projects / ceph.git / blame
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| 6 | <head> | |
| 7 | <!-- | |
| 8 | Copyright 2009-2010 Intel Corporation | |
| 9 | license banner | |
| 10 | --> | |
| 11 | <title>Boost Polygon Library: Polygon 45 Set Concept</title> | |
| 12 | <meta http-equiv="content-type" content="text/html;charset=ISO-8859-1" /> | |
| 13 | <!-- <link type="text/css" rel="stylesheet" href="adobe_source.css"> --> | |
| 14 | </head> | |
| 15 | <body> | |
| 16 | <table style="margin: 0pt; padding: 0pt; width: 100%;" border="0" | |
| 17 | cellpadding="0" cellspacing="0"> | |
| 18 | <tbody> | |
| 19 | <tr> | |
| 20 | <td style="background-color: rgb(238, 238, 238);" nowrap="1" | |
| 21 | valign="top"> | |
| 22 | <div style="padding: 5px;" align="center"> <img | |
| 23 | src="images/boost.png" border="0" height="86" width="277" /><a | |
| 24 | title="www.boost.org home page" href="http://www.boost.org/" | |
| 25 | tabindex="2" style="border: medium none ;"> </a> </div> | |
| 26 | <div style="margin: 5px;"> | |
| 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><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> | |
| 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>Polygon 45 Set Concept</li> | |
| 49 | <li><a href="gtl_polygon_set_concept.htm">Polygon Set Concept</a></li> | |
| 50 | <li><a href="gtl_connectivity_extraction_90.htm">Connectivity | |
| 51 | Extraction 90</a></li> | |
| 52 | <li><a href="gtl_connectivity_extraction_45.htm">Connectivity | |
| 53 | Extraction 45</a></li> | |
| 54 | <li><a href="gtl_connectivity_extraction.htm">Connectivity | |
| 55 | Extraction</a></li> | |
| 56 | <li><a href="gtl_property_merge_90.htm">Property Merge 90</a></li> | |
| 57 | <li><a href="gtl_property_merge_45.htm">Property Merge 45</a></li> | |
| 58 | <li><a href="gtl_property_merge.htm">Property Merge</a></li> | |
| 59 | <li><a href="voronoi_main.htm">Voronoi Main Page<br /> | |
| 60 | </a></li> | |
| 61 | <li><a href="voronoi_benchmark.htm">Voronoi Benchmark</a><br /> | |
| 62 | </li> | |
| 63 | <li><a href="voronoi_builder.htm">Voronoi Builder</a></li> | |
| 64 | <li><a href="voronoi_diagram.htm">Voronoi Diagram</a></li> | |
| 65 | </ul> | |
| 66 | <h3 class="navbar">Other Resources</h3> | |
| 67 | <ul> | |
| 68 | <li><a href="GTL_boostcon2009.pdf">GTL Boostcon 2009 Paper</a></li> | |
| 69 | <li><a href="GTL_boostcon_draft03.pdf">GTL Boostcon 2009 | |
| 70 | Presentation</a></li> | |
| 71 | <li><a href="analysis.htm">Performance Analysis</a></li> | |
| 72 | <li><a href="gtl_tutorial.htm">Layout Versus Schematic Tutorial</a></li> | |
| 73 | <li><a href="gtl_minkowski_tutorial.htm">Minkowski Sum Tutorial</a></li> | |
| 74 | <li><a href="voronoi_basic_tutorial.htm">Voronoi Basic Tutorial</a></li> | |
| 75 | <li><a href="voronoi_advanced_tutorial.htm">Voronoi Advanced | |
| 76 | Tutorial</a></li> | |
| 77 | </ul> | |
| 78 | </div> | |
| 79 | <h3 class="navbar">Polygon Sponsor</h3> | |
| 80 | <div style="padding: 5px;" align="center"> <img | |
| 81 | src="images/intlogo.gif" border="0" height="51" width="127" /><a | |
| 82 | title="www.adobe.com home page" href="http://www.adobe.com/" | |
| 83 | tabindex="2" style="border: medium none ;"> </a> </div> | |
| 84 | </td> | |
| 85 | <td | |
| 86 | style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" | |
| 87 | valign="top" width="100%"> | |
| 88 | <!-- End Header --><br /> | |
| 89 | <p> | |
| 90 | </p> | |
| 91 | <h1>Polygon 45 Set Concept</h1> | |
| 92 | <p> </p> | |
| 93 | <p>The polygon_45_set concept tag is <font face="Courier New"> | |
| 94 | polygon_45_set_concept</font></p> | |
| 95 | <p> <font face="Times New Roman">The semantic of a | |
| 96 | polygon_45_set is zero or more geometry regions which have angles at | |
| 97 | the vertices that are multiples of 45-degrees relative to the | |
| 98 | coordinate axis. A Polygon 45 Set Concept makes no sense in | |
| 99 | floating point, but currently does not provide a static assert to | |
| 100 | prevent it from being used with floating point coordinates. The | |
| 101 | result of such use is undefined. When the intersection of two 45 | |
| 102 | degree edges results in a vertex that is off the integer grid that case | |
| 103 | is handled by inserting a unit length edge between the two 45 degree | |
| 104 | edges near the off grid intersection point. In the case that data | |
| 105 | represented contains no 45-degree angles and is Manhattan a runtime | |
| 106 | check will default to the Manhattan algorithm. The results of | |
| 107 | which are identical to what the 45-degree algorithm would do, but | |
| 108 | obtained more efficiently.</font></p> | |
| 109 | <p> <font face="Times New Roman">The motivation for providing | |
| 110 | the polygon_45_set is to extend the special case of Manhattan geometry | |
| 111 | capability of the library to encompass the slightly less common, but | |
| 112 | still important special case of geometry that is described by angles | |
| 113 | that are multiples of 45-degress with respect to the coordinate | |
| 114 | axis. This simplifies the implementation of geometry algorithms | |
| 115 | and affords many opportunities for optimization. 45-degree | |
| 116 | algorithms can be 50X faster than arbitrary angle algorithms and are | |
| 117 | required to provide a complete feature set that meets the performance | |
| 118 | requirements of application domains in which Manhattan and 45-degree | |
| 119 | geometry are a common special case.</font></p> | |
| 120 | <p>Users are recommended to use std::vector and std::list of user | |
| 121 | defined polygons or library provided | |
| 122 | polygon_45_set_data<coordinate_type> objects. Lists and | |
| 123 | vectors of models of polygon_45_concept or | |
| 124 | polygon_45_with_holes_concept are automatically models of | |
| 125 | polygon_45_set_concept.</p> | |
| 126 | <p>An object that is a model of <font face="Courier New"> | |
| 127 | polygon_45_set_concept</font> can be viewed as a model of <font | |
| 128 | face="Courier New"> | |
| 129 | polygon_90_set_concept</font> if it is determined at runtime to conform | |
| 130 | to the restriction that all edges are axis-parallel. This concept | |
| 131 | casting is accomplished through the <font face="Courier New">view_as<>()</font> | |
| 132 | function.</p> | |
| 133 | <p><font face="Courier New">view_as<polygon_90_set_concept>(polygon_set_object)</font></p> | |
| 134 | <p>The return value of <font face="Courier New">view_as<>()</font> | |
| 135 | can be passed into any interface that expects an object of the | |
| 136 | conceptual type specified in its template parameter. Polygon sets | |
| 137 | cannot be viewed as single polygons or rectangles since it generally | |
| 138 | cannot be known whether a polygon set contains only a single polygon | |
| 139 | without converting to polygons.</p> | |
| 140 | <h2>Operators</h2> | |
| 141 | <p>The return type of some operators is the <font | |
| 142 | face="Courier New">polygon_45_set_view</font> operator template | |
| 143 | type. This type is itself a model of the polygon 90 set concept, | |
| 144 | but furthermore can be used as an argument to the <font | |
| 145 | face="Courier New">polygon_45_set_data</font> constructor and | |
| 146 | assignment operator. The operator template exists to eliminate | |
| 147 | temp copies of intermediate results when Boolean operators are chained | |
| 148 | together.</p> | |
| 149 | <p>Operators are declared inside the namespace <font | |
| 150 | face="Courier New">boost::polygon::operators</font>.</p> | |
| 151 | <table id="table5" border="1" width="100%"> | |
| 152 | <tbody> | |
| 153 | <tr> | |
| 154 | <td width="586"><font face="Courier New">template | |
| 155 | <typename T1, typename T2><br /> | |
| 156 | polygon_45_set_view <b>operator</b>|(const T1& l, const T2& r)</font></td> | |
| 157 | <td>Boolean OR operation (polygon set union). Accepts | |
| 158 | two objects that model polygon_45_set or one of its refinements. | |
| 159 | Returns an operator template that performs the operation on demand when | |
| 160 | chained or or nested in a library function call such as assign(). | |
| 161 | O( n log n) runtime complexity and O(n) memory wrt vertices + | |
| 162 | intersections.</td> | |
| 163 | </tr> | |
| 164 | <tr> | |
| 165 | <td width="586"><font face="Courier New">template | |
| 166 | <typename T1, typename T2><br /> | |
| 167 | polygon_45_set_view <b>operator</b>+(const T1& l, const T2& r)</font></td> | |
| 168 | <td>Same as operator|. The plus sign is also used for | |
| 169 | OR operations in Boolean logic expressions. O( n log n) runtime | |
| 170 | complexity and O(n) memory wrt vertices + intersections.</td> | |
| 171 | </tr> | |
| 172 | <tr> | |
| 173 | <td width="586"><font face="Courier New">template | |
| 174 | <typename T1, typename T2><br /> | |
| 175 | polygon_45_set_view <b>operator</b>&(const T1& l, const | |
| 176 | T2& r)</font></td> | |
| 177 | <td>Boolean AND operation (polygon set intersection). | |
| 178 | Accepts two objects that model polygon_45_set or one of its | |
| 179 | refinements. O( n log n) runtime complexity and O(n) memory wrt | |
| 180 | vertices + intersections.</td> | |
| 181 | </tr> | |
| 182 | <tr> | |
| 183 | <td width="586"><font face="Courier New">template | |
| 184 | <typename T1, typename T2><br /> | |
| 185 | polygon_45_set_view <b>operator</b>*(const T1& l, const T2& r)</font></td> | |
| 186 | <td>Same as operator&. The multiplication symbol | |
| 187 | is also used for AND operations in Boolean logic expressions. O( | |
| 188 | n log n) runtime complexity and O(n) memory wrt vertices + | |
| 189 | intersections.</td> | |
| 190 | </tr> | |
| 191 | <tr> | |
| 192 | <td width="586"><font face="Courier New">template | |
| 193 | <typename T1, typename T2><br /> | |
| 194 | polygon_45_set_view <b>operator</b>^(const T1& l, const T2& r)</font></td> | |
| 195 | <td>Boolean XOR operation (polygon set | |
| 196 | disjoint-union). Accepts two objects that model polygon_45_set or | |
| 197 | one of its refinements. O( n log n) runtime complexity and O(n) | |
| 198 | memory wrt vertices + intersections.</td> | |
| 199 | </tr> | |
| 200 | <tr> | |
| 201 | <td width="586"><font face="Courier New">template | |
| 202 | <typename T1, typename T2><br /> | |
| 203 | polygon_45_set_view <b>operator</b>-(const T1& l, const T2& r)</font></td> | |
| 204 | <td>Boolean SUBTRACT operation (polygon set | |
| 205 | difference). Accepts two objects that model polygon_45_set or one | |
| 206 | of its refinements. O( n log n) runtime complexity and O(n) | |
| 207 | memory wrt vertices + intersections.</td> | |
| 208 | </tr> | |
| 209 | <tr> | |
| 210 | <td width="586"><font face="Courier New">template | |
| 211 | <typename T1, typename T2><br /> | |
| 212 | T1& <b>operator</b>|=(const T1& l, const T2& r)</font></td> | |
| 213 | <td>Same as operator|, but with self assignment, left | |
| 214 | operand must model polygon_45_set and not one of it's | |
| 215 | refinements. O( n log n) runtime complexity and O(n) memory wrt | |
| 216 | vertices + intersections.</td> | |
| 217 | </tr> | |
| 218 | <tr> | |
| 219 | <td width="586"><font face="Courier New">template | |
| 220 | <typename T1, typename T2><br /> | |
| 221 | T1& <b>operator</b>+=(T1& l, const T2& r)</font></td> | |
| 222 | <td>Same as operator+, but with self assignment, left | |
| 223 | operand must model polygon_45_set and not one of it's | |
| 224 | refinements. O( n log n) runtime complexity and O(n) memory wrt | |
| 225 | vertices + intersections.</td> | |
| 226 | </tr> | |
| 227 | <tr> | |
| 228 | <td width="586"><font face="Courier New">template | |
| 229 | <typename T1, typename T2><br /> | |
| 230 | T1& <b>operator</b>&=(const T1& l, const T2& r)</font></td> | |
| 231 | <td>Same as operator&, but with self assignment, left | |
| 232 | operand must model polygon_45_set and not one of it's | |
| 233 | refinements. O( n log n) runtime complexity and O(n) memory wrt | |
| 234 | vertices + intersections.</td> | |
| 235 | </tr> | |
| 236 | <tr> | |
| 237 | <td width="586"><font face="Courier New">template | |
| 238 | <typename T1, typename T2><br /> | |
| 239 | T1& <b>operator</b>*=(T1& l, const T2& r)</font></td> | |
| 240 | <td>Same as operator*, but with self assignment, left | |
| 241 | operand must model polygon_45_set and not one of it's | |
| 242 | refinements. O( n log n) runtime complexity and O(n) memory wrt | |
| 243 | vertices + intersections.</td> | |
| 244 | </tr> | |
| 245 | <tr> | |
| 246 | <td width="586"><font face="Courier New">template | |
| 247 | <typename T1, typename T2><br /> | |
| 248 | T1& <b>operator</b>^=(const T1& l, const T2& r)</font></td> | |
| 249 | <td>Same as operator^, but with self assignment, left | |
| 250 | operand must model polygon_45_set and not one of it's | |
| 251 | refinements. O( n log n) runtime complexity and O(n) memory wrt | |
| 252 | vertices + intersections.</td> | |
| 253 | </tr> | |
| 254 | <tr> | |
| 255 | <td width="586"><font face="Courier New">template | |
| 256 | <typename T1, typename T2><br /> | |
| 257 | T1& <b>operator</b>-=(T1& l, const T2& r)</font></td> | |
| 258 | <td>Same as operator-, but with self assignment, left | |
| 259 | operand must model polygon_45_set and not one of it's | |
| 260 | refinements. O( n log n) runtime complexity and O(n) memory wrt | |
| 261 | vertices + intersections.</td> | |
| 262 | </tr> | |
| 263 | <tr> | |
| 264 | <td width="586"><font face="Courier New">template | |
| 265 | <typename T1><br /> | |
| 266 | T1 <b>operator</b>+(const T1&, coordinate_type bloating)</font></td> | |
| 267 | <td>Performs resize operation, inflating by bloating | |
| 268 | ammount. If negative the result is a shrink instead of | |
| 269 | bloat. Note: returns result by value. O( n log n) runtime | |
| 270 | complexity and O(n) memory wrt vertices + intersections.</td> | |
| 271 | </tr> | |
| 272 | <tr> | |
| 273 | <td width="586"><font face="Courier New">template | |
| 274 | <typename T1, typename T2><br /> | |
| 275 | T1 <b>operator</b>-(const T1&, coordinate_type shrinking)</font></td> | |
| 276 | <td>Performs resize operation, deflating by bloating | |
| 277 | ammount. If negative the result is a bloat instead of | |
| 278 | shrink. Note: returns result by value. O( n log n) runtime | |
| 279 | complexity and O(n) memory wrt vertices + intersections.</td> | |
| 280 | </tr> | |
| 281 | <tr> | |
| 282 | <td width="586"><font face="Courier New">template | |
| 283 | <typename T1, typename T2><br /> | |
| 284 | T1& <b>operator</b>+=(const T1&, coordinate_type bloating)</font></td> | |
| 285 | <td>Performs resize operation, inflating by bloating | |
| 286 | ammount. If negative the result is a shrink instead of | |
| 287 | bloat. Returns reference to modified argument. O( n log n) | |
| 288 | runtime complexity and O(n) memory wrt vertices + intersections.</td> | |
| 289 | </tr> | |
| 290 | <tr> | |
| 291 | <td width="586"><font face="Courier New">template | |
| 292 | <typename T1, typename T2><br /> | |
| 293 | T1& <b>operator</b>-=(const T1&, coordinate_type shrinking)</font></td> | |
| 294 | <td>Performs resize operation, deflating by bloating | |
| 295 | ammount. If negative the result is a bloat instead of | |
| 296 | shrink. Returns reference to modified argument. O( n log n) | |
| 297 | runtime complexity and O(n) memory wrt vertices + intersections.</td> | |
| 298 | </tr> | |
| 299 | </tbody> | |
| 300 | </table> | |
| 301 | <h2>Functions</h2> | |
| 302 | <table id="table3" border="1" width="100%"> | |
| 303 | <tbody> | |
| 304 | <tr> | |
| 305 | <td width="586"><font face="Courier New">template | |
| 306 | <typename T1, typename T2><br /> | |
| 307 | T1& <b>assign</b>(T1& lvalue, const T2& rvalue)</font></td> | |
| 308 | <td>Eliminates overlaps in geometry and copies from an | |
| 309 | object that models polygon_45_set or any of its refinements into an | |
| 310 | object that models polygon_45_set. O( n log n) runtime complexity | |
| 311 | and O(n) memory wrt vertices + intersections.</td> | |
| 312 | </tr> | |
| 313 | <tr> | |
| 314 | <td width="586"><font face="Courier New">template | |
| 315 | <typename T1, typename T2><br /> | |
| 316 | bool <b>equivalence</b>(const T1& lvalue, const T2& rvalue) </font></td> | |
| 317 | <td>Returns true if an object that models polygon_45_set or | |
| 318 | one of its refinements covers the exact same geometric regions as | |
| 319 | another object that models polygon_45_set or one of its | |
| 320 | refinements. For example: two of polygon_45 objects. O( n | |
| 321 | log n) runtime complexity and O(n) memory wrt vertices + intersections.</td> | |
| 322 | </tr> | |
| 323 | <tr> | |
| 324 | <td width="586"><font face="Courier New">template | |
| 325 | <typename output_container_type, typename T><br /> | |
| 326 | void <b>get_trapezoids</b>(output_container_type& output, <br /> | |
| 327 | | |
| 328 | const T& polygon_set)</font></td> | |
| 329 | <td>Output container is expected to be a standard | |
| 330 | container. Slices geometry of an object that models | |
| 331 | polygon_45_set or one of its refinements into non overlapping | |
| 332 | trapezoids along a vertical slicing orientation and appends them to the | |
| 333 | output, which must have a value type that models polygon_45, | |
| 334 | polygon_45_with_holes, polygon or polygon_with_holes. O( n | |
| 335 | log n) runtime complexity and O(n) memory wrt vertices.</td> | |
| 336 | </tr> | |
| 337 | <tr> | |
| 338 | <td width="586"><font face="Courier New">template | |
| 339 | <typename output_container_type, typename T><br /> | |
| 340 | void <b>get_trapezoids</b>(output_container_type& output, <br /> | |
| 341 | | |
| 342 | const T& polygon_set,<br /> | |
| 343 | | |
| 344 | orientation_2d orient)</font></td> | |
| 345 | <td>Output container is expected to be a standard | |
| 346 | container. Slices geometry of an object that models | |
| 347 | polygon_45_set or one of its refinements into non overlapping | |
| 348 | trapezoids along a the specified slicing orientation and appends them | |
| 349 | to the output, which must have a value type that models polygon_45, | |
| 350 | polygon_45_with_holes, polygon or polygon_with_holes. O( n | |
| 351 | log n) runtime complexity and O(n) memory wrt vertices.</td> | |
| 352 | </tr> | |
| 353 | <tr> | |
| 354 | <td width="586"><font face="Courier New">template | |
| 355 | <typename polygon_set_type><br /> | |
| 356 | void <b>clear</b>(polygon_set_type& polygon_set)</font></td> | |
| 357 | <td>Makes the object empty of geometry.</td> | |
| 358 | </tr> | |
| 359 | <tr> | |
| 360 | <td width="586"><font face="Courier New">template | |
| 361 | <typename polygon_set_type><br /> | |
| 362 | bool <b>empty</b>(const polygon_set_type& polygon_set)</font></td> | |
| 363 | <td>Checks whether the object is empty of geometry. | |
| 364 | Polygons that are completely covered by holes will result in empty | |
| 365 | returning true. O( n log n) runtime complexity and O(n) | |
| 366 | memory wrt vertices.</td> | |
| 367 | </tr> | |
| 368 | <tr> | |
| 369 | <td width="586"><font face="Courier New">template | |
| 370 | <typename T, typename rectangle_type><br /> | |
| 371 | bool <b>extents</b>(rectangle_type& extents_rectangle, <br /> | |
| 372 | | |
| 373 | const T& polygon_set)</font></td> | |
| 374 | <td>Computes bounding box of an object that models | |
| 375 | polygon_45_set and stores it in an object that models rectangle. | |
| 376 | If the polygon set is empty returns false. If there are holes | |
| 377 | outside of shells they do not contribute to the extents of the polygon | |
| 378 | set. O( n log n) runtime complexity and O(n) memory wrt | |
| 379 | vertices.</td> | |
| 380 | </tr> | |
| 381 | <tr> | |
| 382 | <td width="586"><font face="Courier New">template | |
| 383 | <typename T><br /> | |
| 384 | area_type <b>area</b>(const T& polygon_set)</font></td> | |
| 385 | <td>Computes the area covered by geometry in an object that | |
| 386 | models polygon_45_set. O( n log n) runtime complexity and | |
| 387 | O(n) memory wrt vertices.</td> | |
| 388 | </tr> | |
| 389 | <tr> | |
| 390 | <td width="586"><font face="Courier New">template | |
| 391 | <typename T1, typename T2><br /> | |
| 392 | T1& <b>interact</b>(T1& a, const T2& b)</font></td> | |
| 393 | <td>Given an object that models polygon_45_set and an | |
| 394 | object that models polygon_45_set or one of its refinements, modifies a | |
| 395 | to retain only regions that overlap or touch regions in b. | |
| 396 | O( n log n) runtime complexity and O(n) memory wrt vertices plus | |
| 397 | intersections.</td> | |
| 398 | </tr> | |
| 399 | <tr> | |
| 400 | <td width="586"><font face="Courier New">template | |
| 401 | <typename T><br /> | |
| 402 | T& <b>self_intersect</b>(T& polygon_set)</font></td> | |
| 403 | <td>Given an object that models polygon_45_set that has | |
| 404 | self overlapping regions, modifies the argument to contain only the | |
| 405 | regions of overlap. O( n log n) runtime complexity and O(n) | |
| 406 | memory wrt vertices + intersections.</td> | |
| 407 | </tr> | |
| 408 | <tr> | |
| 409 | <td width="586"><font face="Courier New">template | |
| 410 | <typename T><br /> | |
| 411 | T& <b>self_xor</b>(T& polygon_set)</font></td> | |
| 412 | <td>Given an object that models polygon_45_set that has | |
| 413 | self overlapping regions, modifies the argument to contain only the | |
| 414 | regions that do not overlap. O( n log n) runtime complexity and | |
| 415 | O(n) memory wrt vertices + intersections.</td> | |
| 416 | </tr> | |
| 417 | <tr> | |
| 418 | <td width="586"><font face="Courier New">template | |
| 419 | <typename T><br /> | |
| 420 | T& <b>bloat</b>(T& polygon_set, unsigned_area_type bloating)</font></td> | |
| 421 | <td>Same as getting all the polygons, bloating them and | |
| 422 | putting them back. O( n log n) runtime complexity and O(n) memory | |
| 423 | wrt vertices + intersections.</td> | |
| 424 | </tr> | |
| 425 | <tr> | |
| 426 | <td width="586"><font face="Courier New">template | |
| 427 | <typename T><br /> | |
| 428 | T& <b>shrink</b>(T& polygon_set, unsigned_area_type shrinking)</font></td> | |
| 429 | <td>Same as getting all the polygons, shrinking them and | |
| 430 | overwriting the polygon set with the resulting regions. O( n log | |
| 431 | n) runtime complexity and O(n) memory wrt vertices + intersections.</td> | |
| 432 | </tr> | |
| 433 | <tr> | |
| 434 | <td width="586"><font face="Courier New">template | |
| 435 | <typename T, typename coord_type><br /> | |
| 436 | T& <b>resize</b>(T& polygon_set, coord_type resizing,<br /> | |
| 437 | RoundingOption | |
| 438 | rounding = CLOSEST, <br /> | |
| 439 | CornerOption | |
| 440 | corner = INTERSECTION)</font></td> | |
| 441 | <td>Same as bloat if resizing is positive, same as shrink | |
| 442 | if resizing is negative. RoundingOption is an enum that controls | |
| 443 | snapping of non-integer results of resizing 45 degree edges. | |
| 444 | CornerOption is an enum that controls how corner filling is | |
| 445 | performed. polygon_45_set_data.hpp defines these enums. O( | |
| 446 | n log n) runtime complexity and O(n) memory wrt vertices + | |
| 447 | intersections.</td> | |
| 448 | </tr> | |
| 449 | <tr> | |
| 450 | <td width="586"><font face="Courier New">template | |
| 451 | <typename T><br /> | |
| 452 | T& <b>grow_and</b>(T& polygon_set, unsigned_area_type bloating)</font></td> | |
| 453 | <td>Same as bloating non-overlapping regions and then | |
| 454 | applying self intersect to retain only the overlaps introduced by the | |
| 455 | bloat. O( n log n) runtime complexity and O(n) memory wrt | |
| 456 | vertices + intersections.</td> | |
| 457 | </tr> | |
| 458 | <tr> | |
| 459 | <td width="586"><font face="Courier New">template | |
| 460 | <typename T><br /> | |
| 461 | T& <b>scale_up</b>(T& polygon_set, unsigned_area_type factor)</font></td> | |
| 462 | <td>Scales geometry up by unsigned factor. O( n log | |
| 463 | n) runtime complexity and O(n) memory wrt vertices.</td> | |
| 464 | </tr> | |
| 465 | <tr> | |
| 466 | <td width="586"><font face="Courier New">template | |
| 467 | <typename T><br /> | |
| 468 | T& <b>scale_down</b>(T& polygon_set, unsigned_area_type factor)</font></td> | |
| 469 | <td>Scales geometry down by unsigned factor. Snaps 45 | |
| 470 | degree edges back to 45 degrees after division truncation leads to | |
| 471 | small changes in angle. O( n log n) runtime complexity and O(n) | |
| 472 | memory wrt vertices.</td> | |
| 473 | </tr> | |
| 474 | <tr> | |
| 475 | <td width="586"><font face="Courier New">template | |
| 476 | <typename T, typename scaling_type><br /> | |
| 477 | T& <b>scale</b>(polygon_set_type& polygon_set, double scaling)</font></td> | |
| 478 | <td>Scales geometry by multiplying by floating point | |
| 479 | factor. Snaps 45 degree edges back to 45 degrees after | |
| 480 | truncation of fractional results of multiply leads to small changes in | |
| 481 | angle. O( n log n) runtime complexity and O(n) memory wrt | |
| 482 | vertices.</td> | |
| 483 | </tr> | |
| 484 | <tr> | |
| 485 | <td width="586"><font face="Courier New">template | |
| 486 | <typename T, typename transformation_type><br /> | |
| 487 | T& <b>transform</b>(T& polygon_set,<br /> | |
| 488 | | |
| 489 | const transformation_type& transformation)</font></td> | |
| 490 | <td>Applies transformation.transform() on all | |
| 491 | vertices. O( n log n) runtime complexity and O(n) memory wrt | |
| 492 | vertices.</td> | |
| 493 | </tr> | |
| 494 | <tr> | |
| 495 | <td width="586"><font face="Courier New">template | |
| 496 | <typename T><br /> | |
| 497 | T& <b>keep</b>(T& polygon_set, <br /> | |
| 498 | unsigned_area_type min_area,<br /> | |
| 499 | unsigned_area_type max_area,<br /> | |
| 500 | unsigned_area_type min_width,<br /> | |
| 501 | unsigned_area_type max_width,<br /> | |
| 502 | unsigned_area_type | |
| 503 | min_height,<br /> | |
| 504 | unsigned_area_type | |
| 505 | max_height)</font></td> | |
| 506 | <td>Retains only regions that satisfy the min/max criteria | |
| 507 | in the argument list. Note: useful for visualization to cull too | |
| 508 | small polygons. O( n log n) runtime complexity and O(n) memory | |
| 509 | wrt vertices.</td> | |
| 510 | </tr> | |
| 511 | </tbody> | |
| 512 | </table> | |
| 513 | <h1>Polygon 45 Set Data Object</h1> | |
| 514 | <p> </p> | |
| 515 | <p>The polygon 45 set data type encapsulates the internal data | |
| 516 | format that serves as the input to the sweep-line algorithm that | |
| 517 | implements polygon-clipping Boolean operations. It also | |
| 518 | internally keeps track of whether that data has been sorted or scanned | |
| 519 | and maintains the invariant that when its flags indicate that the data | |
| 520 | is sorted or scanned the data has not been changed to violate that | |
| 521 | assumption. Using the Polygon 45 Set Data type directly can be | |
| 522 | more efficient than using lists and vectors of polygons in the | |
| 523 | functions above because of the invariants it can enforce which provide | |
| 524 | the opportunity to maintain the data is sorted form rather than going | |
| 525 | all the way out to polygons then resorting those vertices for a | |
| 526 | subsequent operation.</p> | |
| 527 | <p>The declaration of Polygon 45 Set Data is the following:</p> | |
| 528 | <p><font face="Courier New">template <typename T><br /> | |
| 529 | class polygon_45_set_data;</font></p> | |
| 530 | <p>The class is parameterized on the coordinate data type. | |
| 531 | Algorithms that benefit from knowledge of the invariants enforced by | |
| 532 | the class are implemented as member functions to provide them access to | |
| 533 | information about those invariants. </p> | |
| 534 | <h2>Member Functions</h2> | |
| 535 | <table id="table4" border="1" width="100%"> | |
| 536 | <tbody> | |
| 537 | <tr> | |
| 538 | <td width="586"><font face="Courier New"><b>polygon_45_set_data</b>()</font></td> | |
| 539 | <td>Default constructor. </td> | |
| 540 | </tr> | |
| 541 | <tr> | |
| 542 | <td width="586"><font face="Courier New">template | |
| 543 | <typename iT><br /> | |
| 544 | <b>polygon_45_set_data</b>(iT input_begin, iT input_end)</font></td> | |
| 545 | <td>Construct from an iterator range of insertable objects.</td> | |
| 546 | </tr> | |
| 547 | <tr> | |
| 548 | <td width="586"><font face="Courier New"> <b>polygon_45_set_data</b>(const | |
| 549 | polygon_45_set_data& that)</font></td> | |
| 550 | <td>Copy construct.</td> | |
| 551 | </tr> | |
| 552 | <tr> | |
| 553 | <td width="586"><font face="Courier New">template | |
| 554 | <typename l, typename r, typename op><br /> | |
| 555 | <b>polygon_45_set_data</b>(const | |
| 556 | polygon_45_set_view<l,r,op>& t)</font></td> | |
| 557 | <td>Copy construct from a Boolean operator template.</td> | |
| 558 | </tr> | |
| 559 | <tr> | |
| 560 | <td width="586"><font face="Courier New">polygon_45_set_data& | |
| 561 | <br /> | |
| 562 | <b>operator=</b>(const polygon_45_set_data& that)</font></td> | |
| 563 | <td>Assignment from another polygon set, may change | |
| 564 | scanning orientation.</td> | |
| 565 | </tr> | |
| 566 | <tr> | |
| 567 | <td width="586"><font face="Courier New">template | |
| 568 | <typename l, typename r, typename op><br /> | |
| 569 | polygon_45_set_data& <br /> | |
| 570 | <b>operator=</b>(const polygon_45_set_view<l, r, | |
| 571 | op>& that)</font></td> | |
| 572 | <td>Assignment from a Boolean operator template.</td> | |
| 573 | </tr> | |
| 574 | <tr> | |
| 575 | <td width="586"><font face="Courier New">template | |
| 576 | <typename geometry_object><br /> | |
| 577 | polygon_45_set_data& <b>operator=</b>(const geometry_object& | |
| 578 | geo)</font></td> | |
| 579 | <td>Assignment from an insertable object.</td> | |
| 580 | </tr> | |
| 581 | <tr> | |
| 582 | <td width="586"><font face="Courier New"> | |
| 583 | template <typename iT><br /> | |
| 584 | void <b>insert</b>(iT input_begin, iT input_end, <br /> | |
| 585 | bool | |
| 586 | is_hole = false)</font></td> | |
| 587 | <td>Insert objects of an iterator range. If is_hole | |
| 588 | is true inserts subtractive regions. Linear wrt the number of | |
| 589 | vertices added.</td> | |
| 590 | </tr> | |
| 591 | <tr> | |
| 592 | <td width="586"><font face="Courier New"> | |
| 593 | void <b>insert</b>(const polygon_45_set_data& polygon_set, <br /> | |
| 594 | bool | |
| 595 | is_hole = false)</font></td> | |
| 596 | <td>Insert a polygon set. Linear wrt the number of | |
| 597 | vertices added.</td> | |
| 598 | </tr> | |
| 599 | <tr> | |
| 600 | <td width="586"><font face="Courier New"> | |
| 601 | template <typename geometry_type><br /> | |
| 602 | void <b>insert</b>(const geometry_type& geometry_object, <br /> | |
| 603 | bool | |
| 604 | is_hole = false)</font></td> | |
| 605 | <td>Insert a geometry object, if is_hole is true then the | |
| 606 | inserted region is subtractive rather than additive. Linear wrt | |
| 607 | the number of vertices added.</td> | |
| 608 | </tr> | |
| 609 | <tr> | |
| 610 | <td width="586"><font face="Courier New">template | |
| 611 | <typename output_container><br /> | |
| 612 | void <b>get</b>(output_container& output) const</font></td> | |
| 613 | <td>Expects a standard container of geometry objects. | |
| 614 | Will scan and eliminate overlaps. Converts polygon set geometry | |
| 615 | to objects of that type and appends them to the container. | |
| 616 | Polygons will be output with counterclockwise winding, hole polygons | |
| 617 | will be output with clockwise winding. The last vertex of an | |
| 618 | output polygon is not the duplicate of the first, and the number of | |
| 619 | points is equal to the number of edges. O(n log n) runtime and | |
| 620 | O(n) memory wrt. vertices + intersections.</td> | |
| 621 | </tr> | |
| 622 | <tr> | |
| 623 | <td width="586"><font face="Courier New">template | |
| 624 | <typename output_container><br /> | |
| 625 | void <b>get_polygons</b>(output_container& output) const</font></td> | |
| 626 | <td>Expects a standard container of polygon objects. | |
| 627 | Will scan and eliminate overlaps. Converts polygon set geometry | |
| 628 | to polygons and appends them to the container. Polygons will have | |
| 629 | holes fractured out to the outer boundary along the positive y | |
| 630 | direction. O(n log n) runtime and O(n) memory wrt. vertices + | |
| 631 | intersections.</td> | |
| 632 | </tr> | |
| 633 | <tr> | |
| 634 | <td width="586"><font face="Courier New">template | |
| 635 | <typename output_container><br /> | |
| 636 | void <b>get_polygons_with_holes</b>(output_container& o) const</font></td> | |
| 637 | <td>Expects a standard container of polygon with holes | |
| 638 | objects. Will scan and eliminate overlaps. Converts polygon | |
| 639 | set geometry to polygons and appends them to the container. O(n | |
| 640 | log n) runtime and O(n) memory wrt. vertices + intersections.</td> | |
| 641 | </tr> | |
| 642 | <tr> | |
| 643 | <td width="586"><font face="Courier New">template | |
| 644 | <typename output_container><br /> | |
| 645 | void <b>get_trapezoids</b>(output_container& output) const</font></td> | |
| 646 | <td>Expects a standard container of polygon objects. | |
| 647 | Will scan and eliminate overlaps. Slices polygon set geometry to | |
| 648 | trapezoids vertically and appends them to the container. O(n log | |
| 649 | n) runtime and O(n) memory wrt. vertices + intersections.</td> | |
| 650 | </tr> | |
| 651 | <tr> | |
| 652 | <td width="586"><font face="Courier New"> | |
| 653 | template <typename output_container><br /> | |
| 654 | void <b>get_trapezoids</b>(output_container& output, <br /> | |
| 655 | orientation_2d slicing_orientation) const </font> </td> | |
| 656 | <td>Expects a standard container of polygon objects. | |
| 657 | Will scan and eliminate overlaps. Slices polygon set geometry to | |
| 658 | trapezoids along the given orientation and appends them to the | |
| 659 | container. O(n log n) runtime and O(n) memory wrt. vertices + | |
| 660 | intersections.</td> | |
| 661 | </tr> | |
| 662 | <tr> | |
| 663 | <td width="586"><font face="Courier New"> | |
| 664 | bool <b>operator==</b>(const polygon_45_set_data& p) const</font></td> | |
| 665 | <td>Once scanned the data representation of geometry within | |
| 666 | a polygon set is in a mathematically canonical form. Comparison | |
| 667 | between two sets is therefore a linear time operation once they are in | |
| 668 | the scanned state. Will scan and eliminate overlaps in both polygon | |
| 669 | sets. O(n log n) runtime and O(n) memory wrt. vertices + | |
| 670 | intersections the first time and linear runtime and constant memory | |
| 671 | subsequently. </td> | |
| 672 | </tr> | |
| 673 | <tr> | |
| 674 | <td width="586"><font face="Courier New">bool <b>operator!=</b>(const | |
| 675 | polygon_45_set_data& p) const</font></td> | |
| 676 | <td>Inverse logic of equivalence operator.</td> | |
| 677 | </tr> | |
| 678 | <tr> | |
| 679 | <td width="586"><font face="Courier New">void <b>clear</b>()</font></td> | |
| 680 | <td>Make the polygon set empty. Note: does not | |
| 681 | de-allocate memory. Use shrink to fit idiom and assign default | |
| 682 | constructed polygon set to de-allocate.</td> | |
| 683 | </tr> | |
| 684 | <tr> | |
| 685 | <td width="586"><font face="Courier New">bool <b>empty</b>() | |
| 686 | const </font> </td> | |
| 687 | <td>Check whether the polygon set contains no | |
| 688 | geometry. Will scan and eliminate overlaps because subtractive | |
| 689 | regions might make the polygon set empty. O(n log n) runtime and | |
| 690 | O(n) memory wrt. vertices + intersections the first time and linear | |
| 691 | runtime and constant memory subsequently. </td> | |
| 692 | </tr> | |
| 693 | <tr> | |
| 694 | <td width="586"><font face="Courier New">bool <b>is_manhattan</b>() | |
| 695 | const</font></td> | |
| 696 | <td>Returns in constant time the information about whether | |
| 697 | the geometry contains only Manhattan (axis-parallel rectilinear) | |
| 698 | edges. Constant time.</td> | |
| 699 | </tr> | |
| 700 | <tr> | |
| 701 | <td width="586"><font face="Courier New">void <b>clean</b>() | |
| 702 | const</font></td> | |
| 703 | <td>Scan and eliminate overlaps. O(n log n) runtime | |
| 704 | and O(n) memory wrt. vertices + intersections the first time and linear | |
| 705 | runtime and constant memory subsequently. </td> | |
| 706 | </tr> | |
| 707 | <tr> | |
| 708 | <td width="586"><font face="Courier New">template | |
| 709 | <typename input_iterator_type><br /> | |
| 710 | void <b>set</b>(input_iterator_type input_begin, <br /> | |
| 711 | input_iterator_type | |
| 712 | input_end) </font> </td> | |
| 713 | <td>Overwrite geometry in polygon set with insertable | |
| 714 | objects in the iterator range. </td> | |
| 715 | </tr> | |
| 716 | <tr> | |
| 717 | <td width="586"><font face="Courier New">template | |
| 718 | <typename rectangle_type><br /> | |
| 719 | bool <b>extents</b>(rectangle_type& extents_rectangle) const</font></td> | |
| 720 | <td>Given an object that models rectangle, scans and | |
| 721 | eliminates overlaps in the polygon set because subtractive regions may | |
| 722 | alter its extents then computes the bounding box and assigns it to | |
| 723 | extents_rectangle. O(n log n) runtime and O(n) memory wrt. | |
| 724 | vertices the first time and linear runtime and constant memory | |
| 725 | subsequently. </td> | |
| 726 | </tr> | |
| 727 | <tr> | |
| 728 | <td width="586"><font face="Courier New">polygon_45_set_data&<br /> | |
| 729 | <b>resize</b>(coord_type resizing,<br /> | |
| 730 | RoundingOption rounding = CLOSEST, | |
| 731 | <br /> | |
| 732 | CornerOption corner = INTERSECTION)</font></td> | |
| 733 | <td>Same as bloat if resizing is positive, same as shrink | |
| 734 | if resizing is negative. RoundingOption is an enum that controls | |
| 735 | snapping of non-integer results of resizing 45 degree edges. | |
| 736 | CornerOption is an enum that controls how corner filling is | |
| 737 | performed. polygon_45_set_data.hpp defines these enums. O(n | |
| 738 | log n) runtime and O(n) memory wrt. vertices + intersections.</td> | |
| 739 | </tr> | |
| 740 | <tr> | |
| 741 | <td width="586"><font face="Courier New">template | |
| 742 | <typename transformation_type><br /> | |
| 743 | polygon_45_set_data& <br /> | |
| 744 | <b>transform</b>(const transformation_type& | |
| 745 | transformation) </font> </td> | |
| 746 | <td>Applies transformation.transform() on vertices stored | |
| 747 | within the polygon set. O(n log n) runtime and O(n) memory wrt. | |
| 748 | vertices + intersections.</td> | |
| 749 | </tr> | |
| 750 | <tr> | |
| 751 | <td width="586"><font face="Courier New">polygon_45_set_data& | |
| 752 | <b>scale_up</b>(unsigned_area_type factor)</font></td> | |
| 753 | <td>Scales vertices stored within the polygon set up by | |
| 754 | factor. Linear wrt vertices.</td> | |
| 755 | </tr> | |
| 756 | <tr> | |
| 757 | <td width="586"><font face="Courier New">polygon_45_set_data& | |
| 758 | <b>scale_down</b>(unsigned_area_type factor)</font> </td> | |
| 759 | <td>Scales vertices stored within the polygon set down by | |
| 760 | factor. Linear wrt vertices.</td> | |
| 761 | </tr> | |
| 762 | <tr> | |
| 763 | <td width="586"><font face="Courier New">polygon_45_set_data& | |
| 764 | <b>scale</b>(double factor) </font></td> | |
| 765 | <td>Scales vertices stored within the polygon set by | |
| 766 | floating point factor. Linear wrt vertices.</td> | |
| 767 | </tr> | |
| 768 | <tr> | |
| 769 | <td width="586"><font face="Courier New">polygon_45_set_data& | |
| 770 | <b>self_xor</b>()</font></td> | |
| 771 | <td>Retain only non-overlapping regions of geometry within | |
| 772 | polygon set. O(n log n) runtime and O(n) memory wrt. vertices + | |
| 773 | intersections.</td> | |
| 774 | </tr> | |
| 775 | <tr> | |
| 776 | <td width="586"><font face="Courier New">polygon_45_set_data& | |
| 777 | <b>self_intersect</b>()</font></td> | |
| 778 | <td>Retain only overlapping regions of geometry within a | |
| 779 | polygon set. O(n log n) runtime and O(n) memory wrt. vertices + | |
| 780 | intersections.</td> | |
| 781 | </tr> | |
| 782 | <tr> | |
| 783 | <td width="586"><font face="Courier New">bool <b>has_error_data</b>() | |
| 784 | const </font></td> | |
| 785 | <td>Returns true if non-integer intersections resulted in | |
| 786 | small artifacts in the output of a boolean. Constant time.</td> | |
| 787 | </tr> | |
| 788 | <tr> | |
| 789 | <td width="586"><font face="Courier New">std::size_t <b>error_count</b>() | |
| 790 | const</font></td> | |
| 791 | <td>Returns the number of artifacts that may potentially be | |
| 792 | present in the output due to non-integer intersections. Constant | |
| 793 | time.</td> | |
| 794 | </tr> | |
| 795 | <tr> | |
| 796 | <td width="586"><font face="Courier New">void <b>get_error_data</b>(polygon_45_set_data& | |
| 797 | p) const</font></td> | |
| 798 | <td>Populates the input polygon set with 1x1 unit squares | |
| 799 | that bound the error that may be present in the output due to | |
| 800 | non-integer intersections. Linear wrt. vertices of error data.</td> | |
| 801 | </tr> | |
| 802 | <tr> | |
| 803 | <td width="586"><font face="Courier New">polygon_45_set_data& | |
| 804 | <b>self_intersect</b>()</font></td> | |
| 805 | <td>Retain only overlapping regions of geometry within a | |
| 806 | polygon set. O(n log n) runtime and O(n) memory wrt. vertices + | |
| 807 | intersections.</td> | |
| 808 | </tr> | |
| 809 | </tbody> | |
| 810 | </table> | |
| 811 | </td> | |
| 812 | </tr> | |
| 813 | <tr> | |
| 814 | <td style="background-color: rgb(238, 238, 238);" nowrap="1" | |
| 815 | valign="top"> </td> | |
| 816 | <td | |
| 817 | style="padding-left: 10px; padding-right: 10px; padding-bottom: 10px;" | |
| 818 | valign="top" width="100%"> | |
| 819 | <table class="docinfo" id="table6" frame="void" rules="none"> | |
| 820 | <colgroup> <col class="docinfo-name" /><col | |
| 821 | class="docinfo-content" /> </colgroup> <tbody valign="top"> | |
| 822 | <tr> | |
| 823 | <th class="docinfo-name">Copyright:</th> | |
| 824 |