsp; <br />
 385             </b>polygon_90_data&amp; <b>operator=</b>(const T2&amp;
 386 that) const</font></td>
 387             <td>Assign from an object that is a model of polygon 90.</td>
 388           </tr>
 389           <tr>
 390             <td width="586"><font face="Courier New">iterator_type <b>begin</b>()
 391 const</font></td>
 392             <td>Get the begin iterator over vertices of the polygon.</td>
 393           </tr>
 394           <tr>
 395             <td width="586"><font face="Courier New">iterator_type <b>end</b>()
 396 const</font></td>
 397             <td>Get the end iterator over vertices of the polygon.</td>
 398           </tr>
 399           <tr>
 400             <td width="586"><font face="Courier New">compact_iterator_type
 401             <b> begin_compact</b>() const</font></td>
 402             <td>Get the begin compact iterator over non-redundant
 403 coordinates of the polygon.</td>
 404           </tr>
 405           <tr>
 406             <td width="586"><font face="Courier New">compact_iterator_type
 407             <b> end_compact</b>() const</font></td>
 408             <td>Get the end compact iterator over non-redundant
 409 coordinates of the polygon.</td>
 410           </tr>
 411           <tr>
 412             <td width="586"><font face="Courier New">std::size_t <b>size</b>()
 413 const</font></td>
 414             <td>Get the number of elements in the sequence stored to
 415 the polygon, usually equal to the number of edges of the polygon.</td>
 416           </tr>
 417           <tr>
 418             <td width="586"><font face="Courier New">template
 419 &lt;typename iT&gt;<b>&nbsp; <br />
 420             </b>void <b>set</b>(iT begin_points, iT end_points)</font></td>
 421             <td>Sets the polygon to the iterator range of points.&nbsp;
 422 No check is performed to ensure the points describe a Manhattan figure,
 423 every other x and y value of the points is used to initialize the
 424 polygon.</td>
 425           </tr>
 426           <tr>
 427             <td width="586"><font face="Courier New">template
 428 &lt;typename iT&gt;<b>&nbsp; <br />
 429             </b>void <b>set_compact</b>(iT begin_coords, iT end_coords)</font></td>
 430             <td>Sets the polygon to the iterator range of
 431 coordinates.&nbsp; These coordinates correspond to the x values of
 432 vertical edges and y values of horizontal edges.&nbsp; It is expected
 433 that the sequence start with an x value and proceed x then y then x
 434 then y.</td>
 435           </tr>
 436         </tbody>
 437       </table>
 438       </td>
 439     </tr>
 440     <tr>
 441       <td style="background-color: rgb(238, 238, 238);" nowrap="1"
 442  valign="top"> &nbsp;</td>
 443       <td
 444  style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;"
 445  valign="top" width="100%">
 446       <table class="docinfo" id="table3" frame="void" rules="none">
 447         <colgroup> <col class="docinfo-name" /><col
 448  class="docinfo-content" /> </colgroup> <tbody valign="top">
 449           <tr>
 450             <th class="docinfo-name">Copyright:</th>
 451             <td>Copyright © Intel Corporation 2008-2010.</td>
 452           </tr>
 453           <tr class="field">
 454             <th class="docinfo-name">License:</th>
 455             <td class="field-body">Distributed under the Boost Software
 456 License, Version 1.0. (See accompanying file <tt class="literal"> <span
 457  class="pre">LICENSE_1_0.txt</span></tt> or copy at <a
 458  class="reference" target="_top"
 459  href="http://www.boost.org/LICENSE_1_0.txt">
 460 http://www.boost.org/LICENSE_1_0.txt</a>)</td>
 461           </tr>
 462         </tbody>
 463       </table>
 464       </td>
 465     </tr>
 466   </tbody>
 467 </table>
 468 </body>
 469 </html>