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  25 <div class="section">
  26 <div class="titlepage"><div><div><h5 class="title">
  27 <a name="geometry.reference.algorithms.area.area_1"></a><a class="link" href="area_1.html" title="area">area</a>
  28 </h5></div></div></div>
  29 <p>
  30             <a class="indexterm" name="idm46187009970336"></a>
  31 Calculates the area of a geometry.
  32           </p>
  33 <h6>
  34 <a name="geometry.reference.algorithms.area.area_1.h0"></a>
  35             <span class="phrase"><a name="geometry.reference.algorithms.area.area_1.description"></a></span><a class="link" href="area_1.html#geometry.reference.algorithms.area.area_1.description">Description</a>
  36           </h6>
  37 <p>
  38             The free function area calculates the area of a geometry. It uses the
  39             default strategy, based on the coordinate system of the geometry.
  40           </p>
  41 <p>
  42             The area algorithm calculates the surface area of all geometries having
  43             a surface, namely box, polygon, ring, multipolygon. The units are the
  44             square of the units used for the points defining the surface. If subject
  45             geometry is defined in meters, then area is calculated in square meters.
  46           </p>
  47 <p>
  48             The area calculation can be done in all three common coordinate systems,
  49             Cartesian, Spherical and Geographic as well.
  50           </p>
  51 <h6>
  52 <a name="geometry.reference.algorithms.area.area_1.h1"></a>
  53             <span class="phrase"><a name="geometry.reference.algorithms.area.area_1.synopsis"></a></span><a class="link" href="area_1.html#geometry.reference.algorithms.area.area_1.synopsis">Synopsis</a>
  54           </h6>
  55 <p>
  56 </p>
  57 <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">Geometry</span><span class="special">&gt;</span>
  58 <span class="identifier">area_result</span><span class="special">&lt;</span><span class="identifier">Geometry</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">area</span><span class="special">(</span><span class="identifier">Geometry</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">geometry</span><span class="special">)</span></pre>
  59 <p>
  60           </p>
  61 <h6>
  62 <a name="geometry.reference.algorithms.area.area_1.h2"></a>
  63             <span class="phrase"><a name="geometry.reference.algorithms.area.area_1.parameters"></a></span><a class="link" href="area_1.html#geometry.reference.algorithms.area.area_1.parameters">Parameters</a>
  64           </h6>
  65 <div class="informaltable"><table class="table">
  66 <colgroup>
  67 <col>
  68 <col>
  69 <col>
  70 <col>
  71 </colgroup>
  72 <thead><tr>
  73 <th>
  74                     <p>
  75                       Type
  76                     </p>
  77                   </th>
  78 <th>
  79                     <p>
  80                       Concept
  81                     </p>
  82                   </th>
  83 <th>
  84                     <p>
  85                       Name
  86                     </p>
  87                   </th>
  88 <th>
  89                     <p>
  90                       Description
  91                     </p>
  92                   </th>
  93 </tr></thead>
  94 <tbody><tr>
  95 <td>
  96                     <p>
  97                       Geometry const &amp;
  98                     </p>
  99                   </td>
 100 <td>
 101                     <p>
 102                       Any type fulfilling a Geometry Concept
 103                     </p>
 104                   </td>
 105 <td>
 106                     <p>
 107                       geometry
 108                     </p>
 109                   </td>
 110 <td>
 111                     <p>
 112                       A model of the specified concept
 113                     </p>
 114                   </td>
 115 </tr></tbody>
 116 </table></div>
 117 <h6>
 118 <a name="geometry.reference.algorithms.area.area_1.h3"></a>
 119             <span class="phrase"><a name="geometry.reference.algorithms.area.area_1.returns"></a></span><a class="link" href="area_1.html#geometry.reference.algorithms.area.area_1.returns">Returns</a>
 120           </h6>
 121 <p>
 122             The calculated area
 123           </p>
 124 <h6>
 125 <a name="geometry.reference.algorithms.area.area_1.h4"></a>
 126             <span class="phrase"><a name="geometry.reference.algorithms.area.area_1.header"></a></span><a class="link" href="area_1.html#geometry.reference.algorithms.area.area_1.header">Header</a>
 127           </h6>
 128 <p>
 129             Either
 130           </p>
 131 <p>
 132             <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">geometry</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>
 133           </p>
 134 <p>
 135             Or
 136           </p>
 137 <p>
 138             <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">geometry</span><span class="special">/</span><span class="identifier">algorithms</span><span class="special">/</span><span class="identifier">area</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>
 139           </p>
 140 <h6>
 141 <a name="geometry.reference.algorithms.area.area_1.h5"></a>
 142             <span class="phrase"><a name="geometry.reference.algorithms.area.area_1.conformance"></a></span><a class="link" href="area_1.html#geometry.reference.algorithms.area.area_1.conformance">Conformance</a>
 143           </h6>
 144 <p>
 145             The function area implements function Area from the <a href="http://www.opengeospatial.org/standards/sfa" target="_top">OGC
 146             Simple Feature Specification</a>.
 147           </p>
 148 <h6>
 149 <a name="geometry.reference.algorithms.area.area_1.h6"></a>
 150             <span class="phrase"><a name="geometry.reference.algorithms.area.area_1.behavior"></a></span><a class="link" href="area_1.html#geometry.reference.algorithms.area.area_1.behavior">Behavior</a>
 151           </h6>
 152 <div class="informaltable"><table class="table">
 153 <colgroup>
 154 <col>
 155 <col>
 156 </colgroup>
 157 <thead><tr>
 158 <th>
 159                     <p>
 160                       Case
 161                     </p>
 162                   </th>
 163 <th>
 164                     <p>
 165                       Behavior
 166                     </p>
 167                   </th>
 168 </tr></thead>
 169 <tbody>
 170 <tr>
 171 <td>
 172                     <p>
 173                       pointlike (e.g. point)
 174                     </p>
 175                   </td>
 176 <td>
 177                     <p>
 178                       Returns 0
 179                     </p>
 180                   </td>
 181 </tr>
 182 <tr>
 183 <td>
 184                     <p>
 185                       linear (e.g. linestring)
 186                     </p>
 187                   </td>
 188 <td>
 189                     <p>
 190                       Returns 0
 191                     </p>
 192                   </td>
 193 </tr>
 194 <tr>
 195 <td>
 196                     <p>
 197                       areal (e.g. polygon)
 198                     </p>
 199                   </td>
 200 <td>
 201                     <p>
 202                       Returns the area
 203                     </p>
 204                   </td>
 205 </tr>
 206 <tr>
 207 <td>
 208                     <p>
 209                       Cartesian
 210                     </p>
 211                   </td>
 212 <td>
 213                     <p>
 214                       Returns the area in the same units as the input coordinates
 215                     </p>
 216                   </td>
 217 </tr>
 218 <tr>
 219 <td>
 220                     <p>
 221                       Spherical
 222                     </p>
 223                   </td>
 224 <td>
 225                     <p>
 226                       Returns the area on a unit sphere (or another sphere, if specified
 227                       as such in the constructor of the strategy)
 228                     </p>
 229                   </td>
 230 </tr>
 231 <tr>
 232 <td>
 233                     <p>
 234                       Reversed polygon (coordinates not according their orientiation)
 235                     </p>
 236                   </td>
 237 <td>
 238                     <p>
 239                       Returns the negative area
 240                     </p>
 241                   </td>
 242 </tr>
 243 </tbody>
 244 </table></div>
 245 <h6>
 246 <a name="geometry.reference.algorithms.area.area_1.h7"></a>
 247             <span class="phrase"><a name="geometry.reference.algorithms.area.area_1.supported_geometries"></a></span><a class="link" href="area_1.html#geometry.reference.algorithms.area.area_1.supported_geometries">Supported
 248             geometries</a>
 249           </h6>
 250 <div class="informaltable"><table class="table">
 251 <colgroup>
 252 <col>
 253 <col>
 254 </colgroup>
 255 <thead><tr>
 256 <th>
 257                     <p>
 258                       Geometry
 259                     </p>
 260                   </th>
 261 <th>
 262                     <p>
 263                       Status
 264                     </p>
 265                   </th>
 266 </tr></thead>
 267 <tbody>
 268 <tr>
 269 <td>
 270                     <p>
 271                       Point
 272                     </p>
 273                   </td>
 274 <td>
 275                     <p>
 276                       <span class="inlinemediaobject"><img src="../../../../img/ok.png" alt="ok"></span>
 277                     </p>
 278                   </td>
 279 </tr>
 280 <tr>
 281 <td>
 282                     <p>
 283                       Segment
 284                     </p>
 285                   </td>
 286 <td>
 287                     <p>
 288                       <span class="inlinemediaobject"><img src="../../../../img/ok.png" alt="ok"></span>
 289                     </p>
 290                   </td>
 291 </tr>
 292 <tr>
 293 <td>
 294                     <p>
 295                       Box
 296                     </p>
 297                   </td>
 298 <td>
 299                     <p>
 300                       <span class="inlinemediaobject"><img src="../../../../img/ok.png" alt="ok"></span>
 301                     </p>
 302                   </td>
 303 </tr>
 304 <tr>
 305 <td>
 306                     <p>
 307                       Linestring
 308                     </p>
 309                   </td>
 310 <td>
 311                     <p>
 312                       <span class="inlinemediaobject"><img src="../../../../img/ok.png" alt="ok"></span>
 313                     </p>
 314                   </td>
 315 </tr>
 316 <tr>
 317 <td>
 318                     <p>
 319                       Ring
 320                     </p>
 321                   </td>
 322 <td>
 323                     <p>
 324                       <span class="inlinemediaobject"><img src="../../../../img/ok.png" alt="ok"></span>
 325                     </p>
 326                   </td>
 327 </tr>
 328 <tr>
 329 <td>
 330                     <p>
 331                       Polygon
 332                     </p>
 333                   </td>
 334 <td>
 335                     <p>
 336                       <span class="inlinemediaobject"><img src="../../../../img/ok.png" alt="ok"></span>
 337                     </p>
 338                   </td>
 339 </tr>
 340 <tr>
 341 <td>
 342                     <p>
 343                       MultiPoint
 344                     </p>
 345                   </td>
 346 <td>
 347                     <p>
 348                       <span class="inlinemediaobject"><img src="../../../../img/ok.png" alt="ok"></span>
 349                     </p>
 350                   </td>
 351 </tr>
 352 <tr>
 353 <td>
 354                     <p>
 355                       MultiLinestring
 356                     </p>
 357                   </td>
 358 <td>
 359                     <p>
 360                       <span class="inlinemediaobject"><img src="../../../../img/ok.png" alt="ok"></span>
 361                     </p>
 362                   </td>
 363 </tr>
 364 <tr>
 365 <td>
 366                     <p>
 367                       MultiPolygon
 368                     </p>
 369                   </td>
 370 <td>
 371                     <p>
 372                       <span class="inlinemediaobject"><img src="../../../../img/ok.png" alt="ok"></span>
 373                     </p>
 374                   </td>
 375 </tr>
 376 <tr>
 377 <td>
 378                     <p>
 379                       Variant
 380                     </p>
 381                   </td>
 382 <td>
 383                     <p>
 384                       <span class="inlinemediaobject"><img src="../../../../img/ok.png" alt="ok"></span>
 385                     </p>
 386                   </td>
 387 </tr>
 388 </tbody>
 389 </table></div>
 390 <h6>
 391 <a name="geometry.reference.algorithms.area.area_1.h8"></a>
 392             <span class="phrase"><a name="geometry.reference.algorithms.area.area_1.complexity"></a></span><a class="link" href="area_1.html#geometry.reference.algorithms.area.area_1.complexity">Complexity</a>
 393           </h6>
 394 <p>
 395             Linear
 396           </p>
 397 <h6>
 398 <a name="geometry.reference.algorithms.area.area_1.h9"></a>
 399             <span class="phrase"><a name="geometry.reference.algorithms.area.area_1.examples"></a></span><a class="link" href="area_1.html#geometry.reference.algorithms.area.area_1.examples">Examples</a>
 400           </h6>
 401 <p>
 402             Calculate the area of a polygon
 403           </p>
 404 <p>
 405 </p>
 406 <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
 407
 408 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">geometry</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 409 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">geometry</span><span class="special">/</span><span class="identifier">geometries</span><span class="special">/</span><span class="identifier">point_xy</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 410 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">geometry</span><span class="special">/</span><span class="identifier">geometries</span><span class="special">/</span><span class="identifier">polygon</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 411
 412 <span class="keyword">namespace</span> <span class="identifier">bg</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">geometry</span><span class="special">;</span> <a class="co" name="geometry.reference.algorithms.area.area_1.c0" href="area_1.html#geometry.reference.algorithms.area.area_1.c1"><img src="../../../../../../../../doc/src/images/callouts/1.png" alt="1" border="0"></a>
 413
 414 <span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
 415 <span class="special">{</span>
 416     <span class="comment">// Calculate the area of a cartesian polygon</span>
 417     <span class="identifier">bg</span><span class="special">::</span><span class="identifier">model</span><span class="special">::</span><span class="identifier">polygon</span><span class="special">&lt;</span><span class="identifier">bg</span><span class="special">::</span><span class="identifier">model</span><span class="special">::</span><span class="identifier">d2</span><span class="special">::</span><span class="identifier">point_xy</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">poly</span><span class="special">;</span>
 418     <span class="identifier">bg</span><span class="special">::</span><span class="identifier">read_wkt</span><span class="special">(</span><span class="string">"POLYGON((0 0,0 7,4 2,2 0,0 0))"</span><span class="special">,</span> <span class="identifier">poly</span><span class="special">);</span>
 419     <span class="keyword">double</span> <span class="identifier">area</span> <span class="special">=</span> <span class="identifier">bg</span><span class="special">::</span><span class="identifier">area</span><span class="special">(</span><span class="identifier">poly</span><span class="special">);</span>
 420     <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Area: "</span> <span class="special">&lt;&lt;</span> <span class="identifier">area</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 421
 422     <span class="comment">// Calculate the area of a spherical equatorial polygon</span>
 423     <span class="identifier">bg</span><span class="special">::</span><span class="identifier">model</span><span class="special">::</span><span class="identifier">polygon</span><span class="special">&lt;</span><span class="identifier">bg</span><span class="special">::</span><span class="identifier">model</span><span class="special">::</span><span class="identifier">point</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">,</span> <span class="number">2</span><span class="special">,</span> <span class="identifier">bg</span><span class="special">::</span><span class="identifier">cs</span><span class="special">::</span><span class="identifier">spherical_equatorial</span><span class="special">&lt;</span><span class="identifier">bg</span><span class="special">::</span><span class="identifier">degree</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">sph_poly</span><span class="special">;</span>
 424     <span class="identifier">bg</span><span class="special">::</span><span class="identifier">read_wkt</span><span class="special">(</span><span class="string">"POLYGON((0 0,0 45,45 0,0 0))"</span><span class="special">,</span> <span class="identifier">sph_poly</span><span class="special">);</span>
 425     <span class="identifier">area</span> <span class="special">=</span> <span class="identifier">bg</span><span class="special">::</span><span class="identifier">area</span><span class="special">(</span><span class="identifier">sph_poly</span><span class="special">);</span>
 426     <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Area: "</span> <span class="special">&lt;&lt;</span> <span class="identifier">area</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 427
 428     <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
 429 <span class="special">}</span>
 430 </pre>
 431 <p>
 432           </p>
 433 <div class="calloutlist"><table border="0" summary="Callout list"><tr>
 434 <td width="5%" valign="top" align="left"><p><a name="geometry.reference.algorithms.area.area_1.c1"></a><a href="#geometry.reference.algorithms.area.area_1.c0"><img src="../../../../../../../../doc/src/images/callouts/1.png" alt="1" border="0"></a> </p></td>
 435 <td valign="top" align="left"><p>
 436                 Convenient namespace alias
 437               </p></td>
 438 </tr></table></div>
 439 <p>
 440             Output:
 441           </p>
 442 <pre class="programlisting">Area: 16
 443 Area: 0.339837
 444 </pre>
 445 </div>
 446 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 447 <td align="left"></td>
 448 <td align="right"><div class="copyright-footer">Copyright &#169; 2009-2019 Barend Gehrels, Bruno Lalande, Mateusz Loskot, Adam
 449       Wulkiewicz, Oracle and/or its affiliates<p>
 450         Distributed under the Boost Software License, Version 1.0. (See accompanying
 451         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
 452       </p>
 453 </div></td>
 454 </tr></table>
 455 <hr>
 456 <div class="spirit-nav">
 457 <a accesskey="p" href="../area.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../area.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="area_2_with_strategy.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a>
 458 </div>
 459 </body>
 460 </html>