boost/polygon/polygon_traits.hpp

0001 /*
0002   Copyright 2008 Intel Corporation
0003
0004   Use, modification and distribution are subject to the Boost Software License,
0005   Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
0006   http://www.boost.org/LICENSE_1_0.txt).
0007 */
0008 #ifndef BOOST_POLYGON_POLYGON_TRAITS_HPP
0009 #define BOOST_POLYGON_POLYGON_TRAITS_HPP
0010 namespace boost { namespace polygon{
0011
0012   template <typename T, typename enable = gtl_yes>
0013   struct polygon_90_traits {
0014     typedef typename T::coordinate_type coordinate_type;
0015     typedef typename T::compact_iterator_type compact_iterator_type;
0016
0017     // Get the begin iterator
0018     static inline compact_iterator_type begin_compact(const T& t) {
0019       return t.begin_compact();
0020     }
0021
0022     // Get the end iterator
0023     static inline compact_iterator_type end_compact(const T& t) {
0024       return t.end_compact();
0025     }
0026
0027     // Get the number of sides of the polygon
0028     static inline std::size_t size(const T& t) {
0029       return t.size();
0030     }
0031
0032     // Get the winding direction of the polygon
0033     static inline winding_direction winding(const T&) {
0034       return unknown_winding;
0035     }
0036   };
0037
0038   template <typename T>
0039   struct polygon_traits_general {
0040     typedef typename T::coordinate_type coordinate_type;
0041     typedef typename T::iterator_type iterator_type;
0042     typedef typename T::point_type point_type;
0043
0044     // Get the begin iterator
0045     static inline iterator_type begin_points(const T& t) {
0046       return t.begin();
0047     }
0048
0049     // Get the end iterator
0050     static inline iterator_type end_points(const T& t) {
0051       return t.end();
0052     }
0053
0054     // Get the number of sides of the polygon
0055     static inline std::size_t size(const T& t) {
0056       return t.size();
0057     }
0058
0059     // Get the winding direction of the polygon
0060     static inline winding_direction winding(const T&) {
0061       return unknown_winding;
0062     }
0063   };
0064
0065   template <typename T>
0066   struct polygon_traits_90 {
0067     typedef typename polygon_90_traits<T>::coordinate_type coordinate_type;
0068     typedef iterator_compact_to_points<typename polygon_90_traits<T>::compact_iterator_type, point_data<coordinate_type> > iterator_type;
0069     typedef point_data<coordinate_type> point_type;
0070
0071     // Get the begin iterator
0072     static inline iterator_type begin_points(const T& t) {
0073       return iterator_type(polygon_90_traits<T>::begin_compact(t),
0074                            polygon_90_traits<T>::end_compact(t));
0075     }
0076
0077     // Get the end iterator
0078     static inline iterator_type end_points(const T& t) {
0079       return iterator_type(polygon_90_traits<T>::end_compact(t),
0080                            polygon_90_traits<T>::end_compact(t));
0081     }
0082
0083     // Get the number of sides of the polygon
0084     static inline std::size_t size(const T& t) {
0085       return polygon_90_traits<T>::size(t);
0086     }
0087
0088     // Get the winding direction of the polygon
0089     static inline winding_direction winding(const T& t) {
0090       return polygon_90_traits<T>::winding(t);
0091     }
0092   };
0093
0094 #ifndef BOOST_VERY_LITTLE_SFINAE
0095
0096   template <typename T, typename enable = gtl_yes>
0097   struct polygon_traits {};
0098
0099   template <typename T>
0100   struct polygon_traits<T,
0101                         typename gtl_or_4<
0102     typename gtl_same_type<typename geometry_concept<T>::type, polygon_concept>::type,
0103     typename gtl_same_type<typename geometry_concept<T>::type, polygon_45_concept>::type,
0104     typename gtl_same_type<typename geometry_concept<T>::type, polygon_with_holes_concept>::type,
0105     typename gtl_same_type<typename geometry_concept<T>::type, polygon_45_with_holes_concept>::type
0106   >::type> : public polygon_traits_general<T> {};
0107
0108   template <typename T>
0109   struct polygon_traits< T,
0110                          typename gtl_or<
0111     typename gtl_same_type<typename geometry_concept<T>::type, polygon_90_concept>::type,
0112     typename gtl_same_type<typename geometry_concept<T>::type, polygon_90_with_holes_concept>::type
0113   >::type > : public polygon_traits_90<T> {};
0114
0115 #else
0116
0117   template <typename T, typename T_IF, typename T_ELSE>
0118   struct gtl_ifelse {};
0119   template <typename T_IF, typename T_ELSE>
0120   struct gtl_ifelse<gtl_no, T_IF, T_ELSE> {
0121     typedef T_ELSE type;
0122   };
0123   template <typename T_IF, typename T_ELSE>
0124   struct gtl_ifelse<gtl_yes, T_IF, T_ELSE> {
0125     typedef T_IF type;
0126   };
0127
0128   template <typename T, typename enable = gtl_yes>
0129   struct polygon_traits {};
0130
0131   template <typename T>
0132   struct polygon_traits<T, typename gtl_or<typename gtl_or_4<
0133     typename gtl_same_type<typename geometry_concept<T>::type, polygon_concept>::type,
0134     typename gtl_same_type<typename geometry_concept<T>::type, polygon_45_concept>::type,
0135     typename gtl_same_type<typename geometry_concept<T>::type, polygon_with_holes_concept>::type,
0136     typename gtl_same_type<typename geometry_concept<T>::type, polygon_45_with_holes_concept>::type
0137   >::type, typename gtl_or<
0138     typename gtl_same_type<typename geometry_concept<T>::type, polygon_90_concept>::type,
0139     typename gtl_same_type<typename geometry_concept<T>::type, polygon_90_with_holes_concept>::type
0140   >::type>::type > : public gtl_ifelse<typename gtl_or<
0141     typename gtl_same_type<typename geometry_concept<T>::type, polygon_90_concept>::type,
0142     typename gtl_same_type<typename geometry_concept<T>::type, polygon_90_with_holes_concept>::type >::type,
0143       polygon_traits_90<T>,
0144       polygon_traits_general<T> >::type {
0145   };
0146
0147 #endif
0148
0149   template <typename T, typename enable = void>
0150   struct polygon_with_holes_traits {
0151     typedef typename T::iterator_holes_type iterator_holes_type;
0152     typedef typename T::hole_type hole_type;
0153
0154     // Get the begin iterator
0155     static inline iterator_holes_type begin_holes(const T& t) {
0156       return t.begin_holes();
0157     }
0158
0159     // Get the end iterator
0160     static inline iterator_holes_type end_holes(const T& t) {
0161       return t.end_holes();
0162     }
0163
0164     // Get the number of holes
0165     static inline std::size_t size_holes(const T& t) {
0166       return t.size_holes();
0167     }
0168   };
0169
0170   template <typename T, typename enable = void>
0171   struct polygon_90_mutable_traits {
0172
0173     // Set the data of a polygon with the unique coordinates in an iterator, starting with an x
0174     template <typename iT>
0175     static inline T& set_compact(T& t, iT input_begin, iT input_end) {
0176       t.set_compact(input_begin, input_end);
0177       return t;
0178     }
0179
0180   };
0181
0182   template <typename T, typename enable = void>
0183   struct polygon_mutable_traits {
0184
0185     // Set the data of a polygon with the unique coordinates in an iterator, starting with an x
0186     template <typename iT>
0187     static inline T& set_points(T& t, iT input_begin, iT input_end) {
0188       t.set(input_begin, input_end);
0189       return t;
0190     }
0191
0192   };
0193
0194   template <typename T, typename enable = void>
0195   struct polygon_with_holes_mutable_traits {
0196
0197     // Set the data of a polygon with the unique coordinates in an iterator, starting with an x
0198     template <typename iT>
0199     static inline T& set_holes(T& t, iT inputBegin, iT inputEnd) {
0200       t.set_holes(inputBegin, inputEnd);
0201       return t;
0202     }
0203
0204   };
0205 }
0206 }
0207 #include "isotropy.hpp"
0208
0209 //point
0210 #include "point_data.hpp"
0211 #include "point_traits.hpp"
0212 #include "point_concept.hpp"
0213
0214 //interval
0215 #include "interval_data.hpp"
0216 #include "interval_traits.hpp"
0217 #include "interval_concept.hpp"
0218
0219 //rectangle
0220 #include "rectangle_data.hpp"
0221 #include "rectangle_traits.hpp"
0222 #include "rectangle_concept.hpp"
0223
0224 //algorithms needed by polygon types
0225 #include "detail/iterator_points_to_compact.hpp"
0226 #include "detail/iterator_compact_to_points.hpp"
0227
0228 //polygons
0229 #include "polygon_45_data.hpp"
0230 #include "polygon_data.hpp"
0231 #include "polygon_90_data.hpp"
0232 #include "polygon_90_with_holes_data.hpp"
0233 #include "polygon_45_with_holes_data.hpp"
0234 #include "polygon_with_holes_data.hpp"
0235
0236 namespace boost { namespace polygon{
0237   struct polygon_concept {};
0238   struct polygon_with_holes_concept {};
0239   struct polygon_45_concept {};
0240   struct polygon_45_with_holes_concept {};
0241   struct polygon_90_concept {};
0242   struct polygon_90_with_holes_concept {};
0243
0244
0245   template <typename T>
0246   struct is_polygon_90_type {
0247     typedef typename geometry_concept<T>::type GC;
0248     typedef typename gtl_same_type<polygon_90_concept, GC>::type type;
0249   };
0250
0251   template <typename T>
0252   struct is_polygon_45_type {
0253     typedef typename geometry_concept<T>::type GC;
0254     typedef typename gtl_or<typename is_polygon_90_type<T>::type,
0255                             typename gtl_same_type<polygon_45_concept, GC>::type>::type type;
0256   };
0257
0258   template <typename T>
0259   struct is_polygon_type {
0260     typedef typename geometry_concept<T>::type GC;
0261     typedef typename gtl_or<typename is_polygon_45_type<T>::type,
0262                             typename gtl_same_type<polygon_concept, GC>::type>::type type;
0263   };
0264
0265   template <typename T>
0266   struct is_polygon_90_with_holes_type {
0267     typedef typename geometry_concept<T>::type GC;
0268     typedef typename gtl_or<typename is_polygon_90_type<T>::type,
0269                             typename gtl_same_type<polygon_90_with_holes_concept, GC>::type>::type type;
0270   };
0271
0272   template <typename T>
0273   struct is_polygon_45_with_holes_type {
0274     typedef typename geometry_concept<T>::type GC;
0275     typedef typename gtl_or_3<typename is_polygon_90_with_holes_type<T>::type,
0276                               typename is_polygon_45_type<T>::type,
0277                               typename gtl_same_type<polygon_45_with_holes_concept, GC>::type>::type type;
0278   };
0279
0280   template <typename T>
0281   struct is_polygon_with_holes_type {
0282     typedef typename geometry_concept<T>::type GC;
0283     typedef typename gtl_or_3<typename is_polygon_45_with_holes_type<T>::type,
0284                               typename is_polygon_type<T>::type,
0285                               typename gtl_same_type<polygon_with_holes_concept, GC>::type>::type type;
0286   };
0287
0288   template <typename T>
0289   struct is_mutable_polygon_90_type {
0290     typedef typename geometry_concept<T>::type GC;
0291     typedef typename gtl_same_type<polygon_90_concept, GC>::type type;
0292   };
0293
0294   template <typename T>
0295   struct is_mutable_polygon_45_type {
0296     typedef typename geometry_concept<T>::type GC;
0297     typedef typename gtl_same_type<polygon_45_concept, GC>::type type;
0298   };
0299
0300   template <typename T>
0301   struct is_mutable_polygon_type {
0302     typedef typename geometry_concept<T>::type GC;
0303     typedef typename gtl_same_type<polygon_concept, GC>::type type;
0304   };
0305
0306   template <typename T>
0307   struct is_mutable_polygon_90_with_holes_type {
0308     typedef typename geometry_concept<T>::type GC;
0309     typedef typename gtl_same_type<polygon_90_with_holes_concept, GC>::type type;
0310   };
0311
0312   template <typename T>
0313   struct is_mutable_polygon_45_with_holes_type {
0314     typedef typename geometry_concept<T>::type GC;
0315     typedef typename gtl_same_type<polygon_45_with_holes_concept, GC>::type type;
0316   };
0317
0318   template <typename T>
0319   struct is_mutable_polygon_with_holes_type {
0320     typedef typename geometry_concept<T>::type GC;
0321     typedef typename gtl_same_type<polygon_with_holes_concept, GC>::type type;
0322   };
0323
0324   template <typename T>
0325   struct is_any_mutable_polygon_with_holes_type {
0326     typedef typename gtl_or_3<typename is_mutable_polygon_90_with_holes_type<T>::type,
0327                               typename is_mutable_polygon_45_with_holes_type<T>::type,
0328                               typename is_mutable_polygon_with_holes_type<T>::type>::type type;
0329   };
0330   template <typename T>
0331   struct is_any_mutable_polygon_without_holes_type {
0332     typedef typename gtl_or_3<
0333       typename is_mutable_polygon_90_type<T>::type,
0334       typename is_mutable_polygon_45_type<T>::type,
0335       typename is_mutable_polygon_type<T>::type>::type type; };
0336
0337   template <typename T>
0338   struct is_any_mutable_polygon_type {
0339     typedef typename gtl_or<typename is_any_mutable_polygon_with_holes_type<T>::type,
0340                             typename is_any_mutable_polygon_without_holes_type<T>::type>::type type;
0341   };
0342
0343   template <typename T>
0344   struct polygon_from_polygon_with_holes_type {};
0345   template <>
0346   struct polygon_from_polygon_with_holes_type<polygon_with_holes_concept> { typedef polygon_concept type; };
0347   template <>
0348   struct polygon_from_polygon_with_holes_type<polygon_45_with_holes_concept> { typedef polygon_45_concept type; };
0349   template <>
0350   struct polygon_from_polygon_with_holes_type<polygon_90_with_holes_concept> { typedef polygon_90_concept type; };
0351
0352   template <>
0353   struct geometry_domain<polygon_45_concept> { typedef forty_five_domain type; };
0354   template <>
0355   struct geometry_domain<polygon_45_with_holes_concept> { typedef forty_five_domain type; };
0356   template <>
0357   struct geometry_domain<polygon_90_concept> { typedef manhattan_domain type; };
0358   template <>
0359   struct geometry_domain<polygon_90_with_holes_concept> { typedef manhattan_domain type; };
0360
0361   template <typename domain_type, typename coordinate_type>
0362   struct distance_type_by_domain { typedef typename coordinate_traits<coordinate_type>::coordinate_distance type; };
0363   template <typename coordinate_type>
0364   struct distance_type_by_domain<manhattan_domain, coordinate_type> {
0365     typedef typename coordinate_traits<coordinate_type>::coordinate_difference type; };
0366
0367   // \brief Sets the boundary of the polygon to the points in the iterator range
0368   // \tparam T A type that models polygon_concept
0369   // \tparam iT Iterator type over objects that model point_concept
0370   // \param t The polygon to set
0371   // \param begin_points The start of the range of points
0372   // \param end_points The end of the range of points
0373
0374   /// \relatesalso polygon_concept
0375   template <typename T, typename iT>
0376   typename enable_if <typename is_any_mutable_polygon_type<T>::type, T>::type &
0377   set_points(T& t, iT begin_points, iT end_points) {
0378     polygon_mutable_traits<T>::set_points(t, begin_points, end_points);
0379     return t;
0380   }
0381
0382   // \brief Sets the boundary of the polygon to the non-redundant coordinates in the iterator range
0383   // \tparam T A type that models polygon_90_concept
0384   // \tparam iT Iterator type over objects that model coordinate_concept
0385   // \param t The polygon to set
0386   // \param begin_compact_coordinates The start of the range of coordinates
0387   // \param end_compact_coordinates The end of the range of coordinates
0388
0389 /// \relatesalso polygon_90_concept
0390   template <typename T, typename iT>
0391   typename enable_if <typename gtl_or<
0392     typename is_mutable_polygon_90_type<T>::type,
0393     typename is_mutable_polygon_90_with_holes_type<T>::type>::type, T>::type &
0394   set_compact(T& t, iT begin_compact_coordinates, iT end_compact_coordinates) {
0395     polygon_90_mutable_traits<T>::set_compact(t, begin_compact_coordinates, end_compact_coordinates);
0396     return t;
0397   }
0398
0399 /// \relatesalso polygon_with_holes_concept
0400   template <typename T, typename iT>
0401   typename enable_if< typename gtl_and <
0402     typename is_any_mutable_polygon_with_holes_type<T>::type,
0403     typename gtl_different_type<typename geometry_domain<typename geometry_concept<T>::type>::type,
0404                                 manhattan_domain>::type>::type,
0405                        T>::type &
0406   set_compact(T& t, iT begin_compact_coordinates, iT end_compact_coordinates) {
0407     iterator_compact_to_points<iT, point_data<typename polygon_traits<T>::coordinate_type> >
0408       itrb(begin_compact_coordinates, end_compact_coordinates),
0409       itre(end_compact_coordinates, end_compact_coordinates);
0410     return set_points(t, itrb, itre);
0411   }
0412
0413 /// \relatesalso polygon_with_holes_concept
0414   template <typename T, typename iT>
0415   typename enable_if <typename is_any_mutable_polygon_with_holes_type<T>::type, T>::type &
0416   set_holes(T& t, iT begin_holes, iT end_holes) {
0417     polygon_with_holes_mutable_traits<T>::set_holes(t, begin_holes, end_holes);
0418     return t;
0419   }
0420
0421 /// \relatesalso polygon_90_concept
0422   template <typename T>
0423   typename polygon_90_traits<T>::compact_iterator_type
0424   begin_compact(const T& polygon,
0425     typename enable_if<
0426       typename gtl_and <typename is_polygon_with_holes_type<T>::type,
0427                         typename gtl_same_type<typename geometry_domain<typename geometry_concept<T>::type>::type,
0428                 manhattan_domain>::type>::type>::type * = 0
0429   ) {
0430     return polygon_90_traits<T>::begin_compact(polygon);
0431   }
0432
0433 /// \relatesalso polygon_90_concept
0434   template <typename T>
0435   typename polygon_90_traits<T>::compact_iterator_type
0436   end_compact(const T& polygon,
0437     typename enable_if<
0438     typename gtl_and <typename is_polygon_with_holes_type<T>::type,
0439                       typename gtl_same_type<typename geometry_domain<typename geometry_concept<T>::type>::type,
0440               manhattan_domain>::type>::type>::type * = 0
0441   ) {
0442     return polygon_90_traits<T>::end_compact(polygon);
0443   }
0444
0445   /// \relatesalso polygon_concept
0446   template <typename T>
0447   typename enable_if < typename gtl_if<
0448     typename is_polygon_with_holes_type<T>::type>::type,
0449                         typename polygon_traits<T>::iterator_type>::type
0450   begin_points(const T& polygon) {
0451     return polygon_traits<T>::begin_points(polygon);
0452   }
0453
0454   /// \relatesalso polygon_concept
0455   template <typename T>
0456   typename enable_if < typename gtl_if<
0457     typename is_polygon_with_holes_type<T>::type>::type,
0458                         typename polygon_traits<T>::iterator_type>::type
0459   end_points(const T& polygon) {
0460     return polygon_traits<T>::end_points(polygon);
0461   }
0462
0463   /// \relatesalso polygon_concept
0464   template <typename T>
0465   typename enable_if <typename is_polygon_with_holes_type<T>::type,
0466                        std::size_t>::type
0467   size(const T& polygon) {
0468     return polygon_traits<T>::size(polygon);
0469   }
0470
0471 /// \relatesalso polygon_with_holes_concept
0472   template <typename T>
0473   typename enable_if < typename gtl_if<
0474     typename is_polygon_with_holes_type<T>::type>::type,
0475                         typename polygon_with_holes_traits<T>::iterator_holes_type>::type
0476   begin_holes(const T& polygon) {
0477     return polygon_with_holes_traits<T>::begin_holes(polygon);
0478   }
0479
0480 /// \relatesalso polygon_with_holes_concept
0481   template <typename T>
0482   typename enable_if < typename gtl_if<
0483     typename is_polygon_with_holes_type<T>::type>::type,
0484                         typename polygon_with_holes_traits<T>::iterator_holes_type>::type
0485   end_holes(const T& polygon) {
0486     return polygon_with_holes_traits<T>::end_holes(polygon);
0487   }
0488
0489 /// \relatesalso polygon_with_holes_concept
0490   template <typename T>
0491   typename enable_if <typename is_polygon_with_holes_type<T>::type,
0492                        std::size_t>::type
0493   size_holes(const T& polygon) {
0494     return polygon_with_holes_traits<T>::size_holes(polygon);
0495   }
0496
0497   // \relatesalso polygon_concept
0498   template <typename T1, typename T2>
0499   typename enable_if<
0500     typename gtl_and< typename is_mutable_polygon_type<T1>::type,
0501                       typename is_polygon_type<T2>::type>::type, T1>::type &
0502   assign(T1& lvalue, const T2& rvalue) {
0503     polygon_mutable_traits<T1>::set_points(lvalue, polygon_traits<T2>::begin_points(rvalue),
0504                                            polygon_traits<T2>::end_points(rvalue));
0505     return lvalue;
0506   }
0507
0508 // \relatesalso polygon_with_holes_concept
0509   template <typename T1, typename T2>
0510   typename enable_if<
0511     typename gtl_and< typename is_mutable_polygon_with_holes_type<T1>::type,
0512                       typename is_polygon_with_holes_type<T2>::type>::type, T1>::type &
0513   assign(T1& lvalue, const T2& rvalue) {
0514     polygon_mutable_traits<T1>::set_points(lvalue, polygon_traits<T2>::begin_points(rvalue),
0515                                            polygon_traits<T2>::end_points(rvalue));
0516     polygon_with_holes_mutable_traits<T1>::set_holes(lvalue, polygon_with_holes_traits<T2>::begin_holes(rvalue),
0517                                                      polygon_with_holes_traits<T2>::end_holes(rvalue));
0518     return lvalue;
0519   }
0520
0521   // \relatesalso polygon_45_concept
0522   template <typename T1, typename T2>
0523   typename enable_if< typename gtl_and< typename is_mutable_polygon_45_type<T1>::type, typename is_polygon_45_type<T2>::type>::type, T1>::type &
0524   assign(T1& lvalue, const T2& rvalue) {
0525     polygon_mutable_traits<T1>::set_points(lvalue, polygon_traits<T2>::begin_points(rvalue),
0526                                            polygon_traits<T2>::end_points(rvalue));
0527     return lvalue;
0528   }
0529
0530 // \relatesalso polygon_45_with_holes_concept
0531   template <typename T1, typename T2>
0532   typename enable_if<
0533     typename gtl_and< typename is_mutable_polygon_45_with_holes_type<T1>::type,
0534                       typename is_polygon_45_with_holes_type<T2>::type>::type, T1>::type &
0535   assign(T1& lvalue, const T2& rvalue) {
0536     polygon_mutable_traits<T1>::set_points(lvalue, polygon_traits<T2>::begin_points(rvalue),
0537                                            polygon_traits<T2>::end_points(rvalue));
0538     polygon_with_holes_mutable_traits<T1>::set_holes(lvalue, polygon_with_holes_traits<T2>::begin_holes(rvalue),
0539                                                      polygon_with_holes_traits<T2>::end_holes(rvalue));
0540     return lvalue;
0541   }
0542
0543   // \relatesalso polygon_90_concept
0544   template <typename T1, typename T2>
0545   typename enable_if<
0546     typename gtl_and< typename is_mutable_polygon_90_type<T1>::type,
0547                       typename is_polygon_90_type<T2>::type>::type, T1>::type &
0548   assign(T1& lvalue, const T2& rvalue) {
0549     polygon_90_mutable_traits<T1>::set_compact(lvalue, polygon_90_traits<T2>::begin_compact(rvalue),
0550                                                polygon_90_traits<T2>::end_compact(rvalue));
0551     return lvalue;
0552   }
0553
0554 // \relatesalso polygon_90_with_holes_concept
0555   template <typename T1, typename T2>
0556   typename enable_if<
0557     typename gtl_and< typename is_mutable_polygon_90_with_holes_type<T1>::type,
0558                       typename is_polygon_90_with_holes_type<T2>::type>::type, T1>::type &
0559   assign(T1& lvalue, const T2& rvalue) {
0560     polygon_90_mutable_traits<T1>::set_compact(lvalue, polygon_90_traits<T2>::begin_compact(rvalue),
0561                                                polygon_90_traits<T2>::end_compact(rvalue));
0562     polygon_with_holes_mutable_traits<T1>::set_holes(lvalue, polygon_with_holes_traits<T2>::begin_holes(rvalue),
0563                                                      polygon_with_holes_traits<T2>::end_holes(rvalue));
0564     return lvalue;
0565   }
0566
0567   // \relatesalso polygon_90_concept
0568   template <typename T1, typename T2>
0569   typename enable_if<
0570     typename gtl_and< typename is_any_mutable_polygon_type<T1>::type,
0571                       typename is_rectangle_concept<typename geometry_concept<T2>::type>::type>::type, T1>::type &
0572   assign(T1& polygon, const T2& rect) {
0573     typedef point_data<typename polygon_traits<T1>::coordinate_type> PT;
0574     PT points[4] = {PT(xl(rect), yl(rect)), PT(xh(rect), yl(rect)), PT(xh(rect), yh(rect)), PT(xl(rect), yh(rect))};
0575     set_points(polygon, points, points+4);
0576     return polygon;
0577   }
0578
0579 /// \relatesalso polygon_90_concept
0580   template <typename polygon_type, typename point_type>
0581   typename enable_if< typename gtl_and< typename is_mutable_polygon_90_type<polygon_type>::type,
0582                                          typename is_point_concept<typename geometry_concept<point_type>::type>::type>::type,
0583                        polygon_type>::type &
0584   convolve(polygon_type& polygon, const point_type& point) {
0585     std::vector<typename polygon_90_traits<polygon_type>::coordinate_type> coords;
0586     coords.reserve(::boost::polygon::size(polygon));
0587     bool pingpong = true;
0588     for(typename polygon_90_traits<polygon_type>::compact_iterator_type iter = begin_compact(polygon);
0589         iter != end_compact(polygon); ++iter) {
0590       coords.push_back((*iter) + (pingpong ? x(point) : y(point)));
0591       pingpong = !pingpong;
0592     }
0593     polygon_90_mutable_traits<polygon_type>::set_compact(polygon, coords.begin(), coords.end());
0594     return polygon;
0595   }
0596
0597 /// \relatesalso polygon_concept
0598   template <typename polygon_type, typename point_type>
0599   typename enable_if< typename gtl_and< typename gtl_or<
0600     typename is_mutable_polygon_45_type<polygon_type>::type,
0601     typename is_mutable_polygon_type<polygon_type>::type>::type,
0602                                          typename is_point_concept<typename geometry_concept<point_type>::type>::type>::type,
0603                        polygon_type>::type &
0604   convolve(polygon_type& polygon, const point_type& point) {
0605     std::vector<typename std::iterator_traits<typename polygon_traits<polygon_type>::iterator_type>::value_type> points;
0606     points.reserve(::boost::polygon::size(polygon));
0607     for(typename polygon_traits<polygon_type>::iterator_type iter = begin_points(polygon);
0608         iter != end_points(polygon); ++iter) {
0609       points.push_back(*iter);
0610       convolve(points.back(), point);
0611     }
0612     polygon_mutable_traits<polygon_type>::set_points(polygon, points.begin(), points.end());
0613     return polygon;
0614   }
0615
0616 /// \relatesalso polygon_with_holes_concept
0617   template <typename polygon_type, typename point_type>
0618   typename enable_if<
0619     typename gtl_and< typename is_any_mutable_polygon_with_holes_type<polygon_type>::type,
0620                       typename is_point_concept<typename geometry_concept<point_type>::type>::type>::type,
0621     polygon_type>::type &
0622   convolve(polygon_type& polygon, const point_type& point) {
0623     typedef typename polygon_with_holes_traits<polygon_type>::hole_type hole_type;
0624     hole_type h;
0625     set_points(h, begin_points(polygon), end_points(polygon));
0626     convolve(h, point);
0627     std::vector<hole_type> holes;
0628     holes.reserve(size_holes(polygon));
0629     for(typename polygon_with_holes_traits<polygon_type>::iterator_holes_type itr = begin_holes(polygon);
0630         itr != end_holes(polygon); ++itr) {
0631       holes.push_back(*itr);
0632       convolve(holes.back(), point);
0633     }
0634     assign(polygon, h);
0635     set_holes(polygon, holes.begin(), holes.end());
0636     return polygon;
0637   }
0638
0639 /// \relatesalso polygon_concept
0640   template <typename T>
0641   typename enable_if< typename is_any_mutable_polygon_type<T>::type, T>::type &
0642   move(T& polygon, orientation_2d orient, typename polygon_traits<T>::coordinate_type displacement) {
0643     typedef typename polygon_traits<T>::coordinate_type Unit;
0644     if(orient == HORIZONTAL) return convolve(polygon, point_data<Unit>(displacement, Unit(0)));
0645     return convolve(polygon, point_data<Unit>(Unit(0), displacement));
0646   }
0647
0648 /// \relatesalso polygon_concept
0649 /// \brief Applies a transformation to the polygon.
0650 /// \tparam polygon_type A type that models polygon_concept
0651 /// \tparam transform_type A type that may be either axis_transformation or transformation or that overloads point_concept::transform
0652 /// \param polygon The polygon to transform
0653 /// \param tr The transformation to apply
0654   template <typename polygon_type, typename transform_type>
0655   typename enable_if< typename is_any_mutable_polygon_without_holes_type<polygon_type>::type, polygon_type>::type &
0656   transform(polygon_type& polygon, const transform_type& tr) {
0657     std::vector<typename std::iterator_traits<typename polygon_traits<polygon_type>::iterator_type>::value_type> points;
0658     points.reserve(::boost::polygon::size(polygon));
0659     for(typename polygon_traits<polygon_type>::iterator_type iter = begin_points(polygon);
0660         iter != end_points(polygon); ++iter) {
0661       points.push_back(*iter);
0662       transform(points.back(), tr);
0663     }
0664     polygon_mutable_traits<polygon_type>::set_points(polygon, points.begin(), points.end());
0665     return polygon;
0666   }
0667
0668 /// \relatesalso polygon_with_holes_concept
0669   template <typename T, typename transform_type>
0670   typename enable_if< typename is_any_mutable_polygon_with_holes_type<T>::type, T>::type &
0671   transform(T& polygon, const transform_type& tr) {
0672     typedef typename polygon_with_holes_traits<T>::hole_type hole_type;
0673     hole_type h;
0674     set_points(h, begin_points(polygon), end_points(polygon));
0675     transform(h, tr);
0676     std::vector<hole_type> holes;
0677     holes.reserve(size_holes(polygon));
0678     for(typename polygon_with_holes_traits<T>::iterator_holes_type itr = begin_holes(polygon);
0679         itr != end_holes(polygon); ++itr) {
0680       holes.push_back(*itr);
0681       transform(holes.back(), tr);
0682     }
0683     assign(polygon, h);
0684     set_holes(polygon, holes.begin(), holes.end());
0685     return polygon;
0686   }
0687
0688   template <typename polygon_type>
0689   typename enable_if< typename is_any_mutable_polygon_without_holes_type<polygon_type>::type, polygon_type>::type &
0690   scale_up(polygon_type& polygon, typename coordinate_traits<typename polygon_traits<polygon_type>::coordinate_type>::unsigned_area_type factor) {
0691     std::vector<typename std::iterator_traits<typename polygon_traits<polygon_type>::iterator_type>::value_type> points;
0692     points.reserve(::boost::polygon::size(polygon));
0693     for(typename polygon_traits<polygon_type>::iterator_type iter = begin_points(polygon);
0694         iter != end_points(polygon); ++iter) {
0695       points.push_back(*iter);
0696       scale_up(points.back(), factor);
0697     }
0698     polygon_mutable_traits<polygon_type>::set_points(polygon, points.begin(), points.end());
0699     return polygon;
0700   }
0701
0702   template <typename T>
0703   typename enable_if< typename is_any_mutable_polygon_with_holes_type<T>::type, T>::type &
0704   scale_up(T& polygon, typename coordinate_traits<typename polygon_traits<T>::coordinate_type>::unsigned_area_type factor) {
0705     typedef typename polygon_with_holes_traits<T>::hole_type hole_type;
0706     hole_type h;
0707     set_points(h, begin_points(polygon), end_points(polygon));
0708     scale_up(h, factor);
0709     std::vector<hole_type> holes;
0710     holes.reserve(size_holes(polygon));
0711     for(typename polygon_with_holes_traits<T>::iterator_holes_type itr = begin_holes(polygon);
0712         itr != end_holes(polygon); ++itr) {
0713       holes.push_back(*itr);
0714       scale_up(holes.back(), factor);
0715     }
0716     assign(polygon, h);
0717     set_holes(polygon, holes.begin(), holes.end());
0718     return polygon;
0719   }
0720
0721   //scale non-45 down
0722   template <typename polygon_type>
0723   typename enable_if<
0724     typename gtl_and< typename is_any_mutable_polygon_without_holes_type<polygon_type>::type,
0725                       typename gtl_not<typename gtl_same_type
0726                                        < forty_five_domain,
0727                                          typename geometry_domain<typename geometry_concept<polygon_type>::type>::type>::type>::type>::type,
0728     polygon_type>::type &
0729   scale_down(polygon_type& polygon, typename coordinate_traits<typename polygon_traits<polygon_type>::coordinate_type>::unsigned_area_type factor) {
0730     std::vector<typename std::iterator_traits<typename polygon_traits<polygon_type>::iterator_type>::value_type> points;
0731     points.reserve(::boost::polygon::size(polygon));
0732     for(typename polygon_traits<polygon_type>::iterator_type iter = begin_points(polygon);
0733         iter != end_points(polygon); ++iter) {
0734       points.push_back(*iter);
0735       scale_down(points.back(), factor);
0736     }
0737     polygon_mutable_traits<polygon_type>::set_points(polygon, points.begin(), points.end());
0738     return polygon;
0739   }
0740
0741   template <typename Unit>
0742   Unit local_abs(Unit value) { return value < 0 ? (Unit)-value : value; }
0743
0744   template <typename Unit>
0745   void snap_point_vector_to_45(std::vector<point_data<Unit> >& pts) {
0746     typedef point_data<Unit> Point;
0747     if(pts.size() < 3) { pts.clear(); return; }
0748     typename std::vector<point_data<Unit> >::iterator endLocation = std::unique(pts.begin(), pts.end());
0749     if(endLocation != pts.end()){
0750       pts.resize(endLocation - pts.begin());
0751     }
0752     if(pts.back() == pts[0]) pts.pop_back();
0753     //iterate over point triplets
0754     int numPts = pts.size();
0755     bool wrap_around = false;
0756     for(int i = 0; i < numPts; ++i) {
0757       Point& pt1 = pts[i];
0758       Point& pt2 = pts[(i + 1) % numPts];
0759       Point& pt3 = pts[(i + 2) % numPts];
0760       //check if non-45 edge
0761       Unit deltax = x(pt2) - x(pt1);
0762       Unit deltay = y(pt2) - y(pt1);
0763       if(deltax && deltay &&
0764          local_abs(deltax) != local_abs(deltay)) {
0765         //adjust the middle point
0766         Unit ndx = x(pt3) - x(pt2);
0767         Unit ndy = y(pt3) - y(pt2);
0768         if(ndx && ndy) {
0769           Unit diff = local_abs(local_abs(deltax) - local_abs(deltay));
0770           Unit halfdiff = diff/2;
0771           if((deltax > 0 && deltay > 0) ||
0772              (deltax < 0 && deltay < 0)) {
0773             //previous edge is rising slope
0774             if(local_abs(deltax + halfdiff + (diff % 2)) ==
0775                local_abs(deltay - halfdiff)) {
0776               x(pt2, x(pt2) + halfdiff + (diff % 2));
0777               y(pt2, y(pt2) - halfdiff);
0778             } else if(local_abs(deltax - halfdiff - (diff % 2)) ==
0779                       local_abs(deltay + halfdiff)) {
0780               x(pt2, x(pt2) - halfdiff - (diff % 2));
0781               y(pt2, y(pt2) + halfdiff);
0782             } else{
0783               //std::cout << "fail1\n";
0784             }
0785           } else {
0786             //previous edge is falling slope
0787             if(local_abs(deltax + halfdiff + (diff % 2)) ==
0788                local_abs(deltay + halfdiff)) {
0789               x(pt2, x(pt2) + halfdiff + (diff % 2));
0790               y(pt2, y(pt2) + halfdiff);
0791             } else if(local_abs(deltax - halfdiff - (diff % 2)) ==
0792                       local_abs(deltay - halfdiff)) {
0793               x(pt2, x(pt2) - halfdiff - (diff % 2));
0794               y(pt2, y(pt2) - halfdiff);
0795             } else {
0796               //std::cout << "fail2\n";
0797             }
0798           }
0799           if(i == numPts - 1 && (diff % 2)) {
0800             //we have a wrap around effect
0801             if(!wrap_around) {
0802               wrap_around = true;
0803               i = -1;
0804             }
0805           }
0806         } else if(ndx) {
0807           //next edge is horizontal
0808           //find the x value for pt1 that would make the abs(deltax) == abs(deltay)
0809           Unit newDeltaX = local_abs(deltay);
0810           if(deltax < 0) newDeltaX *= -1;
0811           x(pt2, x(pt1) + newDeltaX);
0812         } else { //ndy
0813           //next edge is vertical
0814           //find the y value for pt1 that would make the abs(deltax) == abs(deltay)
0815           Unit newDeltaY = local_abs(deltax);
0816           if(deltay < 0) newDeltaY *= -1;
0817           y(pt2, y(pt1) + newDeltaY);
0818         }
0819       }
0820     }
0821   }
0822
0823   template <typename polygon_type>
0824   typename enable_if< typename is_any_mutable_polygon_without_holes_type<polygon_type>::type, polygon_type>::type &
0825   snap_to_45(polygon_type& polygon) {
0826     std::vector<typename std::iterator_traits<typename polygon_traits<polygon_type>::iterator_type>::value_type> points;
0827     points.reserve(::boost::polygon::size(polygon));
0828     for(typename polygon_traits<polygon_type>::iterator_type iter = begin_points(polygon);
0829         iter != end_points(polygon); ++iter) {
0830       points.push_back(*iter);
0831     }
0832     snap_point_vector_to_45(points);
0833     polygon_mutable_traits<polygon_type>::set_points(polygon, points.begin(), points.end());
0834     return polygon;
0835   }
0836
0837   template <typename polygon_type>
0838   typename enable_if< typename is_any_mutable_polygon_with_holes_type<polygon_type>::type, polygon_type>::type &
0839   snap_to_45(polygon_type& polygon) {
0840     typedef typename polygon_with_holes_traits<polygon_type>::hole_type hole_type;
0841     hole_type h;
0842     set_points(h, begin_points(polygon), end_points(polygon));
0843     snap_to_45(h);
0844     std::vector<hole_type> holes;
0845     holes.reserve(size_holes(polygon));
0846     for(typename polygon_with_holes_traits<polygon_type>::iterator_holes_type itr = begin_holes(polygon);
0847         itr != end_holes(polygon); ++itr) {
0848       holes.push_back(*itr);
0849       snap_to_45(holes.back());
0850     }
0851     assign(polygon, h);
0852     set_holes(polygon, holes.begin(), holes.end());
0853     return polygon;
0854   }
0855
0856   //scale specifically 45 down
0857   template <typename polygon_type>
0858   typename enable_if<
0859     typename gtl_and< typename is_any_mutable_polygon_without_holes_type<polygon_type>::type,
0860                       typename gtl_same_type
0861                       < forty_five_domain,
0862                         typename geometry_domain<typename geometry_concept<polygon_type>::type>::type>::type>::type,
0863     polygon_type>::type &
0864   scale_down(polygon_type& polygon, typename coordinate_traits<typename polygon_traits<polygon_type>::coordinate_type>::unsigned_area_type factor) {
0865     std::vector<typename std::iterator_traits<typename polygon_traits<polygon_type>::iterator_type>::value_type> points;
0866     points.reserve(::boost::polygon::size(polygon));
0867     for(typename polygon_traits<polygon_type>::iterator_type iter = begin_points(polygon);
0868         iter != end_points(polygon); ++iter) {
0869       points.push_back(*iter);
0870       scale_down(points.back(), factor);
0871     }
0872     snap_point_vector_to_45(points);
0873     polygon_mutable_traits<polygon_type>::set_points(polygon, points.begin(), points.end());
0874     return polygon;
0875   }
0876
0877   template <typename T>
0878   typename enable_if< typename is_any_mutable_polygon_with_holes_type<T>::type, T>::type &
0879   scale_down(T& polygon, typename coordinate_traits<typename polygon_traits<T>::coordinate_type>::unsigned_area_type factor) {
0880     typedef typename polygon_with_holes_traits<T>::hole_type hole_type;
0881     hole_type h;
0882     set_points(h, begin_points(polygon), end_points(polygon));
0883     scale_down(h, factor);
0884     std::vector<hole_type> holes;
0885     holes.reserve(size_holes(polygon));
0886     for(typename polygon_with_holes_traits<T>::iterator_holes_type itr = begin_holes(polygon);
0887         itr != end_holes(polygon); ++itr) {
0888       holes.push_back(*itr);
0889       scale_down(holes.back(), factor);
0890     }
0891     assign(polygon, h);
0892     set_holes(polygon, holes.begin(), holes.end());
0893     return polygon;
0894   }
0895
0896   //scale non-45
0897   template <typename polygon_type>
0898   typename enable_if<
0899     typename gtl_and< typename is_any_mutable_polygon_without_holes_type<polygon_type>::type,
0900                       typename gtl_not<typename gtl_same_type
0901                                        < forty_five_domain,
0902                                          typename geometry_domain<typename geometry_concept<polygon_type>::type>::type>::type>::type>::type,
0903     polygon_type>::type &
0904   scale(polygon_type& polygon, double factor) {
0905     std::vector<typename std::iterator_traits<typename polygon_traits<polygon_type>::iterator_type>::value_type> points;
0906     points.reserve(::boost::polygon::size(polygon));
0907     for(typename polygon_traits<polygon_type>::iterator_type iter = begin_points(polygon);
0908         iter != end_points(polygon); ++iter) {
0909       points.push_back(*iter);
0910       scale(points.back(), anisotropic_scale_factor<double>(factor, factor));
0911     }
0912     polygon_mutable_traits<polygon_type>::set_points(polygon, points.begin(), points.end());
0913     return polygon;
0914   }
0915
0916   //scale specifically 45
0917   template <typename polygon_type>
0918   polygon_type&
0919   scale(polygon_type& polygon, double factor,
0920     typename enable_if<
0921     typename gtl_and< typename is_any_mutable_polygon_without_holes_type<polygon_type>::type,
0922                       typename gtl_same_type
0923                       < forty_five_domain,
0924         typename geometry_domain<typename geometry_concept<polygon_type>::type>::type>::type>::type>::type * = 0
0925   ) {
0926     std::vector<typename std::iterator_traits<typename polygon_traits<polygon_type>::iterator_type>::value_type> points;
0927     points.reserve(::boost::polygon::size(polygon));
0928     for(typename polygon_traits<polygon_type>::iterator_type iter = begin_points(polygon);
0929         iter != end_points(polygon); ++iter) {
0930       points.push_back(*iter);
0931       scale(points.back(), anisotropic_scale_factor<double>(factor, factor));
0932     }
0933     snap_point_vector_to_45(points);
0934     polygon_mutable_traits<polygon_type>::set_points(polygon, points.begin(), points.end());
0935     return polygon;
0936   }
0937
0938   template <typename T>
0939   T&
0940   scale(T& polygon, double factor,
0941   typename enable_if< typename is_any_mutable_polygon_with_holes_type<T>::type>::type * = 0
0942   ) {
0943     typedef typename polygon_with_holes_traits<T>::hole_type hole_type;
0944     hole_type h;
0945     set_points(h, begin_points(polygon), end_points(polygon));
0946     scale(h, factor);
0947     std::vector<hole_type> holes;
0948     holes.reserve(size_holes(polygon));
0949     for(typename polygon_with_holes_traits<T>::iterator_holes_type itr = begin_holes(polygon);
0950         itr != end_holes(polygon); ++itr) {
0951       holes.push_back(*itr);
0952       scale(holes.back(), factor);
0953     }
0954     assign(polygon, h);
0955     set_holes(polygon, holes.begin(), holes.end());
0956     return polygon;
0957   }
0958
0959   template <typename iterator_type, typename area_type>
0960   static area_type
0961   point_sequence_area(iterator_type begin_range, iterator_type end_range) {
0962     typedef typename std::iterator_traits<iterator_type>::value_type point_type;
0963     if(begin_range == end_range) return area_type(0);
0964     point_type first = *begin_range;
0965     point_type previous = first;
0966     ++begin_range;
0967     // Initialize trapezoid base line
0968     area_type y_base = (area_type)y(first);
0969     // Initialize area accumulator
0970
0971     area_type area(0);
0972     while (begin_range != end_range) {
0973       area_type x1 = (area_type)x(previous);
0974       area_type x2 = (area_type)x(*begin_range);
0975 #ifdef BOOST_POLYGON_ICC
0976 #pragma warning (push)
0977 #pragma warning (disable:1572)
0978 #endif
0979       if(x1 != x2) {
0980 #ifdef BOOST_POLYGON_ICC
0981 #pragma warning (pop)
0982 #endif
0983         // do trapezoid area accumulation
0984         area += (x2 - x1) * (((area_type)y(*begin_range) - y_base) +
0985                              ((area_type)y(previous) - y_base)) / 2;
0986       }
0987       previous = *begin_range;
0988       // go to next point
0989       ++begin_range;
0990     }
0991     //wrap around to evaluate the edge between first and last if not closed
0992     if(!equivalence(first, previous)) {
0993       area_type x1 = (area_type)x(previous);
0994       area_type x2 = (area_type)x(first);
0995       area += (x2 - x1) * (((area_type)y(first) - y_base) +
0996                            ((area_type)y(previous) - y_base)) / 2;
0997     }
0998     return area;
0999   }
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