ceph/src/boost/libs/geometry/test/algorithms/is_valid.cpp

   1 // Boost.Geometry (aka GGL, Generic Geometry Library)
   2 // Unit Test
   3
   4 // Copyright (c) 2014-2021, Oracle and/or its affiliates.
   5
   6 // Contributed and/or modified by Menelaos Karavelas, on behalf of Oracle
   7 // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
   8
   9 // Licensed under the Boost Software License version 1.0.
  10 // http://www.boost.org/users/license.html
  11
  12 #ifndef BOOST_TEST_MODULE
  13 #define BOOST_TEST_MODULE test_is_valid
  14 #endif
  15
  16 #include <limits>
  17 #include <iostream>
  18
  19 #include <boost/test/included/unit_test.hpp>
  20
  21 #if defined(TEST_WITH_SVG)
  22 #  include <boost/geometry/io/svg/svg_mapper.hpp>
  23 #else
  24 #  include <boost/core/ignore_unused.hpp>
  25 #endif
  26
  27 #include "geometry_test_common.hpp"
  28 #include "test_is_valid.hpp"
  29 #include "overlay/overlay_cases.hpp"
  30
  31 #include <boost/geometry/core/coordinate_type.hpp>
  32
  33 #include <boost/geometry/algorithms/correct.hpp>
  34 #include <boost/geometry/algorithms/intersection.hpp>
  35 #include <boost/geometry/algorithms/reverse.hpp>
  36
  37 #include <boost/geometry/geometries/geometry_collection.hpp>
  38
  39 template <typename Geometry>
  40 void geometry_to_svg(Geometry const& geometry, const std::string& case_id)
  41 {
  42 #if defined(TEST_WITH_SVG)
  43     {
  44         using point_type = typename bg::point_type<Geometry>::type;
  45
  46         std::ostringstream filename;
  47         filename << "/tmp/svg/" << case_id << ".svg";
  48         std::ofstream svg(filename.str().c_str());
  49         bg::svg_mapper<point_type> mapper(svg, 1200, 800);
  50         mapper.add(geometry);
  51         mapper.map(geometry, "fill-opacity:0.5;fill:rgb(153,204,0);"
  52                 "stroke:rgb(153,204,0);stroke-width:1");
  53
  54         // Get self-turns and map them
  55
  56         using turn_info = bg::detail::overlay::turn_info
  57         <
  58             point_type,
  59             typename bg::detail::segment_ratio_type<point_type, bg::detail::no_rescale_policy>::type
  60         >;
  61         using strategy_type = typename bg::strategies::relate::services::default_strategy
  62             <
  63                 Geometry, Geometry
  64             >::type;
  65
  66
  67         strategy_type strategy;
  68
  69 #if defined(BOOST_GEOMETRY_NO_ROBUSTNESS)
  70         bg::detail::no_rescale_policy rescale_policy;
  71 #else
  72         using rescale_policy_type = typename bg::rescale_policy_type<point_type>::type;
  73         rescale_policy_type rescale_policy = bg::get_rescale_policy<rescale_policy_type>(geometry, strategy);
  74 #endif
  75
  76         std::vector<turn_info> turns;
  77
  78         bg::detail::self_get_turn_points::no_interrupt_policy policy;
  79         bg::self_turns
  80             <
  81                 bg::detail::overlay::assign_null_policy
  82             >(geometry, strategy,  rescale_policy, turns, policy);
  83
  84         for (turn_info const& turn : turns)
  85         {
  86             if (turn.method == bg::detail::overlay::method_none)
  87             {
  88                 continue;
  89             }
  90
  91             mapper.map(turn.point, "fill:rgb(255,128,0);stroke:rgb(0,0,100);stroke-width:1", 2);
  92             std::ostringstream out;
  93             out << bg::method_char(turn.method)
  94                 << std::setprecision(16) << " " << bg::get<0>(turn.point) << " " << bg::get<1>(turn.point);
  95             mapper.text(turn.point, out.str(), "fill:rgb(0,0,0);font-family:Arial;font-size:10px", 5, 5);
  96         }
  97     }
  98 #else
  99     boost::ignore_unused(geometry, case_id);
 100 #endif
 101
 102 }
 103
 104 BOOST_AUTO_TEST_CASE( test_is_valid_point )
 105 {
 106 #ifdef BOOST_GEOMETRY_TEST_DEBUG
 107     std::cout << std::endl << std::endl;
 108     std::cout << "************************************" << std::endl;
 109     std::cout << " is_valid: POINT " << std::endl;
 110     std::cout << "************************************" << std::endl;
 111 #endif
 112
 113     typedef point_type G;
 114     typedef default_validity_tester tester;
 115     typedef test_valid<tester, G> test;
 116
 117     test::apply("p01", "POINT(0 0)", true);
 118 }
 119
 120 BOOST_AUTO_TEST_CASE( test_is_valid_multipoint )
 121 {
 122 #ifdef BOOST_GEOMETRY_TEST_DEBUG
 123     std::cout << std::endl << std::endl;
 124     std::cout << "************************************" << std::endl;
 125     std::cout << " is_valid: MULTIPOINT " << std::endl;
 126     std::cout << "************************************" << std::endl;
 127 #endif
 128
 129     typedef multi_point_type G;
 130     typedef default_validity_tester tester;
 131     typedef test_valid<tester, G> test;
 132
 133     test::apply("mp01", "MULTIPOINT()", true);
 134     test::apply("mp02", "MULTIPOINT(0 0,0 0)", true);
 135     test::apply("mp03", "MULTIPOINT(0 0,1 0,1 1,0 1)", true);
 136     test::apply("mp04", "MULTIPOINT(0 0,1 0,1 1,1 0,0 1)", true);
 137 }
 138
 139 BOOST_AUTO_TEST_CASE( test_is_valid_segment )
 140 {
 141 #ifdef BOOST_GEOMETRY_TEST_DEBUG
 142     std::cout << std::endl << std::endl;
 143     std::cout << "************************************" << std::endl;
 144     std::cout << " is_valid: SEGMENT " << std::endl;
 145     std::cout << "************************************" << std::endl;
 146 #endif
 147
 148     typedef segment_type G;
 149     typedef default_validity_tester tester;
 150     typedef test_valid<tester, G> test;
 151
 152     test::apply("s01", "SEGMENT(0 0,0 0)", false);
 153     test::apply("s02", "SEGMENT(0 0,1 0)", true);
 154 }
 155
 156 BOOST_AUTO_TEST_CASE( test_is_valid_box )
 157 {
 158 #ifdef BOOST_GEOMETRY_TEST_DEBUG
 159     std::cout << std::endl << std::endl;
 160     std::cout << "************************************" << std::endl;
 161     std::cout << " is_valid: BOX " << std::endl;
 162     std::cout << "************************************" << std::endl;
 163 #endif
 164
 165     typedef box_type G;
 166     typedef default_validity_tester tester;
 167     typedef test_valid<tester, G> test;
 168
 169     // boxes where the max corner and below and/or to the left of min corner
 170     test::apply("b01", "BOX(0 0,-1 0)", false);
 171     test::apply("b02", "BOX(0 0,0 -1)", false);
 172     test::apply("b03", "BOX(0 0,-1 -1)", false);
 173
 174     // boxes of zero area; they are not 2-dimensional, so invalid
 175     test::apply("b04", "BOX(0 0,0 0)", false);
 176     test::apply("b05", "BOX(0 0,1 0)", false);
 177     test::apply("b06", "BOX(0 0,0 1)", false);
 178
 179     test::apply("b07", "BOX(0 0,1 1)", true);
 180 }
 181
 182 template <typename G, bool AllowSpikes>
 183 void test_linestrings()
 184 {
 185 #ifdef BOOST_GEOMETRY_TEST_DEBUG
 186     std::cout << "SPIKES ALLOWED? "
 187               << std::boolalpha
 188               << AllowSpikes
 189               << std::noboolalpha
 190               << std::endl;
 191 #endif
 192
 193     typedef validity_tester_linear<AllowSpikes> tester;
 194     typedef test_valid<tester, G> test;
 195
 196     // empty linestring
 197     test::apply("l01", "LINESTRING()", false);
 198
 199     // 1-point linestrings
 200     test::apply("l02", "LINESTRING(0 0)", false);
 201     test::apply("l03", "LINESTRING(0 0,0 0)", false);
 202     test::apply("l04", "LINESTRING(0 0,0 0,0 0)", false);
 203
 204     // 2-point linestrings
 205     test::apply("l05", "LINESTRING(0 0,1 2)", true);
 206     test::apply("l06", "LINESTRING(0 0,1 2,1 2)", true);
 207     test::apply("l07", "LINESTRING(0 0,0 0,1 2,1 2)", true);
 208     test::apply("l08", "LINESTRING(0 0,0 0,0 0,1 2,1 2)", true);
 209
 210     // 3-point linestrings
 211     test::apply("l09", "LINESTRING(0 0,1 0,2 10)", true);
 212     test::apply("l10", "LINESTRING(0 0,1 0,2 10,0 0)", true);
 213     test::apply("l11", "LINESTRING(0 0,10 0,10 10,5 0)", true);
 214
 215     // linestrings with spikes
 216     test::apply("l12", "LINESTRING(0 0,1 2,0 0)", AllowSpikes);
 217     test::apply("l13", "LINESTRING(0 0,1 2,1 2,0 0)", AllowSpikes);
 218     test::apply("l14", "LINESTRING(0 0,0 0,1 2,1 2,0 0)", AllowSpikes);
 219     test::apply("l15", "LINESTRING(0 0,0 0,0 0,1 2,1 2,0 0,0 0)", AllowSpikes);
 220     test::apply("l16", "LINESTRING(0 0,10 0,5 0)", AllowSpikes);
 221     test::apply("l17", "LINESTRING(0 0,10 0,10 10,5 0,0 0)", AllowSpikes);
 222     test::apply("l18", "LINESTRING(0 0,10 0,10 10,5 0,4 0,6 0)", AllowSpikes);
 223     test::apply("l19", "LINESTRING(0 0,1 0,1 1,5 5,4 4)", AllowSpikes);
 224     test::apply("l20", "LINESTRING(0 0,1 0,1 1,5 5,4 4,6 6)", AllowSpikes);
 225     test::apply("l21", "LINESTRING(0 0,1 0,1 1,5 5,4 4,4 0)", AllowSpikes);
 226     test::apply("l22",
 227                 "LINESTRING(0 0,0 0,1 0,1 0,1 0,0 0,0 0,2 0)",
 228                 AllowSpikes);
 229     test::apply("l23",
 230                 "LINESTRING(0 0,1 0,0 0,2 0,0 0,3 0,0 0,4 0)",
 231                 AllowSpikes);
 232     test::apply("l24",
 233                 "LINESTRING(0 0,1 0,0 0,2 0,0 0,3 0,0 0,4 0,0 0)",
 234                 AllowSpikes);
 235
 236     // other examples
 237     test::apply("l25", "LINESTRING(0 0,10 0,10 10,5 0,4 0)", true);
 238     test::apply("l26", "LINESTRING(0 0,10 0,10 10,5 0,4 0,3 0)", true);
 239     test::apply("l27", "LINESTRING(0 0,10 0,10 10,5 0,4 0,-1 0)", true);
 240     test::apply("l28", "LINESTRING(0 0,1 0,1 1,-1 1,-1 0,0 0)", true);
 241     test::apply("l29", "LINESTRING(0 0,1 0,1 1,-1 1,-1 0,0.5 0)", true);
 242 }
 243
 244 BOOST_AUTO_TEST_CASE( test_is_valid_linestring )
 245 {
 246 #ifdef BOOST_GEOMETRY_TEST_DEBUG
 247     std::cout << std::endl << std::endl;
 248     std::cout << "************************************" << std::endl;
 249     std::cout << " is_valid: LINESTRING " << std::endl;
 250     std::cout << "************************************" << std::endl;
 251 #endif
 252
 253     bool const allow_spikes = true;
 254     bool const do_not_allow_spikes = !allow_spikes;
 255
 256     test_linestrings<linestring_type, allow_spikes>();
 257     test_linestrings<linestring_type, do_not_allow_spikes>();
 258 }
 259
 260 template <typename G, bool AllowSpikes>
 261 void test_multilinestrings()
 262 {
 263 #ifdef BOOST_GEOMETRY_TEST_DEBUG
 264     std::cout << "SPIKES ALLOWED? "
 265               << std::boolalpha
 266               << AllowSpikes
 267               << std::noboolalpha
 268               << std::endl;
 269 #endif
 270
 271     typedef validity_tester_linear<AllowSpikes> tester;
 272     typedef test_valid<tester, G> test;
 273
 274     // empty multilinestring
 275     test::apply("mls01", "MULTILINESTRING()", true);
 276
 277     // multilinestring with empty linestring(s)
 278     test::apply("mls02", "MULTILINESTRING(())", false);
 279     test::apply("mls03", "MULTILINESTRING((),(),())", false);
 280     test::apply("mls04", "MULTILINESTRING((),(0 1,1 0))", false);
 281
 282     // multilinestring with invalid linestrings
 283     test::apply("mls05", "MULTILINESTRING((0 0),(0 1,1 0))", false);
 284     test::apply("mls06", "MULTILINESTRING((0 0,0 0),(0 1,1 0))", false);
 285     test::apply("mls07", "MULTILINESTRING((0 0),(1 0))", false);
 286     test::apply("mls08", "MULTILINESTRING((0 0,0 0),(1 0,1 0))", false);
 287     test::apply("mls09", "MULTILINESTRING((0 0),(0 0))", false);
 288     test::apply("mls10", "MULTILINESTRING((0 0,1 0,0 0),(5 0))", false);
 289
 290     // multilinstring that has linestrings with spikes
 291     test::apply("mls11",
 292                 "MULTILINESTRING((0 0,1 0,0 0),(5 0,1 0,4 1))",
 293                 AllowSpikes);
 294     test::apply("mls12",
 295                 "MULTILINESTRING((0 0,1 0,0 0),(1 0,2 0))",
 296                 AllowSpikes);
 297
 298     // valid multilinestrings
 299     test::apply("mls13", "MULTILINESTRING((0 0,1 0,2 0),(5 0,1 0,4 1))", true);
 300     test::apply("mls14", "MULTILINESTRING((0 0,1 0,2 0),(1 0,2 0))", true);
 301     test::apply("mls15", "MULTILINESTRING((0 0,1 1),(0 1,1 0))", true);
 302     test::apply("mls16", "MULTILINESTRING((0 0,1 1,2 2),(0 1,1 0,2 2))", true);
 303 }
 304
 305 BOOST_AUTO_TEST_CASE( test_is_valid_multilinestring )
 306 {
 307 #ifdef BOOST_GEOMETRY_TEST_DEBUG
 308     std::cout << std::endl << std::endl;
 309     std::cout << "************************************" << std::endl;
 310     std::cout << " is_valid: MULTILINESTRING " << std::endl;
 311     std::cout << "************************************" << std::endl;
 312 #endif
 313
 314     bool const allow_spikes = true;
 315     bool const do_not_allow_spikes = !allow_spikes;
 316
 317     test_multilinestrings<multi_linestring_type, allow_spikes>();
 318     test_multilinestrings<multi_linestring_type, do_not_allow_spikes>();
 319 }
 320
 321 template <typename Point, bool AllowDuplicates>
 322 inline void test_open_rings()
 323 {
 324 #ifdef BOOST_GEOMETRY_TEST_DEBUG
 325     std::cout << std::endl << std::endl;
 326     std::cout << "************************************" << std::endl;
 327     std::cout << " is_valid: RING (open) " << std::endl;
 328     std::cout << "************************************" << std::endl;
 329     std::cout << "DUPLICATES ALLOWED? "
 330               << std::boolalpha
 331               << AllowDuplicates
 332               << std::noboolalpha
 333               << std::endl;
 334 #endif
 335
 336     typedef bg::model::ring<Point, false, false> OG; // ccw, open ring
 337     typedef bg::model::ring<Point, false, true> CG; // ccw, closed ring
 338     typedef bg::model::ring<Point, true, false> CW_OG; // cw, open ring
 339     typedef bg::model::ring<Point, true, true> CW_CG; // cw, closed ring
 340
 341     typedef validity_tester_areal<AllowDuplicates> tester;
 342     typedef test_valid<tester, OG, CG, CW_OG, CW_CG> test;
 343
 344     // not enough points
 345     test::apply("r01", "POLYGON(())", false);
 346     test::apply("r02", "POLYGON((0 0))", false);
 347     test::apply("r03", "POLYGON((0 0,1 0))", false);
 348
 349     // duplicate points
 350     test::apply("r04", "POLYGON((0 0,0 0,0 0))", false);
 351     test::apply("r05", "POLYGON((0 0,1 0,1 0))", false);
 352     test::apply("r06", "POLYGON((0 0,1 0,0 0))", false);
 353     test::apply("r07", "POLYGON((0 0,1 0,1 1,0 0,0 0))", AllowDuplicates);
 354     test::apply("r08", "POLYGON((0 0,1 0,1 0,1 1))", AllowDuplicates);
 355     test::apply("r09", "POLYGON((0 0,1 0,1 0,1 1,0 0))", AllowDuplicates);
 356
 357     // with spikes
 358     test::apply("r10", "POLYGON((0 0,2 0,2 2,0 2,1 2))", false);
 359     test::apply("r11", "POLYGON((0 0,2 0,1 0,2 2))", false);
 360     test::apply("r12", "POLYGON((0 0,1 0,2 0,1 0,4 0,4 4))", false);
 361     test::apply("r13", "POLYGON((0 0,2 0,2 2,1 0))", false);
 362     test::apply("r14", "POLYGON((0 0,2 0,1 0))", false);
 363     test::apply("r15", "POLYGON((0 0,5 0,5 5,4 4,5 5,0 5))", false);
 364     test::apply("r16", "POLYGON((0 0,5 0,5 5,4 4,3 3,5 5,0 5))", false);
 365
 366     // with spikes and duplicate points
 367     test::apply("r17", "POLYGON((0 0,0 0,2 0,2 0,1 0,1 0))", false);
 368
 369     // with self-crossings
 370     test::apply("r18", "POLYGON((0 0,5 0,5 5,3 -1,0 5))", false);
 371
 372     // with self-crossings and duplicate points
 373     test::apply("r19", "POLYGON((0 0,5 0,5 5,5 5,3 -1,0 5,0 5))", false);
 374
 375     // with self-intersections
 376     test::apply("r20", "POLYGON((0 0,5 0,5 5,3 5,3 0,2 0,2 5,0 5))", false);
 377
 378     test::apply("r21", "POLYGON((0 0,5 0,5 5,3 5,3 0,2 5,0 5))", false);
 379
 380     test::apply("r22",
 381                 "POLYGON((0 0,5 0,5 1,1 1,1 2,2 2,3 1,4 2,5 2,5 5,0 5))",
 382                 false);
 383
 384     // with self-intersections and duplicate points
 385     test::apply("r23",
 386                 "POLYGON((0 0,5 0,5 5,3 5,3 5,3 0,3 0,2 0,2 0,2 5,2 5,0 5))",
 387                 false);
 388
 389     // next two suggested by Adam Wulkiewicz
 390     test::apply("r24",
 391                 "POLYGON((0 0,5 0,5 5,0 5,4 4,2 2,0 5))",
 392                 false);
 393     test::apply("r25",
 394                 "POLYGON((0 0,5 0,5 5,1 4,4 4,4 1,0 5))",
 395                 false);
 396
 397     // and a few more
 398     test::apply("r26",
 399                 "POLYGON((0 0,5 0,5 5,4 4,1 4,1 1,4 1,4 4,0 5))",
 400                 false);
 401     test::apply("r27",
 402                 "POLYGON((0 0,5 0,5 5,4 4,4 1,1 1,1 4,4 4,0 5))",
 403                 false);
 404
 405     // valid rings
 406     test::apply("r28", "POLYGON((0 0,1 0,1 1))", true);
 407     test::apply("r29", "POLYGON((1 0,1 1,0 0))", true);
 408     test::apply("r30", "POLYGON((0 0,1 0,1 1,0 1))", true);
 409     test::apply("r31", "POLYGON((1 0,1 1,0 1,0 0))", true);
 410
 411     // test cases coming from buffer
 412     test::apply("r32",
 413                 "POLYGON((1.1713032141645456 -0.9370425713316364,\
 414                           5.1713032141645456 4.0629574286683638,\
 415                           4.7808688094430307 4.3753049524455756,\
 416                           4.7808688094430307 4.3753049524455756,\
 417                           0.7808688094430304 -0.6246950475544243,\
 418                           0.7808688094430304 -0.6246950475544243))",
 419                 AllowDuplicates);
 420
 421     // wrong orientation
 422     test::apply("r33", "POLYGON((0 0,0 1,1 1))", false);
 423
 424     // Normal case, plus spikes formed in two different ways
 425     test::apply("r34", "POLYGON((0 0,4 0,4 4,0 4,0 0))", true);
 426     test::apply("r35", "POLYGON((0 0,5 0,4 0,4 4,0 4,0 0))", false);
 427     test::apply("r36", "POLYGON((0 0,4 0,4 -1,4 4,0 4,0 0))", false);
 428 }
 429
 430
 431 template <typename Point, bool AllowDuplicates>
 432 inline void test_closed_rings()
 433 {
 434 #ifdef BOOST_GEOMETRY_TEST_DEBUG
 435     std::cout << std::endl << std::endl;
 436     std::cout << "************************************" << std::endl;
 437     std::cout << " is_valid: RING (closed) " << std::endl;
 438     std::cout << "************************************" << std::endl;
 439     std::cout << "DUPLICATES ALLOWED? "
 440               << std::boolalpha
 441               << AllowDuplicates
 442               << std::noboolalpha
 443               << std::endl;
 444 #endif
 445
 446     typedef bg::model::ring<Point, false, true> CG; // ccw, closed ring
 447     typedef bg::model::ring<Point, true, true> CW_CG; // cw, closed ring
 448
 449     typedef validity_tester_areal<AllowDuplicates> tester;
 450     typedef test_valid<tester, CG, CG, CW_CG> test;
 451
 452     // not enough points
 453     test::apply("r01c", "POLYGON(())", false);
 454     test::apply("r02c", "POLYGON((0 0))", false);
 455     test::apply("r03c", "POLYGON((0 0,0 0))", false);
 456     test::apply("r04c", "POLYGON((0 0,1 0))", false);
 457     test::apply("r05c", "POLYGON((0 0,1 0,1 0))", false);
 458     test::apply("r06c", "POLYGON((0 0,1 0,2 0))", false);
 459     test::apply("r07c", "POLYGON((0 0,1 0,1 0,2 0))", false);
 460     test::apply("r08c", "POLYGON((0 0,1 0,2 0,2 0))", false);
 461
 462     // boundary not closed
 463     test::apply("r09c", "POLYGON((0 0,1 0,1 1,1 2))", false);
 464     test::apply("r10c", "POLYGON((0 0,1 0,1 0,1 1,1 1,1 2))", false);
 465
 466     // with spikes
 467     test::apply("r11c", "POLYGON((0 0,1 0,1 0,2 0,0 0))", false);
 468     test::apply("r12c", "POLYGON((0 0,1 0,1 1,2 2,0.5 0.5,0 1,0 0))", false);
 469
 470     // wrong orientation
 471     test::apply("r13c", "POLYGON((0 0,0 1,1 1,2 0,0 0))", false);
 472 }
 473
 474 BOOST_AUTO_TEST_CASE( test_is_valid_ring )
 475 {
 476     bool const allow_duplicates = true;
 477     bool const do_not_allow_duplicates = !allow_duplicates;
 478
 479     test_open_rings<point_type, allow_duplicates>();
 480     test_open_rings<point_type, do_not_allow_duplicates>();
 481
 482     test_closed_rings<point_type, allow_duplicates>();
 483     test_closed_rings<point_type, do_not_allow_duplicates>();
 484 }
 485
 486 template <typename Point, bool AllowDuplicates>
 487 inline void test_open_polygons()
 488 {
 489 #ifdef BOOST_GEOMETRY_TEST_DEBUG
 490     std::cout << std::endl << std::endl;
 491     std::cout << "************************************" << std::endl;
 492     std::cout << " is_valid: POLYGON (open) " << std::endl;
 493     std::cout << "************************************" << std::endl;
 494     std::cout << "DUPLICATES ALLOWED? "
 495               << std::boolalpha
 496               << AllowDuplicates
 497               << std::noboolalpha
 498               << std::endl;
 499 #endif
 500
 501     typedef bg::model::polygon<Point, false, false> OG; // ccw, open
 502     typedef bg::model::polygon<Point, false, true> CG; // ccw, closed
 503     typedef bg::model::polygon<Point, true, false> CW_OG; // cw, open
 504     typedef bg::model::polygon<Point, true, true> CW_CG; // cw, closed
 505
 506     typedef validity_tester_areal<AllowDuplicates> tester;
 507     typedef test_valid<tester, OG, CG, CW_OG, CW_CG> test;
 508
 509     // not enough points in exterior ring
 510     test::apply("pg001", "POLYGON(())", false);
 511     test::apply("pg002", "POLYGON((0 0))", false);
 512     test::apply("pg003", "POLYGON((0 0,1 0))", false);
 513
 514     // not enough points in interior ring
 515     test::apply("pg004", "POLYGON((0 0,10 0,10 10,0 10),())", false);
 516     test::apply("pg005", "POLYGON((0 0,10 0,10 10,0 10),(1 1))", false);
 517     test::apply("pg006", "POLYGON((0 0,10 0,10 10,0 10),(1 1,2 2))", false);
 518
 519     // duplicate points in exterior ring
 520     test::apply("pg007", "POLYGON((0 0,0 0,0 0))", false);
 521     test::apply("pg008", "POLYGON((0 0,1 0,1 0))", false);
 522     test::apply("pg009", "POLYGON((0 0,1 0,0 0))", false);
 523     test::apply("pg010", "POLYGON((0 0,1 0,1 1,0 0,0 0))", AllowDuplicates);
 524     test::apply("pg011", "POLYGON((0 0,1 0,1 0,1 1))", AllowDuplicates);
 525     test::apply("pg012", "POLYGON((0 0,1 0,1 0,1 1,0 0))",  AllowDuplicates);
 526
 527     // duplicate points in interior ring
 528     test::apply("pg013", "POLYGON((0 0,10 0,10 10,0 10),(1 1,1 1,1 1))", false);
 529     test::apply("pg014", "POLYGON((0 0,10 0,10 10,0 10),(1 1,2 1,2 1))", false);
 530     test::apply("pg015", "POLYGON((0 0,10 0,10 10,0 10),(1 1,2 1,1 1))", false);
 531     test::apply("pg016",
 532                 "POLYGON((0 0,10 0,10 10,0 10),(1 1,2 2,2 1,1 1,1 1))",
 533                 AllowDuplicates);
 534     test::apply("pg017",
 535                 "POLYGON((0 0,10 0,10 10,0 10),(1 1,2 2,2 2,2 1))",
 536                 AllowDuplicates);
 537     test::apply("pg018",
 538                 "POLYGON((0 0,10 0,10 10,0 10),(1 1,2 2,2 1,2 1,1 1))",
 539                 AllowDuplicates);
 540
 541     // with spikes in exterior ring
 542     test::apply("pg019", "POLYGON((0 0,2 0,2 2,0 2,1 2))", false);
 543     test::apply("pg020", "POLYGON((0 0,2 0,1 0,2 2))", false);
 544     test::apply("pg021", "POLYGON((0 0,1 0,2 0,1 0,4 0,4 4))", false);
 545     test::apply("pg022", "POLYGON((0 0,2 0,2 2,1 0))", false);
 546     test::apply("pg023", "POLYGON((0 0,2 0,1 0))", false);
 547     test::apply("pg024", "POLYGON((0 0,5 0,5 5,4 4,5 5,0 5))", false);
 548     test::apply("pg025", "POLYGON((0 0,5 0,5 5,4 4,3 3,5 5,0 5))", false);
 549
 550     // with spikes in interior ring
 551     test::apply("pg026",
 552                 "POLYGON((0 0,10 0,10 10,0 10),(1 1,3 1,3 3,1 3,2 3))",
 553                 false);
 554     test::apply("pg027",
 555                 "POLYGON((0 0,10 0,10 10,0 10),(1 1,3 1,2 1,3 3))",
 556                 false);
 557     test::apply("pg028",
 558                 "POLYGON((0 0,10 0,10 10,0 10),(1 1,2 1,3 1,2 1,4 1,4 4))",
 559                 false);
 560     test::apply("pg029",
 561                 "POLYGON((0 0,10 0,10 10,0 10),(1 1,3 1,3 3,2 1))",
 562                 false);
 563     test::apply("pg030", "POLYGON((0 0,10 0,10 10,0 10),(1 1,3 1,2 1))", false);
 564
 565     // with self-crossings in exterior ring
 566     test::apply("pg031", "POLYGON((0 0,5 0,5 5,3 -1,0 5))", false);
 567
 568     // example from Norvald Ryeng
 569     test::apply("pg032",
 570                 "POLYGON((100 1300,140 1300,140 170,100 1700))",
 571                 false);
 572     // and with point order reversed
 573     test::apply("pg033",
 574                 "POLYGON((100 1300,100 1700,140 170,140 1300))",
 575                 false);
 576
 577     // with self-crossings in interior ring
 578     test::apply("pg034",
 579                 "POLYGON((0 0,10 0,10 10,0 10),(3 3,3 7,4 6,2 6))",
 580                 false);
 581
 582     // with self-crossings between rings
 583     test::apply("pg035", "POLYGON((0 0,5 0,5 5,0 5),(1 1,2 1,1 -1))", false);
 584
 585     // with self-intersections in exterior ring
 586     test::apply("pg036", "POLYGON((0 0,5 0,5 5,3 5,3 0,2 0,2 5,0 5))", false);
 587     test::apply("pg037", "POLYGON((0 0,5 0,5 5,3 5,3 0,2 5,0 5))", false);
 588     test::apply("pg038",
 589                 "POLYGON((0 0,5 0,5 1,1 1,1 2,2 2,3 1,4 2,5 2,5 5,0 5))",
 590                 false);
 591
 592     // next two suggested by Adam Wulkiewicz
 593     test::apply("pg039", "POLYGON((0 0,5 0,5 5,0 5,4 4,2 2,0 5))", false);
 594     test::apply("pg040", "POLYGON((0 0,5 0,5 5,1 4,4 4,4 1,0 5))", false);
 595     test::apply("pg041",
 596                 "POLYGON((0 0,5 0,5 5,4 4,1 4,1 1,4 1,4 4,0 5))",
 597                 false);
 598     test::apply("pg042",
 599                 "POLYGON((0 0,5 0,5 5,4 4,4 1,1 1,1 4,4 4,0 5))",
 600                 false);
 601
 602     // with self-intersections in interior ring
 603     test::apply("pg043",
 604                 "POLYGON((-10 -10,10 -10,10 10,-10 10),(0 0,5 0,5 5,3 5,3 0,2 0,2 5,0 5))",
 605                 false);
 606     test::apply("pg044",
 607                 "POLYGON((-10 -10,10 -10,10 10,-10 10),(0 0,5 0,5 5,3 5,3 0,2 5,0 5))",
 608                 false);
 609
 610     test::apply("pg045",
 611                 "POLYGON((-10 -10,10 -10,10 10,-10 10),(0 0,5 0,5 1,1 1,1 2,2 2,3 1,4 2,5 2,5 5,0 5))",
 612                 false);
 613
 614     // with self-intersections between rings
 615     // hole has common segment with exterior ring
 616     test::apply("pg046",
 617                 "POLYGON((0 0,10 0,10 10,0 10),(1 1,1 10,2 10,2 1))",
 618                 false);
 619     test::apply("pg047",
 620                 "POLYGON((0 0,0 0,10 0,10 10,0 10,0 10),(1 1,1 10,1 10,2 10,2 10,2 1))",
 621                 false);
 622     // hole touches exterior ring at one point
 623     test::apply("pg048", "POLYGON((0 0,10 0,10 10,0 10),(1 1,1 10,2 1))", true);
 624
 625     // "hole" is outside the exterior ring, but touches it
 626     test::apply("pg049",
 627                 "POLYGON((0 0,10 0,10 10,0 10),(5 10,4 11,6 11))",
 628                 false);
 629
 630     // hole touches exterior ring at vertex
 631     test::apply("pg050", "POLYGON((0 0,10 0,10 10,0 10),(0 0,1 4,4 1))", true);
 632
 633     // "hole" is completely outside the exterior ring
 634     test::apply("pg051",
 635                 "POLYGON((0 0,10 0,10 10,0 10),(20 20,20 21,21 21,21 20))",
 636                 false);
 637
 638     // two "holes" completely outside the exterior ring, that touch
 639     // each other
 640     test::apply("pg052",
 641                 "POLYGON((0 0,10 0,10 10,0 10),(20 0,25 10,21 0),(30 0,25 10,31 0))",
 642                 false);
 643
 644     // example from Norvald Ryeng
 645     test::apply("pg053",
 646                 "POLYGON((58 31,56.57 30,62 33),(35 9,28 14,31 16),(23 11,29 5,26 4))",
 647                 false);
 648     // and with points reversed
 649     test::apply("pg054",
 650                 "POLYGON((58 31,62 33,56.57 30),(35 9,31 16,28 14),(23 11,26 4,29 5))",
 651                 false);
 652
 653     // "hole" is completely inside another "hole"
 654     test::apply("pg055",
 655                 "POLYGON((0 0,10 0,10 10,0 10),(1 1,1 9,9 9,9 1),(2 2,2 8,8 8,8 2))",
 656                 false);
 657     test::apply("pg056",
 658                 "POLYGON((0 0,10 0,10 10,0 10),(1 1,1 9,9 9,9 1),(2 2,8 2,8 8,2 8))",
 659                 false);
 660
 661     // "hole" is inside another "hole" (touching)
 662     test::apply("pg057",
 663                 "POLYGON((0 0,10 0,10 10,0 10),(1 1,1 9,9 9,9 1),(2 2,2 8,8 8,9 6,8 2))",
 664                 false);
 665     test::apply("pg058",
 666                 "POLYGON((0 0,10 0,10 10,0 10),(1 1,1 9,9 9,9 1),(2 2,2 8,8 8,9 6,8 2))",
 667                 false);
 668     test::apply("pg058a",
 669                 "POLYGON((0 0,10 0,10 10,0 10),(1 1,1 9,9 9,9 1),(2 2,8 2,9 6,8 8,2 8))",
 670                 false);
 671     test::apply("pg059",
 672                 "POLYGON((0 0,10 0,10 10,0 10),(1 1,1 9,9 9,9 1),(2 2,2 8,8 8,9 6,8 2))",
 673                 false);
 674     test::apply("pg059a",
 675                 "POLYGON((0 0,10 0,10 10,0 10),(1 1,9 1,9 9,1 9),(2 2,2 8,8 8,9 6,8 2))",
 676                 false);
 677     test::apply("pg060",
 678                 "POLYGON((0 0,10 0,10 10,0 10),(1 1,1 9,9 9,9 1),(2 2,2 8,8 8,9 6,8 2))",
 679                 false);
 680     test::apply("pg060a",
 681                 "POLYGON((0 0,10 0,10 10,0 10),(1 1,9 1,9 9,1 9),(2 2,8 2,9 6,8 8,2 8))",
 682                 false);
 683     // hole touches exterior ring at two points
 684     test::apply("pg061", "POLYGON((0 0,10 0,10 10,0 10),(5 0,0 5,5 5))", false);
 685
 686     // cases with more holes
 687     // two holes, touching the exterior at the same point
 688     test::apply("pg062",
 689                 "POLYGON((0 0,10 0,10 10,0 10),(0 0,1 9,2 9),(0 0,9 2,9 1))",
 690                 true);
 691     test::apply("pg063",
 692                 "POLYGON((0 0,0 0,10 0,10 10,0 10,0 0),(0 0,0 0,1 9,2 9),(0 0,0 0,9 2,9 1))",
 693                 AllowDuplicates);
 694     test::apply("pg063",
 695                 "POLYGON((0 10,0 0,0 0,0 0,10 0,10 10),(2 9,0 0,0 0,1 9),(9 1,0 0,0 0,9 2))",
 696                 AllowDuplicates);
 697     // two holes, one inside the other
 698     test::apply("pg064",
 699                 "POLYGON((0 0,10 0,10 10,0 10),(0 0,1 9,9 1),(0 0,4 5,5 4))",
 700                 false);
 701     // 1st hole touches has common segment with 2nd hole
 702     test::apply("pg066",
 703                 "POLYGON((0 0,10 0,10 10,0 10),(1 1,1 5,5 5,5 1),(5 4,5 8,8 8,8 4))",
 704                 false);
 705     // 1st hole touches 2nd hole at two points
 706     test::apply("pg067",
 707                 "POLYGON((0 0,10 0,10 10,0 10),(1 1,1 9,9 9,9 8,2 8,2 1),(2 5,5 8,5 5))",
 708                 false);
 709     // polygon with many holes, where the last two touch at two points
 710     test::apply("pg068",
 711                 "POLYGON((0 0,20 0,20 20,0 20),(1 18,1 19,2 19,2 18),(3 18,3 19,4 19,4 18),(5 18,5 19,6 19,6 18),(7 18,7 19,8 19,8 18),(9 18,9 19,10 19,10 18),(11 18,11 19,12 19,12 18),(13 18,13 19,14 19,14 18),(15 18,15 19,16 19,16 18),(17 18,17 19,18 19,18 18),(1 1,1 9,9 9,9 8,2 8,2 1),(2 5,5 8,5 5))",
 712                 false);
 713     // two holes completely inside exterior ring but touching each
 714     // other at a point
 715     test::apply("pg069",
 716                 "POLYGON((0 0,10 0,10 10,0 10),(1 1,1 9,2 9),(1 1,9 2,9 1))",
 717                 true);
 718     // four holes, each two touching at different points
 719     test::apply("pg070",
 720                 "POLYGON((0 0,10 0,10 10,0 10),(0 10,2 1,1 1),(0 10,4 1,3 1),(10 10,9 1,8 1),(10 10,7 1,6 1))",
 721                 true);
 722     // five holes, with two pairs touching each at some point, and
 723     // fifth hole creating a disconnected component for the interior
 724     test::apply("pg071",
 725                 "POLYGON((0 0,10 0,10 10,0 10),(0 10,2 1,1 1),(0 10,4 1,3 1),(10 10,9 1,8 1),(10 10,7 1,6 1),(4 1,4 4,6 4,6 1))",
 726                 false);
 727     // five holes, with two pairs touching each at some point, and
 728     // fifth hole creating three disconnected components for the interior
 729     test::apply("pg072",
 730                 "POLYGON((0 0,10 0,10 10,0 10),(0 10,2 1,1 1),(0 10,4 1,3 1),(10 10,9 1,8 1),(10 10,7 1,6 1),(4 1,4 4,6 4,6 1,5 0))",
 731                 false);
 732
 733     // both examples: a polygon with one hole, where the hole contains
 734     // the exterior ring
 735     test::apply("pg073",
 736                 "POLYGON((0 0,1 0,1 1,0 1),(-10 -10,-10 10,10 10,10 -10))",
 737                 false);
 738     test::apply("pg074",
 739                 "POLYGON((-10 -10,1 0,1 1,0 1),(-10 -10,-10 10,10 10,10 -10))",
 740                 false);
 741
 742     test::apply
 743         ("pg075",
 744          "POLYGON((-6 -10,-6.6923076923076925 -6.711538461538462,\
 745                    -9 -7,-8.824742268041238 -6.123711340206185,\
 746                    -10 -6,-8.583333333333332 -4.916666666666667,\
 747                    -8.094117647058823 -2.4705882352941173,-10 -3,\
 748                    -8.526315789473683 -0.05263157894736803,-10 1,\
 749                    -10 10,-7.764705882352941 8.509803921568627,\
 750                    -7.65090909090909 7.789090909090909,-10 10,\
 751                    -7.574468085106383 7.304964539007091,-7.4375 6.4375,\
 752                    -6.5 5.5,-6.4 6,-7.574468085106383 7.304964539007091,\
 753                    -7.65090909090909 7.789090909090909,\
 754                    -6.297029702970297 6.514851485148515,\
 755                    0 0,-6.297029702970297 6.514851485148515,\
 756                    -4.848484848484849 5.151515151515151,-4 6,\
 757                    -6.117647058823529 7.411764705882352,\
 758                    0 0,-6.11764705882353 7.411764705882353,\
 759                    -7.764705882352941 8.509803921568627,-8 10,\
 760                    -2.9473684210526314 7.052631578947368,-2 8,\
 761                    -0.17821782178217824 6.633663366336634,1 10,\
 762                    1.8095238095238098 5.142857142857142,\
 763                    3.2038834951456314 4.097087378640777,7 7,\
 764                    3.7142857142857144 3.7142857142857144,\
 765                    4.4 3.1999999999999997,8 2,\
 766                    6.540540540540541 1.5945945945945947,10 -1,\
 767                    7.454545454545455 -4.393939393939394,8 -5,\
 768                    7.320754716981132 -4.716981132075472,7 -6,\
 769                    6.062068965517241 -5.117241379310345,\
 770                    4.9504132231404965 -5.256198347107438,\
 771                    6.1506849315068495 -7.123287671232877,9 -8,\
 772                    6.548387096774194 -7.741935483870968,8 -10,\
 773                    5.906976744186046 -7.674418604651163,\
 774                    3.9107142857142856 -7.464285714285714,4 -8,\
 775                    2.8043478260869565 -7.3478260869565215,\
 776                    1.7829457364341086 -7.24031007751938,2 -8,\
 777                    1.0728476821192054 -7.1655629139072845,\
 778                    -4.3583617747440275 -6.593856655290103,-5 -9,\
 779                    -5.2020725388601035 -7.720207253886011,-6 -10),\
 780                   (5.127659574468085 -6.808510638297872,\
 781                    3.72972972972973 -6.378378378378379,\
 782                    3.571428571428571 -5.428571428571429,\
 783                    3.8539325842696632 -5.393258426966292,\
 784                    5.127659574468085 -6.808510638297872),\
 785                   (-5.5 4.5,-6.5 5.5,-6.4 6,\
 786                    -5.263157894736842 4.736842105263158,-5.5 4.5))",
 787          false);
 788
 789     // test cases coming from buffer
 790     test::apply
 791         ("pg076",
 792          "POLYGON((1.1713032141645456 -0.9370425713316364,\
 793                    5.1713032141645456 4.0629574286683638,\
 794                    4.7808688094430307 4.3753049524455756,\
 795                    4.7808688094430307 4.3753049524455756,\
 796                    0.7808688094430304 -0.6246950475544243,\
 797                    0.7808688094430304 -0.6246950475544243))",
 798          AllowDuplicates);
 799
 800
 801     // MySQL report on Sep 30, 2015
 802     test::apply
 803         ("pg077",
 804          "POLYGON((72.8714768817168 -167.0048853643874,9274.40641550926 3433.5957427942167,-58.09039811390054 187.50989457746405,-81.09039811390053 179.50989457746405,-207.99999999999997 135.36742435621204,-208 1,-208 0,-208 -276.9111154485375,49.8714768817168 -176.0048853643874))",
 805          true);
 806
 807     test::apply("pg077-simplified",
 808                 "POLYGON((-200 0,-207.99999999999997 135.36742435621204,-208 1,-208 0,-208 -276.9111154485375))",
 809                 true);
 810
 811     test::apply
 812         ("pg078",
 813          "POLYGON((0 10,-10 0,0 0,10 0))",
 814          true);
 815
 816     test::apply
 817         ("pg078spike1",
 818          "POLYGON((0 10,-10 0,0 0,-10 0,10 0))",
 819          false);
 820
 821     test::apply
 822         ("pg078spike2",
 823          "POLYGON((0 10,-10 0,0 0,-8 0,10 0))",
 824          false);
 825
 826     test::apply
 827         ("pg078spike3",
 828          "POLYGON((0 10,-10 0,0 0,-11 0,10 0))",
 829          false);
 830
 831     test::apply
 832         ("pg078reversed",
 833          "POLYGON((0 10,10 0,0 0,-10 0))",
 834          false);
 835
 836     test::apply
 837         ("pg079",
 838          "POLYGON((10 0,0 10,0 0,0 -10))",
 839          true);
 840
 841     test::apply
 842         ("pg079spike1",
 843          "POLYGON((10 0,0 10,0 0,0 10,0 -10))",
 844          false);
 845
 846     test::apply
 847         ("pg079spike2",
 848          "POLYGON((10 0,0 10,0 0,0 8,0 -10))",
 849          false);
 850
 851     test::apply
 852         ("pg079spike3",
 853          "POLYGON((10 0,0 10,0 0,0 11,0 -10))",
 854          false);
 855
 856     test::apply
 857         ("pg079reversed",
 858          "POLYGON((10 0,0 -10,0 0,0 10))",
 859          false);
 860 }
 861
 862
 863 template <typename Point>
 864 inline void test_doc_example_polygon()
 865 {
 866 #ifdef BOOST_GEOMETRY_TEST_DEBUG
 867     std::cout << std::endl << std::endl;
 868     std::cout << "************************************" << std::endl;
 869     std::cout << " is_valid: doc example polygon " << std::endl;
 870     std::cout << "************************************" << std::endl;
 871 #endif
 872
 873     typedef bg::model::polygon<Point> ClockwiseClosedPolygon;
 874     typedef validity_tester_areal<true> tester;
 875     typedef test_valid<tester, ClockwiseClosedPolygon> test;
 876
 877     test::apply("pg-doc",
 878                 "POLYGON((0 0,0 10,10 10,10 0,0 0),(0 0,9 1,9 2,0 0),(0 0,2 9,1 9,0 0),(2 9,9 2,9 9,2 9))",
 879                 false);
 880
 881     // Containing a self touching point, which should be valid
 882     test::apply("ggl_list_20190307_matthieu_2", ggl_list_20190307_matthieu_2[1], true);
 883 }
 884
 885 BOOST_AUTO_TEST_CASE( test_is_valid_polygon )
 886 {
 887     bool const allow_duplicates = true;
 888     bool const do_not_allow_duplicates = !allow_duplicates;
 889
 890     test_open_polygons<point_type, allow_duplicates>();
 891     test_open_polygons<point_type, do_not_allow_duplicates>();
 892     test_doc_example_polygon<point_type>();
 893 }
 894
 895 template <typename Point, bool AllowDuplicates>
 896 inline void test_open_multipolygons()
 897 {
 898     // WKT of multipolygons should be defined as ccw, open
 899
 900 #ifdef BOOST_GEOMETRY_TEST_DEBUG
 901     std::cout << std::endl << std::endl;
 902     std::cout << "************************************" << std::endl;
 903     std::cout << " is_valid: MULTIPOLYGON (open) " << std::endl;
 904     std::cout << "************************************" << std::endl;
 905     std::cout << "DUPLICATES ALLOWED? "
 906               << std::boolalpha
 907               << AllowDuplicates
 908               << std::noboolalpha
 909               << std::endl;
 910 #endif
 911
 912     // cw, ccw, open and closed polygons
 913     typedef bg::model::polygon<point_type,false,false> ccw_open_polygon_type;
 914     typedef bg::model::polygon<point_type,false,true>  ccw_closed_polygon_type;
 915     typedef bg::model::polygon<point_type,true,false>  cw_open_polygon_type;
 916     typedef bg::model::polygon<point_type,true,true>   cw_closed_polygon_type;
 917
 918     typedef bg::model::multi_polygon<ccw_open_polygon_type> OG;
 919     typedef bg::model::multi_polygon<ccw_closed_polygon_type> CG;
 920     typedef bg::model::multi_polygon<cw_open_polygon_type> CW_OG;
 921     typedef bg::model::multi_polygon<cw_closed_polygon_type> CW_CG;
 922
 923     typedef validity_tester_areal<AllowDuplicates> tester;
 924     typedef test_valid<tester, OG, CG, CW_OG, CW_CG> test;
 925
 926     // not enough points
 927     test::apply("mpg01", "MULTIPOLYGON()", true);
 928     test::apply("mpg02", "MULTIPOLYGON((()))", false);
 929     test::apply("mpg03", "MULTIPOLYGON(((0 0)),(()))", false);
 930     test::apply("mpg04", "MULTIPOLYGON(((0 0,1 0)))", false);
 931
 932     // two disjoint polygons
 933     test::apply("mpg05",
 934                 "MULTIPOLYGON(((0 0,1 0,1 1,0 1)),((2 2,3 2,3 3,2 3)))",
 935                 true);
 936
 937     // two disjoint polygons with multiple points
 938     test::apply("mpg06",
 939                 "MULTIPOLYGON(((0 0,1 0,1 0,1 1,0 1)),((2 2,3 2,3 3,3 3,2 3)))",
 940                 AllowDuplicates);
 941
 942     // two polygons touch at a point
 943     test::apply("mpg07",
 944                 "MULTIPOLYGON(((0 0,1 0,1 1,0 1)),((1 1,2 1,2 2,1 2)))",
 945                 true);
 946
 947     // two polygons share a segment at a point
 948     test::apply("mpg08",
 949                 "MULTIPOLYGON(((0 0,1.5 0,1.5 1,0 1)),((1 1,2 1,2 2,1 2)))",
 950                 false);
 951
 952     // one polygon inside another and boundaries touching
 953     test::apply("mpg09",
 954                 "MULTIPOLYGON(((0 0,10 0,10 10,0 10)),((0 0,9 1,9 2)))",
 955                 false);
 956     test::apply("mpg09_2",
 957                 "MULTIPOLYGON(((0 0,5 1,10 0,10 10,0 10)),((1 1,9 1,9 2)))",
 958                 false);
 959
 960     // one polygon inside another and boundaries not touching
 961     test::apply("mpg10",
 962                 "MULTIPOLYGON(((0 0,10 0,10 10,0 10)),((1 1,9 1,9 2)))",
 963                 false);
 964
 965     // free space is disconnected
 966     test::apply("mpg11",
 967                 "MULTIPOLYGON(((0 0,1 0,1 1,0 1)),((1 1,2 1,2 2,1 2)),((0 1,0 2,-1 2,-1 -1)),((1 2,1 3,0 3,0 2)))",
 968                 true);
 969
 970     // multi-polygon with a polygon inside the hole of another polygon
 971     test::apply("mpg12",
 972                 "MULTIPOLYGON(((0 0,100 0,100 100,0 100),(1 1,1 99,99 99,99 1)),((2 2,98 2,98 98,2 98)))",
 973                 true);
 974     test::apply("mpg13",
 975                 "MULTIPOLYGON(((0 0,100 0,100 100,0 100),(1 1,1 99,99 99,99 1)),((1 1,98 2,98 98,2 98)))",
 976                 true);
 977
 978     // test case suggested by Barend Gehrels: take two valid polygons P1 and
 979     // P2 with holes H1 and H2, respectively, and consider P2 to be
 980     // fully inside H1; now invalidate the multi-polygon by
 981     // considering H2 as a hole of P1 and H1 as a hole of P2; this
 982     // should be invalid
 983     //
 984     // first the valid case:
 985     test::apply("mpg14",
 986                 "MULTIPOLYGON(((0 0,100 0,100 100,0 100),(1 1,1 99,99 99,99 1)),((2 2,98 2,98 98,2 98),(3 3,3 97,97 97,97 3)))",
 987                 true);
 988     // and the invalid case:
 989     test::apply("mpg15",
 990                 "MULTIPOLYGON(((0 0,100 0,100 100,0 100),(3 3,3 97,97 97,97 3)),((2 2,98 2,98 98,2 98),(1 1,1 99,99 99,99 1)))",
 991                 false);
 992
 993     test::apply
 994         ("mpg16",
 995          "MULTIPOLYGON(((-1 4,8 -10,-10 10,7 -6,8 -2,\
 996                       -10 10,-10 1,-3 -4,4 1,-1 2,4 3,-8 10,-5 -9,-1 6,-5 0)),\
 997                       ((-10 -3,-8 1,2 -8,-2 6,-4 0,8 -5,-1 5,8 2)),\
 998                       ((-6 -10,1 10,4 -8,-7 -2,2 0,-4 3,-10 9)),\
 999                       ((10 -1,-2 8,-7 3,-6 8,-9 -7,7 -5)),\
1000                       ((7 7,-4 -4,9 -8,-10 -6)))",
1001          false);
1002
1003     test::apply
1004         ("mpg17",
1005          "MULTIPOLYGON(((-1 4,8 -10,-10 10,7 -6,8 -2,\
1006                       -10 10,-10 1,-3 -4,4 1,-1 2,4 3,-8 10,-5 -9,-1 6,-5 0)),\
1007                       ((-10 -3,-8 1,2 -8,-2 6,-4 0,8 -5,-1 5,8 2)),\
1008                       ((-6 -10,-10 9,-4 3,2 0,-7 -2,4 -8,1 10)),\
1009                       ((10 -1,-2 8,-7 3,-6 8,-9 -7,7 -5)),\
1010                       ((7 7,-10 -6,9 -8,-4 -4)))",
1011          false);
1012
1013     // test cases coming from buffer
1014     {
1015         std::string wkt = "MULTIPOLYGON(((1.1713032141645456 -0.9370425713316364,5.1713032141645456 4.0629574286683638,4.7808688094430307 4.3753049524455756,4.7808688094430307 4.3753049524455756,0.7808688094430304 -0.6246950475544243,0.7808688094430304 -0.6246950475544243,1.1713032141645456 -0.9370425713316364)))";
1016
1017         OG open_mpgn = from_wkt<OG>(wkt);
1018         bg::reverse(open_mpgn);
1019
1020         test::apply("mpg18", open_mpgn, false);
1021     }
1022     {
1023         // the polygon has a self-touching point at (7,8),
1024         // defining an interior ring which is not part of its definition,
1025         // and is therefore invalid
1026         std::string wkt = "MULTIPOLYGON(((5.2811206375710933 9.9800205994776228,5.2446420208654896 10.0415020265598844,5.1807360092909640 10.1691699739962242,5.1261005500004773 10.3010716408018013,5.0810140527710059 10.4365348863171388,5.0457062680576819 10.5748694208940446,5.0203571162381344 10.7153703234534277,5.0050957707794934 10.8573216336015328,5.0000000000000000 10.9999999999999964,5.0050957707794925 11.1426783663984619,5.0203571162381344 11.2846296765465670,5.0457062680576801 11.4251305791059501,5.0810140527710042 11.5634651136828559,5.1261005500004755 11.6989283591981934,5.1807360092909622 11.8308300260037704,5.2446420208654869 11.9584979734401102,5.3174929343376363 12.0812816349111927,5.3989175181512774 12.1985553330226910,5.4885008512914810 12.3097214678905669,5.5857864376269024 12.4142135623730923,5.6902785321094269 12.5114991487085145,5.8014446669773028 12.6010824818487190,5.9187183650888020 12.6825070656623602,6.0415020265598844 12.7553579791345104,6.1691699739962260 12.8192639907090360,6.3010716408018030 12.8738994499995236,6.4365348863171405 12.9189859472289950,6.5748694208940472 12.9542937319423199,6.7153703234534312 12.9796428837618656,6.8573216336015381 12.9949042292205075,7.0000000000000036 13.0000000000000000,7.1426783663984690 12.9949042292205075,7.2846296765465750 12.9796428837618656,7.4251305791059590 12.9542937319423181,7.5634651136828657 12.9189859472289932,7.6989283591982032 12.8738994499995201,7.8308300260037802 12.8192639907090324,7.9584979734401209 12.7553579791345069,8.0812816349112033 12.6825070656623566,8.1985553330227017 12.6010824818487137,8.3097214678905793 12.5114991487085092,8.4142135623731029 12.4142135623730869,8.5114991487085252 12.3097214678905598,8.6010824818487297 12.1985553330226821,8.6825070656623708 12.0812816349111838,8.7553579791345193 11.9584979734400996,8.8192639907090431 11.8308300260037580,8.8738994499995290 11.6989283591981810,8.9189859472290003 11.5634651136828417,8.9542937319423235 11.4251305791059359,8.9796428837618691 11.2846296765465510,8.9949042292205093 11.1426783663984441,9.0000000000000000 11.0000000000000000,8.9949042292205075 10.8573216336015346,8.9796428837618656 10.7153703234534294,8.9542937319423181 10.5748694208940464,8.9189859472289950 10.4365348863171405,8.8738994499995236 10.3010716408018030,8.8192639907090360 10.1691699739962278,8.7553579791345122 10.0415020265598862,8.7188787869375428 9.9800200826281831,8.8573216336015381 9.9949042292205075,9.0000000000000036 10.0000000000000000,9.1426783663984690 9.9949042292205075,9.2846296765465759 9.9796428837618656,9.4251305791059590 9.9542937319423181,9.5634651136828648 9.9189859472289932,9.6989283591982041 9.8738994499995201,9.8308300260037793 9.8192639907090324,9.9584979734401209 9.7553579791345069,10.0812816349112033 9.6825070656623566,10.1985553330227017 9.6010824818487137,10.3097214678905793 9.5114991487085092,10.4142135623731029 9.4142135623730869,10.5114991487085252 9.3097214678905598,10.6010824818487297 9.1985553330226821,10.6825070656623708 9.0812816349111838,10.7553579791345193 8.9584979734400996,10.8192639907090431 8.8308300260037580,10.8738994499995290 8.6989283591981810,10.9189859472290003 8.5634651136828417,10.9542937319423235 8.4251305791059359,10.9796428837618691 8.2846296765465510,10.9949042292205093 8.1426783663984441,11.0000000000000000 8.0000000000000000,10.9949042292205075 7.8573216336015355,10.9796428837618656 7.7153703234534294,10.9542937319423181 7.5748694208940464,10.9189859472289950 7.4365348863171405,10.8738994499995236 7.3010716408018030,10.8192639907090360 7.1691699739962269,10.7553579791345122 7.0415020265598862,10.6825070656623620 6.9187183650888047,10.6010824818487208 6.8014446669773063,10.5114991487085163 6.6902785321094296,10.4142135623730958 6.5857864376269051,10.3097214678905704 6.4885008512914837,10.1985553330226946 6.3989175181512792,10.0812816349111962 6.3174929343376380,9.9584979734401138 6.2446420208654887,9.8308300260037740 6.1807360092909640,9.6989283591981970 6.1261005500004764,9.5634651136828595 6.0810140527710050,9.4251305791059536 6.0457062680576810,9.2846296765465706 6.0203571162381344,9.1426783663984654 6.0050957707794925,9.0000000000000018 6.0000000000000000,8.8573216336015363 6.0050957707794925,8.7153703234534312 6.0203571162381344,8.5748694208940481 6.0457062680576810,8.4365348863171423 6.0810140527710050,8.3010716408018048 6.1261005500004764,8.1691699739962278 6.1807360092909622,8.0415020265598880 6.2446420208654878,7.9187183650888064 6.3174929343376363,7.8014446669773072 6.3989175181512783,7.6902785321094314 6.4885008512914819,7.5857864376269060 6.5857864376269033,7.4885008512914846 6.6902785321094278,7.3989175181512810 6.8014446669773045,7.3174929343376389 6.9187183650888029,7.2446420208654896 7.0415020265598844,7.1807360092909640 7.1691699739962251,7.1261005500004773 7.3010716408018013,7.0810140527710059 7.4365348863171379,7.0457062680576819 7.5748694208940437,7.0203571162381344 7.7153703234534268,7.0050957707794934 7.8573216336015328,"
1027           "7.0000000000000000 8.0000000000000000,7.0050957707794925 8.1426783663984619,7.0203571162381344 8.2846296765465670,7.0457062680576801 8.4251305791059501,7.0810140527710042 8.5634651136828559,7.1261005500004755 8.6989283591981934,7.1807360092909622 8.8308300260037704,7.2446420208654869 8.9584979734401102,7.2811219724467575 9.0199799990140797,7.1426783663984654 9.0050957707794925,7.0000000000000009 9.0000000000000000,6.8573216336015363 9.0050957707794925,6.7188786030357956 9.0199806804111571,6.7553579791345184 8.9584979734400996,6.8192639907090431 8.8308300260037580,6.8738994499995290 8.6989283591981810,6.9189859472290003 8.5634651136828417,6.9542937319423235 8.4251305791059359,6.9796428837618683 8.2846296765465510,6.9949042292205084 8.1426783663984441,"
1028           "7.0000000000000000 8.0000000000000000,6.9949042292205075 7.8573216336015355,6.9796428837618656 7.7153703234534294,6.9542937319423190 7.5748694208940464,6.9189859472289950 7.4365348863171405,6.8738994499995236 7.3010716408018030,6.8192639907090369 7.1691699739962269,6.7553579791345113 7.0415020265598862,6.6825070656623620 6.9187183650888047,6.6010824818487208 6.8014446669773063,6.5114991487085163 6.6902785321094296,6.4142135623730949 6.5857864376269051,6.3097214678905704 6.4885008512914837,6.1985553330226946 6.3989175181512792,6.0812816349111953 6.3174929343376380,5.9584979734401138 6.2446420208654887,5.8308300260037731 6.1807360092909640,5.6989283591981970 6.1261005500004764,5.5634651136828603 6.0810140527710050,5.4251305791059536 6.0457062680576810,5.2846296765465715 6.0203571162381344,5.1426783663984654 6.0050957707794925,5.0000000000000009 6.0000000000000000,4.8573216336015363 6.0050957707794925,4.7153703234534312 6.0203571162381344,4.5748694208940481 6.0457062680576810,4.4365348863171423 6.0810140527710050,4.3010716408018048 6.1261005500004764,4.1691699739962287 6.1807360092909622,4.0415020265598880 6.2446420208654878,3.9187183650888064 6.3174929343376363,3.8014446669773077 6.3989175181512783,3.6902785321094314 6.4885008512914819,3.5857864376269064 6.5857864376269033,3.4885008512914846 6.6902785321094278,3.3989175181512805 6.8014446669773045,3.3174929343376389 6.9187183650888029,3.2446420208654896 7.0415020265598844,3.1807360092909640 7.1691699739962251,3.1261005500004773 7.3010716408018013,3.0810140527710059 7.4365348863171379,3.0457062680576819 7.5748694208940437,3.0203571162381349 7.7153703234534268,3.0050957707794934 7.8573216336015328,3.0000000000000000 7.9999999999999973,3.0050957707794925 8.1426783663984619,3.0203571162381344 8.2846296765465670,3.0457062680576801 8.4251305791059501,3.0810140527710042 8.5634651136828559,3.1261005500004755 8.6989283591981934,3.1807360092909618 8.8308300260037704,3.2446420208654869 8.9584979734401102,3.3174929343376358 9.0812816349111927,3.3989175181512770 9.1985553330226910,3.4885008512914810 9.3097214678905669,3.5857864376269024 9.4142135623730923,3.6902785321094269 9.5114991487085145,3.8014446669773028 9.6010824818487190,3.9187183650888020 9.6825070656623602,4.0415020265598844 9.7553579791345104,4.1691699739962260 9.8192639907090360,4.3010716408018030 9.8738994499995236,4.4365348863171405 9.9189859472289950,4.5748694208940472 9.9542937319423199,4.7153703234534312 9.9796428837618656,4.8573216336015381 9.9949042292205075,5.0000000000000036 10.0000000000000000,5.1426783663984690 9.9949042292205075)))";
1029
1030         OG open_mpgn = from_wkt<OG>(wkt);
1031         bg::reverse(open_mpgn);
1032
1033         test::apply("mpg19", open_mpgn, false);
1034         geometry_to_svg(open_mpgn, "mpg19");
1035     }
1036     {
1037         std::string wkt = "MULTIPOLYGON(((-1.1713032141645421 0.9370425713316406,-1.2278293047051545 0.8616467945203863,-1.2795097139219473 0.7828504914601357,-1.3261404828502752 0.7009646351604617,-1.3675375811487496 0.6163123916860891,-1.4035376333829217 0.5292278447680804,-1.4339985637934827 0.4400546773279756,-1.4588001570043776 0.3491448151183161,-1.4778445324579732 0.2568570378324778,-1.4910565307049013 0.1635555631651331,-1.4983840100240693 0.0696086094114048,-1.4997980522022116 -0.0246130577225216,-1.4952930766608652 -0.1187375883622537,-1.4848868624803642 -0.2123935159867641,-1.4686204782339323 -0.3052112234370423,-1.4465581199087858 -0.3968244016261590,-1.4187868575539013 -0.4868714951938814,-1.3854162916543107 -0.5749971294005020,-1.3465781205880585 -0.6608535126285795,-1.3024256208728704 -0.7441018089575634,-1.2531330422537639 -0.8244134753943718,-1.1988949200189114 -0.9014715584824893,-1.1399253072577331 -0.9749719451724563,-1.0764569300911435 -1.0446245630171400,-1.0087402692078766 -1.1101545249551616,-0.9370425713316382 -1.1713032141645441,-0.8616467945203836 -1.2278293047051563,-0.7828504914601331 -1.2795097139219491,-0.7009646351604588 -1.3261404828502767,-0.6163123916860862 -1.3675375811487509,-0.5292278447680773 -1.4035376333829228,-0.4400546773279725 -1.4339985637934838,-0.3491448151183129 -1.4588001570043785,-0.2568570378324746 -1.4778445324579736,-0.1635555631651299 -1.4910565307049017,-0.0696086094114016 -1.4983840100240695,0.0246130577225248 -1.4997980522022114,0.1187375883622569 -1.4952930766608650,0.2123935159867673 -1.4848868624803639,0.3052112234370455 -1.4686204782339316,0.3968244016261621 -1.4465581199087849,0.4868714951938845 -1.4187868575539002,0.5749971294005050 -1.3854162916543096,0.6608535126285824 -1.3465781205880569,0.7441018089575662 -1.3024256208728686,0.8244134753943745 -1.2531330422537621,0.9014715584824917 -1.1988949200189096,0.9749719451724583 -1.1399253072577313,1.0446245630171418 -1.0764569300911420,1.1101545249551634 -1.0087402692078746,1.1713032141645456 -0.9370425713316364,5.1713032141645456 4.0629574286683638,5.1713032141645439 4.0629574286683621,5.2278293047051561 4.1383532054796159,5.2795097139219491 4.2171495085398671,5.3261404828502767 4.2990353648395407,5.3675375811487509 4.3836876083139131,5.4035376333829230 4.4707721552319217,5.4339985637934838 4.5599453226720268,5.4588001570043785 4.6508551848816859,5.4778445324579739 4.7431429621675241,5.4910565307049017 4.8364444368348689,5.4983840100240693 4.9303913905885972,5.4997980522022116 5.0246130577225232,5.4952930766608645 5.1187375883622552,5.4848868624803639 5.2123935159867658,5.4686204782339320 5.3052112234370439,5.4465581199087856 5.3968244016261604,5.4187868575539007 5.4868714951938822,5.3854162916543107 5.5749971294005025,5.3465781205880578 5.6608535126285799,5.3024256208728699 5.7441018089575637,5.2531330422537632 5.8244134753943726,5.1988949200189110 5.9014715584824895,5.1399253072577329 5.9749719451724559,5.0764569300911440 6.0446245630171394,5.0087402692078768 6.1101545249551616,4.9370425713316379 6.1713032141645439,4.8616467945203841 6.2278293047051561,4.7828504914601337 6.2795097139219482,4.7009646351604593 6.3261404828502759,4.6163123916860869 6.3675375811487509,4.5292278447680783 6.4035376333829230,4.4400546773279732 6.4339985637934838,4.3491448151183141 6.4588001570043785,4.2568570378324750 6.4778445324579739,4.1635555631651311 6.4910565307049017,4.0696086094114028 6.4983840100240693,3.9753869422774759 6.4997980522022116,3.8812624116377439 6.4952930766608645,3.7876064840132333 6.4848868624803639,3.6947887765629552 6.4686204782339320,3.6031755983738387 6.4465581199087847,3.5131285048061165 6.4187868575539007,3.4250028705994957 6.3854162916543098,3.3391464873714183 6.3465781205880578,3.2558981910424345 6.3024256208728691,3.1755865246056261 6.2531330422537623,3.0985284415175087 6.1988949200189101,3.0250280548275423 6.1399253072577320,2.9553754369828584 6.0764569300911422,2.8898454750448366 6.0087402692078751,2.8286967858354544 5.9370425713316362,-1.1713032141645456 0.9370425713316364,-1.1713032141645421 0.9370425713316406)))";
1038
1039         OG open_mpgn = from_wkt<OG>(wkt);
1040         bg::reverse(open_mpgn);
1041
1042         // polygon contains a spike
1043         test::apply("mpg20", open_mpgn, false);
1044     }
1045
1046     // Interior ring touches exterior ring, which at that same point touches another exterior ring in (1 2)
1047     test::apply
1048         ("mpg21",
1049         "MULTIPOLYGON(((2 3,1 2,1 0,2 0,2 1,4 3),(2 2,1.5 1.5,1 2)),((0 3,0 2,1 2)))",
1050          true);
1051
1052     // Two interior rings touch each other in (10 5)
1053     test::apply
1054         ("mpg22",
1055         "MULTIPOLYGON(((10 5,5 10,0 5,5 0),(10 5,5 4,4 6)),((10 5,10 0,20 0,20 10,10 10),(10 5,18 8,15 3)))",
1056          true);
1057
1058     // Two polygons, one inside interior of other one, touching all at same point (0,0)
1059     test::apply
1060         ("mpg23",
1061         "MULTIPOLYGON(((0 0,10 0,10 10,0 10),(0 0,1 9,9 9,9 1)),((0 0,8 2,8 8,2 8)))",
1062          true);
1063
1064     test::apply
1065         ("ticket_12503",
1066         "MULTIPOLYGON(((15 20,12 23,15 17,15 20)),((36 25,35 25,34 24,34 23,35 23,36 25)),((15 15,10 13,11 23,12 23,12 25,10 25,7 24,8 6,15 15)),((12 29,11 30,12 30,11 31,13 31,13 34,6 38,6 32,8 31,12 27,12 29)),((9 26,6 31,7 26,7 24,9 26)),((15 48,15 45,18 44,15 48)),((38 39,18 44,26 34,38 39)),((15 45,13 34,15 33,15 45)),((17 32,15 33,15 32,17 32)),((21 31,16 38,18 32,17 32,19 30,21 31)),((15 32,13 31,13 30,15 29,15 32)),((17 29,15 29,15 28,17 29)),((15 28,13 30,12 29,14 27,15 28)),((26 27,28 30,31 27,26 34,21 31,22 29,19 30,18 30,17 29,19 29,19 28,23 28,24 27,25 27,24 26,25 24,30 24,26 27)),((17 26,15 28,15 26,17 26)),((32 26,34 27,31 27,27 27,32 26)),((19 26,17 26,19 25,19 26)),((35 23,33 18,41 15,35 23)),((24 26,24 27,19 26,20 25,23 24,24 26)),((32 13,49 1,48 4,46 5,33 15,32 13)),((33 25,32 26,32 25,31 24,32 23,33 25)),((42 15,43 22,44 22,44 23,43 23,35 23,42 15)),((44 42,38 39,40 39,39 34,34 27,33 25,35 25,38 31,36 25,43 23,44 42)),((48 46,44 23,48 22,48 46)),((15 3,23 2,18 11,15 3)),((30 19,28 20,27 21,25 24,23 24,22 23,26 20,29 17,30 19)),((24 19,21 21,21 20,22 19,24 19)),((31 24,30 24,27 21,31 22,30 19,31 19,34 23,31 23,31 24)),((21 20,20 21,21 18,21 20)),((14 26,12 26,12 25,15 25,15 20,17 17,20 21,21 21,22 23,20 24,19 25,16 25,15 26,14 27,14 26),(17 24,20 22,20 21,17 24)),((23 18,22 19,22 17,23 18)),((28 13,31 10,32 13,30 15,28 13)),((18 17,17 17,16 16,18 17)),((16 16,15 17,15 15,16 16)),((30 17,29 17,29 16,30 15,30 17)),((33 18,31 19,30 17,33 15,33 18)),((42 13,47 7,48 4,48 22,44 22,43 14,42 13)),((42 15,41 15,42 14,43 14,42 15)),((24 2,49 1,27 11,23 13,25 6,27 10,24 2)),((29 16,24 19,23 18,28 13,29 16)),((17 13,16 15,15 15,15 11,17 13)),((20 14,23 13,22 17,20 15,21 17,21 18,18 17,19 15,17 13,18 11,20 14)),((5 3,15 3,15 11,8 5,8 6,5 3)))",
1067          true);
1068
1069     // MySQL report 12.06.2015
1070     {
1071         std::string wkt = "MULTIPOLYGON("
1072             "((-40.314872143936725 -85.6567579487603,-53.1473643859603 -98.48925019078388,-41.29168745244485 -90.56754012573627,-40.314872143936725 -85.6567579487603)),"
1073             "((-186.91433298215597 -88.80210078879976,-192.54783347494038 -75.53420159905284,-192.7944062150986 -78.03769664281869,-186.91433298215597 -88.80210078879976)),"
1074             "((170.89089207158912 -44.35600339378721,191.8949969913326 -31.3460752560506,169.32805525181837 -43.07341636227523,170.89089207158912 -44.35600339378721)),"
1075             "((-2.6035109435630504 -13.058121512403435,26.839412016794036 43.97610638055074,26.974733141577826 43.72289807427111,26.97470368529088 43.722907009738066,-2.6035109435630504 -13.058121512403435))"
1076             ")";
1077
1078         std::string msg;
1079         CG mpoly = from_wkt<CG>(wkt);
1080         BOOST_CHECK_MESSAGE(! bg::is_valid(mpoly, msg), msg);
1081         BOOST_CHECK_MESSAGE(bg::is_valid(mpoly[0], msg), msg);
1082         BOOST_CHECK_MESSAGE(bg::is_valid(mpoly[1], msg), msg);
1083         BOOST_CHECK_MESSAGE(bg::is_valid(mpoly[2], msg), msg);
1084         BOOST_CHECK_MESSAGE(! bg::is_valid(mpoly[3], msg), msg);
1085
1086         // The last Polygon has wrong orientation, so correct it
1087         bg::reverse(mpoly[3]);
1088         BOOST_CHECK_MESSAGE(bg::is_valid(mpoly, msg), msg);
1089         BOOST_CHECK_MESSAGE(bg::is_valid(mpoly[0], msg), msg);
1090         BOOST_CHECK_MESSAGE(bg::is_valid(mpoly[1], msg), msg);
1091         BOOST_CHECK_MESSAGE(bg::is_valid(mpoly[2], msg), msg);
1092         BOOST_CHECK_MESSAGE(bg::is_valid(mpoly[3], msg), msg);
1093     }
1094
1095     // MySQL report 30.06.2015
1096 #ifdef BOOST_GEOMETRY_TEST_FAILURES
1097     {
1098         std::string wkt = "MULTIPOLYGON(((153.60036248974487 -86.4072234353084,134.8924761503673 -92.0821987136617,151.87887755950274 -92.0821987136617,153.60036248974487 -86.4072234353084)),((-162.3619975827558 -20.37135271519032,-170.42498886764488 -34.35970444494861,-168.21072335866987 -37.67358696575207,-162.3619975827558 -20.37135271519032)),((25.982352329146433 -1.793573272167862,25.81900562736861 -2.0992322130216032,24.216310496207715 -2.737558757030656,25.9822948153016 -1.7936204725604972,25.982352329146433 -1.793573272167862)))";
1099
1100         std::string msg;
1101         CG mpoly = from_wkt<CG>(wkt);
1102         bg::correct(mpoly);
1103
1104         BOOST_CHECK_MESSAGE(bg::is_valid(mpoly, msg), msg);
1105         BOOST_CHECK_MESSAGE(bg::is_valid(mpoly[2], msg), msg);
1106     }
1107     {
1108         std::string wkt = "MULTIPOLYGON(("
1109             "(176.37937452790632 33.81070321484654,165.31874654406195 30.429623478264823,164.22653456196667 40.57205841516082,169.96584109309163 43.760662373477935,169.96717084197783 43.76157019827226,169.96831223949295 43.76270579928938,169.96922682269394 43.76403090891733,169.96988377185227 43.76550087346144,169.97026094902066 43.767066157889666,169.97034564404004 43.768674015069664,169.97013500284808 43.77027026324768,169.96963612365553 43.77180111187144,169.9688658177501 43.773214974230235,169.9678500429876 43.77446420582984,169.96662302906125 43.775506709921984,169.96522612402566 43.77630735608547,169.96370640094523 43.77683916405498,169.96211507162087 43.777084212905194,169.96050576084875 43.777034244952155,163.96123663641703 43.03565247280777,161.69252016076334 64.10327452950632,161.69220086043657 64.10485513588213,161.69159759286657 64.10635057476519,161.6907307489143 64.1077102992874,161.68962962850455 64.10888834981994,161.68833145026844 64.10984490744038,161.6868800935278 64.11054763983988,161.68532461514377 64.11097279417753,161.68371759136113 64.11110599994278,161.68211334069463 64.1109427546887,161.68056608792585 64.11048857621772,161.67912813126807 64.10975881607614,127.83620579794024 42.81253476817878,91.03182023020634 47.701488147167275,136.39039242955064 83.14688773021612,136.39163693720113 83.14807413530517,136.39262607583518 83.14948053535137,136.39332183340986 83.15105288318968,136.39369747235173 83.15273075437446,136.3937385570669 83.15444966925705,136.39344350869288 83.15614357090246,136.39282366577314 83.15774736362043,136.39190284852347 83.15919941455623,136.39071644343446 83.1604439222067,136.38931004338824 83.16143306084076,136.38773769554993 83.16212881841544,136.38605982436513 83.16250445735731,136.38434090948257 83.16254554207251,136.38264700783714 83.16225049369845,136.38104321511918 83.1616306507787,136.37959116418338 83.16070983352907,91.00745759860087 47.70471273777429,-11.691678619246499 61.34689554994591,-33.79755445921219 85.09421525362518,-33.7987816906185 85.09530774427819,-33.80019114476049 85.09615218005024,-33.80173336063651 85.09671892773947,-33.80335421832898 85.0969880988603,-33.8049968381973 85.09695024757627,-33.80660357691587 85.09660670217643,-33.808118050311506 85.09596951846243,-33.80948711201435 85.09506105668265,-33.81066271848674 85.0939131968595,-33.81160361498191 85.09256622004571,-33.812276783268395 85.09106739476917,-33.81265860031601 85.08946931827111,-33.812735667282574 85.08782807074738,-32.830674277011205 64.15491927762633,-166.9120300852194 81.96578933819151,-166.91372994506622 81.96584876974394,-166.9154093128506 81.96557899307163,-166.91700503326308 81.96499015355748,-166.91845709668723 81.96410439545254,-166.91971089595725 81.96295502910593,-166.92071927994778 81.96158527827609,-166.92144432676722 81.96004665463211,-166.9218587698712 81.95839702057518,-166.92194702346433 81.95669841323047,-166.9217057686293 81.95501471144192,-135.70224400417752 -45.9322191166313,-138.57126185553517 -49.74180297177792,-161.44988958707904 -54.37476978072864,-161.45143808151082 -54.37523543008462,-161.45287478035848 -54.37597742789392,-161.45415085337137 -54.37697055527431,-161.4552229296195 -54.37818105799885,-161.45605457157663 -54.3795677937282,-161.45661751355206 -54.381083630348755,-161.4568926223796 -54.382677047890056,-161.4568705477121 -54.384293889575865,-161.45655203981923 -54.38587920249453,-161.4559479240874 -54.38737910532821,-161.45507873308873 -54.388742619660995,-161.45397400872366 -54.38992340262376,-161.4526712981565 -54.39088132198683,-161.45121487766946 -54.391583820166765,-161.44965424780858 -54.39200702078731,-161.44804245096856 -54.392136540185234,-141.89488089543744 -54.15502243957519,-153.27347396169714 -69.26392265746459,-153.2743589702193 -69.26537072588309,-153.2749485381606 -69.26696212522691,-153.2752205928412 -69.26863727551263,-153.27516494887718 -69.27033346122717,-153.27478368950827 -69.27198717931759,-153.27409108860425 -69.27353651666519,-153.27311307626903 -69.27492346803459,-153.2718862680504 -69.27609610771653,-153.27045659410012 -69.27701053356093,-153.268877579607 -69.27763251061793,-153.2672083408813 -69.27793875285136,-153.26551137211467 -69.27791779493838,-153.26385020567662 -69.27757042151681,-107.17294666067983 -54.86628398298008,-106.1185414985015 -57.820838687964276,-161.49299710582102 -75.80397143603332,-161.49452500826962 -75.80463385281091,-161.49590016714416 -75.80557311845463,-161.4970730084222 -75.80675537274882,-161.49800125156384 -75.8081379958174,-161.49865143371088 -75.80967114455622,-161.4990001160121 -75.81129954946056,-161.4990347285859 -75.81296450707245,-161.49875402366052 -75.81460599622092,-161.49816812055553 -75.81616484176531,-161.49729814088408 -75.81758484783957,-161.4961754471254 -75.81881482369457,-161.49484051201802 -75.81981042910776,-161.49334145953082 -75.82053577283341,-161.49173233000997 -75.82096470647024,-161.49007113204223 -75.82108176710256,-100.22898834625123 -74.30605444452195,-100.22734583448315 -74.30585777708335,-100.22576946346221 -74.30535620216963,-100.22431530761126 -74.30456756172502,-100.22303509393429 -74.30351990914377,-100.22197436199151 -74.30225051135928,-100.22117084397333 -74.30080452319054,-100.22065312249669 -74.299233381102,-100.22043961386883 -74.29759297351377,-100.2205379129852 -74.2959416527474,-100.220944523165 -74.29433815932634,-106.0959583598649 -57.83192845601232,-92.94623645293606 -53.56150642974892,0.5168968571681063 -52.42819495175221,42.552398940491486 -80.15392826171708,42.553823957605765 -80.15468988561345,42.55536450400553 -80.15517718585528,42.55696829838054 -80.15537362500162,42.55858091298275 -80.15527253652432,42.56014762073331 -80.15487735104905,42.56161525248782 -80.15420147993068,42.56293400143029 -80.15326786011391,42.56405911336014 -80.15210817572546,42.564952405509295 -80.15076178281409,42.56558356234557 -80.14927437372997,42.56593116438665 -80.14769642646958,42.56598341511011 -80.14608149161101,42.565738541290365 -80.14448437497535,42.5652048531764 -80.1429592776891,42.56440046246796 -80.14155795676808,22.856549024752262 -52.14358082479128,22.85544171929926 -52.14229333196901,22.854107064023683 -52.14124335176489,22.852595089554377 -52.14047024353326,22.850962473473096 -52.14000298785936,22.849270415709668 -52.13985910019877,0.5220842171561202 -52.41060241052812,-8.41778896463083 -46.51405003506674,2.082503817262605 -45.5265842190059,82.16974873985578 -55.61946094607285,82.17129108418781 -55.61951844683097,82.17281962817947 -55.61930470483393,82.17428704023979 -55.6188263386343,82.17564788173712 -55.61809816091227,82.17686001401307 -55.61714271979877,82.17788590321227 -55.61598960066932,87.42894995498656 -48.54817950299798,90.86025690382013 -48.842320647346625,90.86187779422266 -48.842309257891365,90.86346890919046 -48.841999792907956,90.8649759064788 -48.84140282172809,90.86634731676145 -48.84053873304434,90.86753630149138 -48.839437038563695,90.86850225260417 -48.838135365077605,90.86921217942799 -48.836678169372995,90.86964183543259 -48.83511521987464,90.8697765463347 -48.83349989687612,90.8696117112771 -48.831887369412634,90.86915295996427 -48.83033271104191,90.86841596038786 -48.82888901888599,90.8674258837091 -48.827605600175325,88.83971158165615 -46.64932716144001,92.40269805720794 -41.853630224309256,126.8456757419591 -63.47440298320586,126.84713519537095 -63.47513926788542,126.84870592800237 -63.475591947011644,126.85033338098 -63.4757452969263,126.85196102526822 -63.47559399107129,126.8535323251863 -63.47514328500498,126.85499270215635 -63.47440883385204,126.85629143047208 -63.47341614852797,126.85738339923923 -63.472199709625954,126.85823067928733 -63.47080176974498,126.85880384062692 -63.46927088585993,126.8590829746903 -63.46766023271123,126.85905838584898 -63.466025755798086,126.85873092818818 -63.46442422813017,126.85811197584037 -63.46291127823613,126.85722302790863 -63.461539457925234,126.85609496170247 -63.46035641691782,97.38483049679773 -37.827161184361024,99.87187230030216 -36.330501626203954,171.77091226660818 -29.569125763297997,171.77242885150693 -29.568846999536735,171.7738731802143 -29.568306949932698,171.77520061136264 -29.567522306359965,171.7763701166585 -29.566517320612498,171.777345548987 -29.565323054828713,171.77809675964784 -29.56397642142174,171.77860053019282 -29.562519042189095,171.77884129006245 -29.56099596186458,171.77881159784133 -29.559454255873884,165.32871350322802 30.33706888582541,176.38762884933539 33.794883447557986,176.38920864287232 33.79555326659214,176.3906277904606 33.79651785214075,176.39183197552205 33.79774028557272,176.39277510897307 33.799173779364644,176.39342109324193 33.80076346785056,176.3937452038706 33.80244850715521,176.39373503582075 33.80416440393784,176.3933909782652 33.80584548381587,176.39272619969265 33.80742740499197,176.39176614389606 33.80884962087758,176.39054755613435 33.810057697458305,176.38911707674143 33.811005396706115,176.3875294560099 33.81165644629765,176.38584545867357 33.81198592790426,176.38412953819284 33.81198123091831,176.3824473698573 33.81164253511265,176.38239992262746 33.811606862577534,176.38239393445264 33.81162601425782,176.37937452790632 33.81070321484654),"
1110             "(31.940896057402718 -11.516674682385004,31.735090184010808 -11.433768531594366,34.28637780994461 -10.636047228893936,31.940896057402718 -11.516674682385004),"
1111             "(30.28283959927952 -10.848748755534567,-3.4172969820295727 2.7269017301769836,-13.569154489871252 9.18584944133385,-12.274858999116972 9.628378040430327,21.92730276845213 2.385649455001494,38.84218041215776 -8.23228345814529,30.28283959927952 -10.848748755534567),"
1112             "(-3.506381078742539 2.7627880702187406,-16.750651901766318 8.098065902036172,-13.590409501346059 9.178582205591375,-3.506381078742539 2.7627880702187406),"
1113             "(31.709407405831065 -11.423422566994818,30.308715440626955 -10.859172493055892,38.861820878026606 -8.244612297573639,39.53325186684806 -8.666087271928937,34.579078645088416 -10.526151567651766,31.709407405831065 -11.423422566994818),"
1114             "(31.96495469130859 -11.526366382128769,34.5846215239078 -10.542808015164859,39.883544951634676 -8.885975497800693,42.787058225913796 -10.708574699971027,37.770908594399415 -13.865217464656103,31.96495469130859 -11.526366382128769),"
1115             "(48.77877229519879 -5.194821637047497,38.86437999888012 -8.225507106217272,21.97711163867511 2.3751018026608763,48.385785409894076 -3.2172657509225715,49.85165664674822 -4.7920077720156655,48.77877229519879 -5.194821637047497),"
1116             "(52.035281286546805 -3.9721613339210506,48.39482899889053 -3.201249949645277,24.68775090776513 22.266150556743217,27.256969910296846 23.144584341056124,56.359252044298216 -2.1676440520591687,55.64595593834196 -2.6165186152963713,52.035281286546805 -3.9721613339210506),"
1117             "(21.0523618078348 -15.604823171775074,20.044774220126357 -15.088996753249816,23.066991360577624 -14.144024584675869,23.763240995171685 -14.58700084866993,21.0523618078348 -15.604823171775074),"
1118             "(49.86941225561311 -4.785336300805852,48.41562983381898 -3.2235856816187862,52.00474175020747 -3.9836250990190427,49.86941225561311 -4.785336300805852),"
1119             "(56.52330868895917 -2.287118069864981,56.3885724075448 -2.1699191303695926,106.52503218338835 29.380766897799347,127.67871416131852 24.428460971650335,56.52330868895917 -2.287118069864981),"
1120             "(23.783784057718577 -14.579279673235199,23.088894501216046 -14.137168734379976,31.708657690867156 -11.442032284077861,31.91659602271336 -11.525797467311321,23.783784057718577 -14.579279673235199),"
1121             "(39.55390791690693 -8.65834200124904,38.88402046337834 -8.237835944785246,48.51602741760274 -5.293470218105426,39.55390791690693 -8.65834200124904),(56.50463609360271 -2.2941260112243,55.727564043439656 -2.5858892138401472,56.373071028355454 -2.1796740901332754,56.50463609360271 -2.2941260112243),(21.03014957321752 -15.613158799416311,10.569260752810493 -19.54075189827794,-2.9464639789869125 -22.277697151591028,20.02087042017853 -15.096466397529603,21.03014957321752 -15.613158799416311),"
1122             "(52.47436796255111 -4.065143439019163,52.0671665340097 -3.978913434571549,55.572196226218196 -2.6629353253941694,54.16542157313718 -3.5482133364501145,52.47436796255111 -4.065143439019163),"
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1127             "(56.963208077106145 -2.6929774535282007,54.22943361944536 -3.5286570687708547,55.65380423765296 -2.6323059828796573,56.51967220394539 -2.3072039455782374,56.963208077106145 -2.6929774535282007),"
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1138             "(21.933986962464473 2.402164887728272,2.4189169499386907 14.652281880490598,24.669574614144935 22.25993595597394,48.36498457496562 -3.1949300189490657,21.933986962464473 2.402164887728272),"
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1141             "(52.5097940270921 -4.072645352049953,54.108776779744645 -3.583859692404417,53.12503062771869 -4.202927454922124,52.5097940270921 -4.072645352049953),"
1142             "(43.28546691270277 -26.986883767640755,42.97679823939298 -26.79048854796605,56.466941170357856 -19.295797633524103,64.08900802970163 -24.08037950217483,45.2669261914462 -28.001268064806617,43.28546691270277 -26.986883767640755),"
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1146             "(9.350288473315587 38.74248379268954,-6.585012056625516 55.86103593692023,70.2680521039453 37.868910337863355,40.90146758060325 27.828271548502038,24.262734733742946 25.772111264832496,9.350288473315587 38.74248379268954),"
1147             "(73.09089007444824 -29.731095597924465,85.69919539743492 -37.64566996857491,80.88024981899486 -38.09884440280534,73.09089007444824 -29.731095597924465),"
1148             "(73.04450471090416 -29.681265947851927,69.3379197794863 -25.699470542214453,79.58321142449617 -22.367138852695543,96.03221445150848 -36.67396648552466,85.72790431968778 -37.64297969856965,73.04450471090416 -29.681265947851927),"
1149             "(9.46387079270287 38.62046756176968,24.239338321979417 25.769211949937343,21.716979498625832 25.45751975956489,9.46387079270287 38.62046756176968),"
1150             "(50.56156943063165 -5.528888731813538,49.937839204058804 -4.858844205801361,52.475136061040715 -4.083236988055326,53.10370484197959 -4.216347691874761,51.46866317625423 -5.24527327754466,50.56156943063165 -5.528888731813538),"
1151             "(9.224408992818482 38.851964794507175,-11.711265479809555 57.06114671556529,-6.615650355906411 55.86820869061986,9.224408992818482 38.851964794507175),"
1152             "(60.55579159384646 -5.794417042185758,69.30386052897589 -7.646930246489353,63.93552683381575 -8.734031540594103,60.55579159384646 -5.794417042185758),"
1153             "(57.688459366105995 -3.3005293657993064,56.99858293272367 -2.7004966111511806,122.14822367585627 17.214748146233596,120.66377698176358 16.39003571587255,57.688459366105995 -3.3005293657993064),"
1154             "(73.03324406984439 -29.694914662490135,80.85821729038376 -38.100921377000205,63.342896321792594 -39.748050882541506,50.75959180753584 -31.74216343806383,67.57943285376581 -26.271427096622276,73.03324406984439 -29.694914662490135),"
1155             "(39.86400285729009 -8.873708408777603,34.87732280230907 -10.432912187499966,39.551916707235804 -8.677803685461726,39.86400285729009 -8.873708408777603),"
1156             "(43.44410013402389 -27.087801782144677,45.239552804641725 -28.00697030328185,44.975318735147916 -28.06201375436441,43.44410013402389 -27.087801782144677),"
1157             "(-15.257389373944136 10.259973914784002,-12.30836353977779 9.635461489231913,-13.588110003575826 9.197907303291592,-15.257389373944136 10.259973914784002),"
1158             "(23.069529991534154 -14.124848414588413,21.951827586412705 -13.413730431788267,30.282022284527198 -10.86733124094458,31.682974917738175 -11.431686321512942,23.069529991534154 -14.124848414588413),"
1159             "(23.80229280523764 -14.591055529795597,31.94065465827722 -11.53548916772298,37.76851162339057 -13.883163606614682,37.770097848105024 -13.883634342409975,37.771744254525196 -13.883798801928782,37.77339225172808 -13.883651132524463,37.774983192179256 -13.883196589331225,37.77646045883184 -13.882451348248843,42.80353701408153 -10.718930933297813,45.567034652447205 -12.45365217013186,26.508719800762194 -16.312970859703256,23.80229280523764 -14.591055529795597),"
1160             "(43.276761579565346 -27.002134145623014,44.95069160862587 -28.067143910504445,38.11630436469161 -29.49083715589638,42.92240688088259 -26.820725087652352,43.276761579565346 -27.002134145623014),"
1161             "(126.75959213687518 -63.39967008039708,92.41319098322936 -41.83950698990248,93.78447601919933 -39.99379341951623,97.3690323884615 -37.83666821790139,126.75959213687518 -63.39967008039708),"
1162             "(72.98685869023261 -29.645084995156807,67.60116781362723 -26.264357693619786,69.31952721664192 -25.70545281408542,72.98685869023261 -29.645084995156807),"
1163             "(39.886037618944634 -8.866828591799006,39.57257275758669 -8.67005841496514,48.78439784949424 -5.211447043733159,49.91918587276122 -4.864551295334174,50.543010064128545 -5.534696763377852,39.886037618944634 -8.866828591799006),"
1164             "(9.337991159717035 38.729948727398885,21.695490271536684 25.454859141680437,-8.788846562680476 21.687676810037537,-31.489294946971892 35.93737116944357,-32.81216829744508 64.1347806843964,-11.700243714994912 61.33035113568702,-6.637054435703233 55.89123580798307,-11.741701242558069 57.08628824654891,-11.743347393206076 57.086512042263855,-11.745006213819227 57.08642142961937,-11.746618193091077 57.08601965940509,-11.748125500179835 57.08532114539797,-11.749474059428762 57.084350947258365,-11.75061549036676 57.0831438714978,-11.751508843390358 57.08174322277196,-11.752122068858302 57.08019925029701,-11.752433166894022 57.07856734512509,-11.752430976646009 57.076906052953085,-11.752115576690887 57.07527497375627,-11.751498282214417 57.07373262359911,-11.750601239071592 57.07233433533203,-11.749456629289176 57.07113027348812,9.337991159717035 38.729948727398885),"
1165             "(19.998587701357646 -15.085058937588059,-3.1132193245213102 -22.311465244718235,-15.089019545185295 -24.73657453178888,18.684739096779687 -14.412444637400831,19.998587701357646 -15.085058937588059),"
1166             "(21.051250846321395 -15.623961427658536,23.562530114275848 -16.909590792795676,10.677531366771717 -19.518827010871995,21.051250846321395 -15.623961427658536),"
1167             "(54.09086078489642 -4.42538694225184,51.53408460058219 -5.224830093565444,53.128334513377965 -4.221574604966094,54.09086078489642 -4.42538694225184),"
1168             "(173.75757156169772 32.99091541934996,165.3267971738516 30.354864191440612,165.32065635283269 30.411888723916427,173.75757156169772 32.99091541934996),"
1169             "(10.465747395220248 -19.57961137948609,-12.894911802992752 -28.350460831776864,-14.505090251111184 -25.891736822767676,-3.10897552967657 -22.328503814897203,10.465747395220248 -19.57961137948609),"
1170             "(-27.610965806972345 -33.8756481721416,-38.00614396293315 -37.7785591589894,-43.02265457370873 -37.34856959661485,-29.167463128681774 -32.849015266607424,-27.610965806972345 -33.8756481721416),"
1171             "(-38.04432250117674 -37.79289279162382,-43.34682819058996 -39.783739126387225,-48.515464191322366 -39.13238742407438,-43.065536969219835 -37.36249587240486,-38.04432250117674 -37.79289279162382),"
1172             "(-43.38210310004821 -39.796974297919405,-78.87353889947534 -53.12237586126752,-78.87504724430607 -53.12311387651708,-78.87638729989119 -53.124125816073466,-78.87750994786981 -53.125374588331766,-78.87837403873353 -53.126814420827664,-78.87894790011936 -53.128392537980105,-78.87921049772773 -53.130051095526014,-78.87915220631305 -53.1317293007423,-78.87877516248726 -53.13336564074071,-78.87809318640446 -53.13490013715957,-78.87713127519739 -53.136276544608954,-78.87592468673323 -53.13744441228774,-78.87451764727265 -53.13836093320586,-78.87296173040167 -53.138992513230576,-78.87131396665488 -53.13931600244487,-78.86963475311974 -53.1393195436839,-8.445695735047487 -46.516657330884335,0.49077562272833575 -52.4109659347568,-92.89011328794561 -53.543280146805785,-48.55468477896229 -39.14512450915579,-43.38210310004821 -39.796974297919405),"
1173             "(-27.590643470202913 -33.86803834336524,-29.146094667189693 -32.84209543970167,-19.625029335662298 -29.750071937783378,-19.62345393418427 -29.749383122488545,-19.62204318480157 -29.748400197004802,-19.620851301821823 -29.747160934607262,-19.61992408863952 -29.745712959454867,-19.619297177537277 -29.7441119164207,-19.61899466035717 -29.742419332690684,-19.619028162664783 -29.74070025330835,-19.61939639698522 -29.739020741530297,-19.620085212280053 -29.73744534005227,-19.621068137763796 -29.73603459066957,-19.622307400161336 -29.734842707689822,-19.62375537531373 -29.73391549450752,-19.6253564183479 -29.733288583405276,-19.627049002077914 -29.73298606622517,-19.628768081460247 -29.733019568532782,-19.6304475932383 -29.73338780285322,-29.164834804336436 -32.82973483928127,-31.586344616113706 -31.2325578835804,-14.522499048949383 -25.897172872851705,-12.911746604589299 -28.356773367533684,-27.590643470202913 -33.86803834336524),"
1174             "(-15.440268307843084 -24.82560063405746,-33.11063724365916 -30.227166517161177,-35.22563117058885 -28.832160994115174,-15.440268307843084 -24.82560063405746),"
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1176             "(-33.13242765496227 -30.23380803484376,-53.47598660261661 -36.452516973556065,-67.09295594277563 -35.28529916770173,-35.25002833910638 -28.837083149550402,-33.13242765496227 -30.23380803484376),"
1177             "(-53.520970953712265 -36.466267226310144,-58.2354762927896 -37.90741924457058,-71.67669094887043 -36.21351002448205,-67.15404194693704 -35.29766922081722,-53.520970953712265 -36.466267226310144),"
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1199             "(63.338554000982406 -39.76607948751283,75.50811715621062 -47.508744406950505,26.068801349075883 -43.27092792395031,63.338554000982406 -39.76607948751283),"
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1201             "(44.97189605739587 -28.080645200533002,50.71876939527397 -31.736994677353735,17.512462576017413 -42.53750991301251,15.017806026020082 -42.32364842620168,38.064721701858005 -29.51950096385712,44.97189605739587 -28.080645200533002),"
1202             "(63.31443324277529 -39.750733090438565,25.97083832848871 -43.262530741061205,17.557355750597907 -42.54135463818072,50.737959125026705 -31.74919957485254,63.31443324277529 -39.750733090438565),"
1203             "(85.75231357643165 -37.6583020340463,96.05049525434477 -36.68986655103241,96.15182157912969 -36.77798293714598,93.77244835997257 -39.980558168609235,91.56652005301999 -41.308048394369706,85.75231357643165 -37.6583020340463),"
1204             "(45.61355673842014 -12.462143693709407,55.186990966922515 -10.523510597075763,60.993339532379515 -16.76100411965765,56.46747536013181 -19.27543354028412,45.61355673842014 -12.462143693709407),"
1205             "(64.13520076257863 -24.088675402162217,67.2169128156077 -23.446714026907344,69.14521649458379 -25.51818851852844,67.33723331195878 -26.098671354979363,64.13520076257863 -24.088675402162217),"
1206             "(64.11378371141129 -24.075218400024625,56.48444685596549 -19.286072018869127,61.00566269662134 -16.774225066753985,67.20295566340234 -23.431703029161305,64.11378371141129 -24.075218400024625),"
1207             "(45.591992977695206 -12.448607551276503,42.82001730414031 -10.708559948596815,50.72722514027072 -5.7325837246547025,55.17296905968835 -10.508447510846764,45.591992977695206 -12.448607551276503),"
1208             "(90.83906500907895 -48.82288432501792,87.44124588861607 -48.531629462280534,88.82907600317388 -46.66364240274166,90.83906500907895 -48.82288432501792),"
1209             "(23.58758948005409 -16.922419734971612,42.90360027945853 -26.81109719825043,38.05849031533148 -29.502880586949516,-6.114132515913077 -38.70463297488126,-12.88506814740878 -28.365491980870296,10.5740180759243 -19.557686478564662,23.58758948005409 -16.922419734971612),"
1210             "(-3.2757307439501204 -22.362271881443974,-14.515075742325166 -25.876489092295138,-15.231034498305647 -24.783228289527237,-3.2757307439501204 -22.362271881443974),"
1211             "(-103.408268267121 -53.67082036628739,-107.56298077416507 -53.72117660087794,-107.79361648076426 -53.07491097499442,-58.233960524270685 -37.92529090694332,-54.5393407101279 -38.390899910893495,-103.408268267121 -53.67082036628739),"
1212             "(-31.626870337402607 -31.22684198473644,-49.444973181371616 -36.79804691662782,-53.42912203896892 -36.45653410481242,-33.113427002687885 -30.246340465564593,-31.626870337402607 -31.22684198473644),"
1213             "(-49.48916830524817 -36.811864820269555,-54.49901880228574 -38.378300779876625,-58.192985934280664 -37.912774029229915,-53.47410637084559 -36.47028435921391,-49.48916830524817 -36.811864820269555),"
1214             "(-31.605236430328155 -31.220097240155404,-33.0916365938955 -30.239698946225996,-15.262540010301606 -24.789610509222257,-15.249551258319446 -24.786972494086065,-14.532484538870866 -25.881925144352813,-31.605236430328155 -31.220097240155404),"
1215             "(-103.46664127579638 -53.6890713586619,-107.16209180873788 -54.84450985214174,-107.55674612108137 -53.73864675776175,-103.46664127579638 -53.6890713586619),"
1216             "(-110.00462741884331 -53.750805850432336,-107.81040256225506 -53.08006517376252,-107.58151701429983 -53.72142667015059,-110.00462741884331 -53.750805850432336),"
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1218             "(-27.592871920864 -33.887582518965544,-19.25708965943322 -39.38568922534542,-37.965533667372725 -37.78204018761589,-27.592871920864 -33.887582518965544),"
1219             "(-38.0037121954104 -37.796373821125144,-19.22641600937537 -39.405920919960636,-12.821155357361697 -43.63069616509796,-43.309481338204634 -39.78844570828592,-38.0037121954104 -37.796373821125144),"
1220             "(-43.34475623878629 -39.801680880936765,-12.788017983898143 -43.65255287986782,-8.469056186486533 -46.50124926830628,-78.80591177161446 -53.11570776137347,-43.34475623878629 -39.801680880936765),"
1221             "(-27.572549585136507 -33.87997268950195,-12.901902948535914 -28.37180451734392,-6.125539187747014 -38.71923420248274,-6.124615012752566 -38.72041215386896,-6.1235039573952275 -38.72141575980836,-6.12223839702193 -38.72221577595208,-6.120855209143663 -38.72278889041018,-6.119394698851558 -38.7231184030432,-6.11789942435578 -38.723194712092116,-6.116412956870168 -38.72301559396661,38.006907672851085 -29.531544390670412,14.986494714540797 -42.320976703350695,-19.220444896885056 -39.3888453254074,-27.572549585136507 -33.87997268950195),"
1222             "(163.85356981584565 38.01045640606598,150.78183751989167 33.1026264373484,160.43346758187292 38.46477202131451,163.85356981584565 38.01045640606598),"
1223             "(127.70830325425007 24.439550041637304,106.54590505913245 29.393902120191427,119.4559466211646 37.51814283753344,144.37633145980607 40.59773643801638,160.4042990486444 38.46863420514055,150.67036889056672 33.060765246572494,127.70830325425007 24.439550041637304),"
1224             "(137.87665775262624 22.04101325621122,122.3018982810747 17.280057664991475,132.94821653533805 23.194814080812744,137.87665775262624 22.04101325621122),"
1225             "(137.91007347628613 22.051206470998714,132.97106197457936 23.207481912287477,150.67791335246926 33.044889401030915,163.89246423334544 38.00632192281352,163.89395437188944 38.00704878327708,163.89528110506717 38.00804307603519,163.89639702613067 38.00926927308045,163.89726226105742 38.01068356001573,163.89784589332643 38.0122354016276,163.8981270686255 38.01386934760742,163.89809574001623 38.01552701389832,163.8977530269305 38.01714916887077,163.8971111751712 38.018677849783465,163.8961931193457 38.020058433904424,163.8950316633681 38.02124159028708,163.89366830831162 38.02218504246065,163.892151769495 38.02285507905031,163.8905362357896 38.02322775835002,160.45914599302486 38.479038148184,164.20988616119448 40.562819558817196,165.3016644430351 30.424412023824377,137.91007347628613 22.051206470998714),"
1226             "(138.43525780056368 21.928255201073114,165.3116438348011 30.33174198050335,171.7604175947424 -29.552483202131402,99.90657434057331 -36.30961852717998,149.90557033770168 -6.2210711003068075,149.90688874767233 -6.220099211525472,149.9080034680365 -6.2188991402094,149.90887562498716 -6.217512736621926,149.90947480366685 -6.215988349019058,149.9097801088294 -6.214379137593647,149.90978089352305 -6.212741220612166,149.90947713038307 -6.211131717394169,149.90887941258603 -6.209606756381856,149.9080085844325 -6.20821951776467,149.90689501444066 -6.207018378918731,149.90557753630043 -6.206045227335496,149.90410209462055 -6.205333999873108,149.90252014269552 -6.204909499271364,149.90088684816726 -6.204786529202118,149.89925916915584 -6.204969378018662,113.2096851912215 -13.847909418407404,115.57854716414471 -10.659476291875812,122.98695766373115 -8.24983286863276,122.99248836987037 -8.24805714415804,122.99248165360493 -8.248036225546489,122.99252002096307 -8.24804691580876,122.99409329720051 -8.247358404482963,122.99550225424824 -8.246376525670339,122.99669287690277 -8.24513892167087,122.99761952024896 -8.243693038524139,122.99824665954954 -8.242094307069925,122.99855025215751 -8.240404017895434,122.9985186592394 -8.238686971637309,122.99815309197326 -8.237008994718828,122.99746756511585 -8.235434415761524,122.99648835971863 -8.234023599418036,122.99525301559079 -8.232830632171684,122.99380889213523 -8.231901248822297,122.99221135273041 -8.231271079150648,122.99052164226393 -8.230964281979102,122.98880453918649 -8.230992618994556,122.98712587209964 -8.231355003840502,122.98709746667338 -8.231375211028098,122.98709422100694 -8.23136523218978,122.98445994390397 -8.232210944081352,115.62680134884883 -10.59450865345169,139.5811057192091 21.647409332212078,139.58192836390296 21.648754158529584,139.58249698017912 21.650224525030524,139.58279319818183 21.651772929697092,139.58280744822028 21.653349349391526,139.58253926992927 21.65490285591575,139.58199732714186 21.65638326131015,139.58119912799356 21.65774273923798,139.5801704593002 21.65893737007465,139.5789445534828 21.659928559785786,139.5775610149529 21.660684286755505,139.57606454064265 21.661180136284507,138.43525780056368 21.928255201073114),"
1227             "(-11.672901457713799 61.32672411402214,90.98812319335303 47.68960389094599,84.7626026713778 42.82467865599619,70.29932468799596 37.879602651101656,-6.606416144696235 55.884063056220455,-11.672901457713799 61.32672411402214),"
1228             "(21.731752401457072 25.441649913510176,24.257151920623585 25.753718243894582,27.241673724801043 23.15789335269138,24.67466474051967 22.280215188935983,21.731752401457072 25.441649913510176),"
1229             "(27.27614200608447 23.151139413488384,40.90533858676494 27.81105618886412,88.24260741703002 33.66087553733939,106.50102688198155 29.386386724583776,56.37475342083092 -2.1578890939673077,27.27614200608447 23.151139413488384),"
1230             "(24.280548333299286 25.756617557996357,40.820431510930504 27.800564754617064,27.26084581815643 23.16444842429204,24.280548333299286 25.756617557996357),"
1231             "(-8.816428652507156 21.684268290604805,-29.245606398615163 19.15968622376516,-30.746990152471433 20.114940195264964,-31.488293120007164 35.91601695199151,-8.816428652507156 21.684268290604805),"
1232             "(-29.272966059430175 19.15630519150303,-30.693779343676994 18.980737162403244,-30.745984888163573 20.09351270989812,-29.272966059430175 19.15630519150303),"
1233             "(-8.765268372199529 21.672915212812164,21.710263177057982 25.43898929273592,24.6564884472217 22.274000588276877,2.399797039244074 14.664283533978011,-8.765268372199529 21.672915212812164),"
1234             "(-11.719020876527594 61.35052257161079,-32.813002816538585 64.15256868853093,-33.794092220123524 85.06475931794377,-11.719020876527594 61.35052257161079),"
1235             "(138.36863398834245 21.92583635515323,120.74643517661659 16.41589072499998,122.22857097659741 17.23931929444039,137.91059951928324 22.033067125450867,138.36863398834245 21.92583635515323),"
1236             "(138.40162314694612 21.936129433384743,137.94401525032401 22.043260338510414,165.30357425200395 30.40667726763579,165.30972750566778 30.349537283861128,138.40162314694612 21.936129433384743),"
1237             "(127.7390129190668 24.432360580502113,150.56644469028546 33.00302819199967,132.94563868010746 23.21343377755938,127.7390129190668 24.432360580502113),"
1238             "(-161.35503387993074 -54.37346556730929,-138.5871756703948 -49.76293390065463,-141.88154531641396 -54.13731498386075,-161.35503387993074 -54.37346556730929),"
1239             "(-35.27079817688228 -28.823383801272726,-67.15508315200245 -35.279973754753655,-104.45438672212283 -32.08275635744238,-104.45608427388785 -32.08277574513043,-104.45774629244461 -32.083121797430444,-104.45931051252892 -32.08378154996377,-104.46071833276328 -32.084730285999285,-104.46191701107783 -32.08593246243208,-104.46286164062022 -32.08734304135757,-104.46351683212971 -32.088909177355255,-104.46385803974773 -32.09057219727058,-104.46387248059507 -32.0922697983248,-104.46355961366501 -32.09393838220386,-104.46293116009147 -32.09551543768267,-104.46201066403262 -32.096941882523176,-104.46083261062104 -32.09816427690997,-104.4594411340252 -32.0991368255003,-104.45788836402274 -32.099823093084304,-104.45623247302943 -32.10019736958055,-71.78503500133692 -36.217536765212955,-110.97726480920838 -44.153991877456086,-118.48907838644061 -23.105096307062404,-86.1530711337859 19.831784241114434,-76.17018886097277 -1.845422238170359,-76.16937610532348 -1.846827817505229,-76.16831819663724 -1.848059505056384,-76.1670513874113 -1.8490750932589226,-35.27079817688228 -28.823383801272726),"
1240             "(-104.01746970265641 -32.1378111596404,-67.21616917021902 -35.29234380666436,-71.7311963690772 -36.20664105942231,-104.01746970265641 -32.1378111596404),"
1241             "(-19.189771245865394 -39.40907702065701,14.959045315399937 -42.33622673608511,10.708277693154 -44.69782106654718,2.082853933046394 -45.50894770194591,-12.781743251109447 -43.63567754687929,-19.189771245865394 -39.40907702065701),"
1242             "(25.87291249723667 -43.271742962131206,11.016303004296148 -44.66886433771501,17.514523291044114 -42.55528610711852,25.87291249723667 -43.271742962131206),"
1243             "(-12.74860587593394 -43.65753426277832,2.0024981350794633 -45.51650162110258,-8.441149421139997 -46.49864196914455,-12.74860587593394 -43.65753426277832),"
1244             "(0.5482054515958907 -52.42783142752352,22.844877876175584 -52.15747591132524,42.52338780560707 -80.11376900277862,0.5482054515958907 -52.42783142752352),"
1245             "(70.30021875120347 37.86136945403442,88.19316357634735 33.672450869505475,40.98637445712528 27.838762914602786,70.30021875120347 37.86136945403442),"
1246             "(70.33149133386337 37.8720617667972,84.7697194975705 42.80859204783613,84.77105909891975 42.80917893165259,84.77228255716334 42.80998025200993,91.0124858249585 47.68637930033897,127.81301147359562 42.79793866689235,119.44990642462011 37.5350680374038,88.24355226977912 33.67867053045407,70.33149133386337 37.8720617667972),"
1247             "(144.3073988767456 40.60689326310742,119.4909083116505 37.540144098182196,127.84021527260577 42.79433164264914,144.3073988767456 40.60689326310742),"
1248             "(88.29299612070747 33.66709519588936,119.4149447434929 37.5130667826444,106.52189974628405 29.399521939775685,88.29299612070747 33.66709519588936),"
1249             "(144.44527145744826 40.60625585489642,163.9457022420348 43.01606879557336,164.20784624646586 40.58176249549163,160.4299774597963 38.482900332010054,144.44527145744826 40.60625585489642),"
1250             "(144.37633892649745 40.61541268642703,127.86340960426224 42.808927748536924,161.67658544228874 64.08740831841152,163.94382395897412 43.0335107977197,144.37633892649745 40.61541268642703),"
1251             "(-41.90900718265291 15.92171071110581,-65.04965636135107 20.822031166079725,-65.63127790159731 28.752476130223627,-42.58516701826829 16.9541990192793,-41.90900718265291 15.92171071110581),"
1252             "(-42.60459058740299 16.983858586408623,-65.63278027468877 28.772961078412454,-66.67261586220584 42.95118235795973,-54.565741638677004 35.24839895429071,-42.60459058740299 16.983858586408623),"
1253             "(-54.58907517986818 35.28402900387246,-66.6742146811002 42.97298235051845,-66.98910868886206 47.26628926429717,-62.12011091968531 46.783833855102905,-54.58907517986818 35.28402900387246),"
1254             "(-54.55313781876444 35.261172150516714,-62.097702142309025 46.78161343185131,-46.30482922656958 45.2167417013382,-31.506387108397742 35.92737383993618,-30.76509132865387 20.12645029297113,-54.55313781876444 35.261172150516714),"
1255             "(-97.83416987317577 45.238498178710174,-65.64955249400556 28.76182418273821,-65.06752232404301 20.825807527637693,-82.6206997737451 24.54292980246981,-82.62234422414674 24.543118386846405,-82.62399482199257 24.54299466157833,-82.62559278256681 24.54256303304157,-82.62708119578785 24.541838873339582,-82.62840705301502 24.540847972838158,-82.62952313490874 24.539625621662307,-83.40757403122092 23.506493075556897,-90.83289438322406 30.035664942125123,-97.83416987317577 45.238498178710174),"
1256             "(-82.61888709171882 24.52458915191082,-65.06618612106601 20.80758831903435,-64.01341032562904 6.452926519952804,-83.39437198775232 23.49488435218103,-82.61888709171882 24.52458915191082),"
1257             "(-65.65105486819753 28.782309145932423,-97.84873506427972 45.26564377964443,-97.85028505214999 45.266259170730656,-97.8519235011197 45.266570062288324,-97.85359117767403 45.26656521490745,-97.85522779165703 45.26624480383146,-97.85677417589265 45.26562041262175,-97.85817442520765 45.26471461438658,-97.85937791752582 45.263560155713826,-97.86034114396688 45.26219877281023,-97.86102928178767 45.260679682646156,-97.86141745330046 45.259057803654485,-97.86149162525584 45.25739177030908,-97.86124911617533 45.255741813360295,-97.86069869329278 45.254167582361575,-90.86536170723733 30.064229436755205,-122.87031432291771 58.20657846684874,-122.87160397462488 58.20751906037725,-122.87304273757687 58.20821034821862,-122.87458295968815 58.20862943479625,-122.87617362852775 58.20876243988797,-122.87776206086001 58.208604958341404,-122.87929564752282 58.20816220597348,-122.88072359585243 58.20744884682156,-122.88199861194552 58.20648850746798,-122.88307846704171 58.20531299452339,-122.88392739614764 58.203961241186136,-122.88451728257994 58.20247801776782,-122.88482858919475 58.20091244889254,-128.50870223166575 4.921332760433136,-128.50874214078485 4.920024935850124,-128.5085870504444 4.918725726527491,-128.508240412044 4.917464045229747,-118.50876745117507 -23.102116039964123,-135.68859242632564 -45.914092066443295,-166.90162006241783 81.94670439205376,-32.82983975785978 64.13713127225718,-31.507388935807747 35.94872806687944,-46.297243998766895 45.232694686742164,-46.298438120776574 45.23332182175007,-46.29971427817714 45.23375845429706,-46.30104229243783 45.233994258910144,-62.110046067823596 46.80046435131626,-67.56717234515712 55.133453500144235,-67.56820100882734 55.134741527678834,-67.56945250271089 55.1358143403073,-67.5708826237989 55.13663404607767,-67.5724408599347 55.13717169282173,-67.5740721739131 55.13740829075129,-67.57571894740512 55.137335483181175,-67.57732301604885 55.136955841689016,-67.57882772382588 55.13628277528659,-67.5801799241631 55.13534005681094,-67.58133185708003 55.13416098326309,-67.58224283608062 55.13278719975146,-67.58288068520834 55.1312672285785,-67.58322287550715 55.12965475542346,-67.58325732074876 55.12800673315368,-67.00809756718309 47.28579861360277,-74.64384103040652 48.042403137098944,-74.64551355318005 48.04240861420995,-74.64715670691223 48.04209651127949,-74.6487107421129 48.04147817720973,-74.6501191498815 48.04057609629091,-74.65133071672265 48.039423070612024,-74.65230138680663 48.03806102728863,-74.6529958639579 48.03653949388014,-74.65338889511892 48.03491379743455,-74.65346618861936 48.03324305264807,-74.6532249338596 48.0315880122958,-74.65267390351174 48.03000885809735,-74.65183313452161 48.028563012347625,-74.65073319951154 48.02730304988773,-74.64941409507755 48.02627478634224,-66.69106576546662 42.962920784577285,-65.65105486819753 28.782309145932423),"
1258             "(-74.60894342391143 48.02131743628841,-67.00680717272054 47.268042957701205,-66.69266458534088 42.98472079049692,-74.60894342391143 48.02131743628841),"
1259             "(-138.56127670492663 -49.7577037198288,-134.94703094520807 -49.02582406883465,-133.72337212957453 -54.038411653780486,-141.85939298329575 -54.13705971460783,-138.56127670492663 -49.7577037198288),"
1260             "(-134.93399269617888 -49.00526523292734,-135.68321498734667 -45.93611109773349,-118.50171193441933 -23.121886343614484,-110.99462708067594 -44.15753153101153,-134.93399269617888 -49.00526523292734),"
1261             "(-138.54536289076012 -49.736572791872405,-135.69686656519858 -45.95423814792149,-134.95119672848287 -49.00875938278158,-138.54536289076012 -49.736572791872405),"
1262             "(88.82755353245742 -46.63627739859524,86.64413783102847 -44.29072778657896,91.56634116238342 -41.32862933986829,92.38779164183632 -41.84427969841862,88.82755353245742 -46.63627739859524),"
1263             "(96.17559112847069 -36.775403890830276,96.2533145203432 -36.670790012864686,99.8315395547437 -36.33429989598129,97.37090375596762 -37.815068768540016,96.17559112847069 -36.775403890830276),"
1264             "(92.39828457197696 -41.83015645846746,91.58318530508117 -41.31849282059788,93.74495703397014 -40.01757527428385,92.39828457197696 -41.83015645846746),"
1265             "(96.16509920779882 -36.78952577205994,97.35510564997305 -37.824575800671205,93.81196732309566 -39.95677632714469,96.16509920779882 -36.78952577205994),"
1266             "(88.81691795134695 -46.65059264343438,87.42069611419876 -48.52987476642635,80.5749329147718 -47.94307232519108,86.62877983973574 -44.29996996515029,88.81691795134695 -46.65059264343438),"
1267             "(69.32473564139825 -25.685312296376537,69.17686596344828 -25.526450792983923,79.43054197209301 -22.234338902371594,79.56777154519035 -22.35371429782551,69.32473564139825 -25.685312296376537),"
1268             "(79.58722163711042 -22.347388059401556,79.45006045094098 -22.22807217263994,91.24299727724733 -18.441755195353803,92.22218393874856 -18.237804190782946,79.58722163711042 -22.347388059401556),"
1269             "(67.58180682559251 -26.252208498722716,67.35665645137476 -26.110859094265415,69.15841818541341 -25.532373756550623,69.30634307855388 -25.691294568247503,67.58180682559251 -26.252208498722716),"
1270             "(10.713631867610786 -44.714913767695485,10.86035670084666 -44.70114019099129,10.566326319189315 -44.7967750242813,10.713631867610786 -44.714913767695485),"
1271             "(14.990356626143694 -42.338898459344726,17.469630118109404 -42.551441381415,10.93650885434335 -44.676371327096064,10.75178223878234 -44.69371860760433,14.990356626143694 -42.338898459344726),"
1272             "(113.19393813942808 -13.869104583916076,149.85225961536605 -6.232679296303189,99.86624158413852 -36.31341680350249,96.26738808398915 -36.65184732348474,113.19393813942808 -13.869104583916076),"
1273             "(113.18383917989723 -13.853283334263445,92.53313651295461 -18.155111782662388,115.54974201699517 -10.668833135736556,113.18383917989723 -13.853283334263445),"
1274             "(163.96311491920022 43.01821047323797,169.91789145903348 43.754090361605556,164.22449464723803 40.59100135183526,163.96311491920022 43.01821047323797),"
1275             "(92.37537042521268 -18.187979529764235,91.40187377110232 -18.3907452751927,115.58013059889898 -10.627916926612096,115.56781674564326 -10.64450497131272,92.37537042521268 -18.187979529764235),"
1276             "(-86.16139825386244 19.849866063211905,-118.49613390319635 -23.085326003412035,-128.4910459077906 4.921493651135869,-122.86916414947727 58.18220258298618,-90.8472856693717 30.0249784474685,-86.16139825386244 19.849866063211905),"
1277             "(-86.14941695432584 19.865785693545394,-90.81481832588861 29.996413910560918,-83.41817017513736 23.49245140750158,-86.14941695432584 19.865785693545394),"
1278             "(-106.11264211278916 -57.83736939023901,-100.24152662041178 -74.28881727173125,-161.4303237477923 -75.80205692190154,-106.11264211278916 -57.83736939023901),"
1279             "(-67.56328532753739 55.095514517777545,-62.132454845199874 46.802684774567844,-66.99039908239888 47.28404492010701,-67.56328532753739 55.095514517777545),"
1280             "(115.59662188220229 -10.635148141706566,115.6088128566935 -10.618708014427298,118.58211270640945 -9.664081031738045,115.59662188220229 -10.635148141706566)))";
1281         std::string msg;
1282         CG mpoly = from_wkt<CG>(wkt);
1283         bg::correct(mpoly);
1284
1285         BOOST_CHECK_MESSAGE(bg::is_valid(mpoly, msg), msg);
1286     }
1287 #endif // BOOST_GEOMETRY_TEST_FAILURES
1288 }
1289
1290 BOOST_AUTO_TEST_CASE( test_is_valid_multipolygon )
1291 {
1292     test_open_multipolygons<point_type, true>();
1293     test_open_multipolygons<point_type, false>();
1294 }
1295
1296
1297 template <typename CoordinateType, typename Geometry>
1298 inline void check_one(Geometry const& geometry)
1299 {
1300     bool const is_fp = boost::is_floating_point<CoordinateType>::value;
1301
1302     bg::validity_failure_type failure;
1303     bool validity = bg::is_valid(geometry, failure);
1304     if (BOOST_GEOMETRY_CONDITION(is_fp))
1305     {
1306         BOOST_CHECK(! validity);
1307         BOOST_CHECK(failure == bg::failure_invalid_coordinate);
1308     }
1309     else
1310     {
1311         BOOST_CHECK(failure == bg::no_failure
1312                     || failure != bg::failure_invalid_coordinate);
1313     }
1314 }
1315
1316 template <typename P, typename CoordinateType>
1317 inline void test_with_invalid_coordinate(CoordinateType invalid_value)
1318 {
1319     typedef bg::model::segment<P> segment_t;
1320     typedef bg::model::box<P> box_t;
1321     typedef bg::model::linestring<P> linestring_t;
1322     typedef bg::model::ring<P> ring_t; // cw, closed
1323     typedef bg::model::polygon<P> polygon_t; // cw, closed
1324     typedef bg::model::multi_point<P> multi_point_t;
1325     typedef bg::model::multi_linestring<linestring_t> multi_linestring_t;
1326     typedef bg::model::multi_polygon<polygon_t> multi_polygon_t;
1327
1328     typedef typename bg::coordinate_type<P>::type coord_t;
1329
1330     std::string wkt_point = "POINT(1 1)";
1331     std::string wkt_segment = "LINESTRING(1 1,10 20)";
1332     std::string wkt_box = "BOX(1 1,10 20)";
1333     std::string wkt_linestring = "LINESTRING(1 1,2 3,4 -5)";
1334     std::string wkt_ring = "POLYGON((1 1,2 2,2 1,1 1))";
1335     std::string wkt_polygon = "POLYGON((1 1,1 200,200 200,200 1,1 1),(50 50,50 51,49 50,50 50))";
1336     std::string wkt_multipoint = "MULTIPOINT(1 1,2 3,4 -5,-5 2)";
1337     std::string wkt_multilinestring =
1338         "MULTILINESTRING((1 1,2 3,4 -5),(-4 -2,-8 9))";
1339     std::string wkt_multipolygon = "MULTIPOLYGON(((1 1,1 200,200 200,200 1,1 1),(50 50,50 51,49 50,50 50)),((500 500,550 550,550 500,500 500)))";
1340
1341     {
1342         P p;
1343         bg::read_wkt(wkt_point, p);
1344         BOOST_CHECK(bg::is_valid(p));
1345         bg::set<1>(p, invalid_value);
1346         check_one<coord_t>(p);
1347     }
1348     {
1349         segment_t s;
1350         bg::read_wkt(wkt_segment, s);
1351         BOOST_CHECK(bg::is_valid(s));
1352         bg::set<1, 1>(s, invalid_value);
1353         check_one<coord_t>(s);
1354     }
1355     {
1356         box_t b;
1357         bg::read_wkt(wkt_box, b);
1358         BOOST_CHECK(bg::is_valid(b));
1359         bg::set<1, 0>(b, invalid_value);
1360         check_one<coord_t>(b);
1361     }
1362     {
1363         linestring_t ls;
1364         bg::read_wkt(wkt_linestring, ls);
1365         BOOST_CHECK(bg::is_valid(ls));
1366         bg::set<1>(ls[1], invalid_value);
1367         check_one<coord_t>(ls);
1368     }
1369     {
1370         ring_t r;
1371         bg::read_wkt(wkt_ring, r);
1372         BOOST_CHECK(bg::is_valid(r));
1373         bg::set<0>(r[1], invalid_value);
1374         check_one<coord_t>(r);
1375     }
1376     {
1377         polygon_t pgn;
1378         bg::read_wkt(wkt_polygon, pgn);
1379         BOOST_CHECK(bg::is_valid(pgn));
1380         bg::set<0>(bg::interior_rings(pgn)[0][1], invalid_value);
1381         check_one<coord_t>(pgn);
1382     }
1383     {
1384         multi_point_t mp;
1385         bg::read_wkt(wkt_multipoint, mp);
1386         BOOST_CHECK(bg::is_valid(mp));
1387         bg::set<0>(mp[2], invalid_value);
1388         check_one<coord_t>(mp);
1389     }
1390     {
1391         multi_linestring_t mls;
1392         bg::read_wkt(wkt_multilinestring, mls);
1393         BOOST_CHECK(bg::is_valid(mls));
1394         bg::set<0>(mls[1][1], invalid_value);
1395         check_one<coord_t>(mls);
1396     }
1397     {
1398         multi_polygon_t mpgn;
1399         bg::read_wkt(wkt_multipolygon, mpgn);
1400         BOOST_CHECK(bg::is_valid(mpgn));
1401         bg::set<0>(bg::exterior_ring(mpgn[1])[1], invalid_value);
1402         check_one<coord_t>(mpgn);
1403     }
1404 }
1405
1406 template <typename P>
1407 inline void test_with_invalid_coordinate()
1408 {
1409     typedef typename bg::coordinate_type<P>::type coord_t;
1410
1411     coord_t const q_nan = std::numeric_limits<coord_t>::quiet_NaN();
1412     coord_t const inf = std::numeric_limits<coord_t>::infinity();
1413
1414     test_with_invalid_coordinate<P, coord_t>(q_nan);
1415     test_with_invalid_coordinate<P, coord_t>(inf);
1416 }
1417
1418 BOOST_AUTO_TEST_CASE( test_geometries_with_invalid_coordinates )
1419 {
1420     typedef point_type fp_point_type;
1421     typedef bg::model::point<int, 2, bg::cs::cartesian> int_point_type;
1422
1423     test_with_invalid_coordinate<fp_point_type>();
1424     test_with_invalid_coordinate<int_point_type>();
1425 }
1426
1427 BOOST_AUTO_TEST_CASE( test_with_NaN_coordinates )
1428 {
1429 #ifdef BOOST_GEOMETRY_TEST_DEBUG
1430     std::cout << std::endl << std::endl;
1431     std::cout << "************************************" << std::endl;
1432     std::cout << " is_valid: geometry with NaN coordinates" << std::endl;
1433     std::cout << "************************************" << std::endl;
1434 #endif
1435
1436     linestring_type ls1, ls2;
1437     bg::read_wkt("LINESTRING(1 1,1.115235e+308 1.738137e+308)", ls1);
1438     bg::read_wkt("LINESTRING(-1 1,1.115235e+308 1.738137e+308)", ls2);
1439
1440     // the intersection of the two linestrings is a new linestring
1441     // (multilinestring with a single element) that has NaN coordinates
1442     multi_linestring_type mls;
1443     bg::intersection(ls1, ls2, mls);
1444
1445     typedef validity_tester_linear<true> tester_allow_spikes;
1446     typedef validity_tester_linear<false> tester_disallow_spikes;
1447
1448     test_valid
1449         <
1450             tester_allow_spikes, multi_linestring_type
1451         >::apply("mls-NaN", mls, false);
1452
1453     test_valid
1454         <
1455             tester_disallow_spikes, multi_linestring_type
1456         >::apply("mls-NaN", mls, false);
1457 }
1458
1459 BOOST_AUTO_TEST_CASE( test_is_valid_variant )
1460 {
1461 #ifdef BOOST_GEOMETRY_TEST_DEBUG
1462     std::cout << std::endl << std::endl;
1463     std::cout << "************************************" << std::endl;
1464     std::cout << " is_valid: variant support" << std::endl;
1465     std::cout << "************************************" << std::endl;
1466 #endif
1467
1468     typedef bg::model::polygon<point_type> polygon_type; // cw, closed
1469
1470     typedef boost::variant
1471         <
1472             linestring_type, multi_linestring_type, polygon_type
1473         > variant_geometry;
1474     typedef test_valid_variant<variant_geometry> test;
1475
1476     variant_geometry vg;
1477
1478     linestring_type valid_linestring =
1479         from_wkt<linestring_type>("LINESTRING(0 0,1 0)");
1480     multi_linestring_type invalid_multi_linestring =
1481         from_wkt<multi_linestring_type>("MULTILINESTRING((0 0,1 0),(0 0))");
1482     polygon_type valid_polygon =
1483         from_wkt<polygon_type>("POLYGON((0 0,1 1,1 0,0 0))");
1484     polygon_type invalid_polygon =
1485         from_wkt<polygon_type>("POLYGON((0 0,2 2,2 0,1 0))");
1486
1487     vg = valid_linestring;
1488     test::apply("v01", vg, true);
1489     vg = invalid_multi_linestring;
1490     test::apply("v02", vg, false);
1491     vg = valid_polygon;
1492     test::apply("v03", vg, true);
1493     vg = invalid_polygon;
1494     test::apply("v04", vg, false);
1495 }
1496
1497 BOOST_AUTO_TEST_CASE( test_is_valid_geometry_collection )
1498 {
1499 #ifdef BOOST_GEOMETRY_TEST_DEBUG
1500     std::cout << std::endl << std::endl;
1501     std::cout << "************************************" << std::endl;
1502     std::cout << " is_valid: geometry collection" << std::endl;
1503     std::cout << "************************************" << std::endl;
1504 #endif
1505
1506     using polygon_type = bg::model::polygon<point_type>; // cw, closed
1507     using variant_type = boost::variant
1508         <
1509             linestring_type, multi_linestring_type, polygon_type
1510         >;
1511     using gc_type = bg::model::geometry_collection<variant_type>;
1512
1513     typedef test_valid_variant<gc_type> test;
1514
1515     gc_type gc;
1516
1517     linestring_type valid_linestring =
1518         from_wkt<linestring_type>("LINESTRING(0 0,1 0)");
1519     multi_linestring_type invalid_multi_linestring =
1520         from_wkt<multi_linestring_type>("MULTILINESTRING((0 0,1 0),(0 0))");
1521     polygon_type valid_polygon =
1522         from_wkt<polygon_type>("POLYGON((0 0,1 1,1 0,0 0))");
1523     polygon_type invalid_polygon =
1524         from_wkt<polygon_type>("POLYGON((0 0,2 2,2 0,1 0))");
1525
1526     gc = {valid_linestring, valid_polygon};
1527     test::apply("gc01", gc, true);
1528     gc = {invalid_multi_linestring, valid_polygon};
1529     test::apply("gc02", gc, false);
1530     gc = {valid_linestring, invalid_polygon};
1531     test::apply("gc03", gc, false);
1532 }