summaryrefslogtreecommitdiff
path: root/boost/geometry/algorithms/detail/relate/linear_areal.hpp
blob: f1b4fdf81a0bae7e5aa2b612051782f58be6333b (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
// Boost.Geometry (aka GGL, Generic Geometry Library)

// Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands.

// This file was modified by Oracle on 2013, 2014, 2015, 2017.
// Modifications copyright (c) 2013-2017 Oracle and/or its affiliates.

// Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle

// Use, modification and distribution is subject to the Boost Software License,
// Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)

#ifndef BOOST_GEOMETRY_ALGORITHMS_DETAIL_RELATE_LINEAR_AREAL_HPP
#define BOOST_GEOMETRY_ALGORITHMS_DETAIL_RELATE_LINEAR_AREAL_HPP

#include <boost/core/ignore_unused.hpp>
#include <boost/range/size.hpp>

#include <boost/geometry/core/assert.hpp>
#include <boost/geometry/core/topological_dimension.hpp>

#include <boost/geometry/util/condition.hpp>
#include <boost/geometry/util/range.hpp>

#include <boost/geometry/algorithms/num_interior_rings.hpp>
#include <boost/geometry/algorithms/detail/point_on_border.hpp>
#include <boost/geometry/algorithms/detail/sub_range.hpp>
#include <boost/geometry/algorithms/detail/single_geometry.hpp>

#include <boost/geometry/algorithms/detail/relate/point_geometry.hpp>
#include <boost/geometry/algorithms/detail/relate/turns.hpp>
#include <boost/geometry/algorithms/detail/relate/boundary_checker.hpp>
#include <boost/geometry/algorithms/detail/relate/follow_helpers.hpp>

#include <boost/geometry/views/detail/normalized_view.hpp>

namespace boost { namespace geometry
{

#ifndef DOXYGEN_NO_DETAIL
namespace detail { namespace relate {

// WARNING!
// TODO: In the worst case calling this Pred in a loop for MultiLinestring/MultiPolygon may take O(NM)
// Use the rtree in this case!

// may be used to set IE and BE for a Linear geometry for which no turns were generated
template
<
    typename Geometry2,
    typename Result,
    typename PointInArealStrategy,
    typename BoundaryChecker,
    bool TransposeResult
>
class no_turns_la_linestring_pred
{
public:
    no_turns_la_linestring_pred(Geometry2 const& geometry2,
                                Result & res,
                                PointInArealStrategy const& point_in_areal_strategy,
                                BoundaryChecker const& boundary_checker)
        : m_geometry2(geometry2)
        , m_result(res)
        , m_point_in_areal_strategy(point_in_areal_strategy)
        , m_boundary_checker(boundary_checker)
        , m_interrupt_flags(0)
    {
        if ( ! may_update<interior, interior, '1', TransposeResult>(m_result) )
        {
            m_interrupt_flags |= 1;
        }

        if ( ! may_update<interior, exterior, '1', TransposeResult>(m_result) )
        {
            m_interrupt_flags |= 2;
        }

        if ( ! may_update<boundary, interior, '0', TransposeResult>(m_result) )
        {
            m_interrupt_flags |= 4;
        }

        if ( ! may_update<boundary, exterior, '0', TransposeResult>(m_result) )
        {
            m_interrupt_flags |= 8;
        }
    }

    template <typename Linestring>
    bool operator()(Linestring const& linestring)
    {
        std::size_t const count = boost::size(linestring);
        
        // invalid input
        if ( count < 2 )
        {
            // ignore
            // TODO: throw an exception?
            return true;
        }

        // if those flags are set nothing will change
        if ( m_interrupt_flags == 0xF )
        {
            return false;
        }

        int const pig = detail::within::point_in_geometry(range::front(linestring),
                                                          m_geometry2,
                                                          m_point_in_areal_strategy);
        //BOOST_GEOMETRY_ASSERT_MSG(pig != 0, "There should be no IPs");

        if ( pig > 0 )
        {
            update<interior, interior, '1', TransposeResult>(m_result);
            m_interrupt_flags |= 1;
        }
        else
        {
            update<interior, exterior, '1', TransposeResult>(m_result);
            m_interrupt_flags |= 2;
        }

        // check if there is a boundary
        if ( ( m_interrupt_flags & 0xC ) != 0xC // if wasn't already set
          && ( m_boundary_checker.template
                is_endpoint_boundary<boundary_front>(range::front(linestring))
            || m_boundary_checker.template
                is_endpoint_boundary<boundary_back>(range::back(linestring)) ) )
        {
            if ( pig > 0 )
            {
                update<boundary, interior, '0', TransposeResult>(m_result);
                m_interrupt_flags |= 4;
            }
            else
            {
                update<boundary, exterior, '0', TransposeResult>(m_result);
                m_interrupt_flags |= 8;
            }
        }

        return m_interrupt_flags != 0xF
            && ! m_result.interrupt;
    }

private:
    Geometry2 const& m_geometry2;
    Result & m_result;
    PointInArealStrategy const& m_point_in_areal_strategy;
    BoundaryChecker const& m_boundary_checker;
    unsigned m_interrupt_flags;
};

// may be used to set EI and EB for an Areal geometry for which no turns were generated
template <typename Result, bool TransposeResult>
class no_turns_la_areal_pred
{
public:
    no_turns_la_areal_pred(Result & res)
        : m_result(res)
        , interrupt(! may_update<interior, exterior, '2', TransposeResult>(m_result)
                 && ! may_update<boundary, exterior, '1', TransposeResult>(m_result) )
    {}

    template <typename Areal>
    bool operator()(Areal const& areal)
    {
        if ( interrupt )
        {
            return false;
        }

        // TODO:
        // handle empty/invalid geometries in a different way than below?

        typedef typename geometry::point_type<Areal>::type point_type;
        point_type dummy;
        bool const ok = boost::geometry::point_on_border(dummy, areal);

        // TODO: for now ignore, later throw an exception?
        if ( !ok )
        {
            return true;
        }

        update<interior, exterior, '2', TransposeResult>(m_result);
        update<boundary, exterior, '1', TransposeResult>(m_result);
                    
        return false;
    }

private:
    Result & m_result;
    bool const interrupt;
};

// The implementation of an algorithm calculating relate() for L/A
template <typename Geometry1, typename Geometry2, bool TransposeResult = false>
struct linear_areal
{
    // check Linear / Areal
    BOOST_STATIC_ASSERT(topological_dimension<Geometry1>::value == 1
                     && topological_dimension<Geometry2>::value == 2);

    static const bool interruption_enabled = true;

    typedef typename geometry::point_type<Geometry1>::type point1_type;
    typedef typename geometry::point_type<Geometry2>::type point2_type;

    template <typename Geometry>
        struct is_multi
            : boost::is_base_of
                <
                    multi_tag,
                    typename tag<Geometry>::type
                >
        {};

    template <typename Geom1, typename Geom2>
    struct multi_turn_info
        : turns::get_turns<Geom1, Geom2>::turn_info
    {
        multi_turn_info() : priority(0) {}
        int priority; // single-geometry sorting priority
    };

    template <typename Geom1, typename Geom2>
    struct turn_info_type
        : boost::mpl::if_c
            <
                is_multi<Geometry2>::value,
                multi_turn_info<Geom1, Geom2>,
                typename turns::get_turns<Geom1, Geom2>::turn_info
            >
    {};
    
    template <typename Result, typename IntersectionStrategy>
    static inline void apply(Geometry1 const& geometry1, Geometry2 const& geometry2,
                             Result & result,
                             IntersectionStrategy const& intersection_strategy)
    {
// TODO: If Areal geometry may have infinite size, change the following line:

        // The result should be FFFFFFFFF
        relate::set<exterior, exterior, result_dimension<Geometry2>::value, TransposeResult>(result);// FFFFFFFFd, d in [1,9] or T

        if ( BOOST_GEOMETRY_CONDITION( result.interrupt ) )
            return;

        // get and analyse turns
        typedef typename turn_info_type<Geometry1, Geometry2>::type turn_type;
        std::vector<turn_type> turns;

        interrupt_policy_linear_areal<Geometry2, Result> interrupt_policy(geometry2, result);

        turns::get_turns<Geometry1, Geometry2>::apply(turns, geometry1, geometry2, interrupt_policy, intersection_strategy);
        if ( BOOST_GEOMETRY_CONDITION( result.interrupt ) )
            return;

        boundary_checker<Geometry1> boundary_checker1(geometry1);
        no_turns_la_linestring_pred
            <
                Geometry2,
                Result,
                typename IntersectionStrategy::template point_in_geometry_strategy<Geometry1, Geometry2>::type,
                boundary_checker<Geometry1>,
                TransposeResult
            > pred1(geometry2,
                    result,
                    intersection_strategy.template get_point_in_geometry_strategy<Geometry1, Geometry2>(),
                    boundary_checker1);
        for_each_disjoint_geometry_if<0, Geometry1>::apply(turns.begin(), turns.end(), geometry1, pred1);
        if ( BOOST_GEOMETRY_CONDITION( result.interrupt ) )
            return;

        no_turns_la_areal_pred<Result, !TransposeResult> pred2(result);
        for_each_disjoint_geometry_if<1, Geometry2>::apply(turns.begin(), turns.end(), geometry2, pred2);
        if ( BOOST_GEOMETRY_CONDITION( result.interrupt ) )
            return;
        
        if ( turns.empty() )
            return;

        // This is set here because in the case if empty Areal geometry were passed
        // those shouldn't be set
        relate::set<exterior, interior, '2', TransposeResult>(result);// FFFFFF2Fd
        if ( BOOST_GEOMETRY_CONDITION( result.interrupt ) )
            return;

        {
            sort_dispatch(turns.begin(), turns.end(), is_multi<Geometry2>());

            turns_analyser<turn_type> analyser;
            analyse_each_turn(result, analyser,
                              turns.begin(), turns.end(),
                              geometry1, geometry2,
                              boundary_checker1,
                              intersection_strategy.get_side_strategy());

            if ( BOOST_GEOMETRY_CONDITION( result.interrupt ) )
                return;
        }

        // If 'c' (insersection_boundary) was not found we know that any Ls isn't equal to one of the Rings
        if ( !interrupt_policy.is_boundary_found )
        {
            relate::set<exterior, boundary, '1', TransposeResult>(result);
        }
        // Don't calculate it if it's required
        else if ( may_update<exterior, boundary, '1', TransposeResult>(result) )
        {
// TODO: REVISE THIS CODE AND PROBABLY REWRITE SOME PARTS TO BE MORE HUMAN-READABLE
//       IN GENERAL IT ANALYSES THE RINGS OF AREAL GEOMETRY AND DETECTS THE ONES THAT
//       MAY OVERLAP THE INTERIOR OF LINEAR GEOMETRY (NO IPs OR NON-FAKE 'u' OPERATION)
// NOTE: For one case std::sort may be called again to sort data by operations for data already sorted by ring index
//       In the worst case scenario the complexity will be O( NlogN + R*(N/R)log(N/R) )
//       So always should remain O(NlogN) -> for R==1 <-> 1(N/1)log(N/1), for R==N <-> N(N/N)log(N/N)
//       Some benchmarking should probably be done to check if only one std::sort should be used

            // sort by multi_index and rind_index
            std::sort(turns.begin(), turns.end(), less_ring());

            typedef typename std::vector<turn_type>::iterator turn_iterator;

            turn_iterator it = turns.begin();
            segment_identifier * prev_seg_id_ptr = NULL;
            // for each ring
            for ( ; it != turns.end() ; )
            {
                // it's the next single geometry
                if ( prev_seg_id_ptr == NULL
                  || prev_seg_id_ptr->multi_index != it->operations[1].seg_id.multi_index )
                {
                    // if the first ring has no IPs
                    if ( it->operations[1].seg_id.ring_index > -1 )
                    {
                        // we can be sure that the exterior overlaps the boundary
                        relate::set<exterior, boundary, '1', TransposeResult>(result);                    
                        break;
                    }
                    // if there was some previous ring
                    if ( prev_seg_id_ptr != NULL )
                    {
                        signed_size_type const next_ring_index = prev_seg_id_ptr->ring_index + 1;
                        BOOST_GEOMETRY_ASSERT(next_ring_index >= 0);
                        
                        // if one of the last rings of previous single geometry was ommited
                        if ( static_cast<std::size_t>(next_ring_index)
                                < geometry::num_interior_rings(
                                    single_geometry(geometry2, *prev_seg_id_ptr)) )
                        {
                            // we can be sure that the exterior overlaps the boundary
                            relate::set<exterior, boundary, '1', TransposeResult>(result);
                            break;
                        }
                    }
                }
                // if it's the same single geometry
                else /*if ( previous_multi_index == it->operations[1].seg_id.multi_index )*/
                {
                    // and we jumped over one of the rings
                    if ( prev_seg_id_ptr != NULL // just in case
                      && prev_seg_id_ptr->ring_index + 1 < it->operations[1].seg_id.ring_index )
                    {
                        // we can be sure that the exterior overlaps the boundary
                        relate::set<exterior, boundary, '1', TransposeResult>(result);                    
                        break;
                    }
                }

                prev_seg_id_ptr = boost::addressof(it->operations[1].seg_id);

                // find the next ring first iterator and check if the analysis should be performed
                has_boundary_intersection has_boundary_inters;
                turn_iterator next = find_next_ring(it, turns.end(), has_boundary_inters);

                // if there is no 1d overlap with the boundary
                if ( !has_boundary_inters.result )
                {
                    // we can be sure that the exterior overlaps the boundary
                    relate::set<exterior, boundary, '1', TransposeResult>(result);                    
                    break;
                }
                // else there is 1d overlap with the boundary so we must analyse the boundary
                else
                {
                    // u, c
                    typedef turns::less<1, turns::less_op_areal_linear<1> > less;
                    std::sort(it, next, less());

                    // analyse
                    areal_boundary_analyser<turn_type> analyser;
                    for ( turn_iterator rit = it ; rit != next ; ++rit )
                    {
                        // if the analyser requests, break the search
                        if ( !analyser.apply(it, rit, next) )
                            break;
                    }

                    // if the boundary of Areal goes out of the Linear
                    if ( analyser.is_union_detected )
                    {
                        // we can be sure that the boundary of Areal overlaps the exterior of Linear
                        relate::set<exterior, boundary, '1', TransposeResult>(result);
                        break;
                    }
                }

                it = next;
            }

            // if there was some previous ring
            if ( prev_seg_id_ptr != NULL )
            {
                signed_size_type const next_ring_index = prev_seg_id_ptr->ring_index + 1;
                BOOST_GEOMETRY_ASSERT(next_ring_index >= 0);

                // if one of the last rings of previous single geometry was ommited
                if ( static_cast<std::size_t>(next_ring_index)
                        < geometry::num_interior_rings(
                            single_geometry(geometry2, *prev_seg_id_ptr)) )
                {
                    // we can be sure that the exterior overlaps the boundary
                    relate::set<exterior, boundary, '1', TransposeResult>(result);
                }
            }
        }
    }

    template <typename It, typename Pred, typename Comp>
    static void for_each_equal_range(It first, It last, Pred pred, Comp comp)
    {
        if ( first == last )
            return;

        It first_equal = first;
        It prev = first;
        for ( ++first ; ; ++first, ++prev )
        {
            if ( first == last || !comp(*prev, *first) )
            {
                pred(first_equal, first);
                first_equal = first;
            }
            
            if ( first == last )
                break;
        }
    }

    struct same_ip
    {
        template <typename Turn>
        bool operator()(Turn const& left, Turn const& right) const
        {
            return left.operations[0].seg_id == right.operations[0].seg_id
                && left.operations[0].fraction == right.operations[0].fraction;
        }
    };

    struct same_ip_and_multi_index
    {
        template <typename Turn>
        bool operator()(Turn const& left, Turn const& right) const
        {
            return same_ip()(left, right)
                && left.operations[1].seg_id.multi_index == right.operations[1].seg_id.multi_index;
        }
    };

    template <typename OpToPriority>
    struct set_turns_group_priority
    {
        template <typename TurnIt>
        void operator()(TurnIt first, TurnIt last) const
        {
            BOOST_GEOMETRY_ASSERT(first != last);
            static OpToPriority op_to_priority;
            // find the operation with the least priority
            int least_priority = op_to_priority(first->operations[0]);
            for ( TurnIt it = first + 1 ; it != last ; ++it )
            {
                int priority = op_to_priority(it->operations[0]);
                if ( priority < least_priority )
                    least_priority = priority;
            }
            // set the least priority for all turns of the group
            for ( TurnIt it = first ; it != last ; ++it )
            {
                it->priority = least_priority;
            }
        }
    };

    template <typename SingleLess>
    struct sort_turns_group
    {
        struct less
        {
            template <typename Turn>
            bool operator()(Turn const& left, Turn const& right) const
            {
                return left.operations[1].seg_id.multi_index == right.operations[1].seg_id.multi_index ?
                    SingleLess()(left, right) :
                    left.priority < right.priority;
            }
        };

        template <typename TurnIt>
        void operator()(TurnIt first, TurnIt last) const
        {
            std::sort(first, last, less());
        }
    };

    template <typename TurnIt>
    static void sort_dispatch(TurnIt first, TurnIt last, boost::true_type const& /*is_multi*/)
    {
        // sort turns by Linear seg_id, then by fraction, then by other multi_index
        typedef turns::less<0, turns::less_other_multi_index<0> > less;
        std::sort(first, last, less());

        // For the same IP and multi_index - the same other's single geometry
        // set priorities as the least operation found for the whole single geometry
        // so e.g. single geometries containing 'u' will always be before those only containing 'i'
        typedef turns::op_to_int<0,2,3,1,4,0> op_to_int_xuic;
        for_each_equal_range(first, last,
                             set_turns_group_priority<op_to_int_xuic>(), // least operation in xuic order
                             same_ip_and_multi_index()); // other's multi_index

        // When priorities for single geometries are set now sort turns for the same IP
        // if multi_index is the same sort them according to the single-less
        // else use priority of the whole single-geometry set earlier
        typedef turns::less<0, turns::less_op_linear_areal_single<0> > single_less;
        for_each_equal_range(first, last,
                             sort_turns_group<single_less>(),
                             same_ip());
    }

    template <typename TurnIt>
    static void sort_dispatch(TurnIt first, TurnIt last, boost::false_type const& /*is_multi*/)
    {
        // sort turns by Linear seg_id, then by fraction, then
        // for same ring id: x, u, i, c
        // for different ring id: c, i, u, x
        typedef turns::less<0, turns::less_op_linear_areal_single<0> > less;
        std::sort(first, last, less());
    }
    

    // interrupt policy which may be passed to get_turns to interrupt the analysis
    // based on the info in the passed result/mask
    template <typename Areal, typename Result>
    class interrupt_policy_linear_areal
    {
    public:
        static bool const enabled = true;

        interrupt_policy_linear_areal(Areal const& areal, Result & result)
            : m_result(result), m_areal(areal)
            , is_boundary_found(false)
        {}

// TODO: since we update result for some operations here, we may not do it in the analyser!

        template <typename Range>
        inline bool apply(Range const& turns)
        {
            typedef typename boost::range_iterator<Range const>::type iterator;
            
            for (iterator it = boost::begin(turns) ; it != boost::end(turns) ; ++it)
            {
                if ( it->operations[0].operation == overlay::operation_intersection )
                {
                    bool const no_interior_rings
                        = geometry::num_interior_rings(
                                single_geometry(m_areal, it->operations[1].seg_id)) == 0;

                    // WARNING! THIS IS TRUE ONLY IF THE POLYGON IS SIMPLE!
                    // OR WITHOUT INTERIOR RINGS (AND OF COURSE VALID)
                    if ( no_interior_rings )
                        update<interior, interior, '1', TransposeResult>(m_result);
                }
                else if ( it->operations[0].operation == overlay::operation_continue )
                {
                    update<interior, boundary, '1', TransposeResult>(m_result);
                    is_boundary_found = true;
                }
                else if ( ( it->operations[0].operation == overlay::operation_union
                         || it->operations[0].operation == overlay::operation_blocked )
                       && it->operations[0].position == overlay::position_middle )
                {
// TODO: here we could also check the boundaries and set BB at this point
                    update<interior, boundary, '0', TransposeResult>(m_result);
                }
            }

            return m_result.interrupt;
        }

    private:
        Result & m_result;
        Areal const& m_areal;

    public:
        bool is_boundary_found;
    };

    // This analyser should be used like Input or SinglePass Iterator
    // IMPORTANT! It should be called also for the end iterator - last
    template <typename TurnInfo>
    class turns_analyser
    {
        typedef typename TurnInfo::point_type turn_point_type;

        static const std::size_t op_id = 0;
        static const std::size_t other_op_id = 1;

    public:
        turns_analyser()
            : m_previous_turn_ptr(NULL)
            , m_previous_operation(overlay::operation_none)
            , m_boundary_counter(0)
            , m_interior_detected(false)
            , m_first_interior_other_id_ptr(NULL)
            , m_first_from_unknown(false)
            , m_first_from_unknown_boundary_detected(false)
        {}

        template <typename Result,
                  typename TurnIt,
                  typename Geometry,
                  typename OtherGeometry,
                  typename BoundaryChecker,
                  typename SideStrategy>
        void apply(Result & res, TurnIt it,
                   Geometry const& geometry,
                   OtherGeometry const& other_geometry,
                   BoundaryChecker const& boundary_checker,
                   SideStrategy const& side_strategy)
        {
            overlay::operation_type op = it->operations[op_id].operation;

            if ( op != overlay::operation_union
              && op != overlay::operation_intersection
              && op != overlay::operation_blocked
              && op != overlay::operation_continue ) // operation_boundary / operation_boundary_intersection
            {
                return;
            }

            segment_identifier const& seg_id = it->operations[op_id].seg_id;
            segment_identifier const& other_id = it->operations[other_op_id].seg_id;

            const bool first_in_range = m_seg_watcher.update(seg_id);

            // TODO: should apply() for the post-last ip be called if first_in_range ?
            // this would unify how last points in ranges are handled
            // possibly replacing parts of the code below
            // e.g. for is_multi and m_interior_detected

            // handle possible exit
            bool fake_enter_detected = false;
            if ( m_exit_watcher.get_exit_operation() == overlay::operation_union )
            {
                // real exit point - may be multiple
                // we know that we entered and now we exit
                if ( ! turn_on_the_same_ip<op_id>(m_exit_watcher.get_exit_turn(), *it) )
                {
                    m_exit_watcher.reset_detected_exit();
                    
                    update<interior, exterior, '1', TransposeResult>(res);

                    // next single geometry
                    if ( first_in_range && m_previous_turn_ptr )
                    {
                        // NOTE: similar code is in the post-last-ip-apply()
                        segment_identifier const& prev_seg_id = m_previous_turn_ptr->operations[op_id].seg_id;

                        bool const prev_back_b = is_endpoint_on_boundary<boundary_back>(
                                                    range::back(sub_range(geometry, prev_seg_id)),
                                                    boundary_checker);

                        // if there is a boundary on the last point
                        if ( prev_back_b )
                        {
                            update<boundary, exterior, '0', TransposeResult>(res);
                        }
                    }
                }
                // fake exit point, reset state
                else if ( op == overlay::operation_intersection
                        || op == overlay::operation_continue ) // operation_boundary
                {
                    m_exit_watcher.reset_detected_exit();
                    fake_enter_detected = true;
                }
            }
            else if ( m_exit_watcher.get_exit_operation() == overlay::operation_blocked )
            {
                // ignore multiple BLOCKs for this same single geometry1
                if ( op == overlay::operation_blocked
                  && seg_id.multi_index == m_previous_turn_ptr->operations[op_id].seg_id.multi_index )
                {
                    return;
                }

                if ( ( op == overlay::operation_intersection
                    || op == overlay::operation_continue )
                  && turn_on_the_same_ip<op_id>(m_exit_watcher.get_exit_turn(), *it) )
                {
                    fake_enter_detected = true;
                }

                m_exit_watcher.reset_detected_exit();
            }

            if ( BOOST_GEOMETRY_CONDITION( is_multi<OtherGeometry>::value )
              && m_first_from_unknown )
            {
                // For MultiPolygon many x/u operations may be generated as a first IP
                // if for all turns x/u was generated and any of the Polygons doesn't contain the LineString
                // then we know that the LineString is outside
                // Similar with the u/u turns, if it was the first one it doesn't mean that the
                // Linestring came from the exterior
                if ( ( m_previous_operation == overlay::operation_blocked
                    && ( op != overlay::operation_blocked // operation different than block
                        || seg_id.multi_index != m_previous_turn_ptr->operations[op_id].seg_id.multi_index ) ) // or the next single-geometry
                  || ( m_previous_operation == overlay::operation_union
                    && ! turn_on_the_same_ip<op_id>(*m_previous_turn_ptr, *it) )
                   )
                {
                    update<interior, exterior, '1', TransposeResult>(res);
                    if ( m_first_from_unknown_boundary_detected )
                    {
                        update<boundary, exterior, '0', TransposeResult>(res);
                    }

                    m_first_from_unknown = false;
                    m_first_from_unknown_boundary_detected = false;
                }
            }

// NOTE: THE WHOLE m_interior_detected HANDLING IS HERE BECAUSE WE CAN'T EFFICIENTLY SORT TURNS (CORRECTLY)
// BECAUSE THE SAME IP MAY BE REPRESENTED BY TWO SEGMENTS WITH DIFFERENT DISTANCES
// IT WOULD REQUIRE THE CALCULATION OF MAX DISTANCE
// TODO: WE COULD GET RID OF THE TEST IF THE DISTANCES WERE NORMALIZED

// UPDATE: THEY SHOULD BE NORMALIZED NOW

// TODO: THIS IS POTENTIALLY ERROREOUS!
// THIS ALGORITHM DEPENDS ON SOME SPECIFIC SEQUENCE OF OPERATIONS
// IT WOULD GIVE WRONG RESULTS E.G.
// IN THE CASE OF SELF-TOUCHING POINT WHEN 'i' WOULD BE BEFORE 'u' 

            // handle the interior overlap
            if ( m_interior_detected )
            {
                BOOST_GEOMETRY_ASSERT_MSG(m_previous_turn_ptr, "non-NULL ptr expected");

                // real interior overlap
                if ( ! turn_on_the_same_ip<op_id>(*m_previous_turn_ptr, *it) )
                {
                    update<interior, interior, '1', TransposeResult>(res);
                    m_interior_detected = false;

                    // new range detected - reset previous state and check the boundary
                    if ( first_in_range )
                    {
                        segment_identifier const& prev_seg_id = m_previous_turn_ptr->operations[op_id].seg_id;

                        bool const prev_back_b = is_endpoint_on_boundary<boundary_back>(
                                                    range::back(sub_range(geometry, prev_seg_id)),
                                                    boundary_checker);

                        // if there is a boundary on the last point
                        if ( prev_back_b )
                        {
                            update<boundary, interior, '0', TransposeResult>(res);
                        }

                        // The exit_watcher is reset below
                        // m_exit_watcher.reset();
                    }
                }
                // fake interior overlap
                else if ( op == overlay::operation_continue )
                {
                    m_interior_detected = false;
                }
                else if ( op == overlay::operation_union )
                {
// TODO: this probably is not a good way of handling the interiors/enters
//       the solution similar to exit_watcher would be more robust
//       all enters should be kept and handled.
//       maybe integrate it with the exit_watcher -> enter_exit_watcher
                    if ( m_first_interior_other_id_ptr
                      && m_first_interior_other_id_ptr->multi_index == other_id.multi_index )
                    {
                        m_interior_detected = false;
                    }
                }
            }

            // NOTE: If post-last-ip apply() was called this wouldn't be needed
            if ( first_in_range )
            {
                m_exit_watcher.reset();
                m_boundary_counter = 0;
                m_first_from_unknown = false;
                m_first_from_unknown_boundary_detected = false;
            }

            // i/u, c/u
            if ( op == overlay::operation_intersection
              || op == overlay::operation_continue ) // operation_boundary/operation_boundary_intersection
            {
                bool const first_point = first_in_range || m_first_from_unknown;
                bool no_enters_detected = m_exit_watcher.is_outside();
                m_exit_watcher.enter(*it);

                if ( op == overlay::operation_intersection )
                {
                    if ( m_boundary_counter > 0 && it->operations[op_id].is_collinear )
                        --m_boundary_counter;

                    if ( m_boundary_counter == 0 )
                    {
                        // interiors overlaps
                        //update<interior, interior, '1', TransposeResult>(res);

// TODO: think about the implementation of the more robust version
//       this way only the first enter will be handled
                        if ( !m_interior_detected )
                        {
                            // don't update now
                            // we might enter a boundary of some other ring on the same IP
                            m_interior_detected = true;
                            m_first_interior_other_id_ptr = boost::addressof(other_id);
                        }
                    }
                }
                else // operation_boundary
                {
                    // don't add to the count for all met boundaries
                    // only if this is the "new" boundary
                    if ( first_point || !it->operations[op_id].is_collinear )
                        ++m_boundary_counter;

                    update<interior, boundary, '1', TransposeResult>(res);
                }

                bool const this_b
                    = is_ip_on_boundary<boundary_front>(it->point,
                                                        it->operations[op_id],
                                                        boundary_checker,
                                                        seg_id);
                // going inside on boundary point
                if ( this_b )
                {
                    update<boundary, boundary, '0', TransposeResult>(res);
                }
                // going inside on non-boundary point
                else
                {
                    update<interior, boundary, '0', TransposeResult>(res);

                    // if we didn't enter in the past, we were outside
                    if ( no_enters_detected
                      && ! fake_enter_detected
                      && it->operations[op_id].position != overlay::position_front )
                    {
// TODO: calculate_from_inside() is only needed if the current Linestring is not closed
                        bool const from_inside = first_point
                                              && calculate_from_inside(geometry,
                                                                       other_geometry,
                                                                       *it,
                                                                       side_strategy);

                        if ( from_inside )
                            update<interior, interior, '1', TransposeResult>(res);
                        else
                            update<interior, exterior, '1', TransposeResult>(res);

                        // if it's the first IP then the first point is outside
                        if ( first_point )
                        {
                            bool const front_b = is_endpoint_on_boundary<boundary_front>(
                                                    range::front(sub_range(geometry, seg_id)),
                                                    boundary_checker);

                            // if there is a boundary on the first point
                            if ( front_b )
                            {
                                if ( from_inside )
                                    update<boundary, interior, '0', TransposeResult>(res);
                                else
                                    update<boundary, exterior, '0', TransposeResult>(res);
                            }
                        }
                    }
                }

                if ( BOOST_GEOMETRY_CONDITION( is_multi<OtherGeometry>::value ) )
                {
                    m_first_from_unknown = false;
                    m_first_from_unknown_boundary_detected = false;
                }
            }
            // u/u, x/u
            else if ( op == overlay::operation_union || op == overlay::operation_blocked )
            {
                bool const op_blocked = op == overlay::operation_blocked;
                bool const no_enters_detected = m_exit_watcher.is_outside()
// TODO: is this condition ok?
// TODO: move it into the exit_watcher?
                    && m_exit_watcher.get_exit_operation() == overlay::operation_none;
                    
                if ( op == overlay::operation_union )
                {
                    if ( m_boundary_counter > 0 && it->operations[op_id].is_collinear )
                        --m_boundary_counter;
                }
                else // overlay::operation_blocked
                {
                    m_boundary_counter = 0;
                }

                // we're inside, possibly going out right now
                if ( ! no_enters_detected )
                {
                    if ( op_blocked
                      && it->operations[op_id].position == overlay::position_back ) // ignore spikes!
                    {
                        // check if this is indeed the boundary point
                        // NOTE: is_ip_on_boundary<>() should be called here but the result will be the same
                        if ( is_endpoint_on_boundary<boundary_back>(it->point, boundary_checker) )
                        {
                            update<boundary, boundary, '0', TransposeResult>(res);
                        }
                    }
                    // union, inside, but no exit -> collinear on self-intersection point
                    // not needed since we're already inside the boundary
                    /*else if ( !exit_detected )
                    {
                        update<interior, boundary, '0', TransposeResult>(res);
                    }*/
                }
                // we're outside or inside and this is the first turn
                else
                {
                    bool const this_b = is_ip_on_boundary<boundary_any>(it->point,
                                                                        it->operations[op_id],
                                                                        boundary_checker,
                                                                        seg_id);
                    // if current IP is on boundary of the geometry
                    if ( this_b )
                    {
                        update<boundary, boundary, '0', TransposeResult>(res);
                    }
                    // if current IP is not on boundary of the geometry
                    else
                    {
                        update<interior, boundary, '0', TransposeResult>(res);
                    }

                    // TODO: very similar code is used in the handling of intersection
                    if ( it->operations[op_id].position != overlay::position_front )
                    {
// TODO: calculate_from_inside() is only needed if the current Linestring is not closed
                        // NOTE: this is not enough for MultiPolygon and operation_blocked
                        // For LS/MultiPolygon multiple x/u turns may be generated
                        // the first checked Polygon may be the one which LS is outside for.
                        bool const first_point = first_in_range || m_first_from_unknown;
                        bool const first_from_inside = first_point
                                                    && calculate_from_inside(geometry,
                                                                             other_geometry,
                                                                             *it,
                                                                             side_strategy);
                        if ( first_from_inside )
                        {
                            update<interior, interior, '1', TransposeResult>(res);

                            // notify the exit_watcher that we started inside
                            m_exit_watcher.enter(*it);
                            // and reset unknown flags since we know that we started inside
                            m_first_from_unknown = false;
                            m_first_from_unknown_boundary_detected = false;
                        }
                        else
                        {
                            if ( BOOST_GEOMETRY_CONDITION( is_multi<OtherGeometry>::value )
                              /*&& ( op == overlay::operation_blocked
                                || op == overlay::operation_union )*/ ) // if we're here it's u or x
                            {
                                m_first_from_unknown = true;
                            }
                            else
                            {
                                update<interior, exterior, '1', TransposeResult>(res);
                            }
                        }

                        // first IP on the last segment point - this means that the first point is outside or inside
                        if ( first_point && ( !this_b || op_blocked ) )
                        {
                            bool const front_b = is_endpoint_on_boundary<boundary_front>(
                                                    range::front(sub_range(geometry, seg_id)),
                                                    boundary_checker);

                            // if there is a boundary on the first point
                            if ( front_b )
                            {
                                if ( first_from_inside )
                                {
                                    update<boundary, interior, '0', TransposeResult>(res);
                                }
                                else
                                {
                                    if ( BOOST_GEOMETRY_CONDITION( is_multi<OtherGeometry>::value )
                                      /*&& ( op == overlay::operation_blocked
                                        || op == overlay::operation_union )*/ ) // if we're here it's u or x
                                    {
                                        BOOST_GEOMETRY_ASSERT(m_first_from_unknown);
                                        m_first_from_unknown_boundary_detected = true;
                                    }
                                    else
                                    {
                                        update<boundary, exterior, '0', TransposeResult>(res);
                                    }
                                }
                            }
                        }
                    }
                }

                // if we're going along a boundary, we exit only if the linestring was collinear
                if ( m_boundary_counter == 0
                  || it->operations[op_id].is_collinear )
                {
                    // notify the exit watcher about the possible exit
                    m_exit_watcher.exit(*it);
                }
            }

            // store ref to previously analysed (valid) turn
            m_previous_turn_ptr = boost::addressof(*it);
            // and previously analysed (valid) operation
            m_previous_operation = op;
        }

        // it == last
        template <typename Result,
                  typename TurnIt,
                  typename Geometry,
                  typename OtherGeometry,
                  typename BoundaryChecker>
        void apply(Result & res,
                   TurnIt first, TurnIt last,
                   Geometry const& geometry,
                   OtherGeometry const& /*other_geometry*/,
                   BoundaryChecker const& boundary_checker)
        {
            boost::ignore_unused(first, last);
            //BOOST_GEOMETRY_ASSERT( first != last );

            // For MultiPolygon many x/u operations may be generated as a first IP
            // if for all turns x/u was generated and any of the Polygons doesn't contain the LineString
            // then we know that the LineString is outside
            if ( BOOST_GEOMETRY_CONDITION( is_multi<OtherGeometry>::value )
              && m_first_from_unknown )
            {
                update<interior, exterior, '1', TransposeResult>(res);
                if ( m_first_from_unknown_boundary_detected )
                {
                    update<boundary, exterior, '0', TransposeResult>(res);
                }

                // done below
                //m_first_from_unknown = false;
                //m_first_from_unknown_boundary_detected = false;
            }

            // here, the possible exit is the real one
            // we know that we entered and now we exit
            if ( /*m_exit_watcher.get_exit_operation() == overlay::operation_union // THIS CHECK IS REDUNDANT
                ||*/ m_previous_operation == overlay::operation_union
                && !m_interior_detected )
            {
                // for sure
                update<interior, exterior, '1', TransposeResult>(res);

                BOOST_GEOMETRY_ASSERT(first != last);
                BOOST_GEOMETRY_ASSERT(m_previous_turn_ptr);

                segment_identifier const& prev_seg_id = m_previous_turn_ptr->operations[op_id].seg_id;

                bool const prev_back_b = is_endpoint_on_boundary<boundary_back>(
                                            range::back(sub_range(geometry, prev_seg_id)),
                                            boundary_checker);

                // if there is a boundary on the last point
                if ( prev_back_b )
                {
                    update<boundary, exterior, '0', TransposeResult>(res);
                }
            }
            // we might enter some Areal and didn't go out,
            else if ( m_previous_operation == overlay::operation_intersection
                   || m_interior_detected )
            {
                // just in case
                update<interior, interior, '1', TransposeResult>(res);
                m_interior_detected = false;

                BOOST_GEOMETRY_ASSERT(first != last);
                BOOST_GEOMETRY_ASSERT(m_previous_turn_ptr);

                segment_identifier const& prev_seg_id = m_previous_turn_ptr->operations[op_id].seg_id;

                bool const prev_back_b = is_endpoint_on_boundary<boundary_back>(
                                            range::back(sub_range(geometry, prev_seg_id)),
                                            boundary_checker);

                // if there is a boundary on the last point
                if ( prev_back_b )
                {
                    update<boundary, interior, '0', TransposeResult>(res);
                }
            }

            // This condition may be false if the Linestring is lying on the Polygon's collinear spike
            // if Polygon's spikes are not handled in get_turns() or relate() (they currently aren't)
            //BOOST_GEOMETRY_ASSERT_MSG(m_previous_operation != overlay::operation_continue,
            //                    "Unexpected operation! Probably the error in get_turns(L,A) or relate(L,A)");
            // Currently one c/c turn is generated for the exit
            //   when a Linestring is going out on a collinear spike
            // When a Linestring is going in on a collinear spike
            //   the turn is not generated for the entry
            // So assume it's the former
            if ( m_previous_operation == overlay::operation_continue )
            {
                update<interior, exterior, '1', TransposeResult>(res);

                segment_identifier const& prev_seg_id = m_previous_turn_ptr->operations[op_id].seg_id;

                bool const prev_back_b = is_endpoint_on_boundary<boundary_back>(
                                            range::back(sub_range(geometry, prev_seg_id)),
                                            boundary_checker);

                // if there is a boundary on the last point
                if ( prev_back_b )
                {
                    update<boundary, exterior, '0', TransposeResult>(res);
                }
            }

            // Reset exit watcher before the analysis of the next Linestring
            m_exit_watcher.reset();
            m_boundary_counter = 0;
            m_first_from_unknown = false;
            m_first_from_unknown_boundary_detected = false;
        }

        // check if the passed turn's segment of Linear geometry arrived
        // from the inside or the outside of the Areal geometry
        template <typename Turn, typename SideStrategy>
        static inline bool calculate_from_inside(Geometry1 const& geometry1,
                                                 Geometry2 const& geometry2,
                                                 Turn const& turn,
                                                 SideStrategy const& side_strategy)
        {
            typedef typename cs_tag<typename Turn::point_type>::type cs_tag;

            if ( turn.operations[op_id].position == overlay::position_front )
                return false;

            typename sub_range_return_type<Geometry1 const>::type
                range1 = sub_range(geometry1, turn.operations[op_id].seg_id);
            
            typedef detail::normalized_view<Geometry2 const> const range2_type;
            typedef typename boost::range_iterator<range2_type>::type range2_iterator;
            range2_type range2(sub_range(geometry2, turn.operations[other_op_id].seg_id));
            
            BOOST_GEOMETRY_ASSERT(boost::size(range1));
            std::size_t const s2 = boost::size(range2);
            BOOST_GEOMETRY_ASSERT(s2 > 2);
            std::size_t const seg_count2 = s2 - 1;

            std::size_t const p_seg_ij = static_cast<std::size_t>(turn.operations[op_id].seg_id.segment_index);
            std::size_t const q_seg_ij = static_cast<std::size_t>(turn.operations[other_op_id].seg_id.segment_index);

            BOOST_GEOMETRY_ASSERT(p_seg_ij + 1 < boost::size(range1));
            BOOST_GEOMETRY_ASSERT(q_seg_ij + 1 < s2);

            point1_type const& pi = range::at(range1, p_seg_ij);
            point2_type const& qi = range::at(range2, q_seg_ij);
            point2_type const& qj = range::at(range2, q_seg_ij + 1);
            point1_type qi_conv;
            geometry::convert(qi, qi_conv);
            bool const is_ip_qj = equals::equals_point_point(turn.point, qj);
// TODO: test this!
//            BOOST_GEOMETRY_ASSERT(!equals::equals_point_point(turn.point, pi));
//            BOOST_GEOMETRY_ASSERT(!equals::equals_point_point(turn.point, qi));
            point1_type new_pj;
            geometry::convert(turn.point, new_pj);

            if ( is_ip_qj )
            {
                std::size_t const q_seg_jk = (q_seg_ij + 1) % seg_count2;
// TODO: the following function should return immediately, however the worst case complexity is O(N)
// It would be good to replace it with some O(1) mechanism
                range2_iterator qk_it = find_next_non_duplicated(boost::begin(range2),
                                                                 range::pos(range2, q_seg_jk),
                                                                 boost::end(range2));

                // Will this sequence of points be always correct?
                overlay::side_calculator<cs_tag, point1_type, point2_type, SideStrategy>
                    side_calc(qi_conv, new_pj, pi, qi, qj, *qk_it, side_strategy);

                return calculate_from_inside_sides(side_calc);
            }
            else
            {
                point2_type new_qj;
                geometry::convert(turn.point, new_qj);

                overlay::side_calculator<cs_tag, point1_type, point2_type, SideStrategy>
                    side_calc(qi_conv, new_pj, pi, qi, new_qj, qj, side_strategy);

                return calculate_from_inside_sides(side_calc);
            }
        }

        template <typename It>
        static inline It find_next_non_duplicated(It first, It current, It last)
        {
            BOOST_GEOMETRY_ASSERT( current != last );

            It it = current;

            for ( ++it ; it != last ; ++it )
            {
                if ( !equals::equals_point_point(*current, *it) )
                    return it;
            }

            // if not found start from the beginning
            for ( it = first ; it != current ; ++it )
            {
                if ( !equals::equals_point_point(*current, *it) )
                    return it;
            }

            return current;
        }

        // calculate inside or outside based on side_calc
        // this is simplified version of a check from equal<>
        template <typename SideCalc>
        static inline bool calculate_from_inside_sides(SideCalc const& side_calc)
        {
            int const side_pk_p = side_calc.pk_wrt_p1();
            int const side_qk_p = side_calc.qk_wrt_p1();
            // If they turn to same side (not opposite sides)
            if (! overlay::base_turn_handler::opposite(side_pk_p, side_qk_p))
            {
                int const side_pk_q2 = side_calc.pk_wrt_q2();
                return side_pk_q2 == -1;
            }
            else
            {
                return side_pk_p == -1;
            }
        }

    private:
        exit_watcher<TurnInfo, op_id> m_exit_watcher;
        segment_watcher<same_single> m_seg_watcher;
        TurnInfo * m_previous_turn_ptr;
        overlay::operation_type m_previous_operation;
        unsigned m_boundary_counter;
        bool m_interior_detected;
        const segment_identifier * m_first_interior_other_id_ptr;
        bool m_first_from_unknown;
        bool m_first_from_unknown_boundary_detected;
    };

    // call analyser.apply() for each turn in range
    // IMPORTANT! The analyser is also called for the end iterator - last
    template <typename Result,
              typename TurnIt,
              typename Analyser,
              typename Geometry,
              typename OtherGeometry,
              typename BoundaryChecker,
              typename SideStrategy>
    static inline void analyse_each_turn(Result & res,
                                         Analyser & analyser,
                                         TurnIt first, TurnIt last,
                                         Geometry const& geometry,
                                         OtherGeometry const& other_geometry,
                                         BoundaryChecker const& boundary_checker,
                                         SideStrategy const& side_strategy)
    {
        if ( first == last )
            return;

        for ( TurnIt it = first ; it != last ; ++it )
        {
            analyser.apply(res, it,
                           geometry, other_geometry,
                           boundary_checker,
                           side_strategy);

            if ( BOOST_GEOMETRY_CONDITION( res.interrupt ) )
                return;
        }

        analyser.apply(res, first, last,
                       geometry, other_geometry,
                       boundary_checker);
    }

    // less comparator comparing multi_index then ring_index
    // may be used to sort turns by ring
    struct less_ring
    {
        template <typename Turn>
        inline bool operator()(Turn const& left, Turn const& right) const
        {
            return left.operations[1].seg_id.multi_index < right.operations[1].seg_id.multi_index
                || ( left.operations[1].seg_id.multi_index == right.operations[1].seg_id.multi_index
                  && left.operations[1].seg_id.ring_index < right.operations[1].seg_id.ring_index );
        }
    };

    // policy/functor checking if a turn's operation is operation_continue
    struct has_boundary_intersection
    {
        has_boundary_intersection()
            : result(false) {}

        template <typename Turn>
        inline void operator()(Turn const& turn)
        {
            if ( turn.operations[1].operation == overlay::operation_continue )
                result = true;
        }

        bool result;
    };

    // iterate through the range and search for the different multi_index or ring_index
    // also call fun for each turn in the current range
    template <typename It, typename Fun>
    static inline It find_next_ring(It first, It last, Fun & fun)
    {
        if ( first == last )
            return last;

        signed_size_type const multi_index = first->operations[1].seg_id.multi_index;
        signed_size_type const ring_index = first->operations[1].seg_id.ring_index;

        fun(*first);
        ++first;

        for ( ; first != last ; ++first )
        {
            if ( multi_index != first->operations[1].seg_id.multi_index
              || ring_index != first->operations[1].seg_id.ring_index )
            {
                return first;
            }

            fun(*first);
        }

        return last;
    }

    // analyser which called for turns sorted by seg/distance/operation
    // checks if the boundary of Areal geometry really got out
    // into the exterior of Linear geometry
    template <typename TurnInfo>
    class areal_boundary_analyser
    {
    public:
        areal_boundary_analyser()
            : is_union_detected(false)
            , m_previous_turn_ptr(NULL)
        {}

        template <typename TurnIt>
        bool apply(TurnIt /*first*/, TurnIt it, TurnIt last)
        {
            overlay::operation_type op = it->operations[1].operation;

            if ( it != last )
            {
                if ( op != overlay::operation_union
                  && op != overlay::operation_continue )
                {
                    return true;
                }

                if ( is_union_detected )
                {
                    BOOST_GEOMETRY_ASSERT(m_previous_turn_ptr != NULL);
                    if ( !detail::equals::equals_point_point(it->point, m_previous_turn_ptr->point) )
                    {
                        // break
                        return false;
                    }
                    else if ( op == overlay::operation_continue ) // operation_boundary
                    {
                        is_union_detected = false;
                    }
                }

                if ( op == overlay::operation_union )
                {
                    is_union_detected = true;
                    m_previous_turn_ptr = boost::addressof(*it);
                }

                return true;
            }
            else
            {
                return false;
            }            
        }

        bool is_union_detected;

    private:
        const TurnInfo * m_previous_turn_ptr;
    };
};

template <typename Geometry1, typename Geometry2>
struct areal_linear
{
    typedef linear_areal<Geometry2, Geometry1, true> linear_areal_type;

    static const bool interruption_enabled = linear_areal_type::interruption_enabled;

    template <typename Result, typename IntersectionStrategy>
    static inline void apply(Geometry1 const& geometry1, Geometry2 const& geometry2,
                             Result & result,
                             IntersectionStrategy const& intersection_strategy)
    {
        linear_areal_type::apply(geometry2, geometry1, result, intersection_strategy);
    }
};

}} // namespace detail::relate
#endif // DOXYGEN_NO_DETAIL

}} // namespace boost::geometry

#endif // BOOST_GEOMETRY_ALGORITHMS_DETAIL_RELATE_LINEAR_AREAL_HPP