import quincy beta 17.1.0

[ceph.git] / ceph / src / boost / libs / geometry / test / algorithms / is_valid.cpp

// Boost.Geometry (aka GGL, Generic Geometry Library)
// Unit Test

// Copyright (c) 2014-2018, Oracle and/or its affiliates.

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

// Licensed under the Boost Software License version 1.0.
// http://www.boost.org/users/license.html

#ifndef BOOST_TEST_MODULE
#define BOOST_TEST_MODULE test_is_valid
#endif

#include <limits>
#include <iostream>

#include <boost/test/included/unit_test.hpp>

#include "test_is_valid.hpp"
#include "overlay/overlay_cases.hpp"

#include <boost/geometry/core/coordinate_type.hpp>

#include <boost/geometry/algorithms/correct.hpp>
#include <boost/geometry/algorithms/intersection.hpp>
#include <boost/geometry/algorithms/reverse.hpp>

BOOST_AUTO_TEST_CASE( test_is_valid_point )
{
#ifdef BOOST_GEOMETRY_TEST_DEBUG
    std::cout << std::endl << std::endl;
    std::cout << "************************************" << std::endl;
    std::cout << " is_valid: POINT " << std::endl;
    std::cout << "************************************" << std::endl;
#endif

    typedef point_type G;
    typedef default_validity_tester tester;
    typedef test_valid<tester, G> test;

    test::apply("p01", "POINT(0 0)", true);
}

BOOST_AUTO_TEST_CASE( test_is_valid_multipoint )
{
#ifdef BOOST_GEOMETRY_TEST_DEBUG
    std::cout << std::endl << std::endl;
    std::cout << "************************************" << std::endl;
    std::cout << " is_valid: MULTIPOINT " << std::endl;
    std::cout << "************************************" << std::endl;
#endif

    typedef multi_point_type G;
    typedef default_validity_tester tester;
    typedef test_valid<tester, G> test;

    test::apply("mp01", "MULTIPOINT()", true);
    test::apply("mp02", "MULTIPOINT(0 0,0 0)", true);
    test::apply("mp03", "MULTIPOINT(0 0,1 0,1 1,0 1)", true);
    test::apply("mp04", "MULTIPOINT(0 0,1 0,1 1,1 0,0 1)", true);
}

BOOST_AUTO_TEST_CASE( test_is_valid_segment )
{
#ifdef BOOST_GEOMETRY_TEST_DEBUG
    std::cout << std::endl << std::endl;
    std::cout << "************************************" << std::endl;
    std::cout << " is_valid: SEGMENT " << std::endl;
    std::cout << "************************************" << std::endl;
#endif

    typedef segment_type G;
    typedef default_validity_tester tester;
    typedef test_valid<tester, G> test;

    test::apply("s01", "SEGMENT(0 0,0 0)", false);
    test::apply("s02", "SEGMENT(0 0,1 0)", true);
}

BOOST_AUTO_TEST_CASE( test_is_valid_box )
{
#ifdef BOOST_GEOMETRY_TEST_DEBUG
    std::cout << std::endl << std::endl;
    std::cout << "************************************" << std::endl;
    std::cout << " is_valid: BOX " << std::endl;
    std::cout << "************************************" << std::endl;
#endif

    typedef box_type G;
    typedef default_validity_tester tester;
    typedef test_valid<tester, G> test;

    // boxes where the max corner and below and/or to the left of min corner
    test::apply("b01", "BOX(0 0,-1 0)", false);
    test::apply("b02", "BOX(0 0,0 -1)", false);
    test::apply("b03", "BOX(0 0,-1 -1)", false);

    // boxes of zero area; they are not 2-dimensional, so invalid
    test::apply("b04", "BOX(0 0,0 0)", false);
    test::apply("b05", "BOX(0 0,1 0)", false);
    test::apply("b06", "BOX(0 0,0 1)", false);

    test::apply("b07", "BOX(0 0,1 1)", true);
}

template <typename G, bool AllowSpikes>
void test_linestrings()
{
#ifdef BOOST_GEOMETRY_TEST_DEBUG
    std::cout << "SPIKES ALLOWED? "
              << std::boolalpha
              << AllowSpikes
              << std::noboolalpha
              << std::endl;
#endif

    typedef validity_tester_linear<AllowSpikes> tester;
    typedef test_valid<tester, G> test;

    // empty linestring
    test::apply("l01", "LINESTRING()", false);

    // 1-point linestrings
    test::apply("l02", "LINESTRING(0 0)", false);
    test::apply("l03", "LINESTRING(0 0,0 0)", false);
    test::apply("l04", "LINESTRING(0 0,0 0,0 0)", false);

    // 2-point linestrings
    test::apply("l05", "LINESTRING(0 0,1 2)", true);
    test::apply("l06", "LINESTRING(0 0,1 2,1 2)", true);
    test::apply("l07", "LINESTRING(0 0,0 0,1 2,1 2)", true);
    test::apply("l08", "LINESTRING(0 0,0 0,0 0,1 2,1 2)", true);

    // 3-point linestrings
    test::apply("l09", "LINESTRING(0 0,1 0,2 10)", true);
    test::apply("l10", "LINESTRING(0 0,1 0,2 10,0 0)", true);
    test::apply("l11", "LINESTRING(0 0,10 0,10 10,5 0)", true);

    // linestrings with spikes
    test::apply("l12", "LINESTRING(0 0,1 2,0 0)", AllowSpikes);
    test::apply("l13", "LINESTRING(0 0,1 2,1 2,0 0)", AllowSpikes);
    test::apply("l14", "LINESTRING(0 0,0 0,1 2,1 2,0 0)", AllowSpikes);
    test::apply("l15", "LINESTRING(0 0,0 0,0 0,1 2,1 2,0 0,0 0)", AllowSpikes);
    test::apply("l16", "LINESTRING(0 0,10 0,5 0)", AllowSpikes);
    test::apply("l17", "LINESTRING(0 0,10 0,10 10,5 0,0 0)", AllowSpikes);
    test::apply("l18", "LINESTRING(0 0,10 0,10 10,5 0,4 0,6 0)", AllowSpikes);
    test::apply("l19", "LINESTRING(0 0,1 0,1 1,5 5,4 4)", AllowSpikes);
    test::apply("l20", "LINESTRING(0 0,1 0,1 1,5 5,4 4,6 6)", AllowSpikes);
    test::apply("l21", "LINESTRING(0 0,1 0,1 1,5 5,4 4,4 0)", AllowSpikes);
    test::apply("l22",
                "LINESTRING(0 0,0 0,1 0,1 0,1 0,0 0,0 0,2 0)",
                AllowSpikes);
    test::apply("l23",
                "LINESTRING(0 0,1 0,0 0,2 0,0 0,3 0,0 0,4 0)",
                AllowSpikes);
    test::apply("l24",
                "LINESTRING(0 0,1 0,0 0,2 0,0 0,3 0,0 0,4 0,0 0)",
                AllowSpikes);

    // other examples
    test::apply("l25", "LINESTRING(0 0,10 0,10 10,5 0,4 0)", true);
    test::apply("l26", "LINESTRING(0 0,10 0,10 10,5 0,4 0,3 0)", true);
    test::apply("l27", "LINESTRING(0 0,10 0,10 10,5 0,4 0,-1 0)", true);
    test::apply("l28", "LINESTRING(0 0,1 0,1 1,-1 1,-1 0,0 0)", true);
    test::apply("l29", "LINESTRING(0 0,1 0,1 1,-1 1,-1 0,0.5 0)", true);
}

BOOST_AUTO_TEST_CASE( test_is_valid_linestring )
{
#ifdef BOOST_GEOMETRY_TEST_DEBUG
    std::cout << std::endl << std::endl;
    std::cout << "************************************" << std::endl;
    std::cout << " is_valid: LINESTRING " << std::endl;
    std::cout << "************************************" << std::endl;
#endif

    bool const allow_spikes = true;
    bool const do_not_allow_spikes = !allow_spikes;

    test_linestrings<linestring_type, allow_spikes>();
    test_linestrings<linestring_type, do_not_allow_spikes>();
}

template <typename G, bool AllowSpikes>
void test_multilinestrings()
{
#ifdef BOOST_GEOMETRY_TEST_DEBUG
    std::cout << "SPIKES ALLOWED? "
              << std::boolalpha
              << AllowSpikes
              << std::noboolalpha
              << std::endl;
#endif

    typedef validity_tester_linear<AllowSpikes> tester;
    typedef test_valid<tester, G> test;

    // empty multilinestring
    test::apply("mls01", "MULTILINESTRING()", true);

    // multilinestring with empty linestring(s)
    test::apply("mls02", "MULTILINESTRING(())", false);
    test::apply("mls03", "MULTILINESTRING((),(),())", false);
    test::apply("mls04", "MULTILINESTRING((),(0 1,1 0))", false);

    // multilinestring with invalid linestrings
    test::apply("mls05", "MULTILINESTRING((0 0),(0 1,1 0))", false);
    test::apply("mls06", "MULTILINESTRING((0 0,0 0),(0 1,1 0))", false);
    test::apply("mls07", "MULTILINESTRING((0 0),(1 0))", false);
    test::apply("mls08", "MULTILINESTRING((0 0,0 0),(1 0,1 0))", false);
    test::apply("mls09", "MULTILINESTRING((0 0),(0 0))", false);
    test::apply("mls10", "MULTILINESTRING((0 0,1 0,0 0),(5 0))", false);

    // multilinstring that has linestrings with spikes
    test::apply("mls11",
                "MULTILINESTRING((0 0,1 0,0 0),(5 0,1 0,4 1))",
                AllowSpikes);
    test::apply("mls12",
                "MULTILINESTRING((0 0,1 0,0 0),(1 0,2 0))",
                AllowSpikes);

    // valid multilinestrings
    test::apply("mls13", "MULTILINESTRING((0 0,1 0,2 0),(5 0,1 0,4 1))", true);
    test::apply("mls14", "MULTILINESTRING((0 0,1 0,2 0),(1 0,2 0))", true);
    test::apply("mls15", "MULTILINESTRING((0 0,1 1),(0 1,1 0))", true);
    test::apply("mls16", "MULTILINESTRING((0 0,1 1,2 2),(0 1,1 0,2 2))", true);
}

BOOST_AUTO_TEST_CASE( test_is_valid_multilinestring )
{
#ifdef BOOST_GEOMETRY_TEST_DEBUG
    std::cout << std::endl << std::endl;
    std::cout << "************************************" << std::endl;
    std::cout << " is_valid: MULTILINESTRING " << std::endl;
    std::cout << "************************************" << std::endl;
#endif

    bool const allow_spikes = true;
    bool const do_not_allow_spikes = !allow_spikes;

    test_multilinestrings<multi_linestring_type, allow_spikes>();
    test_multilinestrings<multi_linestring_type, do_not_allow_spikes>();
}

template <typename Point, bool AllowDuplicates>
inline void test_open_rings()
{
#ifdef BOOST_GEOMETRY_TEST_DEBUG
    std::cout << std::endl << std::endl;
    std::cout << "************************************" << std::endl;
    std::cout << " is_valid: RING (open) " << std::endl;
    std::cout << "************************************" << std::endl;
    std::cout << "DUPLICATES ALLOWED? "
              << std::boolalpha
              << AllowDuplicates
              << std::noboolalpha
              << std::endl;
#endif

    typedef bg::model::ring<Point, false, false> OG; // ccw, open ring
    typedef bg::model::ring<Point, false, true> CG; // ccw, closed ring
    typedef bg::model::ring<Point, true, false> CW_OG; // cw, open ring
    typedef bg::model::ring<Point, true, true> CW_CG; // cw, closed ring
 
    typedef validity_tester_areal<AllowDuplicates> tester;
    typedef test_valid<tester, OG, CG, CW_OG, CW_CG> test;

    // not enough points
    test::apply("r01", "POLYGON(())", false);
    test::apply("r02", "POLYGON((0 0))", false);
    test::apply("r03", "POLYGON((0 0,1 0))", false);

    // duplicate points
    test::apply("r04", "POLYGON((0 0,0 0,0 0))", false);
    test::apply("r05", "POLYGON((0 0,1 0,1 0))", false);
    test::apply("r06", "POLYGON((0 0,1 0,0 0))", false);
    test::apply("r07", "POLYGON((0 0,1 0,1 1,0 0,0 0))", AllowDuplicates);
    test::apply("r08", "POLYGON((0 0,1 0,1 0,1 1))", AllowDuplicates);
    test::apply("r09", "POLYGON((0 0,1 0,1 0,1 1,0 0))", AllowDuplicates);

    // with spikes
    test::apply("r10", "POLYGON((0 0,2 0,2 2,0 2,1 2))", false);
    test::apply("r11", "POLYGON((0 0,2 0,1 0,2 2))", false);
    test::apply("r12", "POLYGON((0 0,1 0,2 0,1 0,4 0,4 4))", false);
    test::apply("r13", "POLYGON((0 0,2 0,2 2,1 0))", false);
    test::apply("r14", "POLYGON((0 0,2 0,1 0))", false);
    test::apply("r15", "POLYGON((0 0,5 0,5 5,4 4,5 5,0 5))", false);
    test::apply("r16", "POLYGON((0 0,5 0,5 5,4 4,3 3,5 5,0 5))", false);

    // with spikes and duplicate points
    test::apply("r17", "POLYGON((0 0,0 0,2 0,2 0,1 0,1 0))", false);

    // with self-crossings
    test::apply("r18", "POLYGON((0 0,5 0,5 5,3 -1,0 5))", false);

    // with self-crossings and duplicate points
    test::apply("r19", "POLYGON((0 0,5 0,5 5,5 5,3 -1,0 5,0 5))", false);

    // with self-intersections
    test::apply("r20", "POLYGON((0 0,5 0,5 5,3 5,3 0,2 0,2 5,0 5))", false);

    test::apply("r21", "POLYGON((0 0,5 0,5 5,3 5,3 0,2 5,0 5))", false);

    test::apply("r22",
                "POLYGON((0 0,5 0,5 1,1 1,1 2,2 2,3 1,4 2,5 2,5 5,0 5))",
                false);

    // with self-intersections and duplicate points
    test::apply("r23",
                "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))",
                false);

    // next two suggested by Adam Wulkiewicz
    test::apply("r24",
                "POLYGON((0 0,5 0,5 5,0 5,4 4,2 2,0 5))",
                false);
    test::apply("r25",
                "POLYGON((0 0,5 0,5 5,1 4,4 4,4 1,0 5))",
                false);

    // and a few more
    test::apply("r26",
                "POLYGON((0 0,5 0,5 5,4 4,1 4,1 1,4 1,4 4,0 5))",
                false);
    test::apply("r27",
                "POLYGON((0 0,5 0,5 5,4 4,4 1,1 1,1 4,4 4,0 5))",
                false);

    // valid rings
    test::apply("r28", "POLYGON((0 0,1 0,1 1))", true);
    test::apply("r29", "POLYGON((1 0,1 1,0 0))", true);
    test::apply("r30", "POLYGON((0 0,1 0,1 1,0 1))", true);
    test::apply("r31", "POLYGON((1 0,1 1,0 1,0 0))", true);

    // test cases coming from buffer
    test::apply("r32",
                "POLYGON((1.1713032141645456 -0.9370425713316364,\
                          5.1713032141645456 4.0629574286683638,\
                          4.7808688094430307 4.3753049524455756,\
                          4.7808688094430307 4.3753049524455756,\
                          0.7808688094430304 -0.6246950475544243,\
                          0.7808688094430304 -0.6246950475544243))",
                AllowDuplicates);

    // wrong orientation
    test::apply("r33", "POLYGON((0 0,0 1,1 1))", false);

    // Normal case, plus spikes formed in two different ways
    test::apply("r34", "POLYGON((0 0,4 0,4 4,0 4,0 0))", true);
    test::apply("r35", "POLYGON((0 0,5 0,4 0,4 4,0 4,0 0))", false);
    test::apply("r36", "POLYGON((0 0,4 0,4 -1,4 4,0 4,0 0))", false);
}


template <typename Point, bool AllowDuplicates>
inline void test_closed_rings()
{
#ifdef BOOST_GEOMETRY_TEST_DEBUG
    std::cout << std::endl << std::endl;
    std::cout << "************************************" << std::endl;
    std::cout << " is_valid: RING (closed) " << std::endl;
    std::cout << "************************************" << std::endl;
    std::cout << "DUPLICATES ALLOWED? "
              << std::boolalpha
              << AllowDuplicates
              << std::noboolalpha
              << std::endl;
#endif

    typedef bg::model::ring<Point, false, true> CG; // ccw, closed ring
    typedef bg::model::ring<Point, true, true> CW_CG; // cw, closed ring

    typedef validity_tester_areal<AllowDuplicates> tester;
    typedef test_valid<tester, CG, CG, CW_CG> test;

    // not enough points
    test::apply("r01c", "POLYGON(())", false);
    test::apply("r02c", "POLYGON((0 0))", false);
    test::apply("r03c", "POLYGON((0 0,0 0))", false);
    test::apply("r04c", "POLYGON((0 0,1 0))", false);
    test::apply("r05c", "POLYGON((0 0,1 0,1 0))", false);
    test::apply("r06c", "POLYGON((0 0,1 0,2 0))", false);
    test::apply("r07c", "POLYGON((0 0,1 0,1 0,2 0))", false);
    test::apply("r08c", "POLYGON((0 0,1 0,2 0,2 0))", false);

    // boundary not closed
    test::apply("r09c", "POLYGON((0 0,1 0,1 1,1 2))", false);
    test::apply("r10c", "POLYGON((0 0,1 0,1 0,1 1,1 1,1 2))", false);

    // with spikes
    test::apply("r11c", "POLYGON((0 0,1 0,1 0,2 0,0 0))", false);
    test::apply("r12c", "POLYGON((0 0,1 0,1 1,2 2,0.5 0.5,0 1,0 0))", false);

    // wrong orientation
    test::apply("r13c", "POLYGON((0 0,0 1,1 1,2 0,0 0))", false);
}

BOOST_AUTO_TEST_CASE( test_is_valid_ring )
{
    bool const allow_duplicates = true;
    bool const do_not_allow_duplicates = !allow_duplicates;

    test_open_rings<point_type, allow_duplicates>();
    test_open_rings<point_type, do_not_allow_duplicates>();

    test_closed_rings<point_type, allow_duplicates>();
    test_closed_rings<point_type, do_not_allow_duplicates>();
}

template <typename Point, bool AllowDuplicates>
inline void test_open_polygons()
{
#ifdef BOOST_GEOMETRY_TEST_DEBUG
    std::cout << std::endl << std::endl;
    std::cout << "************************************" << std::endl;
    std::cout << " is_valid: POLYGON (open) " << std::endl;
    std::cout << "************************************" << std::endl;
    std::cout << "DUPLICATES ALLOWED? "
              << std::boolalpha
              << AllowDuplicates
              << std::noboolalpha
              << std::endl;
#endif

    typedef bg::model::polygon<Point, false, false> OG; // ccw, open
    typedef bg::model::polygon<Point, false, true> CG; // ccw, closed
    typedef bg::model::polygon<Point, true, false> CW_OG; // cw, open
    typedef bg::model::polygon<Point, true, true> CW_CG; // cw, closed

    typedef validity_tester_areal<AllowDuplicates> tester;
    typedef test_valid<tester, OG, CG, CW_OG, CW_CG> test;

    // not enough points in exterior ring
    test::apply("pg001", "POLYGON(())", false);
    test::apply("pg002", "POLYGON((0 0))", false);
    test::apply("pg003", "POLYGON((0 0,1 0))", false);

    // not enough points in interior ring
    test::apply("pg004", "POLYGON((0 0,10 0,10 10,0 10),())", false);
    test::apply("pg005", "POLYGON((0 0,10 0,10 10,0 10),(1 1))", false);
    test::apply("pg006", "POLYGON((0 0,10 0,10 10,0 10),(1 1,2 2))", false);

    // duplicate points in exterior ring
    test::apply("pg007", "POLYGON((0 0,0 0,0 0))", false);
    test::apply("pg008", "POLYGON((0 0,1 0,1 0))", false);
    test::apply("pg009", "POLYGON((0 0,1 0,0 0))", false);
    test::apply("pg010", "POLYGON((0 0,1 0,1 1,0 0,0 0))", AllowDuplicates);
    test::apply("pg011", "POLYGON((0 0,1 0,1 0,1 1))", AllowDuplicates);
    test::apply("pg012", "POLYGON((0 0,1 0,1 0,1 1,0 0))",  AllowDuplicates);

    // duplicate points in interior ring
    test::apply("pg013", "POLYGON((0 0,10 0,10 10,0 10),(1 1,1 1,1 1))", false);
    test::apply("pg014", "POLYGON((0 0,10 0,10 10,0 10),(1 1,2 1,2 1))", false);
    test::apply("pg015", "POLYGON((0 0,10 0,10 10,0 10),(1 1,2 1,1 1))", false);
    test::apply("pg016",
                "POLYGON((0 0,10 0,10 10,0 10),(1 1,2 2,2 1,1 1,1 1))",
                AllowDuplicates);
    test::apply("pg017",
                "POLYGON((0 0,10 0,10 10,0 10),(1 1,2 2,2 2,2 1))",
                AllowDuplicates);
    test::apply("pg018",
                "POLYGON((0 0,10 0,10 10,0 10),(1 1,2 2,2 1,2 1,1 1))",
                AllowDuplicates);

    // with spikes in exterior ring
    test::apply("pg019", "POLYGON((0 0,2 0,2 2,0 2,1 2))", false);
    test::apply("pg020", "POLYGON((0 0,2 0,1 0,2 2))", false);
    test::apply("pg021", "POLYGON((0 0,1 0,2 0,1 0,4 0,4 4))", false);
    test::apply("pg022", "POLYGON((0 0,2 0,2 2,1 0))", false);
    test::apply("pg023", "POLYGON((0 0,2 0,1 0))", false);
    test::apply("pg024", "POLYGON((0 0,5 0,5 5,4 4,5 5,0 5))", false);
    test::apply("pg025", "POLYGON((0 0,5 0,5 5,4 4,3 3,5 5,0 5))", false);

    // with spikes in interior ring
    test::apply("pg026",
                "POLYGON((0 0,10 0,10 10,0 10),(1 1,3 1,3 3,1 3,2 3))",
                false);
    test::apply("pg027",
                "POLYGON((0 0,10 0,10 10,0 10),(1 1,3 1,2 1,3 3))",
                false);
    test::apply("pg028",
                "POLYGON((0 0,10 0,10 10,0 10),(1 1,2 1,3 1,2 1,4 1,4 4))",
                false);
    test::apply("pg029",
                "POLYGON((0 0,10 0,10 10,0 10),(1 1,3 1,3 3,2 1))",
                false);
    test::apply("pg030", "POLYGON((0 0,10 0,10 10,0 10),(1 1,3 1,2 1))", false);

    // with self-crossings in exterior ring
    test::apply("pg031", "POLYGON((0 0,5 0,5 5,3 -1,0 5))", false);

    // example from Norvald Ryeng
    test::apply("pg032",
                "POLYGON((100 1300,140 1300,140 170,100 1700))",
                false);
    // and with point order reversed
    test::apply("pg033",
                "POLYGON((100 1300,100 1700,140 170,140 1300))",
                false);

    // with self-crossings in interior ring
    test::apply("pg034",
                "POLYGON((0 0,10 0,10 10,0 10),(3 3,3 7,4 6,2 6))",
                false);

    // with self-crossings between rings
    test::apply("pg035", "POLYGON((0 0,5 0,5 5,0 5),(1 1,2 1,1 -1))", false);

    // with self-intersections in exterior ring
    test::apply("pg036", "POLYGON((0 0,5 0,5 5,3 5,3 0,2 0,2 5,0 5))", false);
    test::apply("pg037", "POLYGON((0 0,5 0,5 5,3 5,3 0,2 5,0 5))", false);
    test::apply("pg038",
                "POLYGON((0 0,5 0,5 1,1 1,1 2,2 2,3 1,4 2,5 2,5 5,0 5))",
                false);

    // next two suggested by Adam Wulkiewicz
    test::apply("pg039", "POLYGON((0 0,5 0,5 5,0 5,4 4,2 2,0 5))", false);
    test::apply("pg040", "POLYGON((0 0,5 0,5 5,1 4,4 4,4 1,0 5))", false);
    test::apply("pg041",
                "POLYGON((0 0,5 0,5 5,4 4,1 4,1 1,4 1,4 4,0 5))",
                false);
    test::apply("pg042",
                "POLYGON((0 0,5 0,5 5,4 4,4 1,1 1,1 4,4 4,0 5))",
                false);

    // with self-intersections in interior ring
    test::apply("pg043",
                "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))",
                false);
    test::apply("pg044",
                "POLYGON((-10 -10,10 -10,10 10,-10 10),(0 0,5 0,5 5,3 5,3 0,2 5,0 5))",
                false);

    test::apply("pg045",
                "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))",
                false);

    // with self-intersections between rings
    // hole has common segment with exterior ring
    test::apply("pg046",
                "POLYGON((0 0,10 0,10 10,0 10),(1 1,1 10,2 10,2 1))",
                false);
    test::apply("pg047",
                "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))",
                false);
    // hole touches exterior ring at one point
    test::apply("pg048", "POLYGON((0 0,10 0,10 10,0 10),(1 1,1 10,2 1))", true);

    // "hole" is outside the exterior ring, but touches it
    test::apply("pg049",
                "POLYGON((0 0,10 0,10 10,0 10),(5 10,4 11,6 11))",
                false);

    // hole touches exterior ring at vertex
    test::apply("pg050", "POLYGON((0 0,10 0,10 10,0 10),(0 0,1 4,4 1))", true);

    // "hole" is completely outside the exterior ring
    test::apply("pg051",
                "POLYGON((0 0,10 0,10 10,0 10),(20 20,20 21,21 21,21 20))",
                false);

    // two "holes" completely outside the exterior ring, that touch
    // each other
    test::apply("pg052",
                "POLYGON((0 0,10 0,10 10,0 10),(20 0,25 10,21 0),(30 0,25 10,31 0))",
                false);

    // example from Norvald Ryeng
    test::apply("pg053",
                "POLYGON((58 31,56.57 30,62 33),(35 9,28 14,31 16),(23 11,29 5,26 4))",
                false);
    // and with points reversed
    test::apply("pg054",
                "POLYGON((58 31,62 33,56.57 30),(35 9,31 16,28 14),(23 11,26 4,29 5))",
                false);

    // "hole" is completely inside another "hole"
    test::apply("pg055",
                "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))",
                false);
    test::apply("pg056",
                "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))",
                false);

    // "hole" is inside another "hole" (touching)
    test::apply("pg057",
                "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))",
                false);
    test::apply("pg058",
                "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))",
                false);
    test::apply("pg058a",
                "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))",
                false);
    test::apply("pg059",
                "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))",
                false);
    test::apply("pg059a",
                "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))",
                false);
    test::apply("pg060",
                "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))",
                false);
    test::apply("pg060a",
                "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))",
                false);
    // hole touches exterior ring at two points
    test::apply("pg061", "POLYGON((0 0,10 0,10 10,0 10),(5 0,0 5,5 5))", false);

    // cases with more holes
    // two holes, touching the exterior at the same point
    test::apply("pg062",
                "POLYGON((0 0,10 0,10 10,0 10),(0 0,1 9,2 9),(0 0,9 2,9 1))",
                true);
    test::apply("pg063",
                "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))",
                AllowDuplicates);
    test::apply("pg063",
                "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))",
                AllowDuplicates);
    // two holes, one inside the other
    test::apply("pg064",
                "POLYGON((0 0,10 0,10 10,0 10),(0 0,1 9,9 1),(0 0,4 5,5 4))",
                false);
    // 1st hole touches has common segment with 2nd hole
    test::apply("pg066",
                "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))",
                false);
    // 1st hole touches 2nd hole at two points
    test::apply("pg067",
                "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))",
                false);
    // polygon with many holes, where the last two touch at two points
    test::apply("pg068",
                "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))",
                false);
    // two holes completely inside exterior ring but touching each
    // other at a point
    test::apply("pg069",
                "POLYGON((0 0,10 0,10 10,0 10),(1 1,1 9,2 9),(1 1,9 2,9 1))",
                true);
    // four holes, each two touching at different points
    test::apply("pg070",
                "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))",
                true);
    // five holes, with two pairs touching each at some point, and
    // fifth hole creating a disconnected component for the interior
    test::apply("pg071",
                "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))",
                false);
    // five holes, with two pairs touching each at some point, and
    // fifth hole creating three disconnected components for the interior
    test::apply("pg072",
                "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))",
                false);

    // both examples: a polygon with one hole, where the hole contains
    // the exterior ring
    test::apply("pg073",
                "POLYGON((0 0,1 0,1 1,0 1),(-10 -10,-10 10,10 10,10 -10))",
                false);
    test::apply("pg074",
                "POLYGON((-10 -10,1 0,1 1,0 1),(-10 -10,-10 10,10 10,10 -10))",
                false);

    test::apply
        ("pg075",
         "POLYGON((-6 -10,-6.6923076923076925 -6.711538461538462,\
                   -9 -7,-8.824742268041238 -6.123711340206185,\
                   -10 -6,-8.583333333333332 -4.916666666666667,\
                   -8.094117647058823 -2.4705882352941173,-10 -3,\
                   -8.526315789473683 -0.05263157894736803,-10 1,\
                   -10 10,-7.764705882352941 8.509803921568627,\
                   -7.65090909090909 7.789090909090909,-10 10,\
                   -7.574468085106383 7.304964539007091,-7.4375 6.4375,\
                   -6.5 5.5,-6.4 6,-7.574468085106383 7.304964539007091,\
                   -7.65090909090909 7.789090909090909,\
                   -6.297029702970297 6.514851485148515,\
                   0 0,-6.297029702970297 6.514851485148515,\
                   -4.848484848484849 5.151515151515151,-4 6,\
                   -6.117647058823529 7.411764705882352,\
                   0 0,-6.11764705882353 7.411764705882353,\
                   -7.764705882352941 8.509803921568627,-8 10,\
                   -2.9473684210526314 7.052631578947368,-2 8,\
                   -0.17821782178217824 6.633663366336634,1 10,\
                   1.8095238095238098 5.142857142857142,\
                   3.2038834951456314 4.097087378640777,7 7,\
                   3.7142857142857144 3.7142857142857144,\
                   4.4 3.1999999999999997,8 2,\
                   6.540540540540541 1.5945945945945947,10 -1,\
                   7.454545454545455 -4.393939393939394,8 -5,\
                   7.320754716981132 -4.716981132075472,7 -6,\
                   6.062068965517241 -5.117241379310345,\
                   4.9504132231404965 -5.256198347107438,\
                   6.1506849315068495 -7.123287671232877,9 -8,\
                   6.548387096774194 -7.741935483870968,8 -10,\
                   5.906976744186046 -7.674418604651163,\
                   3.9107142857142856 -7.464285714285714,4 -8,\
                   2.8043478260869565 -7.3478260869565215,\
                   1.7829457364341086 -7.24031007751938,2 -8,\
                   1.0728476821192054 -7.1655629139072845,\
                   -4.3583617747440275 -6.593856655290103,-5 -9,\
                   -5.2020725388601035 -7.720207253886011,-6 -10),\
                  (5.127659574468085 -6.808510638297872,\
                   3.72972972972973 -6.378378378378379,\
                   3.571428571428571 -5.428571428571429,\
                   3.8539325842696632 -5.393258426966292,\
                   5.127659574468085 -6.808510638297872),\
                  (-5.5 4.5,-6.5 5.5,-6.4 6,\
                   -5.263157894736842 4.736842105263158,-5.5 4.5))",
         false);

    // test cases coming from buffer
    test::apply
        ("pg076",
         "POLYGON((1.1713032141645456 -0.9370425713316364,\
                   5.1713032141645456 4.0629574286683638,\
                   4.7808688094430307 4.3753049524455756,\
                   4.7808688094430307 4.3753049524455756,\
                   0.7808688094430304 -0.6246950475544243,\
                   0.7808688094430304 -0.6246950475544243))",
         AllowDuplicates);


    // MySQL report on Sep 30, 2015
    test::apply
        ("pg077",
         "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))",
         true);

    test::apply("pg077-simplified",
                "POLYGON((-200 0,-207.99999999999997 135.36742435621204,-208 1,-208 0,-208 -276.9111154485375))",
                true);

    test::apply
        ("pg078",
         "POLYGON((0 10,-10 0,0 0,10 0))",
         true);

    test::apply
        ("pg078spike1",
         "POLYGON((0 10,-10 0,0 0,-10 0,10 0))",
         false);

    test::apply
        ("pg078spike2",
         "POLYGON((0 10,-10 0,0 0,-8 0,10 0))",
         false);

    test::apply
        ("pg078spike3",
         "POLYGON((0 10,-10 0,0 0,-11 0,10 0))",
         false);

    test::apply
        ("pg078reversed",
         "POLYGON((0 10,10 0,0 0,-10 0))",
         false);

    test::apply
        ("pg079",
         "POLYGON((10 0,0 10,0 0,0 -10))",
         true);

    test::apply
        ("pg079spike1",
         "POLYGON((10 0,0 10,0 0,0 10,0 -10))",
         false);

    test::apply
        ("pg079spike2",
         "POLYGON((10 0,0 10,0 0,0 8,0 -10))",
         false);

    test::apply
        ("pg079spike3",
         "POLYGON((10 0,0 10,0 0,0 11,0 -10))",
         false);

    test::apply
        ("pg079reversed",
         "POLYGON((10 0,0 -10,0 0,0 10))",
         false);
}


template <typename Point>
inline void test_doc_example_polygon()
{
#ifdef BOOST_GEOMETRY_TEST_DEBUG
    std::cout << std::endl << std::endl;
    std::cout << "************************************" << std::endl;
    std::cout << " is_valid: doc example polygon " << std::endl;
    std::cout << "************************************" << std::endl;
#endif

    typedef bg::model::polygon<Point> ClockwiseClosedPolygon;
    typedef validity_tester_areal<true> tester;
    typedef test_valid<tester, ClockwiseClosedPolygon> test;

    test::apply("pg-doc",
                "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))",
                false);

    // Containing a self touching point, which should be valid
    test::apply("ggl_list_20190307_matthieu_2", ggl_list_20190307_matthieu_2[1], true);
}

BOOST_AUTO_TEST_CASE( test_is_valid_polygon )
{
    bool const allow_duplicates = true;
    bool const do_not_allow_duplicates = !allow_duplicates;

    test_open_polygons<point_type, allow_duplicates>();
    test_open_polygons<point_type, do_not_allow_duplicates>();
    test_doc_example_polygon<point_type>();
}

template <typename Point, bool AllowDuplicates>
inline void test_open_multipolygons()
{
    // WKT of multipolygons should be defined as ccw, open

#ifdef BOOST_GEOMETRY_TEST_DEBUG
    std::cout << std::endl << std::endl;
    std::cout << "************************************" << std::endl;
    std::cout << " is_valid: MULTIPOLYGON (open) " << std::endl;
    std::cout << "************************************" << std::endl;
    std::cout << "DUPLICATES ALLOWED? "
              << std::boolalpha
              << AllowDuplicates
              << std::noboolalpha
              << std::endl;
#endif

    // cw, ccw, open and closed polygons
    typedef bg::model::polygon<point_type,false,false> ccw_open_polygon_type;
    typedef bg::model::polygon<point_type,false,true>  ccw_closed_polygon_type;
    typedef bg::model::polygon<point_type,true,false>  cw_open_polygon_type;
    typedef bg::model::polygon<point_type,true,true>   cw_closed_polygon_type;

    typedef bg::model::multi_polygon<ccw_open_polygon_type> OG;
    typedef bg::model::multi_polygon<ccw_closed_polygon_type> CG;
    typedef bg::model::multi_polygon<cw_open_polygon_type> CW_OG;
    typedef bg::model::multi_polygon<cw_closed_polygon_type> CW_CG;

    typedef validity_tester_areal<AllowDuplicates> tester;
    typedef test_valid<tester, OG, CG, CW_OG, CW_CG> test;

    // not enough points
    test::apply("mpg01", "MULTIPOLYGON()", true);
    test::apply("mpg02", "MULTIPOLYGON((()))", false);
    test::apply("mpg03", "MULTIPOLYGON(((0 0)),(()))", false);
    test::apply("mpg04", "MULTIPOLYGON(((0 0,1 0)))", false);

    // two disjoint polygons
    test::apply("mpg05",
                "MULTIPOLYGON(((0 0,1 0,1 1,0 1)),((2 2,3 2,3 3,2 3)))",
                true);

    // two disjoint polygons with multiple points
    test::apply("mpg06",
                "MULTIPOLYGON(((0 0,1 0,1 0,1 1,0 1)),((2 2,3 2,3 3,3 3,2 3)))",
                AllowDuplicates);

    // two polygons touch at a point
    test::apply("mpg07",
                "MULTIPOLYGON(((0 0,1 0,1 1,0 1)),((1 1,2 1,2 2,1 2)))",
                true);

    // two polygons share a segment at a point
    test::apply("mpg08",
                "MULTIPOLYGON(((0 0,1.5 0,1.5 1,0 1)),((1 1,2 1,2 2,1 2)))",
                false);

    // one polygon inside another and boundaries touching
    test::apply("mpg09",
                "MULTIPOLYGON(((0 0,10 0,10 10,0 10)),((0 0,9 1,9 2)))",
                false);
    test::apply("mpg09_2",
                "MULTIPOLYGON(((0 0,5 1,10 0,10 10,0 10)),((1 1,9 1,9 2)))",
                false);

    // one polygon inside another and boundaries not touching
    test::apply("mpg10",
                "MULTIPOLYGON(((0 0,10 0,10 10,0 10)),((1 1,9 1,9 2)))",
                false);

    // free space is disconnected
    test::apply("mpg11",
                "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)))",
                true);

    // multi-polygon with a polygon inside the hole of another polygon
    test::apply("mpg12",
                "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)))",
                true);
    test::apply("mpg13",
                "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)))",
                true);

    // test case suggested by Barend Gehrels: take two valid polygons P1 and
    // P2 with holes H1 and H2, respectively, and consider P2 to be
    // fully inside H1; now invalidate the multi-polygon by
    // considering H2 as a hole of P1 and H1 as a hole of P2; this
    // should be invalid
    //
    // first the valid case:
    test::apply("mpg14",
                "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)))",
                true);
    // and the invalid case:
    test::apply("mpg15",
                "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)))",
                false);

    test::apply
        ("mpg16",
         "MULTIPOLYGON(((-1 4,8 -10,-10 10,7 -6,8 -2,\
                      -10 10,-10 1,-3 -4,4 1,-1 2,4 3,-8 10,-5 -9,-1 6,-5 0)),\
                      ((-10 -3,-8 1,2 -8,-2 6,-4 0,8 -5,-1 5,8 2)),\
                      ((-6 -10,1 10,4 -8,-7 -2,2 0,-4 3,-10 9)),\
                      ((10 -1,-2 8,-7 3,-6 8,-9 -7,7 -5)),\
                      ((7 7,-4 -4,9 -8,-10 -6)))",
         false);

    test::apply
        ("mpg17",
         "MULTIPOLYGON(((-1 4,8 -10,-10 10,7 -6,8 -2,\
                      -10 10,-10 1,-3 -4,4 1,-1 2,4 3,-8 10,-5 -9,-1 6,-5 0)),\
                      ((-10 -3,-8 1,2 -8,-2 6,-4 0,8 -5,-1 5,8 2)),\
                      ((-6 -10,-10 9,-4 3,2 0,-7 -2,4 -8,1 10)),\
                      ((10 -1,-2 8,-7 3,-6 8,-9 -7,7 -5)),\
                      ((7 7,-10 -6,9 -8,-4 -4)))",
         false);

    // test cases coming from buffer
    {
        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)))";

        OG open_mpgn = from_wkt<OG>(wkt);
        bg::reverse(open_mpgn);

        test::apply("mpg18", open_mpgn, false);
    }
    {
        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 7.8573216336015328,7.0000000000000000 7.9999999999999973,7.0050957707794925 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 8.1426783663984441,7.0000000000000000 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)))";

        OG open_mpgn = from_wkt<OG>(wkt);
        bg::reverse(open_mpgn);

        // polygon has a self-touching point
        test::apply("mpg19", open_mpgn, false);
    }
    {
        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)))";

        OG open_mpgn = from_wkt<OG>(wkt);
        bg::reverse(open_mpgn);

        // polygon contains a spike
        test::apply("mpg20", open_mpgn, false);
    }

    // Interior ring touches exterior ring, which at that same point touches another exterior ring in (1 2)
    test::apply
        ("mpg21",
        "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)))",
         true);

    // Two interior rings touch each other in (10 5)
    test::apply
        ("mpg22",
        "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)))",
         true);

    // Two polygons, one inside interior of other one, touching all at same point (0,0)
    test::apply
        ("mpg23",
        "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)))",
         true);

    test::apply
        ("ticket_12503",
        "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)))",
         true);

    // MySQL report 12.06.2015
    {
        std::string wkt = "MULTIPOLYGON("
            "((-40.314872143936725 -85.6567579487603,-53.1473643859603 -98.48925019078388,-41.29168745244485 -90.56754012573627,-40.314872143936725 -85.6567579487603)),"
            "((-186.91433298215597 -88.80210078879976,-192.54783347494038 -75.53420159905284,-192.7944062150986 -78.03769664281869,-186.91433298215597 -88.80210078879976)),"
            "((170.89089207158912 -44.35600339378721,191.8949969913326 -31.3460752560506,169.32805525181837 -43.07341636227523,170.89089207158912 -44.35600339378721)),"
            "((-2.6035109435630504 -13.058121512403435,26.839412016794036 43.97610638055074,26.974733141577826 43.72289807427111,26.97470368529088 43.722907009738066,-2.6035109435630504 -13.058121512403435))"
            ")";

        std::string msg;
        CG mpoly = from_wkt<CG>(wkt);
        BOOST_CHECK_MESSAGE(! bg::is_valid(mpoly, msg), msg);
        BOOST_CHECK_MESSAGE(bg::is_valid(mpoly[0], msg), msg);
        BOOST_CHECK_MESSAGE(bg::is_valid(mpoly[1], msg), msg);
        BOOST_CHECK_MESSAGE(bg::is_valid(mpoly[2], msg), msg);
        BOOST_CHECK_MESSAGE(! bg::is_valid(mpoly[3], msg), msg);

        // The last Polygon has wrong orientation, so correct it
        bg::reverse(mpoly[3]);
        BOOST_CHECK_MESSAGE(bg::is_valid(mpoly, msg), msg);
        BOOST_CHECK_MESSAGE(bg::is_valid(mpoly[0], msg), msg);
        BOOST_CHECK_MESSAGE(bg::is_valid(mpoly[1], msg), msg);
        BOOST_CHECK_MESSAGE(bg::is_valid(mpoly[2], msg), msg);
        BOOST_CHECK_MESSAGE(bg::is_valid(mpoly[3], msg), msg);
    }

    // MySQL report 30.06.2015
#ifdef BOOST_GEOMETRY_TEST_FAILURES
    {
        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)))";

        std::string msg;
        CG mpoly = from_wkt<CG>(wkt);
        bg::correct(mpoly);

        BOOST_CHECK_MESSAGE(bg::is_valid(mpoly, msg), msg);
        BOOST_CHECK_MESSAGE(bg::is_valid(mpoly[2], msg), msg);
    }
    {
        std::string wkt = "MULTIPOLYGON(("
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            "(-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),"
            "(-82.61888709171882 24.52458915191082,-65.06618612106601 20.80758831903435,-64.01341032562904 6.452926519952804,-83.39437198775232 23.49488435218103,-82.61888709171882 24.52458915191082),"
            "(-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),"
            "(-74.60894342391143 48.02131743628841,-67.00680717272054 47.268042957701205,-66.69266458534088 42.98472079049692,-74.60894342391143 48.02131743628841),"
            "(-138.56127670492663 -49.7577037198288,-134.94703094520807 -49.02582406883465,-133.72337212957453 -54.038411653780486,-141.85939298329575 -54.13705971460783,-138.56127670492663 -49.7577037198288),"
            "(-134.93399269617888 -49.00526523292734,-135.68321498734667 -45.93611109773349,-118.50171193441933 -23.121886343614484,-110.99462708067594 -44.15753153101153,-134.93399269617888 -49.00526523292734),"
            "(-138.54536289076012 -49.736572791872405,-135.69686656519858 -45.95423814792149,-134.95119672848287 -49.00875938278158,-138.54536289076012 -49.736572791872405),"
            "(88.82755353245742 -46.63627739859524,86.64413783102847 -44.29072778657896,91.56634116238342 -41.32862933986829,92.38779164183632 -41.84427969841862,88.82755353245742 -46.63627739859524),"
            "(96.17559112847069 -36.775403890830276,96.2533145203432 -36.670790012864686,99.8315395547437 -36.33429989598129,97.37090375596762 -37.815068768540016,96.17559112847069 -36.775403890830276),"
            "(92.39828457197696 -41.83015645846746,91.58318530508117 -41.31849282059788,93.74495703397014 -40.01757527428385,92.39828457197696 -41.83015645846746),"
            "(96.16509920779882 -36.78952577205994,97.35510564997305 -37.824575800671205,93.81196732309566 -39.95677632714469,96.16509920779882 -36.78952577205994),"
            "(88.81691795134695 -46.65059264343438,87.42069611419876 -48.52987476642635,80.5749329147718 -47.94307232519108,86.62877983973574 -44.29996996515029,88.81691795134695 -46.65059264343438),"
            "(69.32473564139825 -25.685312296376537,69.17686596344828 -25.526450792983923,79.43054197209301 -22.234338902371594,79.56777154519035 -22.35371429782551,69.32473564139825 -25.685312296376537),"
            "(79.58722163711042 -22.347388059401556,79.45006045094098 -22.22807217263994,91.24299727724733 -18.441755195353803,92.22218393874856 -18.237804190782946,79.58722163711042 -22.347388059401556),"
            "(67.58180682559251 -26.252208498722716,67.35665645137476 -26.110859094265415,69.15841818541341 -25.532373756550623,69.30634307855388 -25.691294568247503,67.58180682559251 -26.252208498722716),"
            "(10.713631867610786 -44.714913767695485,10.86035670084666 -44.70114019099129,10.566326319189315 -44.7967750242813,10.713631867610786 -44.714913767695485),"
            "(14.990356626143694 -42.338898459344726,17.469630118109404 -42.551441381415,10.93650885434335 -44.676371327096064,10.75178223878234 -44.69371860760433,14.990356626143694 -42.338898459344726),"
            "(113.19393813942808 -13.869104583916076,149.85225961536605 -6.232679296303189,99.86624158413852 -36.31341680350249,96.26738808398915 -36.65184732348474,113.19393813942808 -13.869104583916076),"
            "(113.18383917989723 -13.853283334263445,92.53313651295461 -18.155111782662388,115.54974201699517 -10.668833135736556,113.18383917989723 -13.853283334263445),"
            "(163.96311491920022 43.01821047323797,169.91789145903348 43.754090361605556,164.22449464723803 40.59100135183526,163.96311491920022 43.01821047323797),"
            "(92.37537042521268 -18.187979529764235,91.40187377110232 -18.3907452751927,115.58013059889898 -10.627916926612096,115.56781674564326 -10.64450497131272,92.37537042521268 -18.187979529764235),"
            "(-86.16139825386244 19.849866063211905,-118.49613390319635 -23.085326003412035,-128.4910459077906 4.921493651135869,-122.86916414947727 58.18220258298618,-90.8472856693717 30.0249784474685,-86.16139825386244 19.849866063211905),"
            "(-86.14941695432584 19.865785693545394,-90.81481832588861 29.996413910560918,-83.41817017513736 23.49245140750158,-86.14941695432584 19.865785693545394),"
            "(-106.11264211278916 -57.83736939023901,-100.24152662041178 -74.28881727173125,-161.4303237477923 -75.80205692190154,-106.11264211278916 -57.83736939023901),"
            "(-67.56328532753739 55.095514517777545,-62.132454845199874 46.802684774567844,-66.99039908239888 47.28404492010701,-67.56328532753739 55.095514517777545),"
            "(115.59662188220229 -10.635148141706566,115.6088128566935 -10.618708014427298,118.58211270640945 -9.664081031738045,115.59662188220229 -10.635148141706566)))";
        std::string msg;
        CG mpoly = from_wkt<CG>(wkt);
        bg::correct(mpoly);

        BOOST_CHECK_MESSAGE(bg::is_valid(mpoly, msg), msg);
    }
#endif // BOOST_GEOMETRY_TEST_FAILURES
}

BOOST_AUTO_TEST_CASE( test_is_valid_multipolygon )
{
    test_open_multipolygons<point_type, true>();
    test_open_multipolygons<point_type, false>();
}


template <typename CoordinateType, typename Geometry>
inline void check_one(Geometry const& geometry)
{
    bool const is_fp = boost::is_floating_point<CoordinateType>::value;

    bg::validity_failure_type failure;
    bool validity = bg::is_valid(geometry, failure);
    if (BOOST_GEOMETRY_CONDITION(is_fp))
    {
        BOOST_CHECK(! validity);
        BOOST_CHECK(failure == bg::failure_invalid_coordinate);
    }
    else
    {
        BOOST_CHECK(failure == bg::no_failure
                    || failure != bg::failure_invalid_coordinate);
    }
}

template <typename P, typename CoordinateType>
inline void test_with_invalid_coordinate(CoordinateType invalid_value)
{
    typedef bg::model::segment<P> segment_t;
    typedef bg::model::box<P> box_t;
    typedef bg::model::linestring<P> linestring_t;
    typedef bg::model::ring<P> ring_t; // cw, closed
    typedef bg::model::polygon<P> polygon_t; // cw, closed
    typedef bg::model::multi_point<P> multi_point_t;
    typedef bg::model::multi_linestring<linestring_t> multi_linestring_t;
    typedef bg::model::multi_polygon<polygon_t> multi_polygon_t;

    typedef typename bg::coordinate_type<P>::type coord_t;

    std::string wkt_point = "POINT(1 1)";
    std::string wkt_segment = "LINESTRING(1 1,10 20)";
    std::string wkt_box = "BOX(1 1,10 20)";
    std::string wkt_linestring = "LINESTRING(1 1,2 3,4 -5)";
    std::string wkt_ring = "POLYGON((1 1,2 2,2 1,1 1))";
    std::string wkt_polygon = "POLYGON((1 1,1 200,200 200,200 1,1 1),(50 50,50 51,49 50,50 50))";
    std::string wkt_multipoint = "MULTIPOINT(1 1,2 3,4 -5,-5 2)";
    std::string wkt_multilinestring =
        "MULTILINESTRING((1 1,2 3,4 -5),(-4 -2,-8 9))";
    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)))";

    {
        P p;
        bg::read_wkt(wkt_point, p);
        BOOST_CHECK(bg::is_valid(p));
        bg::set<1>(p, invalid_value);
        check_one<coord_t>(p);
    }
    {
        segment_t s;
        bg::read_wkt(wkt_segment, s);
        BOOST_CHECK(bg::is_valid(s));
        bg::set<1, 1>(s, invalid_value);
        check_one<coord_t>(s);
    }
    {
        box_t b;
        bg::read_wkt(wkt_box, b);
        BOOST_CHECK(bg::is_valid(b));
        bg::set<1, 0>(b, invalid_value);
        check_one<coord_t>(b);
    }
    {
        linestring_t ls;
        bg::read_wkt(wkt_linestring, ls);
        BOOST_CHECK(bg::is_valid(ls));
        bg::set<1>(ls[1], invalid_value);
        check_one<coord_t>(ls);
    }
    {
        ring_t r;
        bg::read_wkt(wkt_ring, r);
        BOOST_CHECK(bg::is_valid(r));
        bg::set<0>(r[1], invalid_value);
        check_one<coord_t>(r);
    }
    {
        polygon_t pgn;
        bg::read_wkt(wkt_polygon, pgn);
        BOOST_CHECK(bg::is_valid(pgn));
        bg::set<0>(bg::interior_rings(pgn)[0][1], invalid_value);
        check_one<coord_t>(pgn);
    }
    {
        multi_point_t mp;
        bg::read_wkt(wkt_multipoint, mp);
        BOOST_CHECK(bg::is_valid(mp));
        bg::set<0>(mp[2], invalid_value);
        check_one<coord_t>(mp);
    }
    {
        multi_linestring_t mls;
        bg::read_wkt(wkt_multilinestring, mls);
        BOOST_CHECK(bg::is_valid(mls));
        bg::set<0>(mls[1][1], invalid_value);
        check_one<coord_t>(mls);
    }
    {
        multi_polygon_t mpgn;
        bg::read_wkt(wkt_multipolygon, mpgn);
        BOOST_CHECK(bg::is_valid(mpgn));
        bg::set<0>(bg::exterior_ring(mpgn[1])[1], invalid_value);
        check_one<coord_t>(mpgn);
    }
}

template <typename P>
inline void test_with_invalid_coordinate()
{
    typedef typename bg::coordinate_type<P>::type coord_t;

    coord_t const q_nan = std::numeric_limits<coord_t>::quiet_NaN();
    coord_t const inf = std::numeric_limits<coord_t>::infinity();

    test_with_invalid_coordinate<P, coord_t>(q_nan);
    test_with_invalid_coordinate<P, coord_t>(inf);
}

BOOST_AUTO_TEST_CASE( test_geometries_with_invalid_coordinates )
{
    typedef point_type fp_point_type;
    typedef bg::model::point<int, 2, bg::cs::cartesian> int_point_type;

    test_with_invalid_coordinate<fp_point_type>();
    test_with_invalid_coordinate<int_point_type>();
}

BOOST_AUTO_TEST_CASE( test_with_NaN_coordinates )
{
#ifdef BOOST_GEOMETRY_TEST_DEBUG
    std::cout << std::endl << std::endl;
    std::cout << "************************************" << std::endl;
    std::cout << " is_valid: geometry with NaN coordinates" << std::endl;
    std::cout << "************************************" << std::endl;
#endif

    linestring_type ls1, ls2;
    bg::read_wkt("LINESTRING(1 1,1.115235e+308 1.738137e+308)", ls1);
    bg::read_wkt("LINESTRING(-1 1,1.115235e+308 1.738137e+308)", ls2);

    // the intersection of the two linestrings is a new linestring
    // (multilinestring with a single element) that has NaN coordinates
    multi_linestring_type mls;
    bg::intersection(ls1, ls2, mls);

    typedef validity_tester_linear<true> tester_allow_spikes;
    typedef validity_tester_linear<false> tester_disallow_spikes;

    test_valid
        <
            tester_allow_spikes, multi_linestring_type
        >::apply("mls-NaN", mls, false);

    test_valid
        <
            tester_disallow_spikes, multi_linestring_type
        >::apply("mls-NaN", mls, false);
}

BOOST_AUTO_TEST_CASE( test_is_valid_variant )
{
#ifdef BOOST_GEOMETRY_TEST_DEBUG
    std::cout << std::endl << std::endl;
    std::cout << "************************************" << std::endl;
    std::cout << " is_valid: variant support" << std::endl;
    std::cout << "************************************" << std::endl;
#endif

    typedef bg::model::polygon<point_type> polygon_type; // cw, closed

    typedef boost::variant
        <
            linestring_type, multi_linestring_type, polygon_type
        > variant_geometry;
    typedef test_valid_variant<variant_geometry> test;

    variant_geometry vg;

    linestring_type valid_linestring =
        from_wkt<linestring_type>("LINESTRING(0 0,1 0)");
    multi_linestring_type invalid_multi_linestring =
        from_wkt<multi_linestring_type>("MULTILINESTRING((0 0,1 0),(0 0))");
    polygon_type valid_polygon =
        from_wkt<polygon_type>("POLYGON((0 0,1 1,1 0,0 0))");
    polygon_type invalid_polygon =
        from_wkt<polygon_type>("POLYGON((0 0,2 2,2 0,1 0))");

    vg = valid_linestring;
    test::apply("v01", vg, true);
    vg = invalid_multi_linestring;
    test::apply("v02", vg, false);
    vg = valid_polygon;
    test::apply("v03", vg, true);
    vg = invalid_polygon;
    test::apply("v04", vg, false);
}