text: // Boost.Geometry (aka GGL, Generic Geometry Library)
  // Unit Test
  
  // Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands.
  // Copyright (c) 2008-2012 Bruno Lalande, Paris, France.
  // Copyright (c) 2009-2012 Mateusz Loskot, London, UK.
  
  // This file was modified by Oracle on 2014, 2015.
  // Modifications copyright (c) 2014-2015 Oracle and/or its affiliates.
  
  // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
  
  // Parts of Boost.Geometry are redesigned from Geodan's Geographic Library
  // (geolib/GGL), copyright (c) 1995-2010 Geodan, Amsterdam, the Netherlands.
  
  // Use, modification and distribution is subject to the Boost Software License,
  // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
  // http://www.boost.org/LICENSE_1_0.txt)
  
  
  #include <geometry_test_common.hpp>
  
  #include <boost/concept_check.hpp>
  
  #include <boost/geometry/strategies/geographic/distance_vincenty.hpp>
  #include <boost/geometry/strategies/geographic/side_vincenty.hpp>
  #include <boost/geometry/algorithms/detail/vincenty_inverse.hpp>
  #include <boost/geometry/algorithms/detail/vincenty_direct.hpp>
  
  #include <boost/geometry/core/srs.hpp>
  #include <boost/geometry/strategies/strategies.hpp>
  #include <boost/geometry/algorithms/assign.hpp>
  #include <boost/geometry/geometries/point.hpp>
  #include <test_common/test_point.hpp>
  
  #ifdef HAVE_TTMATH
  #  include <boost/geometry/extensions/contrib/ttmath_stub.hpp>
  #endif
  
  template <typename T>
  void normalize_deg(T & deg)
  {
      while ( deg > T(180) )
          deg -= T(360);
      while ( deg <= T(-180) )
          deg += T(360);
  }
  
  template <typename T>
  T difference_deg(T const& a1, T const& a2)
  {
      T d = a1 - a2;
      normalize_deg(d);
      return d;
  }
  
  template <typename T>
  void check_deg(std::string const& name, T const& a1, T const& a2, T const& percent, T const& error)
  {
      T diff = bg::math::abs(difference_deg(a1, a2));
      
      if ( bg::math::equals(a1, T(0)) || bg::math::equals(a2, T(0)) )
      {
          if ( diff > error )
          {
              BOOST_ERROR(name << " - the difference {" << diff << "} between {" << a1 << "} and {" << a2 << "} exceeds {" << error << "}");
          }
      }
      else
      {
          T greater = (std::max)(bg::math::abs(a1), bg::math::abs(a2));
  
          if ( diff > greater * percent / T(100) )
          {
              BOOST_ERROR(name << " the difference {" << diff << "} between {" << a1 << "} and {" << a2 << "} exceeds {" << percent << "}%");
          }
      }
  }
  
  double azimuth(double deg, double min, double sec)
  {
      min = fabs(min);
      sec = fabs(sec);
  
      if ( deg < 0 )
      {
          min = -min;
          sec = -sec;
      }
  
      return deg + min/60.0 + sec/3600.0;
  }
  
  double azimuth(double deg, double min)
  {
      return azimuth(deg, min, 0.0);
  }
  
  template <typename P>
  bool non_precise_ct()
  {
      typedef typename bg::coordinate_type<P>::type ct;
      return boost::is_integral<ct>::value || boost::is_float<ct>::value;
  }
  
  template <typename P1, typename P2, typename Spheroid>
  void test_vincenty(double lon1, double lat1, double lon2, double lat2,
                     double expected_distance,
                     double expected_azimuth_12,
                     double /*expected_azimuth_21*/,
                     Spheroid const& spheroid)
  {
      typedef typename bg::promote_floating_point
          <
              typename bg::select_calculation_type<P1, P2, void>::type
          >::type calc_t;
  
      calc_t tolerance = non_precise_ct<P1>() || non_precise_ct<P2>() ?
                         5.0 : 0.001;
      calc_t error = non_precise_ct<P1>() || non_precise_ct<P2>() ?
                     1e-5 : 1e-12;
  
      // formula
      {
          double const d2r = bg::math::d2r<double>();
          double const r2d = bg::math::r2d<double>();
  
          typedef bg::detail::vincenty_inverse<calc_t, true, true> inverse_formula;
          typename inverse_formula::result_type
              result_i = inverse_formula::apply(lon1 * d2r,
                                               lat1 * d2r,
                                               lon2 * d2r,
                                               lat2 * d2r,
                                               spheroid);
          calc_t dist = result_i.distance;
          calc_t az12 = result_i.azimuth;
          //calc_t az21 = vi.azimuth21();
  
          calc_t az12_deg = az12 * r2d;
          //calc_t az21_deg = az21 * r2d;
          
          BOOST_CHECK_CLOSE(dist, calc_t(expected_distance), tolerance);
          check_deg("az12_deg", az12_deg, calc_t(expected_azimuth_12), tolerance, error);
          //check_deg("az21_deg", az21_deg, calc_t(expected_azimuth_21), tolerance, error);
  
          typedef bg::detail::vincenty_direct<calc_t> direct_formula;
          typename direct_formula::result_type
              result_d = direct_formula::apply(lon1 * d2r,
                                               lat1 * d2r,
                                               dist,
                                               az12,
                                               spheroid);
          calc_t direct_lon2 = result_d.lon2;
          calc_t direct_lat2 = result_d.lat2;
          //calc_t direct_az21 = vd.azimuth21();
  
          calc_t direct_lon2_deg = direct_lon2 * r2d;
          calc_t direct_lat2_deg = direct_lat2 * r2d;
          //calc_t direct_az21_deg = direct_az21 * r2d;
          
          check_deg("direct_lon2_deg", direct_lon2_deg, calc_t(lon2), tolerance, error);
          check_deg("direct_lat2_deg", direct_lat2_deg, calc_t(lat2), tolerance, error);
          //check_deg("direct_az21_deg", direct_az21_deg, az21_deg, tolerance, error);
      }
  
      // distance strategy
      {
          typedef bg::strategy::distance::vincenty<Spheroid> vincenty_type;
  
          BOOST_CONCEPT_ASSERT(
              (
                  bg::concept::PointDistanceStrategy<vincenty_type, P1, P2>)
              );
  
          vincenty_type vincenty(spheroid);
          typedef typename bg::strategy::distance::services::return_type<vincenty_type, P1, P2>::type return_type;
  
          P1 p1;
          P2 p2;
  
          bg::assign_values(p1, lon1, lat1);
          bg::assign_values(p2, lon2, lat2);
          
          BOOST_CHECK_CLOSE(vincenty.apply(p1, p2), return_type(expected_distance), tolerance);
          BOOST_CHECK_CLOSE(bg::distance(p1, p2, vincenty), return_type(expected_distance), tolerance);
      }
  }
  
  template <typename P1, typename P2>
  void test_vincenty(double lon1, double lat1, double lon2, double lat2,
                     double expected_distance,
                     double expected_azimuth_12,
                     double expected_azimuth_21)
  {
      test_vincenty<P1, P2>(lon1, lat1, lon2, lat2,
                            expected_distance, expected_azimuth_12, expected_azimuth_21,
                            bg::srs::spheroid<double>());
  }
  
  template <typename PS, typename P>
  void test_side(double lon1, double lat1,
                 double lon2, double lat2,
                 double lon, double lat,
                 int expected_side)
  {
      // Set radius type, but for integer coordinates we want to have floating point radius type
      typedef typename bg::promote_floating_point
          <
              typename bg::coordinate_type<PS>::type
          >::type rtype;
  
      typedef bg::srs::spheroid<rtype> stype;
  
      typedef bg::strategy::side::vincenty<stype> strategy_type;
  
      strategy_type strategy;
  
      PS p1, p2;
      P p;
  
      bg::assign_values(p1, lon1, lat1);
      bg::assign_values(p2, lon2, lat2);
      bg::assign_values(p, lon, lat);
  
      int side = strategy.apply(p1, p2, p);
  
      BOOST_CHECK_EQUAL(side, expected_side);
  }
  
  template <typename P1, typename P2>
  void test_all()
  {
      // See:
      //  - http://www.ga.gov.au/geodesy/datums/vincenty_inverse.jsp
      //  - http://www.ga.gov.au/geodesy/datums/vincenty_direct.jsp
      // Values in the comments below was calculated using the above pages
      // in some cases distances may be different, previously used values was left
  
      // use km
      double gda_a = 6378.1370;
      double gda_f = 1.0 / 298.25722210;
      double gda_b = gda_a * ( 1.0 - gda_f );
      bg::srs::spheroid<double> gda_spheroid(gda_a, gda_b);
  
      // Test fractional coordinates only for non-integral types
      if ( BOOST_GEOMETRY_CONDITION(
              ! boost::is_integral<typename bg::coordinate_type<P1>::type>::value
           && ! boost::is_integral<typename bg::coordinate_type<P2>::type>::value  ) )
      {
          // Flinders Peak -> Buninyong
          test_vincenty<P1, P2>(azimuth(144,25,29.52440), azimuth(-37,57,3.72030),
                                azimuth(143,55,35.38390), azimuth(-37,39,10.15610),
                                54.972271, azimuth(306,52,5.37), azimuth(127,10,25.07),
                                gda_spheroid);
      }
  
      // Lodz -> Trondheim
      test_vincenty<P1, P2>(azimuth(19,28), azimuth(51,47),
                            azimuth(10,21), azimuth(63,23),
                            1399.032724, azimuth(340,54,25.14), azimuth(153,10,0.19),
                            gda_spheroid);
      // London -> New York
      test_vincenty<P1, P2>(azimuth(0,7,39), azimuth(51,30,26),
                            azimuth(-74,0,21), azimuth(40,42,46),
                            5602.044851, azimuth(288,31,36.82), azimuth(51,10,33.43),
                            gda_spheroid);
  
      // Shanghai -> San Francisco
      test_vincenty<P1, P2>(azimuth(121,30), azimuth(31,12),
                            azimuth(-122,25), azimuth(37,47),
                            9899.698550, azimuth(45,12,44.76), azimuth(309,50,20.88),
                            gda_spheroid);
  
      test_vincenty<P1, P2>(0, 0, 0, 50, 5540.847042, 0, 180, gda_spheroid); // N
      test_vincenty<P1, P2>(0, 0, 0, -50, 5540.847042, 180, 0, gda_spheroid); // S
      test_vincenty<P1, P2>(0, 0, 50, 0, 	5565.974540, 90, -90, gda_spheroid); // E
      test_vincenty<P1, P2>(0, 0, -50, 0, 5565.974540, -90, 90, gda_spheroid); // W
      
      test_vincenty<P1, P2>(0, 0, 50, 50, 7284.879297, azimuth(32,51,55.87), azimuth(237,24,50.12), gda_spheroid); // NE
      
      // The original distance values, azimuths calculated using the web form mentioned above
      // Using default spheroid units (meters)
      test_vincenty<P1, P2>(0, 89, 1, 80, 1005153.5769, azimuth(178,53,23.85), azimuth(359,53,18.35)); // sub-polar
      test_vincenty<P1, P2>(4, 52, 4, 52, 0.0, 0, 0); // no point difference
      test_vincenty<P1, P2>(4, 52, 3, 40, 1336039.890, azimuth(183,41,29.08), azimuth(2,58,5.13)); // normal case
  
      test_side<P1, P2>(0, 0, 0, 1, 0, 2, 0);
      test_side<P1, P2>(0, 0, 0, 1, 0, -2, 0);
      test_side<P1, P2>(10, 0, 10, 1, 10, 2, 0);
      test_side<P1, P2>(10, 0, 10, -1, 10, 2, 0);
  
      test_side<P1, P2>(10, 0, 10, 1, 0, 2, 1); // left
      test_side<P1, P2>(10, 0, 10, -1, 0, 2, -1); // right
  
      test_side<P1, P2>(-10, -10, 10, 10, 10, 0, -1); // right
      test_side<P1, P2>(-10, -10, 10, 10, -10, 0, 1); // left
      test_side<P1, P2>(170, -10, -170, 10, -170, 0, -1); // right
      test_side<P1, P2>(170, -10, -170, 10, 170, 0, 1); // left
  }
  
  template <typename P>
  void test_all()
  {
      test_all<P, P>();
  }
  
  int test_main(int, char* [])
  {
      //test_all<float[2]>();
      //test_all<double[2]>();
      test_all<bg::model::point<double, 2, bg::cs::geographic<bg::degree> > >();
      test_all<bg::model::point<float, 2, bg::cs::geographic<bg::degree> > >();
      test_all<bg::model::point<int, 2, bg::cs::geographic<bg::degree> > >();
  
  #if defined(HAVE_TTMATH)
      test_all<bg::model::point<ttmath::Big<1,4>, 2, bg::cs::geographic<bg::degree> > >();
      test_all<bg::model::point<ttmath_big, 2, bg::cs::geographic<bg::degree> > >();
  #endif
  
  
      return 0;
  }
  