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

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  11   <title>Boost Polygon Library: Rectangle Concept</title>
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  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>Rectangle Concept</li>
  37         <li><a href="gtl_polygon_90_concept.htm">Polygon 90 Concept</a></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>
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  46         <li><a href="gtl_polygon_90_set_concept.htm">Polygon 90 Set
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  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>
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  52 Extraction 90</a></li>
  53         <li><a href="gtl_connectivity_extraction_45.htm">Connectivity
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  90       <p>
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  92       <h1>Rectangle Concept</h1>
  93       <p> </p>
  94       <p>The rectangle concept tag is <font face="Courier New">
  95 rectangle_concept</font></p>
  96       <p> To register a user defined type as a model of <font
  97  face="Times New Roman">rectangle </font>concept, specialize the
  98 geometry concept meta-function for that type.&nbsp; In the example
  99 below CRectangle is registered as a model of rectangle&nbsp; concept.</p>
 100       <p> <font face="Courier New">template &lt;&gt;<br />
 101 struct geometry_concept&lt;CRectangle&gt; { typedef rectangle_concept
 102 type; };</font></p>
 103       <p> <font face="Times New Roman">The semantic of a rectangle is
 104 that it has an x and a y interval and these intervals conform to the
 105 semantic of an interval including its invariant.&nbsp; This invariant
 106 on the intervals of a rectangle is enforced by the generic library
 107 functions that operate on rectangles, and is not expected of the data
 108 type itself or the concept mapping of that data type to the rectangle
 109 concept through its traits.&nbsp; In this way a boost::tuple&lt;int,
 110 int, int, int&gt; or boost::array&lt;int, 4&gt; could be made models of
 111 rectangle by simply providing indirect access to their elements through
 112 traits.</font></p>
 113       <p> <font face="Times New Roman">Below is shown the default
 114 rectangle traits.&nbsp; Specialization of these traits is required for
 115 types that don't conform to the default behavior.&nbsp; The interested
 116 reader will note SFINAE is used on the traits to allow only an object
 117 that provides a member type definition of interval_type to work with
 118 the default read only traits.&nbsp; This becomes necessary when
 119 refinements of concepts are used and it is undesirable to attempt to
 120 match default traits to non-rectangle types at compile time.&nbsp;
 121 Specializing rectangle_traits can be done easily by simply providing
 122 gtl_yes as the enable parameter.</font></p>
 123       <p> <font face="Courier New">template &lt;typename T, typename
 124 enable = gtl_yes&gt;<br />
 125 struct rectangle_traits {};</font></p>
 126       <p> <font face="Courier New">template &lt;typename T&gt;<br />
 127 struct rectangle_traits&lt;T, gtl_no&gt; {};<br />
 128       <br />
 129 template &lt;typename T&gt;<br />
 130 struct rectangle_traits&lt;T, typename gtl_same_type&lt;typename
 131 T::interval_type, typename T::interval_type&gt;::type&gt; {<br />
 132 &nbsp;&nbsp;&nbsp;&nbsp; typedef typename T::coordinate_type
 133 coordinate_type;<br />
 134 &nbsp;&nbsp;&nbsp;&nbsp; typedef typename T::interval_type
 135 interval_type;<br />
 136 &nbsp;&nbsp;&nbsp;&nbsp; static inline interval_type get(const T&amp;
 137 rectangle, orientation_2d orient) {<br />
 138 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return
 139 rectangle.get(orient); }<br />
 140 };<br />
 141       <br />
 142 template &lt;typename T&gt;<br />
 143 struct rectangle_mutable_traits {<br />
 144 &nbsp;&nbsp;&nbsp;&nbsp; template &lt;typename T2&gt;<br />
 145 &nbsp;&nbsp;&nbsp;&nbsp; static inline void set(T&amp; rectangle,
 146 orientation_2d orient, const T2&amp; interval) {<br />
 147 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 148 rectangle.set(orient, interval); }<br />
 149 &nbsp;&nbsp;&nbsp;&nbsp; template &lt;typename T2, typename T3&gt;<br />
 150 &nbsp;&nbsp;&nbsp;&nbsp; static inline T construct(const T2&amp;
 151 interval_horizontal, const T3&amp; interval_vertical) {<br />
 152 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return
 153 T(interval_horizontal, interval_vertical); }<br />
 154 };</font></p>
 155       <h2>Functions</h2>
 156       <table id="table1" border="1" width="100%">
 157         <tbody>
 158           <tr>
 159             <td width="586"><font face="Courier New">template
 160 &lt;typename T&gt;<br />
 161 interval_type <b>get</b>(const T&amp; rectangle, orientation_2d)</font></td>
 162             <td><font face="Times New Roman">Expects a model of
 163 rectangle.&nbsp; Returns the x interval or y interval of the rectangle,
 164 depending on the orientation_2d value.</font><font face="Courier New"><br />
 165 &nbsp;</font></td>
 166           </tr>
 167           <tr>
 168             <td width="586"><font face="Courier New">template
 169 &lt;typename T, typename coordinate_type&gt;<br />
 170 void <b>set</b>(T&amp; rectangle, orientation_2d, coordinate_type)</font></td>
 171             <td><font face="Times New Roman">Expects a model of
 172 rectangle.&nbsp;&nbsp; Sets the x interval or y interval of the
 173 rectangle to the coordinate, depending on the orientation_2d value.</font></td>
 174           </tr>
 175           <tr>
 176             <td width="586"><font face="Courier New">template
 177 &lt;typename T&gt;<br />
 178 interval_type <b>get</b>(const T&amp; rectangle, orientation_2d, <br />
 179 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 180 direction_1d)</font></td>
 181             <td><font face="Times New Roman">Expects
 182 a model of rectangle.&nbsp; Returns the coordinate specificed by the
 183 direction_1d value of the x interval or y interval of the rectangle,
 184 depending on the orientation_2d value.</font><font face="Courier New"><br />
 185 &nbsp;</font></td>
 186           </tr>
 187           <tr>
 188             <td width="586"><font face="Courier New">template
 189 &lt;typename T, typename coordinate_type&gt;<br />
 190 void <b>set</b>(T&amp; rectangle, orientation_2d, direction_1d, <br />
 191 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; coordinate_type)</font></td>
 192             <td><font face="Times New Roman">Expects a model of
 193 rectangle.&nbsp;&nbsp; Sets the coordinate specified by the
 194 direction_1d value of the x interval or y interval of the rectangle to
 195 the coordinate, depending on the orientation_2d value.</font></td>
 196           </tr>
 197           <tr>
 198             <td width="586"><font face="Courier New">template
 199 &lt;typename T, typename T2&gt;<br />
 200 T <b>construct</b>(const T2&amp; h, const T2&amp; v)</font></td>
 201             <td>Construct an object that is a model of rectangle given
 202 x interval and y intervals.</td>
 203           </tr>
 204           <tr>
 205             <td width="586"><font face="Courier New">template
 206 &lt;typename T, typename T2&gt;<br />
 207 T <b>construct</b>(coordinate_type xl, coordinate_type yl, <br />
 208 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 209 coordinate_type xh, coordinate_type yh)</font></td>
 210             <td>Construct an object that is a model of rectangle given
 211 four coordinate values.</td>
 212           </tr>
 213           <tr>
 214             <td width="586"><font face="Courier New">template
 215 &lt;typename T1, typename T2&gt;<br />
 216 T1&amp; <b>assign</b>(T1&amp; left, const T2&amp; right)</font></td>
 217             <td>Copies data from right object that models rectangle
 218 into left object that models rectangle.</td>
 219           </tr>
 220           <tr>
 221             <td width="586"><font face="Courier New">template
 222 &lt;typename T, typename T2&gt;<br />
 223 bool <b>equivalence</b>(const T&amp; rectangle1, </font> <br />
 224             <font face="Courier New">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 225 const T2&amp; rectangle2)</font></td>
 226             <td>Given two objects that model rectangle, compares and
 227 returns true if their x and y intervals are respectively equivalent.</td>
 228           </tr>
 229           <tr>
 230             <td width="586"><font face="Courier New">template
 231 &lt;typename T, typename point_type&gt;<br />
 232 bool <b>contains</b>(const T&amp;, const point_type&amp; point, <br />
 233 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 234 bool consider_touch=true)</font></td>
 235             <td>Given an object that models rectangle and an object
 236 that models point, returns true if the rectangle contains the
 237 point.&nbsp; If the consider_touch flag is true will return true if the
 238 point lies along the boundary of the rectangle.</td>
 239           </tr>
 240           <tr>
 241             <td width="586"><font face="Courier New">template
 242 &lt;typename T1, typename T2&gt;<br />
 243 bool <b>contains</b>(const T1&amp; a, const T2&amp; b, <br />
 244 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 245 bool consider_touch = true) </font></td>
 246             <td>Returns true if model of rectangle a contains both
 247 intervals of model of rectangle b.&nbsp; If the consider_touch flag is
 248 true will consider rectangle b contained even if it touches the
 249 boundary of a.</td>
 250           </tr>
 251           <tr>
 252             <td width="586"><font face="Courier New">template
 253 &lt;typename T&gt;<br />
 254 interval_type <b>horizontal</b>(const T&amp; rectangle)</font></td>
 255             <td>Returns the x interval of an object that models
 256 rectangle.</td>
 257           </tr>
 258           <tr>
 259             <td width="586"><font face="Courier New">template
 260 &lt;typename T&gt;<br />
 261 interval_type <b>vertical</b>(const T&amp; rectangle)</font></td>
 262             <td>Returns the y interval of an object that models
 263 rectangle.</td>
 264           </tr>
 265           <tr>
 266             <td width="586"><font face="Courier New">template
 267 &lt;typename T&gt;<br />
 268 coordinate_type <b>xl</b>(const T&amp; rectangle)</font></td>
 269             <td>Returns the west coordinate of an object that models
 270 rectangle.</td>
 271           </tr>
 272           <tr>
 273             <td width="586"><font face="Courier New">template
 274 &lt;typename T&gt;<br />
 275 coordinate_type <b>xh</b>(const T&amp; rectangle)</font></td>
 276             <td>Returns the east coordinate of an object that models
 277 rectangle.</td>
 278           </tr>
 279           <tr>
 280             <td width="586"><font face="Courier New">template
 281 &lt;typename T&gt;<br />
 282 coordinate_type <b>yl</b>(const T&amp; rectangle)</font></td>
 283             <td>Returns the south coordinate of an object that models
 284 rectangle.</td>
 285           </tr>
 286           <tr>
 287             <td width="586"><font face="Courier New">template
 288 &lt;typename T&gt;<br />
 289 coordinate_type <b>yh</b>(const T&amp; rectangle)</font></td>
 290             <td>Returns the north coordinate of an object that models
 291 rectangle.</td>
 292           </tr>
 293           <tr>
 294             <td width="586"><font face="Courier New">template
 295 &lt;typename T&gt;<br />
 296 point_type <b>ll</b>(const T&amp; rectangle)</font></td>
 297             <td>Returns the lower left corner point of an object that
 298 models rectangle.</td>
 299           </tr>
 300           <tr>
 301             <td width="586"><font face="Courier New">template
 302 &lt;typename T&gt;<br />
 303 point_type <b>lr</b>(const T&amp; rectangle)</font></td>
 304             <td>Returns the lower right corner point of an object that
 305 models rectangle.</td>
 306           </tr>
 307           <tr>
 308             <td width="586"><font face="Courier New">template
 309 &lt;typename T&gt;<br />
 310 point_type <b>ul</b>(const T&amp; rectangle)</font></td>
 311             <td>Returns the upper left corner point of an object that
 312 models rectangle.</td>
 313           </tr>
 314           <tr>
 315             <td width="586"><font face="Courier New">template
 316 &lt;typename T&gt;<br />
 317 point_type <b>ur</b>(const T&amp; rectangle)</font></td>
 318             <td>Returns the upper right corner point of an object that
 319 models rectangle.</td>
 320           </tr>
 321           <tr>
 322             <td width="586"><font face="Courier New">// get the center
 323 coordinate<br />
 324 template &lt;typename T, typename point_type&gt;<br />
 325 void <b>center</b>(point_type&amp; p, const T&amp; rectangle)</font></td>
 326             <td>Sets object that models point to the center point of an
 327 object that models rectangle.</td>
 328           </tr>
 329           <tr>
 330             <td width="586"><font face="Courier New">template
 331 &lt;typename T, typename interval_type&gt;<br />
 332 void <b>horizontal</b>(T&amp; rectangle, const interval_type&amp; i)</font></td>
 333             <td>Sets the x interval of the object that models rectangle
 334 to be equal to the value of an object that models interval.</td>
 335           </tr>
 336           <tr>
 337             <td width="586"><font face="Courier New">template
 338 &lt;typename T, typename interval_type&gt;<br />
 339 void <b>vertical</b>(T&amp; rectangle, const interval_type&amp; i )</font></td>
 340             <td>Sets the y interval of the object that models rectangle
 341 to be equal to the value of an object that models interval.</td>
 342           </tr>
 343           <tr>
 344             <td width="586"><font face="Courier New">template
 345 &lt;typename rectangle_type&gt;<br />
 346 void <b>xl</b>(rectangle_type&amp; rectangle, coordinate_type )</font></td>
 347             <td>Sets the west coordinate of the object that models
 348 rectangle to be equal to the coordinate value.</td>
 349           </tr>
 350           <tr>
 351             <td width="586"><font face="Courier New">template
 352 &lt;typename rectangle_type&gt;<br />
 353 void <b>xh</b>(rectangle_type&amp; rectangle, coordinate_type )</font></td>
 354             <td>Sets the east coordinate of the object that models
 355 rectangle to be equal to the coordinate value.</td>
 356           </tr>
 357           <tr>
 358             <td width="586"><font face="Courier New">template
 359 &lt;typename rectangle_type&gt;<br />
 360 void <b>yl</b>(rectangle_type&amp; rectangle, coordinate_type )</font></td>
 361             <td>Sets the south coordinate of the object that models
 362 rectangle to be equal to the coordinate value.</td>
 363           </tr>
 364           <tr>
 365             <td width="586"><font face="Courier New">template
 366 &lt;typename rectangle_type&gt;<br />
 367 void <b>yh</b>(rectangle_type&amp; rectangle, coordinate_type )</font></td>
 368             <td>Sets the north coordinate of the object that models
 369 rectangle to be equal to the coordinate value.</td>
 370           </tr>
 371           <tr>
 372             <td width="586"><font face="Courier New">template
 373 &lt;typename T, typename T1, typename T2&gt;<br />
 374 T&amp; <b>set_points</b>(T&amp; rectangle, const T1&amp; p1, const
 375 T2&amp; p2)</font></td>
 376             <td>Sets the rectangle to the rectangle fully described by
 377 the points p1 and p2.</td>
 378           </tr>
 379           <tr>
 380             <td width="586"><font face="Courier New">template
 381 &lt;typename T&gt;<br />
 382 coordinate_difference <b>delta</b>(const T&amp; rectangle, <br />
 383 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 384 orientation_2d)</font></td>
 385             <td>Returns the delta of the interval specified by
 386 orientation_2d of an object that models rectangle.</td>
 387           </tr>
 388           <tr>
 389             <td width="586"><font face="Courier New">template
 390 &lt;typename T&gt;<br />
 391 manhattan_area_type <b>area</b>(const T&amp; rectangle)</font></td>
 392             <td>Returns the area of an object that models rectangle.</td>
 393           </tr>
 394           <tr>
 395             <td width="586"><font face="Courier New">template
 396 &lt;typename T&gt;<br />
 397 coordinate_difference <b>half_perimeter</b>(const T&amp; rectangle)</font></td>
 398             <td>Returns the length plus width of an object that models
 399 rectangle.</td>
 400           </tr>
 401           <tr>
 402             <td width="586"><font face="Courier New">template
 403 &lt;typename T&gt;<br />
 404 coordinate_difference <b>perimeter</b>(const T&amp; rectangle)</font></td>
 405             <td>Returns the perimeter length of an object that models
 406 rectangle.</td>
 407           </tr>
 408           <tr>
 409             <td width="586"><font face="Courier New">template
 410 &lt;typename T&gt;<br />
 411 orientation_2d <b>quess_orientation</b>(const T&amp; rectangle)</font></td>
 412             <td>Returns the orientation in which the rectangle has a
 413 longer delta.&nbsp; Returns HORIZONTAL if the rectangle is a square.</td>
 414           </tr>
 415           <tr>
 416             <td width="586"><font face="Courier New">template
 417 &lt;typename rectangle_type&gt;<br />
 418 rectangle_type&amp; <b>transform</b>(rectangle_type&amp; rectangle,<br />
 419 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 420 coordinate_type axis = 0)</font></td>
 421             <td>Applies transform() on the two points that fully
 422 describe the rectangle and sets the rectangle to that described by the
 423 result of transforming those points.</td>
 424           </tr>
 425           <tr>
 426             <td width="586"><font face="Courier New">template
 427 &lt;typename rectangle_type&gt;<br />
 428 rectangle_type&amp; <b>scale_up</b>(rectangle_type&amp; rectangle, <br />
 429 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 430 unsigned_area_type factor)</font></td>
 431             <td>Scales up x interval and y interval&nbsp; of an object
 432 that models rectangle by unsigned factor.</td>
 433           </tr>
 434           <tr>
 435             <td width="586"><font face="Courier New">template
 436 &lt;typename rectangle_type&gt;<br />
 437 rectangle_type&amp; <b>scale_down</b>(rectangle_type&amp; rectangle, <br />
 438 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 439 unsigned_area_type factor)</font></td>
 440             <td>Scales down x interval and y interval&nbsp; of an
 441 object that models rectangle by unsigned factor.</td>
 442           </tr>
 443           <tr>
 444             <td width="586"><font face="Courier New">template
 445 &lt;typename rectangle_type, scaling_type&gt;<br />
 446 rectangle_type&amp; <b>scale</b>(rectangle_type&amp; rectangle,<br />
 447 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 448 const scaling_type&amp; scaling) </font></td>
 449             <td>Applies scale() on the two points that fully describe
 450 the rectangle and sets the rectangle to that described by the result of
 451 transforming those points.</td>
 452           </tr>
 453           <tr>
 454             <td width="586"><font face="Courier New">template
 455 &lt;typename T&gt;<br />
 456 T&amp; <b>move</b>(T&amp; rectangle, orientation_2d,<br />
 457 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; coordinate_difference
 458 displacement)</font></td>
 459             <td>Adds displacement value to interval indicated by
 460 orientation_2d of an object that models rectangle.</td>
 461           </tr>
 462           <tr>
 463             <td width="586"><font face="Courier New">template
 464 &lt;typename rectangle_type, typename point_type&gt;<br />
 465 rectangle_type&amp; <b>convolve</b>(rectangle_type&amp; rectangle,<br />
 466 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 467 const point_type&amp; point)</font></td>
 468             <td>Convolves coordinate values of point with x interval
 469 and y interval&nbsp; of an object that models rectangle.</td>
 470           </tr>
 471           <tr>
 472             <td width="586"><font face="Courier New">template
 473 &lt;typename rectangle_type, typename point_type&gt;<br />
 474 rectangle_type&amp; <b>deconvolve</b>(rectangle_type&amp; rectangle,<br />
 475 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 476 const point_type&amp; point)</font></td>
 477             <td>Deconvolves coordinate values of point withx interval
 478 and y interval&nbsp; of an object that models rectangle.</td>
 479           </tr>
 480           <tr>
 481             <td width="586"><font face="Courier New">template
 482 &lt;typename T1, typename T2&gt;<br />
 483 T1&amp; <b>convolve</b>(T1&amp; a, const T2&amp; b)</font></td>
 484             <td>Convolves x interval&nbsp; of b with x interval&nbsp;
 485 of a and convolves y interval&nbsp; of b with y interval&nbsp; of a.</td>
 486           </tr>
 487           <tr>
 488             <td width="586"><font face="Courier New">template
 489 &lt;typename T1, typename T2&gt;<br />
 490 T1&amp; <b>deconvolve</b>(T1&amp; a, const T2&amp; b)</font></td>
 491             <td>Deconvolves x interval&nbsp; of b with x interval&nbsp;
 492 of a and deconvolves y interval&nbsp; of b with y interval&nbsp; of a. </td>
 493           </tr>
 494           <tr>
 495             <td width="586"><font face="Courier New">template
 496 &lt;typename T1, typename T2&gt;<br />
 497 T1&amp; <b>reflected_convolve</b>(T1&amp; a, const T2&amp; b)</font></td>
 498             <td>Reflected convolves y interval&nbsp; of b with x
 499 interval&nbsp; of a and reflected convolves x interval&nbsp; of b with
 500 y interval&nbsp; of a.</td>
 501           </tr>
 502           <tr>
 503             <td width="586"><font face="Courier New">template
 504 &lt;typename T1, typename T2&gt;<br />
 505 T1&amp; <b>reflected_deconvolve</b>(T1&amp; a, const T2&amp; b)</font></td>
 506             <td>Reflected deconvolves y interval&nbsp; of b with x
 507 interval&nbsp; of a and reflected deconvolves x interval&nbsp; of b
 508 with y interval&nbsp; of a.</td>
 509           </tr>
 510           <tr>
 511             <td width="586"><font face="Courier New">template
 512 &lt;typename T, typename point_type&gt;<br />
 513 coordinate_difference <b>euclidean_distance</b>(const T&amp;,<br />
 514 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; const point_type&amp; point,
 515 orienation_2d)</font></td>
 516             <td>Returns the distance from an object that models
 517 rectangle to an object that models point along the given
 518 orientation.&nbsp; Returns zero if the point is contained within the
 519 rectangle along that orientation.</td>
 520           </tr>
 521           <tr>
 522             <td width="586"><font face="Courier New">template
 523 &lt;typename T1, typename T2&gt;<br />
 524 coordinate_difference <b>euclidean_distance</b>(const T1&amp; a,<br />
 525 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; const T2&amp; b, orienation_2d)</font></td>
 526             <td>Returns the distance from an object that models
 527 rectangle to an object that models rectangle along the given
 528 orientation.&nbsp; Returns zero if the intervals of the rectangles
 529 overlap along that orientation.</td>
 530           </tr>
 531           <tr>
 532             <td width="586"><font face="Courier New">template
 533 &lt;typename T, typename point_type&gt;<br />
 534 coordinate_difference <b>square_euclidean_distance</b>(const T&amp;,<br />
 535 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; const point_type&amp; point)</font></td>
 536             <td>Returns the square of the Euclidean distance between a
 537 point and a rectangle.&nbsp; Returns zero if the point is contained
 538 within the rectangle.</td>
 539           </tr>
 540           <tr>
 541             <td width="586"><font face="Courier New">template
 542 &lt;typename T1, typename T2&gt;<br />
 543 coordinate_difference <b>square_euclidean_distance</b><br />
 544 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (const T1&amp; a, const T2&amp; b)</font></td>
 545             <td>Returns the square of the Euclidean distance between
 546 rectangles a and b.&nbsp; Returns zero if the rectangles intersect.</td>
 547           </tr>
 548           <tr>
 549             <td width="586"><font face="Courier New">template
 550 &lt;typename T, typename point_type&gt;<br />
 551 coordinate_difference <b>manhattan_distance</b>(const T&amp;,<br />
 552 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; const point_type&amp; point)</font></td>
 553             <td>Returns the Manhattan distance between a point and a
 554 rectangle.&nbsp; Returns zero if the point is contained within the
 555 rectangle.</td>
 556           </tr>
 557           <tr>
 558             <td width="586"><font face="Courier New">template
 559 &lt;typename T1, typename T2&gt;<br />
 560 coordinate_difference <b>manhattan_distance</b>(const T1&amp; a, <br />
 561 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 562 const T2&amp; b)</font></td>
 563             <td>Returns the Manhattan distance between rectangles a and
 564 b.&nbsp; Returns zero if the rectangles intersect.</td>
 565           </tr>
 566           <tr>
 567             <td width="586"><font face="Courier New">template
 568 &lt;typename T, typename point_type&gt;<br />
 569 coordinate_distance <b>euclidean_distance</b>(const T&amp;,<br />
 570 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; const point_type&amp; point)</font></td>
 571             <td>Returns the Euclidean distance between a point and a
 572 rectangle.&nbsp; Returns zero if the point is contained within the
 573 rectangle.</td>
 574           </tr>
 575           <tr>
 576             <td width="586"><font face="Courier New">template
 577 &lt;typename T1, typename T2&gt;<br />
 578 coordinate_distance <b>euclidean_distance</b>(const T1&amp; a, <br />
 579 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 580 const T2&amp; b)</font></td>
 581             <td>Returns the Euclidean distance between rectangles a and
 582 b.&nbsp; Returns zero if the rectangles intersect.</td>
 583           </tr>
 584           <tr>
 585             <td width="586"><font face="Courier New">template
 586 &lt;typename T1, typename T2&gt;<br />
 587 bool <b>intersects</b>(const T1&amp; a, const T2&amp; b, <br />
 588 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 589 bool consider_touch = true)</font></td>
 590             <td>Returns true if two objects that model rectangle
 591 overlap.&nbsp; If the consider_touch flag is true touching at the sides
 592 or corners is considered overlap.</td>
 593           </tr>
 594           <tr>
 595             <td width="586"><font face="Courier New">template
 596 &lt;typename T1, typename T2&gt;<br />
 597 bool <b>boundaries_intersect</b>(const T1&amp; a, const T2&amp; b, <br />
 598 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 599 bool consider_touch = true)</font></td>
 600             <td>Returns true is two objects that model rectangle
 601 partially overlap such that one there is an intersection between the
 602 edges of the two rectangles&nbsp; If the consider_touch flag is true a
 603 coordinate is considered contained even if the two rectangles touch
 604 only along a side or corner.</td>
 605           </tr>
 606           <tr>
 607             <td width="586"><font face="Courier New">template
 608 &lt;typename T1, typename T2&gt;<br />
 609 bool <b>abuts</b>(const T1&amp; a, const T2&amp; b,<br />
 610 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 611 direction_2d dir) </font></td>
 612             <td>Returns true if rectangle b abuts but down not overlap
 613 rectangle a on the side of rectangle a specified by dir.</td>
 614           </tr>
 615           <tr>
 616             <td width="586"><font face="Courier New">template
 617 &lt;typename T1, typename T2&gt;<br />
 618 bool <b>abuts</b>(const T1&amp; a, const T2&amp; b,<br />
 619 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 620 orientation_2d) </font></td>
 621             <td>Returns true if rectangle b abuts but down not overlap
 622 rectangle a on either side of rectangle a specified by the
 623 orientation_2d.</td>
 624           </tr>
 625           <tr>
 626             <td width="586"><font face="Courier New">template
 627 &lt;typename T1, typename T2&gt;<br />
 628 bool <b>abuts</b>(const T1&amp; a, const T2&amp; b)</font></td>
 629             <td>Returns true if rectangle b abuts but down not overlap
 630 rectangle a on any side.</td>
 631           </tr>
 632           <tr>
 633             <td width="586"><font face="Courier New">template
 634 &lt;typename T1, typename T2&gt;<br />
 635 bool <b>intersect</b>(T1&amp; a, const T2&amp; b, orientation_2d<br />
 636 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 637 bool consider_touch = true) </font></td>
 638             <td>Sets rectangle a to the intersection of rectangle a and
 639 interval b along the orientation_2d and returns true.&nbsp; If the does
 640 not intersect the interval, the rectangle is unchanged and the function
 641 returns false.&nbsp; If the flag consider_touch is true intervals that
 642 abut are considered to intersect.</td>
 643           </tr>
 644           <tr>
 645             <td width="586"><font face="Courier New">template
 646 &lt;typename T1, typename T2&gt;<br />
 647 bool <b>intersect</b>(T1&amp; a, const T2&amp; b,<br />
 648 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 649 bool consider_touch = true) </font></td>
 650             <td>Sets rectangle a to the intersection of rectangle a and
 651 rectangle b and return true.&nbsp; If the two rectangles do not
 652 intersect rectangle a is unchanged and the function returns
 653 false.&nbsp; If the flag consider_touch is true rectangles that abut
 654 are considered to intersect.</td>
 655           </tr>
 656           <tr>
 657             <td width="586"><font face="Courier New">template
 658 &lt;typename T1, typename T2&gt;<br />
 659 T&amp; <b>generalized_intersect</b>(T1&amp; a, const T2&amp; b)</font></td>
 660             <td>Same as intersect, but if they do not intersect set a
 661 to the rectangle between a and b by applying generalized_intersect() on
 662 the intervals of the rectangles.</td>
 663           </tr>
 664           <tr>
 665             <td width="586"><font face="Courier New">template
 666 &lt;typename T&gt;<br />
 667 T&amp; <b>bloat</b>(T&amp; rectangle, coordinate_type)</font></td>
 668             <td>Bloats x and y intervals of rectangle by coordinate
 669 value.</td>
 670           </tr>
 671           <tr>
 672             <td width="586"><font face="Courier New">template
 673 &lt;typename T&gt;<br />
 674 T&amp; <b>bloat</b>(T&amp; rectangle, direction_2d, coordinate_type)</font></td>
 675             <td>Bloats side of rectangle specified by direction_2d by
 676 coordinate value.</td>
 677           </tr>
 678           <tr>
 679             <td width="586"><font face="Courier New">template
 680 &lt;typename T&gt;<br />
 681 T&amp; <b>bloat</b>(T&amp; rectangle, orientation_2d, coordinate_type)</font></td>
 682             <td>Bloats interval of rectangle specified by
 683 orientation_2d by coordinate value.</td>
 684           </tr>
 685           <tr>
 686             <td width="586"><font face="Courier New">template
 687 &lt;typename T&gt;<br />
 688 T&amp; <b>shrink</b>(T&amp; rectangle, coordinate_type)</font></td>
 689             <td>Shrinks x and y intervals of rectangle by coordinate
 690 value.</td>
 691           </tr>
 692           <tr>
 693             <td width="586"><font face="Courier New">template
 694 &lt;typename T&gt;<br />
 695 T&amp; <b>shrink</b>(T&amp; rectangle, direction_2d, coordinate_type)</font></td>
 696             <td>Shrinks side of rectangle specified by direction_2d by
 697 coordinate value.</td>
 698           </tr>
 699           <tr>
 700             <td width="586"><font face="Courier New">template
 701 &lt;typename T&gt;<br />
 702 T&amp; <b>shrink</b>(T&amp; rectangle, orientation_2d, coordinate_type)</font></td>
 703             <td>Shrinks interval of rectangle specified by
 704 orientation_2d by coordinate value.</td>
 705           </tr>
 706           <tr>
 707             <td width="586"><font face="Courier New">template
 708 &lt;typename T1, typename T2&gt;<br />
 709 bool <b>encompass</b>(T1&amp; a, const T2&amp; b)</font></td>
 710             <td>The x and y intervals of a are set to encompass the x
 711 and y intervals of b respectively.</td>
 712           </tr>
 713           <tr>
 714             <td width="586"><font face="Courier New">template
 715 &lt;typename T, typename point_type&gt;<br />
 716 bool <b>encompass</b>(T&amp; rectangle, const point_type&amp; point)</font></td>
 717             <td>The x and y intervals of rectangle are set to encompass
 718 the x and y coordinates of point respectively.</td>
 719           </tr>
 720           <tr>
 721             <td width="586"><font face="Courier New">template
 722 &lt;typename T, typename interval_type&gt;<br />
 723 bool <b>encompass</b>(T&amp; rectangle, const interval_type&amp; i, <br />
 724 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 725 orientation_2d)</font></td>
 726             <td>The interval of rectangle specified by orientation_2d
 727 is set to encompass the interval i.</td>
 728           </tr>
 729           <tr>
 730             <td width="586"><font face="Courier New">template
 731 &lt;typename T, typename point_type&gt;<br />
 732 bool <b>get_corner</b>(point_type&amp; point, const T&amp;
 733 rectangle,&nbsp; <br />
 734 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 735 direction_2d, direction_1d)</font></td>
 736             <td>Sets point to the corner of the rectangle you reach if
 737 you look at its side specified by direction_2d from within the
 738 rectangle and turn in the direction_1d direction (low == left, high =
 739 right).&nbsp; Always returns true.</td>
 740           </tr>
 741         </tbody>
 742       </table>
 743       <h1>Rectangle Data</h1>
 744       <p> </p>
 745       <p>The library provides a model of rectangle concept declared
 746       <font face="Courier New">template&lt;typename T&gt;
 747 rectangle_data </font>where T is the coordinate type.</p>
 748       <p>This data type is used internally when a rectangle is needed
 749 and is available to the library user who finds it convenient to use a
 750 library rectangle data type instead of providing their own.&nbsp; The
 751 data type is implemented to be convenient to use with the library
 752 traits.</p>
 753       <h2>Members</h2>
 754       <table id="table2" border="1" width="100%">
 755         <tbody>
 756           <tr>
 757             <td width="586"><b><font face="Courier New">geometry_type</font></b></td>
 758             <td><font face="Times New Roman">rectangle_concept</font></td>
 759           </tr>
 760           <tr>
 761             <td width="586"><b><font face="Courier New">coordinate_type</font></b></td>
 762             <td><font face="Times New Roman">T</font></td>
 763           </tr>
 764           <tr>
 765             <td width="586"><font face="Courier New"><b>interval_type</b></font></td>
 766             <td><font face="Times New Roman">interval_data&lt;T&gt;</font></td>
 767           </tr>
 768           <tr>
 769             <td width="586"><font face="Courier New"><b>rectangle_data</b>(T
 770 xl, T yl, T xh, T yh)</font></td>
 771             <td><font face="Times New Roman">Constructs a rectangle
 772 with four coordinates.</font></td>
 773           </tr>
 774           <tr>
 775             <td width="586"><font face="Courier New">template
 776 &lt;typename T1, typename T2&gt;<b><br />
 777 rectangle_data</b>(const T1&amp; horizontal_interval,<br />
 778 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 779 const T2&amp; vertical_interval)</font></td>
 780             <td><font face="Times New Roman">Constructs a rectangle
 781 with two objects that model interval.</font></td>
 782           </tr>
 783           <tr>
 784             <td width="586"><font face="Courier New"><b>rectangle_data</b>(const
 785 rectangle_data&amp; that)</font></td>
 786             <td><font face="Times New Roman">Copy construct</font></td>
 787           </tr>
 788           <tr>
 789             <td width="586"><font face="Courier New">rectangle_data&amp;
 790             <b>operator=</b>(const rectangle_data&amp; that)</font></td>
 791             <td>Assignment operator.</td>
 792           </tr>
 793           <tr>
 794             <td width="586"><font face="Courier New">template
 795 &lt;typename T2&gt;<b> <br />
 796             </b>rectangle_data&amp; <b> operator=</b>(const T2&amp;
 797 that) const</font></td>
 798             <td>Assign from an object that is a model of rectangle.</td>
 799           </tr>
 800           <tr>
 801             <td width="586"><font face="Courier New">template
 802 &lt;typename T2&gt;<b> <br />
 803             </b>bool<b> operator==</b>(const T2&amp; that) const</font></td>
 804             <td>Compare equality to an object that is a model of
 805 rectangle.</td>
 806           </tr>
 807           <tr>
 808             <td width="586"><font face="Courier New">template
 809 &lt;typename T2&gt;<b> <br />
 810             </b>bool<b> operator!=</b>(const T2&amp; that) const</font></td>
 811             <td>Compare inequality to an object that is a model of
 812 rectangle.</td>
 813           </tr>
 814           <tr>
 815             <td width="586"><font face="Courier New">interval_data&lt;T&gt;
 816             <b>get</b>(orientation_2d orient) const</font></td>
 817             <td>Get the interval in the given orientation.</td>
 818           </tr>
 819           <tr>
 820             <td width="586"><font face="Courier New">template
 821 &lt;typename T2&gt;<br />
 822 void <b>set</b>(orientation_2d orient, const T2&amp; value)</font></td>
 823             <td>Sets the interval in the given orientation to the value
 824 of an object that models interval.</td>
 825           </tr>
 826         </tbody>
 827       </table>
 828       </td>
 829     </tr>
 830     <tr>
 831       <td style="background-color: rgb(238, 238, 238);" nowrap="1"
 832  valign="top"> &nbsp;</td>
 833       <td
 834  style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;"
 835  valign="top" width="100%">
 836       <table class="docinfo" id="table8" frame="void" rules="none">
 837         <colgroup> <col class="docinfo-name" /><col
 838  class="docinfo-content" /> </colgroup> <tbody valign="top">
 839           <tr>
 840             <th class="docinfo-name">Copyright:</th>
 841             <td>Copyright © Intel Corporation 2008-2010.</td>
 842           </tr>
 843           <tr class="field">
 844             <th class="docinfo-name">License:</th>
 845             <td class="field-body">Distributed under the Boost Software
 846 License, Version 1.0. (See accompanying file <tt class="literal"> <span
 847  class="pre">LICENSE_1_0.txt</span></tt> or copy at <a
 848  class="reference" target="_top"
 849  href="http://www.boost.org/LICENSE_1_0.txt">
 850 http://www.boost.org/LICENSE_1_0.txt</a>)</td>
 851           </tr>
 852         </tbody>
 853       </table>
 854       </td>
 855     </tr>
 856   </tbody>
 857 </table>
 858 </body>
 859 </html>