ceph/src/boost/boost/polygon/polygon_traits.hpp

   1 /*
   2   Copyright 2008 Intel Corporation
   3
   4   Use, modification and distribution are subject to the Boost Software License,
   5   Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
   6   http://www.boost.org/LICENSE_1_0.txt).
   7 */
   8 #ifndef BOOST_POLYGON_POLYGON_TRAITS_HPP
   9 #define BOOST_POLYGON_POLYGON_TRAITS_HPP
  10 namespace boost { namespace polygon{
  11
  12   template <typename T, typename enable = gtl_yes>
  13   struct polygon_90_traits {
  14     typedef typename T::coordinate_type coordinate_type;
  15     typedef typename T::compact_iterator_type compact_iterator_type;
  16
  17     // Get the begin iterator
  18     static inline compact_iterator_type begin_compact(const T& t) {
  19       return t.begin_compact();
  20     }
  21
  22     // Get the end iterator
  23     static inline compact_iterator_type end_compact(const T& t) {
  24       return t.end_compact();
  25     }
  26
  27     // Get the number of sides of the polygon
  28     static inline std::size_t size(const T& t) {
  29       return t.size();
  30     }
  31
  32     // Get the winding direction of the polygon
  33     static inline winding_direction winding(const T&) {
  34       return unknown_winding;
  35     }
  36   };
  37
  38   template <typename T>
  39   struct polygon_traits_general {
  40     typedef typename T::coordinate_type coordinate_type;
  41     typedef typename T::iterator_type iterator_type;
  42     typedef typename T::point_type point_type;
  43
  44     // Get the begin iterator
  45     static inline iterator_type begin_points(const T& t) {
  46       return t.begin();
  47     }
  48
  49     // Get the end iterator
  50     static inline iterator_type end_points(const T& t) {
  51       return t.end();
  52     }
  53
  54     // Get the number of sides of the polygon
  55     static inline std::size_t size(const T& t) {
  56       return t.size();
  57     }
  58
  59     // Get the winding direction of the polygon
  60     static inline winding_direction winding(const T&) {
  61       return unknown_winding;
  62     }
  63   };
  64
  65   template <typename T>
  66   struct polygon_traits_90 {
  67     typedef typename polygon_90_traits<T>::coordinate_type coordinate_type;
  68     typedef iterator_compact_to_points<typename polygon_90_traits<T>::compact_iterator_type, point_data<coordinate_type> > iterator_type;
  69     typedef point_data<coordinate_type> point_type;
  70
  71     // Get the begin iterator
  72     static inline iterator_type begin_points(const T& t) {
  73       return iterator_type(polygon_90_traits<T>::begin_compact(t),
  74                            polygon_90_traits<T>::end_compact(t));
  75     }
  76
  77     // Get the end iterator
  78     static inline iterator_type end_points(const T& t) {
  79       return iterator_type(polygon_90_traits<T>::end_compact(t),
  80                            polygon_90_traits<T>::end_compact(t));
  81     }
  82
  83     // Get the number of sides of the polygon
  84     static inline std::size_t size(const T& t) {
  85       return polygon_90_traits<T>::size(t);
  86     }
  87
  88     // Get the winding direction of the polygon
  89     static inline winding_direction winding(const T& t) {
  90       return polygon_90_traits<T>::winding(t);
  91     }
  92   };
  93
  94 #ifndef BOOST_VERY_LITTLE_SFINAE
  95
  96   template <typename T, typename enable = gtl_yes>
  97   struct polygon_traits {};
  98
  99   template <typename T>
 100   struct polygon_traits<T,
 101                         typename gtl_or_4<
 102     typename gtl_same_type<typename geometry_concept<T>::type, polygon_concept>::type,
 103     typename gtl_same_type<typename geometry_concept<T>::type, polygon_45_concept>::type,
 104     typename gtl_same_type<typename geometry_concept<T>::type, polygon_with_holes_concept>::type,
 105     typename gtl_same_type<typename geometry_concept<T>::type, polygon_45_with_holes_concept>::type
 106   >::type> : public polygon_traits_general<T> {};
 107
 108   template <typename T>
 109   struct polygon_traits< T,
 110                          typename gtl_or<
 111     typename gtl_same_type<typename geometry_concept<T>::type, polygon_90_concept>::type,
 112     typename gtl_same_type<typename geometry_concept<T>::type, polygon_90_with_holes_concept>::type
 113   >::type > : public polygon_traits_90<T> {};
 114
 115 #else
 116
 117   template <typename T, typename T_IF, typename T_ELSE>
 118   struct gtl_ifelse {};
 119   template <typename T_IF, typename T_ELSE>
 120   struct gtl_ifelse<gtl_no, T_IF, T_ELSE> {
 121     typedef T_ELSE type;
 122   };
 123   template <typename T_IF, typename T_ELSE>
 124   struct gtl_ifelse<gtl_yes, T_IF, T_ELSE> {
 125     typedef T_IF type;
 126   };
 127
 128   template <typename T, typename enable = gtl_yes>
 129   struct polygon_traits {};
 130
 131   template <typename T>
 132   struct polygon_traits<T, typename gtl_or<typename gtl_or_4<
 133     typename gtl_same_type<typename geometry_concept<T>::type, polygon_concept>::type,
 134     typename gtl_same_type<typename geometry_concept<T>::type, polygon_45_concept>::type,
 135     typename gtl_same_type<typename geometry_concept<T>::type, polygon_with_holes_concept>::type,
 136     typename gtl_same_type<typename geometry_concept<T>::type, polygon_45_with_holes_concept>::type
 137   >::type, typename gtl_or<
 138     typename gtl_same_type<typename geometry_concept<T>::type, polygon_90_concept>::type,
 139     typename gtl_same_type<typename geometry_concept<T>::type, polygon_90_with_holes_concept>::type
 140   >::type>::type > : public gtl_ifelse<typename gtl_or<
 141     typename gtl_same_type<typename geometry_concept<T>::type, polygon_90_concept>::type,
 142     typename gtl_same_type<typename geometry_concept<T>::type, polygon_90_with_holes_concept>::type >::type,
 143       polygon_traits_90<T>,
 144       polygon_traits_general<T> >::type {
 145   };
 146
 147 #endif
 148
 149   template <typename T, typename enable = void>
 150   struct polygon_with_holes_traits {
 151     typedef typename T::iterator_holes_type iterator_holes_type;
 152     typedef typename T::hole_type hole_type;
 153
 154     // Get the begin iterator
 155     static inline iterator_holes_type begin_holes(const T& t) {
 156       return t.begin_holes();
 157     }
 158
 159     // Get the end iterator
 160     static inline iterator_holes_type end_holes(const T& t) {
 161       return t.end_holes();
 162     }
 163
 164     // Get the number of holes
 165     static inline std::size_t size_holes(const T& t) {
 166       return t.size_holes();
 167     }
 168   };
 169
 170   template <typename T, typename enable = void>
 171   struct polygon_90_mutable_traits {
 172
 173     // Set the data of a polygon with the unique coordinates in an iterator, starting with an x
 174     template <typename iT>
 175     static inline T& set_compact(T& t, iT input_begin, iT input_end) {
 176       t.set_compact(input_begin, input_end);
 177       return t;
 178     }
 179
 180   };
 181
 182   template <typename T, typename enable = void>
 183   struct polygon_mutable_traits {
 184
 185     // Set the data of a polygon with the unique coordinates in an iterator, starting with an x
 186     template <typename iT>
 187     static inline T& set_points(T& t, iT input_begin, iT input_end) {
 188       t.set(input_begin, input_end);
 189       return t;
 190     }
 191
 192   };
 193
 194   template <typename T, typename enable = void>
 195   struct polygon_with_holes_mutable_traits {
 196
 197     // Set the data of a polygon with the unique coordinates in an iterator, starting with an x
 198     template <typename iT>
 199     static inline T& set_holes(T& t, iT inputBegin, iT inputEnd) {
 200       t.set_holes(inputBegin, inputEnd);
 201       return t;
 202     }
 203
 204   };
 205 }
 206 }
 207 #include "isotropy.hpp"
 208
 209 //point
 210 #include "point_data.hpp"
 211 #include "point_traits.hpp"
 212 #include "point_concept.hpp"
 213
 214 //interval
 215 #include "interval_data.hpp"
 216 #include "interval_traits.hpp"
 217 #include "interval_concept.hpp"
 218
 219 //rectangle
 220 #include "rectangle_data.hpp"
 221 #include "rectangle_traits.hpp"
 222 #include "rectangle_concept.hpp"
 223
 224 //algorithms needed by polygon types
 225 #include "detail/iterator_points_to_compact.hpp"
 226 #include "detail/iterator_compact_to_points.hpp"
 227
 228 //polygons
 229 #include "polygon_45_data.hpp"
 230 #include "polygon_data.hpp"
 231 #include "polygon_90_data.hpp"
 232 #include "polygon_90_with_holes_data.hpp"
 233 #include "polygon_45_with_holes_data.hpp"
 234 #include "polygon_with_holes_data.hpp"
 235
 236 namespace boost { namespace polygon{
 237   struct polygon_concept {};
 238   struct polygon_with_holes_concept {};
 239   struct polygon_45_concept {};
 240   struct polygon_45_with_holes_concept {};
 241   struct polygon_90_concept {};
 242   struct polygon_90_with_holes_concept {};
 243
 244
 245   template <typename T>
 246   struct is_polygon_90_type {
 247     typedef typename geometry_concept<T>::type GC;
 248     typedef typename gtl_same_type<polygon_90_concept, GC>::type type;
 249   };
 250
 251   template <typename T>
 252   struct is_polygon_45_type {
 253     typedef typename geometry_concept<T>::type GC;
 254     typedef typename gtl_or<typename is_polygon_90_type<T>::type,
 255                             typename gtl_same_type<polygon_45_concept, GC>::type>::type type;
 256   };
 257
 258   template <typename T>
 259   struct is_polygon_type {
 260     typedef typename geometry_concept<T>::type GC;
 261     typedef typename gtl_or<typename is_polygon_45_type<T>::type,
 262                             typename gtl_same_type<polygon_concept, GC>::type>::type type;
 263   };
 264
 265   template <typename T>
 266   struct is_polygon_90_with_holes_type {
 267     typedef typename geometry_concept<T>::type GC;
 268     typedef typename gtl_or<typename is_polygon_90_type<T>::type,
 269                             typename gtl_same_type<polygon_90_with_holes_concept, GC>::type>::type type;
 270   };
 271
 272   template <typename T>
 273   struct is_polygon_45_with_holes_type {
 274     typedef typename geometry_concept<T>::type GC;
 275     typedef typename gtl_or_3<typename is_polygon_90_with_holes_type<T>::type,
 276                               typename is_polygon_45_type<T>::type,
 277                               typename gtl_same_type<polygon_45_with_holes_concept, GC>::type>::type type;
 278   };
 279
 280   template <typename T>
 281   struct is_polygon_with_holes_type {
 282     typedef typename geometry_concept<T>::type GC;
 283     typedef typename gtl_or_3<typename is_polygon_45_with_holes_type<T>::type,
 284                               typename is_polygon_type<T>::type,
 285                               typename gtl_same_type<polygon_with_holes_concept, GC>::type>::type type;
 286   };
 287
 288   template <typename T>
 289   struct is_mutable_polygon_90_type {
 290     typedef typename geometry_concept<T>::type GC;
 291     typedef typename gtl_same_type<polygon_90_concept, GC>::type type;
 292   };
 293
 294   template <typename T>
 295   struct is_mutable_polygon_45_type {
 296     typedef typename geometry_concept<T>::type GC;
 297     typedef typename gtl_same_type<polygon_45_concept, GC>::type type;
 298   };
 299
 300   template <typename T>
 301   struct is_mutable_polygon_type {
 302     typedef typename geometry_concept<T>::type GC;
 303     typedef typename gtl_same_type<polygon_concept, GC>::type type;
 304   };
 305
 306   template <typename T>
 307   struct is_mutable_polygon_90_with_holes_type {
 308     typedef typename geometry_concept<T>::type GC;
 309     typedef typename gtl_same_type<polygon_90_with_holes_concept, GC>::type type;
 310   };
 311
 312   template <typename T>
 313   struct is_mutable_polygon_45_with_holes_type {
 314     typedef typename geometry_concept<T>::type GC;
 315     typedef typename gtl_same_type<polygon_45_with_holes_concept, GC>::type type;
 316   };
 317
 318   template <typename T>
 319   struct is_mutable_polygon_with_holes_type {
 320     typedef typename geometry_concept<T>::type GC;
 321     typedef typename gtl_same_type<polygon_with_holes_concept, GC>::type type;
 322   };
 323
 324   template <typename T>
 325   struct is_any_mutable_polygon_with_holes_type {
 326     typedef typename gtl_or_3<typename is_mutable_polygon_90_with_holes_type<T>::type,
 327                               typename is_mutable_polygon_45_with_holes_type<T>::type,
 328                               typename is_mutable_polygon_with_holes_type<T>::type>::type type;
 329   };
 330   template <typename T>
 331   struct is_any_mutable_polygon_without_holes_type {
 332     typedef typename gtl_or_3<
 333       typename is_mutable_polygon_90_type<T>::type,
 334       typename is_mutable_polygon_45_type<T>::type,
 335       typename is_mutable_polygon_type<T>::type>::type type; };
 336
 337   template <typename T>
 338   struct is_any_mutable_polygon_type {
 339     typedef typename gtl_or<typename is_any_mutable_polygon_with_holes_type<T>::type,
 340                             typename is_any_mutable_polygon_without_holes_type<T>::type>::type type;
 341   };
 342
 343   template <typename T>
 344   struct polygon_from_polygon_with_holes_type {};
 345   template <>
 346   struct polygon_from_polygon_with_holes_type<polygon_with_holes_concept> { typedef polygon_concept type; };
 347   template <>
 348   struct polygon_from_polygon_with_holes_type<polygon_45_with_holes_concept> { typedef polygon_45_concept type; };
 349   template <>
 350   struct polygon_from_polygon_with_holes_type<polygon_90_with_holes_concept> { typedef polygon_90_concept type; };
 351
 352   template <>
 353   struct geometry_domain<polygon_45_concept> { typedef forty_five_domain type; };
 354   template <>
 355   struct geometry_domain<polygon_45_with_holes_concept> { typedef forty_five_domain type; };
 356   template <>
 357   struct geometry_domain<polygon_90_concept> { typedef manhattan_domain type; };
 358   template <>
 359   struct geometry_domain<polygon_90_with_holes_concept> { typedef manhattan_domain type; };
 360
 361   template <typename domain_type, typename coordinate_type>
 362   struct distance_type_by_domain { typedef typename coordinate_traits<coordinate_type>::coordinate_distance type; };
 363   template <typename coordinate_type>
 364   struct distance_type_by_domain<manhattan_domain, coordinate_type> {
 365     typedef typename coordinate_traits<coordinate_type>::coordinate_difference type; };
 366
 367   // \brief Sets the boundary of the polygon to the points in the iterator range
 368   // \tparam T A type that models polygon_concept
 369   // \tparam iT Iterator type over objects that model point_concept
 370   // \param t The polygon to set
 371   // \param begin_points The start of the range of points
 372   // \param end_points The end of the range of points
 373
 374   /// \relatesalso polygon_concept
 375   template <typename T, typename iT>
 376   typename enable_if <typename is_any_mutable_polygon_type<T>::type, T>::type &
 377   set_points(T& t, iT begin_points, iT end_points) {
 378     polygon_mutable_traits<T>::set_points(t, begin_points, end_points);
 379     return t;
 380   }
 381
 382   // \brief Sets the boundary of the polygon to the non-redundant coordinates in the iterator range
 383   // \tparam T A type that models polygon_90_concept
 384   // \tparam iT Iterator type over objects that model coordinate_concept
 385   // \param t The polygon to set
 386   // \param begin_compact_coordinates The start of the range of coordinates
 387   // \param end_compact_coordinates The end of the range of coordinates
 388
 389 /// \relatesalso polygon_90_concept
 390   template <typename T, typename iT>
 391   typename enable_if <typename gtl_or<
 392     typename is_mutable_polygon_90_type<T>::type,
 393     typename is_mutable_polygon_90_with_holes_type<T>::type>::type, T>::type &
 394   set_compact(T& t, iT begin_compact_coordinates, iT end_compact_coordinates) {
 395     polygon_90_mutable_traits<T>::set_compact(t, begin_compact_coordinates, end_compact_coordinates);
 396     return t;
 397   }
 398
 399 /// \relatesalso polygon_with_holes_concept
 400   template <typename T, typename iT>
 401   typename enable_if< typename gtl_and <
 402     typename is_any_mutable_polygon_with_holes_type<T>::type,
 403     typename gtl_different_type<typename geometry_domain<typename geometry_concept<T>::type>::type,
 404                                 manhattan_domain>::type>::type,
 405                        T>::type &
 406   set_compact(T& t, iT begin_compact_coordinates, iT end_compact_coordinates) {
 407     iterator_compact_to_points<iT, point_data<typename polygon_traits<T>::coordinate_type> >
 408       itrb(begin_compact_coordinates, end_compact_coordinates),
 409       itre(end_compact_coordinates, end_compact_coordinates);
 410     return set_points(t, itrb, itre);
 411   }
 412
 413 /// \relatesalso polygon_with_holes_concept
 414   template <typename T, typename iT>
 415   typename enable_if <typename is_any_mutable_polygon_with_holes_type<T>::type, T>::type &
 416   set_holes(T& t, iT begin_holes, iT end_holes) {
 417     polygon_with_holes_mutable_traits<T>::set_holes(t, begin_holes, end_holes);
 418     return t;
 419   }
 420
 421 /// \relatesalso polygon_90_concept
 422   template <typename T>
 423   typename polygon_90_traits<T>::compact_iterator_type
 424   begin_compact(const T& polygon,
 425     typename enable_if<
 426       typename gtl_and <typename is_polygon_with_holes_type<T>::type,
 427                         typename gtl_same_type<typename geometry_domain<typename geometry_concept<T>::type>::type,
 428                 manhattan_domain>::type>::type>::type * = 0
 429   ) {
 430     return polygon_90_traits<T>::begin_compact(polygon);
 431   }
 432
 433 /// \relatesalso polygon_90_concept
 434   template <typename T>
 435   typename polygon_90_traits<T>::compact_iterator_type
 436   end_compact(const T& polygon,
 437     typename enable_if<
 438     typename gtl_and <typename is_polygon_with_holes_type<T>::type,
 439                       typename gtl_same_type<typename geometry_domain<typename geometry_concept<T>::type>::type,
 440               manhattan_domain>::type>::type>::type * = 0
 441   ) {
 442     return polygon_90_traits<T>::end_compact(polygon);
 443   }
 444
 445   /// \relatesalso polygon_concept
 446   template <typename T>
 447   typename enable_if < typename gtl_if<
 448     typename is_polygon_with_holes_type<T>::type>::type,
 449                         typename polygon_traits<T>::iterator_type>::type
 450   begin_points(const T& polygon) {
 451     return polygon_traits<T>::begin_points(polygon);
 452   }
 453
 454   /// \relatesalso polygon_concept
 455   template <typename T>
 456   typename enable_if < typename gtl_if<
 457     typename is_polygon_with_holes_type<T>::type>::type,
 458                         typename polygon_traits<T>::iterator_type>::type
 459   end_points(const T& polygon) {
 460     return polygon_traits<T>::end_points(polygon);
 461   }
 462
 463   /// \relatesalso polygon_concept
 464   template <typename T>
 465   typename enable_if <typename is_polygon_with_holes_type<T>::type,
 466                        std::size_t>::type
 467   size(const T& polygon) {
 468     return polygon_traits<T>::size(polygon);
 469   }
 470
 471 /// \relatesalso polygon_with_holes_concept
 472   template <typename T>
 473   typename enable_if < typename gtl_if<
 474     typename is_polygon_with_holes_type<T>::type>::type,
 475                         typename polygon_with_holes_traits<T>::iterator_holes_type>::type
 476   begin_holes(const T& polygon) {
 477     return polygon_with_holes_traits<T>::begin_holes(polygon);
 478   }
 479
 480 /// \relatesalso polygon_with_holes_concept
 481   template <typename T>
 482   typename enable_if < typename gtl_if<
 483     typename is_polygon_with_holes_type<T>::type>::type,
 484                         typename polygon_with_holes_traits<T>::iterator_holes_type>::type
 485   end_holes(const T& polygon) {
 486     return polygon_with_holes_traits<T>::end_holes(polygon);
 487   }
 488
 489 /// \relatesalso polygon_with_holes_concept
 490   template <typename T>
 491   typename enable_if <typename is_polygon_with_holes_type<T>::type,
 492                        std::size_t>::type
 493   size_holes(const T& polygon) {
 494     return polygon_with_holes_traits<T>::size_holes(polygon);
 495   }
 496
 497   // \relatesalso polygon_concept
 498   template <typename T1, typename T2>
 499   typename enable_if<
 500     typename gtl_and< typename is_mutable_polygon_type<T1>::type,
 501                       typename is_polygon_type<T2>::type>::type, T1>::type &
 502   assign(T1& lvalue, const T2& rvalue) {
 503     polygon_mutable_traits<T1>::set_points(lvalue, polygon_traits<T2>::begin_points(rvalue),
 504                                            polygon_traits<T2>::end_points(rvalue));
 505     return lvalue;
 506   }
 507
 508 // \relatesalso polygon_with_holes_concept
 509   template <typename T1, typename T2>
 510   typename enable_if<
 511     typename gtl_and< typename is_mutable_polygon_with_holes_type<T1>::type,
 512                       typename is_polygon_with_holes_type<T2>::type>::type, T1>::type &
 513   assign(T1& lvalue, const T2& rvalue) {
 514     polygon_mutable_traits<T1>::set_points(lvalue, polygon_traits<T2>::begin_points(rvalue),
 515                                            polygon_traits<T2>::end_points(rvalue));
 516     polygon_with_holes_mutable_traits<T1>::set_holes(lvalue, polygon_with_holes_traits<T2>::begin_holes(rvalue),
 517                                                      polygon_with_holes_traits<T2>::end_holes(rvalue));
 518     return lvalue;
 519   }
 520
 521   // \relatesalso polygon_45_concept
 522   template <typename T1, typename T2>
 523   typename enable_if< typename gtl_and< typename is_mutable_polygon_45_type<T1>::type, typename is_polygon_45_type<T2>::type>::type, T1>::type &
 524   assign(T1& lvalue, const T2& rvalue) {
 525     polygon_mutable_traits<T1>::set_points(lvalue, polygon_traits<T2>::begin_points(rvalue),
 526                                            polygon_traits<T2>::end_points(rvalue));
 527     return lvalue;
 528   }
 529
 530 // \relatesalso polygon_45_with_holes_concept
 531   template <typename T1, typename T2>
 532   typename enable_if<
 533     typename gtl_and< typename is_mutable_polygon_45_with_holes_type<T1>::type,
 534                       typename is_polygon_45_with_holes_type<T2>::type>::type, T1>::type &
 535   assign(T1& lvalue, const T2& rvalue) {
 536     polygon_mutable_traits<T1>::set_points(lvalue, polygon_traits<T2>::begin_points(rvalue),
 537                                            polygon_traits<T2>::end_points(rvalue));
 538     polygon_with_holes_mutable_traits<T1>::set_holes(lvalue, polygon_with_holes_traits<T2>::begin_holes(rvalue),
 539                                                      polygon_with_holes_traits<T2>::end_holes(rvalue));
 540     return lvalue;
 541   }
 542
 543   // \relatesalso polygon_90_concept
 544   template <typename T1, typename T2>
 545   typename enable_if<
 546     typename gtl_and< typename is_mutable_polygon_90_type<T1>::type,
 547                       typename is_polygon_90_type<T2>::type>::type, T1>::type &
 548   assign(T1& lvalue, const T2& rvalue) {
 549     polygon_90_mutable_traits<T1>::set_compact(lvalue, polygon_90_traits<T2>::begin_compact(rvalue),
 550                                                polygon_90_traits<T2>::end_compact(rvalue));
 551     return lvalue;
 552   }
 553
 554 // \relatesalso polygon_90_with_holes_concept
 555   template <typename T1, typename T2>
 556   typename enable_if<
 557     typename gtl_and< typename is_mutable_polygon_90_with_holes_type<T1>::type,
 558                       typename is_polygon_90_with_holes_type<T2>::type>::type, T1>::type &
 559   assign(T1& lvalue, const T2& rvalue) {
 560     polygon_90_mutable_traits<T1>::set_compact(lvalue, polygon_90_traits<T2>::begin_compact(rvalue),
 561                                                polygon_90_traits<T2>::end_compact(rvalue));
 562     polygon_with_holes_mutable_traits<T1>::set_holes(lvalue, polygon_with_holes_traits<T2>::begin_holes(rvalue),
 563                                                      polygon_with_holes_traits<T2>::end_holes(rvalue));
 564     return lvalue;
 565   }
 566
 567   // \relatesalso polygon_90_concept
 568   template <typename T1, typename T2>
 569   typename enable_if<
 570     typename gtl_and< typename is_any_mutable_polygon_type<T1>::type,
 571                       typename is_rectangle_concept<typename geometry_concept<T2>::type>::type>::type, T1>::type &
 572   assign(T1& polygon, const T2& rect) {
 573     typedef point_data<typename polygon_traits<T1>::coordinate_type> PT;
 574     PT points[4] = {PT(xl(rect), yl(rect)), PT(xh(rect), yl(rect)), PT(xh(rect), yh(rect)), PT(xl(rect), yh(rect))};
 575     set_points(polygon, points, points+4);
 576     return polygon;
 577   }
 578
 579 /// \relatesalso polygon_90_concept
 580   template <typename polygon_type, typename point_type>
 581   typename enable_if< typename gtl_and< typename is_mutable_polygon_90_type<polygon_type>::type,
 582                                          typename is_point_concept<typename geometry_concept<point_type>::type>::type>::type,
 583                        polygon_type>::type &
 584   convolve(polygon_type& polygon, const point_type& point) {
 585     std::vector<typename polygon_90_traits<polygon_type>::coordinate_type> coords;
 586     coords.reserve(::boost::polygon::size(polygon));
 587     bool pingpong = true;
 588     for(typename polygon_90_traits<polygon_type>::compact_iterator_type iter = begin_compact(polygon);
 589         iter != end_compact(polygon); ++iter) {
 590       coords.push_back((*iter) + (pingpong ? x(point) : y(point)));
 591       pingpong = !pingpong;
 592     }
 593     polygon_90_mutable_traits<polygon_type>::set_compact(polygon, coords.begin(), coords.end());
 594     return polygon;
 595   }
 596
 597 /// \relatesalso polygon_concept
 598   template <typename polygon_type, typename point_type>
 599   typename enable_if< typename gtl_and< typename gtl_or<
 600     typename is_mutable_polygon_45_type<polygon_type>::type,
 601     typename is_mutable_polygon_type<polygon_type>::type>::type,
 602                                          typename is_point_concept<typename geometry_concept<point_type>::type>::type>::type,
 603                        polygon_type>::type &
 604   convolve(polygon_type& polygon, const point_type& point) {
 605     std::vector<typename std::iterator_traits<typename polygon_traits<polygon_type>::iterator_type>::value_type> points;
 606     points.reserve(::boost::polygon::size(polygon));
 607     for(typename polygon_traits<polygon_type>::iterator_type iter = begin_points(polygon);
 608         iter != end_points(polygon); ++iter) {
 609       points.push_back(*iter);
 610       convolve(points.back(), point);
 611     }
 612     polygon_mutable_traits<polygon_type>::set_points(polygon, points.begin(), points.end());
 613     return polygon;
 614   }
 615
 616 /// \relatesalso polygon_with_holes_concept
 617   template <typename polygon_type, typename point_type>
 618   typename enable_if<
 619     typename gtl_and< typename is_any_mutable_polygon_with_holes_type<polygon_type>::type,
 620                       typename is_point_concept<typename geometry_concept<point_type>::type>::type>::type,
 621     polygon_type>::type &
 622   convolve(polygon_type& polygon, const point_type& point) {
 623     typedef typename polygon_with_holes_traits<polygon_type>::hole_type hole_type;
 624     hole_type h;
 625     set_points(h, begin_points(polygon), end_points(polygon));
 626     convolve(h, point);
 627     std::vector<hole_type> holes;
 628     holes.reserve(size_holes(polygon));
 629     for(typename polygon_with_holes_traits<polygon_type>::iterator_holes_type itr = begin_holes(polygon);
 630         itr != end_holes(polygon); ++itr) {
 631       holes.push_back(*itr);
 632       convolve(holes.back(), point);
 633     }
 634     assign(polygon, h);
 635     set_holes(polygon, holes.begin(), holes.end());
 636     return polygon;
 637   }
 638
 639 /// \relatesalso polygon_concept
 640   template <typename T>
 641   typename enable_if< typename is_any_mutable_polygon_type<T>::type, T>::type &
 642   move(T& polygon, orientation_2d orient, typename polygon_traits<T>::coordinate_type displacement) {
 643     typedef typename polygon_traits<T>::coordinate_type Unit;
 644     if(orient == HORIZONTAL) return convolve(polygon, point_data<Unit>(displacement, Unit(0)));
 645     return convolve(polygon, point_data<Unit>(Unit(0), displacement));
 646   }
 647
 648 /// \relatesalso polygon_concept
 649 /// \brief Applies a transformation to the polygon.
 650 /// \tparam polygon_type A type that models polygon_concept
 651 /// \tparam transform_type A type that may be either axis_transformation or transformation or that overloads point_concept::transform
 652 /// \param polygon The polygon to transform
 653 /// \param tr The transformation to apply
 654   template <typename polygon_type, typename transform_type>
 655   typename enable_if< typename is_any_mutable_polygon_without_holes_type<polygon_type>::type, polygon_type>::type &
 656   transform(polygon_type& polygon, const transform_type& tr) {
 657     std::vector<typename std::iterator_traits<typename polygon_traits<polygon_type>::iterator_type>::value_type> points;
 658     points.reserve(::boost::polygon::size(polygon));
 659     for(typename polygon_traits<polygon_type>::iterator_type iter = begin_points(polygon);
 660         iter != end_points(polygon); ++iter) {
 661       points.push_back(*iter);
 662       transform(points.back(), tr);
 663     }
 664     polygon_mutable_traits<polygon_type>::set_points(polygon, points.begin(), points.end());
 665     return polygon;
 666   }
 667
 668 /// \relatesalso polygon_with_holes_concept
 669   template <typename T, typename transform_type>
 670   typename enable_if< typename is_any_mutable_polygon_with_holes_type<T>::type, T>::type &
 671   transform(T& polygon, const transform_type& tr) {
 672     typedef typename polygon_with_holes_traits<T>::hole_type hole_type;
 673     hole_type h;
 674     set_points(h, begin_points(polygon), end_points(polygon));
 675     transform(h, tr);
 676     std::vector<hole_type> holes;
 677     holes.reserve(size_holes(polygon));
 678     for(typename polygon_with_holes_traits<T>::iterator_holes_type itr = begin_holes(polygon);
 679         itr != end_holes(polygon); ++itr) {
 680       holes.push_back(*itr);
 681       transform(holes.back(), tr);
 682     }
 683     assign(polygon, h);
 684     set_holes(polygon, holes.begin(), holes.end());
 685     return polygon;
 686   }
 687
 688   template <typename polygon_type>
 689   typename enable_if< typename is_any_mutable_polygon_without_holes_type<polygon_type>::type, polygon_type>::type &
 690   scale_up(polygon_type& polygon, typename coordinate_traits<typename polygon_traits<polygon_type>::coordinate_type>::unsigned_area_type factor) {
 691     std::vector<typename std::iterator_traits<typename polygon_traits<polygon_type>::iterator_type>::value_type> points;
 692     points.reserve(::boost::polygon::size(polygon));
 693     for(typename polygon_traits<polygon_type>::iterator_type iter = begin_points(polygon);
 694         iter != end_points(polygon); ++iter) {
 695       points.push_back(*iter);
 696       scale_up(points.back(), factor);
 697     }
 698     polygon_mutable_traits<polygon_type>::set_points(polygon, points.begin(), points.end());
 699     return polygon;
 700   }
 701
 702   template <typename T>
 703   typename enable_if< typename is_any_mutable_polygon_with_holes_type<T>::type, T>::type &
 704   scale_up(T& polygon, typename coordinate_traits<typename polygon_traits<T>::coordinate_type>::unsigned_area_type factor) {
 705     typedef typename polygon_with_holes_traits<T>::hole_type hole_type;
 706     hole_type h;
 707     set_points(h, begin_points(polygon), end_points(polygon));
 708     scale_up(h, factor);
 709     std::vector<hole_type> holes;
 710     holes.reserve(size_holes(polygon));
 711     for(typename polygon_with_holes_traits<T>::iterator_holes_type itr = begin_holes(polygon);
 712         itr != end_holes(polygon); ++itr) {
 713       holes.push_back(*itr);
 714       scale_up(holes.back(), factor);
 715     }
 716     assign(polygon, h);
 717     set_holes(polygon, holes.begin(), holes.end());
 718     return polygon;
 719   }
 720
 721   //scale non-45 down
 722   template <typename polygon_type>
 723   typename enable_if<
 724     typename gtl_and< typename is_any_mutable_polygon_without_holes_type<polygon_type>::type,
 725                       typename gtl_not<typename gtl_same_type
 726                                        < forty_five_domain,
 727                                          typename geometry_domain<typename geometry_concept<polygon_type>::type>::type>::type>::type>::type,
 728     polygon_type>::type &
 729   scale_down(polygon_type& polygon, typename coordinate_traits<typename polygon_traits<polygon_type>::coordinate_type>::unsigned_area_type factor) {
 730     std::vector<typename std::iterator_traits<typename polygon_traits<polygon_type>::iterator_type>::value_type> points;
 731     points.reserve(::boost::polygon::size(polygon));
 732     for(typename polygon_traits<polygon_type>::iterator_type iter = begin_points(polygon);
 733         iter != end_points(polygon); ++iter) {
 734       points.push_back(*iter);
 735       scale_down(points.back(), factor);
 736     }
 737     polygon_mutable_traits<polygon_type>::set_points(polygon, points.begin(), points.end());
 738     return polygon;
 739   }
 740
 741   template <typename Unit>
 742   Unit local_abs(Unit value) { return value < 0 ? (Unit)-value : value; }
 743
 744   template <typename Unit>
 745   void snap_point_vector_to_45(std::vector<point_data<Unit> >& pts) {
 746     typedef point_data<Unit> Point;
 747     if(pts.size() < 3) { pts.clear(); return; }
 748     typename std::vector<point_data<Unit> >::iterator endLocation = std::unique(pts.begin(), pts.end());
 749     if(endLocation != pts.end()){
 750       pts.resize(endLocation - pts.begin());
 751     }
 752     if(pts.back() == pts[0]) pts.pop_back();
 753     //iterate over point triplets
 754     int numPts = pts.size();
 755     bool wrap_around = false;
 756     for(int i = 0; i < numPts; ++i) {
 757       Point& pt1 = pts[i];
 758       Point& pt2 = pts[(i + 1) % numPts];
 759       Point& pt3 = pts[(i + 2) % numPts];
 760       //check if non-45 edge
 761       Unit deltax = x(pt2) - x(pt1);
 762       Unit deltay = y(pt2) - y(pt1);
 763       if(deltax && deltay &&
 764          local_abs(deltax) != local_abs(deltay)) {
 765         //adjust the middle point
 766         Unit ndx = x(pt3) - x(pt2);
 767         Unit ndy = y(pt3) - y(pt2);
 768         if(ndx && ndy) {
 769           Unit diff = local_abs(local_abs(deltax) - local_abs(deltay));
 770           Unit halfdiff = diff/2;
 771           if((deltax > 0 && deltay > 0) ||
 772              (deltax < 0 && deltay < 0)) {
 773             //previous edge is rising slope
 774             if(local_abs(deltax + halfdiff + (diff % 2)) ==
 775                local_abs(deltay - halfdiff)) {
 776               x(pt2, x(pt2) + halfdiff + (diff % 2));
 777               y(pt2, y(pt2) - halfdiff);
 778             } else if(local_abs(deltax - halfdiff - (diff % 2)) ==
 779                       local_abs(deltay + halfdiff)) {
 780               x(pt2, x(pt2) - halfdiff - (diff % 2));
 781               y(pt2, y(pt2) + halfdiff);
 782             } else{
 783               //std::cout << "fail1\n";
 784             }
 785           } else {
 786             //previous edge is falling slope
 787             if(local_abs(deltax + halfdiff + (diff % 2)) ==
 788                local_abs(deltay + halfdiff)) {
 789               x(pt2, x(pt2) + halfdiff + (diff % 2));
 790               y(pt2, y(pt2) + halfdiff);
 791             } else if(local_abs(deltax - halfdiff - (diff % 2)) ==
 792                       local_abs(deltay - halfdiff)) {
 793               x(pt2, x(pt2) - halfdiff - (diff % 2));
 794               y(pt2, y(pt2) - halfdiff);
 795             } else {
 796               //std::cout << "fail2\n";
 797             }
 798           }
 799           if(i == numPts - 1 && (diff % 2)) {
 800             //we have a wrap around effect
 801             if(!wrap_around) {
 802               wrap_around = true;
 803               i = -1;
 804             }
 805           }
 806         } else if(ndx) {
 807           //next edge is horizontal
 808           //find the x value for pt1 that would make the abs(deltax) == abs(deltay)
 809           Unit newDeltaX = local_abs(deltay);
 810           if(deltax < 0) newDeltaX *= -1;
 811           x(pt2, x(pt1) + newDeltaX);
 812         } else { //ndy
 813           //next edge is vertical
 814           //find the y value for pt1 that would make the abs(deltax) == abs(deltay)
 815           Unit newDeltaY = local_abs(deltax);
 816           if(deltay < 0) newDeltaY *= -1;
 817           y(pt2, y(pt1) + newDeltaY);
 818         }
 819       }
 820     }
 821   }
 822
 823   template <typename polygon_type>
 824   typename enable_if< typename is_any_mutable_polygon_without_holes_type<polygon_type>::type, polygon_type>::type &
 825   snap_to_45(polygon_type& polygon) {
 826     std::vector<typename std::iterator_traits<typename polygon_traits<polygon_type>::iterator_type>::value_type> points;
 827     points.reserve(::boost::polygon::size(polygon));
 828     for(typename polygon_traits<polygon_type>::iterator_type iter = begin_points(polygon);
 829         iter != end_points(polygon); ++iter) {
 830       points.push_back(*iter);
 831     }
 832     snap_point_vector_to_45(points);
 833     polygon_mutable_traits<polygon_type>::set_points(polygon, points.begin(), points.end());
 834     return polygon;
 835   }
 836
 837   template <typename polygon_type>
 838   typename enable_if< typename is_any_mutable_polygon_with_holes_type<polygon_type>::type, polygon_type>::type &
 839   snap_to_45(polygon_type& polygon) {
 840     typedef typename polygon_with_holes_traits<polygon_type>::hole_type hole_type;
 841     hole_type h;
 842     set_points(h, begin_points(polygon), end_points(polygon));
 843     snap_to_45(h);
 844     std::vector<hole_type> holes;
 845     holes.reserve(size_holes(polygon));
 846     for(typename polygon_with_holes_traits<polygon_type>::iterator_holes_type itr = begin_holes(polygon);
 847         itr != end_holes(polygon); ++itr) {
 848       holes.push_back(*itr);
 849       snap_to_45(holes.back());
 850     }
 851     assign(polygon, h);
 852     set_holes(polygon, holes.begin(), holes.end());
 853     return polygon;
 854   }
 855
 856   //scale specifically 45 down
 857   template <typename polygon_type>
 858   typename enable_if<
 859     typename gtl_and< typename is_any_mutable_polygon_without_holes_type<polygon_type>::type,
 860                       typename gtl_same_type
 861                       < forty_five_domain,
 862                         typename geometry_domain<typename geometry_concept<polygon_type>::type>::type>::type>::type,
 863     polygon_type>::type &
 864   scale_down(polygon_type& polygon, typename coordinate_traits<typename polygon_traits<polygon_type>::coordinate_type>::unsigned_area_type factor) {
 865     std::vector<typename std::iterator_traits<typename polygon_traits<polygon_type>::iterator_type>::value_type> points;
 866     points.reserve(::boost::polygon::size(polygon));
 867     for(typename polygon_traits<polygon_type>::iterator_type iter = begin_points(polygon);
 868         iter != end_points(polygon); ++iter) {
 869       points.push_back(*iter);
 870       scale_down(points.back(), factor);
 871     }
 872     snap_point_vector_to_45(points);
 873     polygon_mutable_traits<polygon_type>::set_points(polygon, points.begin(), points.end());
 874     return polygon;
 875   }
 876
 877   template <typename T>
 878   typename enable_if< typename is_any_mutable_polygon_with_holes_type<T>::type, T>::type &
 879   scale_down(T& polygon, typename coordinate_traits<typename polygon_traits<T>::coordinate_type>::unsigned_area_type factor) {
 880     typedef typename polygon_with_holes_traits<T>::hole_type hole_type;
 881     hole_type h;
 882     set_points(h, begin_points(polygon), end_points(polygon));
 883     scale_down(h, factor);
 884     std::vector<hole_type> holes;
 885     holes.reserve(size_holes(polygon));
 886     for(typename polygon_with_holes_traits<T>::iterator_holes_type itr = begin_holes(polygon);
 887         itr != end_holes(polygon); ++itr) {
 888       holes.push_back(*itr);
 889       scale_down(holes.back(), factor);
 890     }
 891     assign(polygon, h);
 892     set_holes(polygon, holes.begin(), holes.end());
 893     return polygon;
 894   }
 895
 896   //scale non-45
 897   template <typename polygon_type>
 898   typename enable_if<
 899     typename gtl_and< typename is_any_mutable_polygon_without_holes_type<polygon_type>::type,
 900                       typename gtl_not<typename gtl_same_type
 901                                        < forty_five_domain,
 902                                          typename geometry_domain<typename geometry_concept<polygon_type>::type>::type>::type>::type>::type,
 903     polygon_type>::type &
 904   scale(polygon_type& polygon, double factor) {
 905     std::vector<typename std::iterator_traits<typename polygon_traits<polygon_type>::iterator_type>::value_type> points;
 906     points.reserve(::boost::polygon::size(polygon));
 907     for(typename polygon_traits<polygon_type>::iterator_type iter = begin_points(polygon);
 908         iter != end_points(polygon); ++iter) {
 909       points.push_back(*iter);
 910       scale(points.back(), anisotropic_scale_factor<double>(factor, factor));
 911     }
 912     polygon_mutable_traits<polygon_type>::set_points(polygon, points.begin(), points.end());
 913     return polygon;
 914   }
 915
 916   //scale specifically 45
 917   template <typename polygon_type>
 918   polygon_type&
 919   scale(polygon_type& polygon, double factor,
 920     typename enable_if<
 921     typename gtl_and< typename is_any_mutable_polygon_without_holes_type<polygon_type>::type,
 922                       typename gtl_same_type
 923                       < forty_five_domain,
 924         typename geometry_domain<typename geometry_concept<polygon_type>::type>::type>::type>::type>::type * = 0
 925   ) {
 926     std::vector<typename std::iterator_traits<typename polygon_traits<polygon_type>::iterator_type>::value_type> points;
 927     points.reserve(::boost::polygon::size(polygon));
 928     for(typename polygon_traits<polygon_type>::iterator_type iter = begin_points(polygon);
 929         iter != end_points(polygon); ++iter) {
 930       points.push_back(*iter);
 931       scale(points.back(), anisotropic_scale_factor<double>(factor, factor));
 932     }
 933     snap_point_vector_to_45(points);
 934     polygon_mutable_traits<polygon_type>::set_points(polygon, points.begin(), points.end());
 935     return polygon;
 936   }
 937
 938   template <typename T>
 939   T&
 940   scale(T& polygon, double factor,
 941   typename enable_if< typename is_any_mutable_polygon_with_holes_type<T>::type>::type * = 0
 942   ) {
 943     typedef typename polygon_with_holes_traits<T>::hole_type hole_type;
 944     hole_type h;
 945     set_points(h, begin_points(polygon), end_points(polygon));
 946     scale(h, factor);
 947     std::vector<hole_type> holes;
 948     holes.reserve(size_holes(polygon));
 949     for(typename polygon_with_holes_traits<T>::iterator_holes_type itr = begin_holes(polygon);
 950         itr != end_holes(polygon); ++itr) {
 951       holes.push_back(*itr);
 952       scale(holes.back(), factor);
 953     }
 954     assign(polygon, h);
 955     set_holes(polygon, holes.begin(), holes.end());
 956     return polygon;
 957   }
 958
 959   template <typename iterator_type, typename area_type>
 960   static area_type
 961   point_sequence_area(iterator_type begin_range, iterator_type end_range) {
 962     typedef typename std::iterator_traits<iterator_type>::value_type point_type;
 963     if(begin_range == end_range) return area_type(0);
 964     point_type first = *begin_range;
 965     point_type previous = first;
 966     ++begin_range;
 967     // Initialize trapezoid base line
 968     area_type y_base = (area_type)y(first);
 969     // Initialize area accumulator
 970
 971     area_type area(0);
 972     while (begin_range != end_range) {
 973       area_type x1 = (area_type)x(previous);
 974       area_type x2 = (area_type)x(*begin_range);
 975 #ifdef BOOST_POLYGON_ICC
 976 #pragma warning (push)
 977 #pragma warning (disable:1572)
 978 #endif
 979       if(x1 != x2) {
 980 #ifdef BOOST_POLYGON_ICC
 981 #pragma warning (pop)
 982 #endif
 983         // do trapezoid area accumulation
 984         area += (x2 - x1) * (((area_type)y(*begin_range) - y_base) +
 985                              ((area_type)y(previous) - y_base)) / 2;
 986       }
 987       previous = *begin_range;
 988       // go to next point
 989       ++begin_range;
 990     }
 991     //wrap around to evaluate the edge between first and last if not closed
 992     if(!equivalence(first, previous)) {
 993       area_type x1 = (area_type)x(previous);
 994       area_type x2 = (area_type)x(first);
 995       area += (x2 - x1) * (((area_type)y(first) - y_base) +
 996                            ((area_type)y(previous) - y_base)) / 2;
 997     }
 998     return area;
 999   }
1000
1001   template <typename T>
1002   typename enable_if<
1003     typename is_polygon_with_holes_type<T>::type,
1004                         typename area_type_by_domain< typename geometry_domain<typename geometry_concept<T>::type>::type,
1005                                                       typename polygon_traits<T>::coordinate_type>::type>::type
1006   area(const T& polygon) {
1007     typedef typename area_type_by_domain< typename geometry_domain<typename geometry_concept<T>::type>::type,
1008       typename polygon_traits<T>::coordinate_type>::type area_type;
1009     area_type retval = point_sequence_area<typename polygon_traits<T>::iterator_type, area_type>
1010       (begin_points(polygon), end_points(polygon));
1011     if(retval < 0) retval *= -1;
1012     for(typename polygon_with_holes_traits<T>::iterator_holes_type itr =
1013           polygon_with_holes_traits<T>::begin_holes(polygon);
1014         itr != polygon_with_holes_traits<T>::end_holes(polygon); ++itr) {
1015       area_type tmp_area = point_sequence_area
1016         <typename polygon_traits<typename polygon_with_holes_traits<T>::hole_type>::iterator_type, area_type>
1017         (begin_points(*itr), end_points(*itr));
1018       if(tmp_area < 0) tmp_area *= -1;
1019       retval -= tmp_area;
1020     }
1021     return retval;
1022   }
1023
1024   template <typename iT>
1025   bool point_sequence_is_45(iT itr, iT itr_end) {
1026     typedef typename std::iterator_traits<iT>::value_type Point;
1027     typedef typename point_traits<Point>::coordinate_type Unit;
1028     if(itr == itr_end) return true;
1029     Point firstPt = *itr;
1030     Point prevPt = firstPt;
1031     ++itr;
1032     while(itr != itr_end) {
1033       Point pt = *itr;
1034       Unit deltax = x(pt) - x(prevPt);
1035       Unit deltay = y(pt) - y(prevPt);
1036       if(deltax && deltay &&
1037          local_abs(deltax) != local_abs(deltay))
1038         return false;
1039       prevPt = pt;
1040       ++itr;
1041     }
1042     Unit deltax = x(firstPt) - x(prevPt);
1043     Unit deltay = y(firstPt) - y(prevPt);
1044     if(deltax && deltay &&
1045        local_abs(deltax) != local_abs(deltay))
1046       return false;
1047     return true;
1048   }
1049
1050   template <typename polygon_type>
1051   typename enable_if< typename is_polygon_with_holes_type<polygon_type>::type, bool>::type
1052   is_45(const polygon_type& polygon) {
1053     typename polygon_traits<polygon_type>::iterator_type itr = begin_points(polygon), itr_end = end_points(polygon);
1054     if(!point_sequence_is_45(itr, itr_end)) return false;
1055     typename polygon_with_holes_traits<polygon_type>::iterator_holes_type itrh = begin_holes(polygon), itrh_end = end_holes(polygon);
1056     typedef typename polygon_with_holes_traits<polygon_type>::hole_type hole_type;
1057     for(; itrh != itrh_end; ++ itrh) {
1058       typename polygon_traits<hole_type>::iterator_type itr1 = begin_points(polygon), itr1_end = end_points(polygon);
1059       if(!point_sequence_is_45(itr1, itr1_end)) return false;
1060     }
1061     return true;
1062   }
1063
1064   template <typename distance_type, typename iterator_type>
1065   distance_type point_sequence_distance(iterator_type itr, iterator_type itr_end) {
1066     typedef distance_type Unit;
1067     typedef iterator_type iterator;
1068     typedef typename std::iterator_traits<iterator>::value_type point_type;
1069     Unit return_value = Unit(0);
1070     point_type previous_point, first_point;
1071     if(itr == itr_end) return return_value;
1072     previous_point = first_point = *itr;
1073     ++itr;
1074     for( ; itr != itr_end; ++itr) {
1075       point_type current_point = *itr;
1076       return_value += (Unit)euclidean_distance(current_point, previous_point);
1077       previous_point = current_point;
1078     }
1079     return_value += (Unit)euclidean_distance(previous_point, first_point);
1080     return return_value;
1081   }
1082
1083   template <typename T>
1084   typename distance_type_by_domain
1085   <typename geometry_domain<typename geometry_concept<T>::type>::type, typename polygon_traits<T>::coordinate_type>::type
1086   perimeter(const T& polygon,
1087   typename enable_if<
1088       typename is_polygon_with_holes_type<T>::type>::type * = 0
1089   ) {
1090     typedef typename distance_type_by_domain
1091       <typename geometry_domain<typename geometry_concept<T>::type>::type, typename polygon_traits<T>::coordinate_type>::type Unit;
1092     typedef typename polygon_traits<T>::iterator_type iterator;
1093     iterator itr = begin_points(polygon);
1094     iterator itr_end = end_points(polygon);
1095     Unit return_value = point_sequence_distance<Unit, iterator>(itr, itr_end);
1096     for(typename polygon_with_holes_traits<T>::iterator_holes_type itr_holes = begin_holes(polygon);
1097         itr_holes != end_holes(polygon); ++itr_holes) {
1098       typedef typename polygon_traits<typename polygon_with_holes_traits<T>::hole_type>::iterator_type hitertype;
1099       return_value += point_sequence_distance<Unit, hitertype>(begin_points(*itr_holes), end_points(*itr_holes));
1100     }
1101     return return_value;
1102   }
1103
1104   template <typename T>
1105   typename enable_if <typename is_polygon_with_holes_type<T>::type,
1106                        direction_1d>::type
1107   winding(const T& polygon) {
1108     winding_direction wd = polygon_traits<T>::winding(polygon);
1109     if(wd != unknown_winding) {
1110       return wd == clockwise_winding ? CLOCKWISE: COUNTERCLOCKWISE;
1111     }
1112     typedef typename area_type_by_domain< typename geometry_domain<typename geometry_concept<T>::type>::type,
1113       typename polygon_traits<T>::coordinate_type>::type area_type;
1114     return point_sequence_area<typename polygon_traits<T>::iterator_type, area_type>(begin_points(polygon), end_points(polygon)) < 0 ?
1115       COUNTERCLOCKWISE : CLOCKWISE;
1116   }
1117
1118   template <typename T, typename input_point_type>
1119   typename enable_if<
1120     typename gtl_and<
1121       typename is_polygon_90_type<T>::type,
1122       typename gtl_same_type<
1123         typename geometry_concept<input_point_type>::type,
1124         point_concept
1125       >::type
1126     >::type,
1127     bool
1128   >::type contains(
1129       const T& polygon,
1130       const input_point_type& point,
1131       bool consider_touch = true) {
1132     typedef T polygon_type;
1133     typedef typename polygon_traits<polygon_type>::coordinate_type coordinate_type;
1134     typedef typename polygon_traits<polygon_type>::iterator_type iterator;
1135     typedef typename std::iterator_traits<iterator>::value_type point_type;
1136     coordinate_type point_x = x(point);
1137     coordinate_type point_y = y(point);
1138     // Check how many intersections has the ray extended from the given
1139     // point in the x-axis negative direction with the polygon edges.
1140     // If the number is odd the point is within the polygon, otherwise not.
1141     // We can safely ignore horizontal edges, however intersections with
1142     // end points of the vertical edges require special handling. We should
1143     // add one intersection in case horizontal edges that extend vertical edge
1144     // point in the same direction.
1145     int num_full_intersections = 0;
1146     int num_half_intersections = 0;
1147     for (iterator iter = begin_points(polygon); iter != end_points(polygon);) {
1148       point_type curr_point = *iter;
1149       ++iter;
1150       point_type next_point = (iter == end_points(polygon)) ? *begin_points(polygon) : *iter;
1151       if (x(curr_point) == x(next_point)) {
1152         if (x(curr_point) > point_x) {
1153           continue;
1154         }
1155         coordinate_type min_y = (std::min)(y(curr_point), y(next_point));
1156         coordinate_type max_y = (std::max)(y(curr_point), y(next_point));
1157         if (point_y > min_y && point_y < max_y) {
1158           if (x(curr_point) == point_x) {
1159             return consider_touch;
1160           }
1161           ++num_full_intersections;
1162         }
1163         if (point_y == min_y || point_y == max_y) {
1164           num_half_intersections += (y(curr_point) < y(next_point) ? 1 : -1);
1165         }
1166       } else {
1167         coordinate_type min_x = (std::min)(x(curr_point), x(next_point));
1168         coordinate_type max_x = (std::max)(x(curr_point), x(next_point));
1169         if (point_x >= min_x && point_x <= max_x) {
1170           if (y(curr_point) == point_y) {
1171             return consider_touch;
1172           }
1173         }
1174       }
1175     }
1176     int total_intersections = num_full_intersections + (num_half_intersections >> 1);
1177     return total_intersections & 1;
1178   }
1179
1180   //TODO: refactor to expose as user APIs
1181   template <typename Unit>
1182   struct edge_utils {
1183     typedef point_data<Unit> Point;
1184     typedef std::pair<Point, Point> half_edge;
1185
1186     class less_point {
1187     public:
1188       typedef Point first_argument_type;
1189       typedef Point second_argument_type;
1190       typedef bool result_type;
1191       inline less_point() {}
1192       inline bool operator () (const Point& pt1, const Point& pt2) const {
1193         if(pt1.get(HORIZONTAL) < pt2.get(HORIZONTAL)) return true;
1194         if(pt1.get(HORIZONTAL) == pt2.get(HORIZONTAL)) {
1195           if(pt1.get(VERTICAL) < pt2.get(VERTICAL)) return true;
1196         }
1197         return false;
1198       }
1199     };
1200
1201     static inline bool between(Point pt, Point pt1, Point pt2) {
1202       less_point lp;
1203       if(lp(pt1, pt2))
1204         return lp(pt, pt2) && lp(pt1, pt);
1205       return lp(pt, pt1) && lp(pt2, pt);
1206     }
1207
1208     template <typename area_type>
1209     static inline bool equal_slope(area_type dx1, area_type dy1, area_type dx2, area_type dy2) {
1210       typedef typename coordinate_traits<Unit>::unsigned_area_type unsigned_product_type;
1211       unsigned_product_type cross_1 = (unsigned_product_type)(dx2 < 0 ? -dx2 :dx2) * (unsigned_product_type)(dy1 < 0 ? -dy1 : dy1);
1212       unsigned_product_type cross_2 = (unsigned_product_type)(dx1 < 0 ? -dx1 :dx1) * (unsigned_product_type)(dy2 < 0 ? -dy2 : dy2);
1213       int dx1_sign = dx1 < 0 ? -1 : 1;
1214       int dx2_sign = dx2 < 0 ? -1 : 1;
1215       int dy1_sign = dy1 < 0 ? -1 : 1;
1216       int dy2_sign = dy2 < 0 ? -1 : 1;
1217       int cross_1_sign = dx2_sign * dy1_sign;
1218       int cross_2_sign = dx1_sign * dy2_sign;
1219       return cross_1 == cross_2 && (cross_1_sign == cross_2_sign || cross_1 == 0);
1220     }
1221
1222     static inline bool equal_slope(const Unit& x, const Unit& y,
1223                                    const Point& pt1, const Point& pt2) {
1224       const Point* pts[2] = {&pt1, &pt2};
1225       typedef typename coordinate_traits<Unit>::manhattan_area_type at;
1226       at dy2 = (at)pts[1]->get(VERTICAL) - (at)y;
1227       at dy1 = (at)pts[0]->get(VERTICAL) - (at)y;
1228       at dx2 = (at)pts[1]->get(HORIZONTAL) - (at)x;
1229       at dx1 = (at)pts[0]->get(HORIZONTAL) - (at)x;
1230       return equal_slope(dx1, dy1, dx2, dy2);
1231     }
1232
1233     template <typename area_type>
1234     static inline bool less_slope(area_type dx1, area_type dy1, area_type dx2, area_type dy2) {
1235       //reflext x and y slopes to right hand side half plane
1236       if(dx1 < 0) {
1237         dy1 *= -1;
1238         dx1 *= -1;
1239       } else if(dx1 == 0) {
1240         //if the first slope is vertical the first cannot be less
1241         return false;
1242       }
1243       if(dx2 < 0) {
1244         dy2 *= -1;
1245         dx2 *= -1;
1246       } else if(dx2 == 0) {
1247         //if the second slope is vertical the first is always less unless it is also vertical, in which case they are equal
1248         return dx1 != 0;
1249       }
1250       typedef typename coordinate_traits<Unit>::unsigned_area_type unsigned_product_type;
1251       unsigned_product_type cross_1 = (unsigned_product_type)(dx2 < 0 ? -dx2 :dx2) * (unsigned_product_type)(dy1 < 0 ? -dy1 : dy1);
1252       unsigned_product_type cross_2 = (unsigned_product_type)(dx1 < 0 ? -dx1 :dx1) * (unsigned_product_type)(dy2 < 0 ? -dy2 : dy2);
1253       int dx1_sign = dx1 < 0 ? -1 : 1;
1254       int dx2_sign = dx2 < 0 ? -1 : 1;
1255       int dy1_sign = dy1 < 0 ? -1 : 1;
1256       int dy2_sign = dy2 < 0 ? -1 : 1;
1257       int cross_1_sign = dx2_sign * dy1_sign;
1258       int cross_2_sign = dx1_sign * dy2_sign;
1259       if(cross_1_sign < cross_2_sign) return true;
1260       if(cross_2_sign < cross_1_sign) return false;
1261       if(cross_1_sign == -1) return cross_2 < cross_1;
1262       return cross_1 < cross_2;
1263     }
1264
1265     static inline bool less_slope(const Unit& x, const Unit& y,
1266                                   const Point& pt1, const Point& pt2) {
1267       const Point* pts[2] = {&pt1, &pt2};
1268       //compute y value on edge from pt_ to pts[1] at the x value of pts[0]
1269       typedef typename coordinate_traits<Unit>::manhattan_area_type at;
1270       at dy2 = (at)pts[1]->get(VERTICAL) - (at)y;
1271       at dy1 = (at)pts[0]->get(VERTICAL) - (at)y;
1272       at dx2 = (at)pts[1]->get(HORIZONTAL) - (at)x;
1273       at dx1 = (at)pts[0]->get(HORIZONTAL) - (at)x;
1274       return less_slope(dx1, dy1, dx2, dy2);
1275     }
1276
1277     //return -1 below, 0 on and 1 above line
1278     //assumes point is on x interval of segment
1279     static inline int on_above_or_below(Point pt, const half_edge& he) {
1280       if(pt == he.first || pt == he.second) return 0;
1281       if(equal_slope(pt.get(HORIZONTAL), pt.get(VERTICAL), he.first, he.second)) return 0;
1282       bool less_result = less_slope(pt.get(HORIZONTAL), pt.get(VERTICAL), he.first, he.second);
1283       int retval = less_result ? -1 : 1;
1284       less_point lp;
1285       if(lp(he.second, he.first)) retval *= -1;
1286       if(!between(pt, he.first, he.second)) retval *= -1;
1287       return retval;
1288     }
1289   };
1290
1291   template <typename T, typename input_point_type>
1292   typename enable_if<
1293     typename gtl_and< typename is_any_mutable_polygon_with_holes_type<T>::type,
1294                       typename gtl_same_type<typename geometry_concept<input_point_type>::type, point_concept>::type>::type,
1295     bool>::type
1296   contains(const T& polygon, const input_point_type& point, bool consider_touch = true) {
1297     typedef typename polygon_with_holes_traits<T>::iterator_holes_type holes_iterator;
1298     bool isInside = contains( view_as< typename polygon_from_polygon_with_holes_type<
1299                               typename geometry_concept<T>::type>::type>( polygon ), point, consider_touch );
1300     if(!isInside) return false; //no need to check holes
1301     holes_iterator itH = begin_holes( polygon );
1302     while( itH != end_holes( polygon ) ) {
1303       if(  contains( *itH, point, !consider_touch )  ) {
1304         isInside = false;
1305         break;
1306       }
1307       ++itH;
1308     }
1309     return isInside;
1310   }
1311
1312   template <typename T, typename input_point_type>
1313   typename enable_if<
1314     typename gtl_and_3<
1315       typename is_polygon_type<T>::type,
1316       typename gtl_different_type<typename geometry_domain<typename geometry_concept<T>::type>::type, manhattan_domain>::type,
1317       typename gtl_same_type<typename geometry_concept<input_point_type>::type, point_concept>::type>::type,
1318     bool>::type
1319   contains(const T& polygon, const input_point_type& point, bool consider_touch = true) {
1320     typedef typename point_traits<input_point_type>::coordinate_type Unit;
1321     typedef point_data<Unit> Point;
1322     typedef std::pair<Point, Point> half_edge;
1323     typedef typename polygon_traits<T>::iterator_type iterator;
1324     iterator itr = begin_points(polygon);
1325     iterator itrEnd = end_points(polygon);
1326     half_edge he;
1327     if(itr == itrEnd) return false;
1328     assign(he.first, *itr);
1329     Point firstPt;
1330     assign(firstPt, *itr);
1331     ++itr;
1332     if(itr == itrEnd) return false;
1333     bool done = false;
1334     int above = 0;
1335     while(!done) {
1336       Point currentPt;
1337       if(itr == itrEnd) {
1338         done = true;
1339         currentPt = firstPt;
1340       } else {
1341         assign(currentPt, *itr);
1342         ++itr;
1343       }
1344       if(currentPt == he.first) {
1345         continue;
1346       } else {
1347         he.second = currentPt;
1348         if(equivalence(point, currentPt)) return consider_touch;
1349         Unit xmin = (std::min)(x(he.first), x(he.second));
1350         Unit xmax = (std::max)(x(he.first), x(he.second));
1351         if(x(point) >= xmin && x(point) < xmax) { //double counts if <= xmax
1352           Point tmppt;
1353           assign(tmppt, point);
1354           int oabedge = edge_utils<Unit>::on_above_or_below(tmppt, he);
1355           if(oabedge == 0) return consider_touch;
1356           if(oabedge == 1) ++above;
1357         } else if(x(point) == xmax) {
1358           if(x(point) == xmin) {
1359             Unit ymin = (std::min)(y(he.first), y(he.second));
1360             Unit ymax = (std::max)(y(he.first), y(he.second));
1361             Unit ypt = y(point);
1362             if(ypt <= ymax && ypt >= ymin)
1363               return consider_touch;
1364           } else {
1365             Point tmppt;
1366             assign(tmppt, point);
1367             if( edge_utils<Unit>::on_above_or_below(tmppt, he) == 0 ) {
1368               return consider_touch;
1369             }
1370           }
1371         }
1372       }
1373       he.first = he.second;
1374     }
1375     return above % 2 != 0; //if the point is above an odd number of edges is must be inside polygon
1376   }
1377
1378   /*
1379   template <typename T, typename input_point_type>
1380   typename enable_if<
1381     typename gtl_and_3<
1382       typename is_polygon_with_holes_type<T>::type,
1383       typename gtl_different_type<typename geometry_domain<typename geometry_concept<T>::type>::type, manhattan_domain>::type,
1384       typename gtl_same_type<typename geometry_concept<input_point_type>::type, point_concept>::type>::type,
1385     bool>::type
1386   contains(const T& polygon, const input_point_type& point, bool consider_touch = true) {
1387     typedef typename point_traits<input_point_type>::coordinate_type Unit;
1388     typedef point_data<Unit> Point;
1389     typedef std::pair<Point, Point> half_edge;
1390     typedef typename polygon_traits<T>::iterator_type iterator;
1391     iterator itr = begin_points(polygon);
1392     iterator itrEnd = end_points(polygon);
1393     half_edge he;
1394     if(itr == itrEnd) return false;
1395     assign(he.first, *itr);
1396     Point firstPt;
1397     assign(firstPt, *itr);
1398     ++itr;
1399     if(itr == itrEnd) return false;
1400     bool done = false;
1401     int above = 0;
1402     while(!done) {
1403       Point currentPt;
1404       if(itr == itrEnd) {
1405         done = true;
1406         currentPt = firstPt;
1407       } else {
1408         assign(currentPt, *itr);
1409         ++itr;
1410       }
1411       if(currentPt == he.first) {
1412         continue;
1413       } else {
1414         he.second = currentPt;
1415         if(equivalence(point, currentPt)) return consider_touch;
1416         Unit xmin = (std::min)(x(he.first), x(he.second));
1417         Unit xmax = (std::max)(x(he.first), x(he.second));
1418         if(x(point) >= xmin && x(point) < xmax) { //double counts if <= xmax
1419           Point tmppt;
1420           assign(tmppt, point);
1421           int oabedge = edge_utils<Unit>::on_above_or_below(tmppt, he);
1422           if(oabedge == 0) return consider_touch;
1423           if(oabedge == 1) ++above;
1424         }
1425       }
1426       he.first = he.second;
1427     }
1428     return above % 2 != 0; //if the point is above an odd number of edges is must be inside polygon
1429   }
1430   */
1431
1432   template <typename T1, typename T2>
1433   typename enable_if<
1434     typename gtl_and< typename is_mutable_rectangle_concept<typename geometry_concept<T1>::type>::type,
1435                       typename is_polygon_with_holes_type<T2>::type>::type,
1436     bool>::type
1437   extents(T1& bounding_box, const T2& polygon) {
1438     typedef typename polygon_traits<T2>::iterator_type iterator;
1439     bool first_iteration = true;
1440     iterator itr_end = end_points(polygon);
1441     for(iterator itr = begin_points(polygon); itr != itr_end; ++itr) {
1442       if(first_iteration) {
1443         set_points(bounding_box, *itr, *itr);
1444         first_iteration = false;
1445       } else {
1446         encompass(bounding_box, *itr);
1447       }
1448     }
1449     if(first_iteration) return false;
1450     return true;
1451   }
1452
1453   template <typename T1, typename T2>
1454   typename enable_if<
1455     typename gtl_and< typename is_mutable_point_concept<typename geometry_concept<T1>::type>::type,
1456                       typename is_polygon_with_holes_type<T2>::type>::type,
1457     bool>::type
1458   center(T1& center_point, const T2& polygon) {
1459     typedef typename polygon_traits<T2>::coordinate_type coordinate_type;
1460     rectangle_data<coordinate_type> bbox;
1461     extents(bbox, polygon);
1462     return center(center_point, bbox);
1463   }
1464
1465   template <class T>
1466   template <class T2>
1467   polygon_90_data<T>& polygon_90_data<T>::operator=(const T2& rvalue) {
1468     assign(*this, rvalue);
1469     return *this;
1470   }
1471
1472   template <class T>
1473   template <class T2>
1474   polygon_45_data<T>& polygon_45_data<T>::operator=(const T2& rvalue) {
1475     assign(*this, rvalue);
1476     return *this;
1477   }
1478
1479   template <class T>
1480   template <class T2>
1481   polygon_data<T>& polygon_data<T>::operator=(const T2& rvalue) {
1482     assign(*this, rvalue);
1483     return *this;
1484   }
1485
1486   template <class T>
1487   template <class T2>
1488   polygon_90_with_holes_data<T>& polygon_90_with_holes_data<T>::operator=(const T2& rvalue) {
1489     assign(*this, rvalue);
1490     return *this;
1491   }
1492
1493   template <class T>
1494   template <class T2>
1495   polygon_45_with_holes_data<T>& polygon_45_with_holes_data<T>::operator=(const T2& rvalue) {
1496     assign(*this, rvalue);
1497     return *this;
1498   }
1499
1500   template <class T>
1501   template <class T2>
1502   polygon_with_holes_data<T>& polygon_with_holes_data<T>::operator=(const T2& rvalue) {
1503     assign(*this, rvalue);
1504     return *this;
1505   }
1506
1507   template <typename T>
1508   struct geometry_concept<polygon_data<T> > {
1509     typedef polygon_concept type;
1510   };
1511   template <typename T>
1512   struct geometry_concept<polygon_45_data<T> > {
1513     typedef polygon_45_concept type;
1514   };
1515   template <typename T>
1516   struct geometry_concept<polygon_90_data<T> > {
1517     typedef polygon_90_concept type;
1518   };
1519   template <typename T>
1520   struct geometry_concept<polygon_with_holes_data<T> > {
1521     typedef polygon_with_holes_concept type;
1522   };
1523   template <typename T>
1524   struct geometry_concept<polygon_45_with_holes_data<T> > {
1525     typedef polygon_45_with_holes_concept type;
1526   };
1527   template <typename T>
1528   struct geometry_concept<polygon_90_with_holes_data<T> > {
1529     typedef polygon_90_with_holes_concept type;
1530   };
1531
1532 //   template <typename T> struct polygon_with_holes_traits<polygon_90_data<T> > {
1533 //     typedef polygon_90_data<T> hole_type;
1534 //     typedef const hole_type* iterator_holes_type;
1535 //     static inline iterator_holes_type begin_holes(const hole_type& t) { return &t; }
1536 //     static inline iterator_holes_type end_holes(const hole_type& t) { return &t; }
1537 //     static inline std::size_t size_holes(const hole_type& t) { return 0; }
1538 //   };
1539 //   template <typename T> struct polygon_with_holes_traits<polygon_45_data<T> > {
1540 //     typedef polygon_45_data<T> hole_type;
1541 //     typedef const hole_type* iterator_holes_type;
1542 //     static inline iterator_holes_type begin_holes(const hole_type& t) { return &t; }
1543 //     static inline iterator_holes_type end_holes(const hole_type& t) { return &t; }
1544 //     static inline std::size_t size_holes(const hole_type& t) { return 0; }
1545 //   };
1546 //   template <typename T> struct polygon_with_holes_traits<polygon_data<T> > {
1547 //     typedef polygon_data<T> hole_type;
1548 //     typedef const hole_type* iterator_holes_type;
1549 //     static inline iterator_holes_type begin_holes(const hole_type& t) { return &t; }
1550 //     static inline iterator_holes_type end_holes(const hole_type& t) { return &t; }
1551 //     static inline std::size_t size_holes(const hole_type& t) { return 0; }
1552 //   };
1553   template <typename T> struct get_void {};
1554   template <> struct get_void<gtl_yes> { typedef void type; };
1555
1556   template <typename T> struct polygon_with_holes_traits<
1557     T, typename get_void<typename is_any_mutable_polygon_without_holes_type<T>::type>::type > {
1558     typedef T hole_type;
1559     typedef const hole_type* iterator_holes_type;
1560     static inline iterator_holes_type begin_holes(const hole_type& t) { return &t; }
1561     static inline iterator_holes_type end_holes(const hole_type& t) { return &t; }
1562   };
1563
1564   template <typename T>
1565   struct view_of<rectangle_concept, T> {
1566     typedef typename polygon_traits<T>::coordinate_type coordinate_type;
1567     typedef interval_data<coordinate_type> interval_type;
1568     rectangle_data<coordinate_type> rect;
1569     view_of(const T& obj) : rect() {
1570       point_data<coordinate_type> pts[2];
1571       typename polygon_traits<T>::iterator_type itr =
1572         begin_points(obj), itre = end_points(obj);
1573       if(itr == itre) return;
1574       assign(pts[0], *itr);
1575       ++itr;
1576       if(itr == itre) return;
1577       ++itr;
1578       if(itr == itre) return;
1579       assign(pts[1], *itr);
1580       set_points(rect, pts[0], pts[1]);
1581     }
1582     inline interval_type get(orientation_2d orient) const {
1583       return rect.get(orient); }
1584   };
1585
1586   template <typename T>
1587   struct geometry_concept<view_of<rectangle_concept, T> > {
1588     typedef rectangle_concept type;
1589   };
1590
1591   template <typename T>
1592   struct view_of<polygon_45_concept, T> {
1593     const T* t;
1594     view_of(const T& obj) : t(&obj) {}
1595     typedef typename polygon_traits<T>::coordinate_type coordinate_type;
1596     typedef typename polygon_traits<T>::iterator_type iterator_type;
1597     typedef typename polygon_traits<T>::point_type point_type;
1598
1599     /// Get the begin iterator
1600     inline iterator_type begin() const {
1601       return polygon_traits<T>::begin_points(*t);
1602     }
1603
1604     /// Get the end iterator
1605     inline iterator_type end() const {
1606       return polygon_traits<T>::end_points(*t);
1607     }
1608
1609     /// Get the number of sides of the polygon
1610     inline std::size_t size() const {
1611       return polygon_traits<T>::size(*t);
1612     }
1613
1614     /// Get the winding direction of the polygon
1615     inline winding_direction winding() const {
1616       return polygon_traits<T>::winding(*t);
1617     }
1618   };
1619
1620   template <typename T>
1621   struct geometry_concept<view_of<polygon_45_concept, T> > {
1622     typedef polygon_45_concept type;
1623   };
1624
1625   template <typename T>
1626   struct view_of<polygon_90_concept, T> {
1627     const T* t;
1628     view_of(const T& obj) : t(&obj) {}
1629     typedef typename polygon_traits<T>::coordinate_type coordinate_type;
1630     typedef typename polygon_traits<T>::iterator_type iterator_type;
1631     typedef typename polygon_traits<T>::point_type point_type;
1632     typedef iterator_points_to_compact<iterator_type, point_type> compact_iterator_type;
1633
1634     /// Get the begin iterator
1635     inline compact_iterator_type begin_compact() const {
1636       return compact_iterator_type(polygon_traits<T>::begin_points(*t),
1637                                    polygon_traits<T>::end_points(*t));
1638     }
1639
1640     /// Get the end iterator
1641     inline compact_iterator_type end_compact() const {
1642       return compact_iterator_type(polygon_traits<T>::end_points(*t),
1643                                    polygon_traits<T>::end_points(*t));
1644     }
1645
1646     /// Get the number of sides of the polygon
1647     inline std::size_t size() const {
1648       return polygon_traits<T>::size(*t);
1649     }
1650
1651     /// Get the winding direction of the polygon
1652     inline winding_direction winding() const {
1653       return polygon_traits<T>::winding(*t);
1654     }
1655   };
1656
1657   template <typename T>
1658   struct geometry_concept<view_of<polygon_90_concept, T> > {
1659     typedef polygon_90_concept type;
1660   };
1661
1662   template <typename T>
1663   struct view_of<polygon_45_with_holes_concept, T> {
1664     const T* t;
1665     view_of(const T& obj) : t(&obj) {}
1666     typedef typename polygon_traits<T>::coordinate_type coordinate_type;
1667     typedef typename polygon_traits<T>::iterator_type iterator_type;
1668     typedef typename polygon_traits<T>::point_type point_type;
1669     typedef view_of<polygon_45_concept, typename polygon_with_holes_traits<T>::hole_type> hole_type;
1670     struct iterator_holes_type {
1671       typedef std::forward_iterator_tag iterator_category;
1672       typedef hole_type value_type;
1673       typedef std::ptrdiff_t difference_type;
1674       typedef const hole_type* pointer; //immutable
1675       typedef const hole_type& reference; //immutable
1676       typedef typename polygon_with_holes_traits<T>::iterator_holes_type iht;
1677       iht internal_itr;
1678       iterator_holes_type() : internal_itr() {}
1679       iterator_holes_type(iht iht_in) : internal_itr(iht_in) {}
1680       inline iterator_holes_type& operator++() {
1681         ++internal_itr;
1682         return *this;
1683       }
1684       inline const iterator_holes_type operator++(int) {
1685         iterator_holes_type tmp(*this);
1686         ++(*this);
1687         return tmp;
1688       }
1689       inline bool operator==(const iterator_holes_type& that) const {
1690         return (internal_itr == that.internal_itr);
1691       }
1692       inline bool operator!=(const iterator_holes_type& that) const {
1693         return (internal_itr != that.internal_itr);
1694       }
1695       inline value_type operator*() const {
1696         return view_as<polygon_45_concept>(*internal_itr);
1697       }
1698     };
1699
1700     /// Get the begin iterator
1701     inline iterator_type begin() const {
1702       return polygon_traits<T>::begin_points(*t);
1703     }
1704
1705     /// Get the end iterator
1706     inline iterator_type end() const {
1707       return polygon_traits<T>::end_points(*t);
1708     }
1709
1710     /// Get the number of sides of the polygon
1711     inline std::size_t size() const {
1712       return polygon_traits<T>::size(*t);
1713     }
1714
1715     /// Get the winding direction of the polygon
1716     inline winding_direction winding() const {
1717       return polygon_traits<T>::winding(*t);
1718     }
1719
1720     /// Get the begin iterator
1721     inline iterator_holes_type begin_holes() const {
1722       return polygon_with_holes_traits<T>::begin_holes(*t);
1723     }
1724
1725     /// Get the end iterator
1726     inline iterator_holes_type end_holes() const {
1727       return polygon_with_holes_traits<T>::end_holes(*t);
1728     }
1729
1730     /// Get the number of sides of the polygon
1731     inline std::size_t size_holes() const {
1732       return polygon_with_holes_traits<T>::size_holes(*t);
1733     }
1734
1735   };
1736
1737   template <typename T>
1738   struct geometry_concept<view_of<polygon_45_with_holes_concept, T> > {
1739     typedef polygon_45_with_holes_concept type;
1740   };
1741
1742   template <typename T>
1743   struct view_of<polygon_90_with_holes_concept, T> {
1744     const T* t;
1745     view_of(const T& obj) : t(&obj) {}
1746     typedef typename polygon_traits<T>::coordinate_type coordinate_type;
1747     typedef typename polygon_traits<T>::iterator_type iterator_type;
1748     typedef typename polygon_traits<T>::point_type point_type;
1749     typedef iterator_points_to_compact<iterator_type, point_type> compact_iterator_type;
1750     typedef view_of<polygon_90_concept, typename polygon_with_holes_traits<T>::hole_type> hole_type;
1751     struct iterator_holes_type {
1752       typedef std::forward_iterator_tag iterator_category;
1753       typedef hole_type value_type;
1754       typedef std::ptrdiff_t difference_type;
1755       typedef const hole_type* pointer; //immutable
1756       typedef const hole_type& reference; //immutable
1757       typedef typename polygon_with_holes_traits<T>::iterator_holes_type iht;
1758       iht internal_itr;
1759       iterator_holes_type() : internal_itr() {}
1760       iterator_holes_type(iht iht_in) : internal_itr(iht_in) {}
1761       inline iterator_holes_type& operator++() {
1762         ++internal_itr;
1763         return *this;
1764       }
1765       inline const iterator_holes_type operator++(int) {
1766         iterator_holes_type tmp(*this);
1767         ++(*this);
1768         return tmp;
1769       }
1770       inline bool operator==(const iterator_holes_type& that) const {
1771         return (internal_itr == that.internal_itr);
1772       }
1773       inline bool operator!=(const iterator_holes_type& that) const {
1774         return (internal_itr != that.internal_itr);
1775       }
1776       inline value_type operator*() const {
1777         return view_as<polygon_90_concept>(*internal_itr);
1778       }
1779     };
1780
1781     /// Get the begin iterator
1782     inline compact_iterator_type begin_compact() const {
1783       return compact_iterator_type(polygon_traits<T>::begin_points(*t),
1784                                    polygon_traits<T>::end_points(*t));
1785     }
1786
1787     /// Get the end iterator
1788     inline compact_iterator_type end_compact() const {
1789       return compact_iterator_type(polygon_traits<T>::end_points(*t),
1790                                    polygon_traits<T>::end_points(*t));
1791     }
1792
1793     /// Get the number of sides of the polygon
1794     inline std::size_t size() const {
1795       return polygon_traits<T>::size(*t);
1796     }
1797
1798     /// Get the winding direction of the polygon
1799     inline winding_direction winding() const {
1800       return polygon_traits<T>::winding(*t);
1801     }
1802
1803     /// Get the begin iterator
1804     inline iterator_holes_type begin_holes() const {
1805       return polygon_with_holes_traits<T>::begin_holes(*t);
1806     }
1807
1808     /// Get the end iterator
1809     inline iterator_holes_type end_holes() const {
1810       return polygon_with_holes_traits<T>::end_holes(*t);
1811     }
1812
1813     /// Get the number of sides of the polygon
1814     inline std::size_t size_holes() const {
1815       return polygon_with_holes_traits<T>::size_holes(*t);
1816     }
1817
1818   };
1819
1820   template <typename T>
1821   struct geometry_concept<view_of<polygon_90_with_holes_concept, T> > {
1822     typedef polygon_90_with_holes_concept type;
1823   };
1824
1825   template <typename T>
1826   struct view_of<polygon_concept, T> {
1827     const T* t;
1828     view_of(const T& obj) : t(&obj) {}
1829     typedef typename polygon_traits<T>::coordinate_type coordinate_type;
1830     typedef typename polygon_traits<T>::iterator_type iterator_type;
1831     typedef typename polygon_traits<T>::point_type point_type;
1832
1833     /// Get the begin iterator
1834     inline iterator_type begin() const {
1835       return polygon_traits<T>::begin_points(*t);
1836     }
1837
1838     /// Get the end iterator
1839     inline iterator_type end() const {
1840       return polygon_traits<T>::end_points(*t);
1841     }
1842
1843     /// Get the number of sides of the polygon
1844     inline std::size_t size() const {
1845       return polygon_traits<T>::size(*t);
1846     }
1847
1848     /// Get the winding direction of the polygon
1849     inline winding_direction winding() const {
1850       return polygon_traits<T>::winding(*t);
1851     }
1852   };
1853
1854   template <typename T>
1855   struct geometry_concept<view_of<polygon_concept, T> > {
1856     typedef polygon_concept type;
1857   };
1858 }
1859 }
1860
1861 #endif