text: // Boost.Geometry - gis-projections (based on PROJ4)
  
  // Copyright (c) 2008-2015 Barend Gehrels, Amsterdam, the Netherlands.
  
  // This file was modified by Oracle on 2017, 2018.
  // Modifications copyright (c) 2017-2018, Oracle and/or its affiliates.
  // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle.
  
  // Use, modification and distribution is subject to the Boost Software License,
  // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
  // http://www.boost.org/LICENSE_1_0.txt)
  
  // This file is converted from PROJ4, http://trac.osgeo.org/proj
  // PROJ4 is originally written by Gerald Evenden (then of the USGS)
  // PROJ4 is maintained by Frank Warmerdam
  // PROJ4 is converted to Boost.Geometry by Barend Gehrels
  
  // Last updated version of proj: 5.0.0
  
  // Original copyright notice:
  
  // Permission is hereby granted, free of charge, to any person obtaining a
  // copy of this software and associated documentation files (the "Software"),
  // to deal in the Software without restriction, including without limitation
  // the rights to use, copy, modify, merge, publish, distribute, sublicense,
  // and/or sell copies of the Software, and to permit persons to whom the
  // Software is furnished to do so, subject to the following conditions:
  
  // The above copyright notice and this permission notice shall be included
  // in all copies or substantial portions of the Software.
  
  // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
  // OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
  // THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
  // FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
  // DEALINGS IN THE SOFTWARE.
  
  #ifndef BOOST_GEOMETRY_PROJECTIONS_IGH_HPP
  #define BOOST_GEOMETRY_PROJECTIONS_IGH_HPP
  
  #include <boost/geometry/util/math.hpp>
  #include <boost/shared_ptr.hpp>
  
  #include <boost/geometry/srs/projections/impl/base_static.hpp>
  #include <boost/geometry/srs/projections/impl/base_dynamic.hpp>
  #include <boost/geometry/srs/projections/impl/projects.hpp>
  #include <boost/geometry/srs/projections/impl/factory_entry.hpp>
  #include <boost/geometry/srs/projections/proj/gn_sinu.hpp>
  #include <boost/geometry/srs/projections/proj/moll.hpp>
  
  namespace boost { namespace geometry
  {
  
  namespace srs { namespace par4
  {
      struct igh {}; // Interrupted Goode Homolosine
  
  }} //namespace srs::par4
  
  namespace projections
  {
      #ifndef DOXYGEN_NO_DETAIL
      namespace detail { namespace igh
      {
              // TODO: consider replacing dynamically created projections
              // with member objects
              template <typename T, typename Parameters>
              struct par_igh
              {
                  boost::shared_ptr<base_v<T, Parameters> > pj[12];
                  T dy0;
              };
  
              /* 40d 44' 11.8" [degrees] */
              template <typename T>
              inline T d4044118() { return (T(40) + T(44)/T(60.) + T(11.8)/T(3600.)) * geometry::math::d2r<T>(); }
  
              template <typename T>
              inline T d10() { return T(10) * geometry::math::d2r<T>(); }
              template <typename T>
              inline T d20() { return T(20) * geometry::math::d2r<T>(); }
              template <typename T>
              inline T d30() { return T(30) * geometry::math::d2r<T>(); }
              template <typename T>
              inline T d40() { return T(40) * geometry::math::d2r<T>(); }
              template <typename T>
              inline T d50() { return T(50) * geometry::math::d2r<T>(); }
              template <typename T>
              inline T d60() { return T(60) * geometry::math::d2r<T>(); }
              template <typename T>
              inline T d80() { return T(80) * geometry::math::d2r<T>(); }
              template <typename T>
              inline T d90() { return T(90) * geometry::math::d2r<T>(); }
              template <typename T>
              inline T d100() { return T(100) * geometry::math::d2r<T>(); }
              template <typename T>
              inline T d140() { return T(140) * geometry::math::d2r<T>(); }
              template <typename T>
              inline T d160() { return T(160) * geometry::math::d2r<T>(); }
              template <typename T>
              inline T d180() { return T(180) * geometry::math::d2r<T>(); }
  
              static const double epsilon = 1.e-10; // allow a little 'slack' on zone edge positions
  
              // Converted from #define SETUP(n, proj, x_0, y_0, lon_0)
              template <template <typename, typename> class Entry, typename Parameters, typename T>
              inline void do_setup(int n, Parameters const& par, par_igh<T, Parameters>& proj_parm,
                                   T const& x_0, T const& y_0,
                                   T const& lon_0)
              {
                  // NOTE: in the original proj4 these projections are initialized
                  // with zeroed parameters which could be done here as well instead
                  // of initializing with parent projection's parameters.
                  Entry<T, Parameters> entry;
                  proj_parm.pj[n-1].reset(entry.create_new(par));
                  proj_parm.pj[n-1]->mutable_params().x0 = x_0;
                  proj_parm.pj[n-1]->mutable_params().y0 = y_0;
                  proj_parm.pj[n-1]->mutable_params().lam0 = lon_0;
              }
  
              // template class, using CRTP to implement forward/inverse
              template <typename T, typename Parameters>
              struct base_igh_spheroid
                  : public base_t_fi<base_igh_spheroid<T, Parameters>, T, Parameters>
              {
                  par_igh<T, Parameters> m_proj_parm;
  
                  inline base_igh_spheroid(const Parameters& par)
                      : base_t_fi<base_igh_spheroid<T, Parameters>, T, Parameters>(*this, par)
                  {}
  
                  // FORWARD(s_forward)  spheroid
                  // Project coordinates from geographic (lon, lat) to cartesian (x, y)
                  inline void fwd(T& lp_lon, T& lp_lat, T& xy_x, T& xy_y) const
                  {
                      static const T d4044118 = igh::d4044118<T>();
                      static const T d20  =  igh::d20<T>();
                      static const T d40  =  igh::d40<T>();
                      static const T d80  =  igh::d80<T>();
                      static const T d100 = igh::d100<T>();
  
                          int z;
                          if (lp_lat >=  d4044118) {          // 1|2
                            z = (lp_lon <= -d40 ? 1: 2);
                          }
                          else if (lp_lat >=  0) {            // 3|4
                            z = (lp_lon <= -d40 ? 3: 4);
                          }
                          else if (lp_lat >= -d4044118) {     // 5|6|7|8
                                 if (lp_lon <= -d100) z =  5; // 5
                            else if (lp_lon <=  -d20) z =  6; // 6
                            else if (lp_lon <=   d80) z =  7; // 7
                            else z = 8;                       // 8
                          }
                          else {                              // 9|10|11|12
                                 if (lp_lon <= -d100) z =  9; // 9
                            else if (lp_lon <=  -d20) z = 10; // 10
                            else if (lp_lon <=   d80) z = 11; // 11
                            else z = 12;                      // 12
                          }
  
                          lp_lon -= this->m_proj_parm.pj[z-1]->params().lam0;
                          this->m_proj_parm.pj[z-1]->fwd(lp_lon, lp_lat, xy_x, xy_y);
                          xy_x += this->m_proj_parm.pj[z-1]->params().x0;
                          xy_y += this->m_proj_parm.pj[z-1]->params().y0;
                  }
  
                  // INVERSE(s_inverse)  spheroid
                  // Project coordinates from cartesian (x, y) to geographic (lon, lat)
                  inline void inv(T& xy_x, T& xy_y, T& lp_lon, T& lp_lat) const
                  {
                      static const T d4044118 = igh::d4044118<T>();
                      static const T d10  =  igh::d10<T>();
                      static const T d20  =  igh::d20<T>();
                      static const T d40  =  igh::d40<T>();
                      static const T d50  =  igh::d50<T>();
                      static const T d60  =  igh::d60<T>();
                      static const T d80  =  igh::d80<T>();
                      static const T d90  =  igh::d90<T>();
                      static const T d100 = igh::d100<T>();
                      static const T d160 = igh::d160<T>();
                      static const T d180 = igh::d180<T>();
  
                      static const T c2 = 2.0;
                      
                      const T y90 = this->m_proj_parm.dy0 + sqrt(c2); // lt=90 corresponds to y=y0+sqrt(2.0)
  
                          int z = 0;
                          if (xy_y > y90+epsilon || xy_y < -y90+epsilon) // 0
                            z = 0;
                          else if (xy_y >=  d4044118)       // 1|2
                            z = (xy_x <= -d40? 1: 2);
                          else if (xy_y >=  0)              // 3|4
                            z = (xy_x <= -d40? 3: 4);
                          else if (xy_y >= -d4044118) {     // 5|6|7|8
                                 if (xy_x <= -d100) z =  5; // 5
                            else if (xy_x <=  -d20) z =  6; // 6
                            else if (xy_x <=   d80) z =  7; // 7
                            else z = 8;                     // 8
                          }
                          else {                            // 9|10|11|12
                                 if (xy_x <= -d100) z =  9; // 9
                            else if (xy_x <=  -d20) z = 10; // 10
                            else if (xy_x <=   d80) z = 11; // 11
                            else z = 12;                    // 12
                          }
  
                          if (z)
                          {
                            int ok = 0;
  
                            xy_x -= this->m_proj_parm.pj[z-1]->params().x0;
                            xy_y -= this->m_proj_parm.pj[z-1]->params().y0;
                            this->m_proj_parm.pj[z-1]->inv(xy_x, xy_y, lp_lon, lp_lat);
                            lp_lon += this->m_proj_parm.pj[z-1]->params().lam0;
  
                            switch (z) {
                              case  1: ok = (lp_lon >= -d180-epsilon && lp_lon <=  -d40+epsilon) ||
                                           ((lp_lon >=  -d40-epsilon && lp_lon <=  -d10+epsilon) &&
                                            (lp_lat >=   d60-epsilon && lp_lat <=   d90+epsilon)); break;
                              case  2: ok = (lp_lon >=  -d40-epsilon && lp_lon <=  d180+epsilon) ||
                                           ((lp_lon >= -d180-epsilon && lp_lon <= -d160+epsilon) &&
                                            (lp_lat >=   d50-epsilon && lp_lat <=   d90+epsilon)) ||
                                           ((lp_lon >=  -d50-epsilon && lp_lon <=  -d40+epsilon) &&
                                            (lp_lat >=   d60-epsilon && lp_lat <=   d90+epsilon)); break;
                              case  3: ok = (lp_lon >= -d180-epsilon && lp_lon <=  -d40+epsilon); break;
                              case  4: ok = (lp_lon >=  -d40-epsilon && lp_lon <=  d180+epsilon); break;
                              case  5: ok = (lp_lon >= -d180-epsilon && lp_lon <= -d100+epsilon); break;
                              case  6: ok = (lp_lon >= -d100-epsilon && lp_lon <=  -d20+epsilon); break;
                              case  7: ok = (lp_lon >=  -d20-epsilon && lp_lon <=   d80+epsilon); break;
                              case  8: ok = (lp_lon >=   d80-epsilon && lp_lon <=  d180+epsilon); break;
                              case  9: ok = (lp_lon >= -d180-epsilon && lp_lon <= -d100+epsilon); break;
                              case 10: ok = (lp_lon >= -d100-epsilon && lp_lon <=  -d20+epsilon); break;
                              case 11: ok = (lp_lon >=  -d20-epsilon && lp_lon <=   d80+epsilon); break;
                              case 12: ok = (lp_lon >=   d80-epsilon && lp_lon <=  d180+epsilon); break;
                            }
  
                            z = (!ok? 0: z); // projectable?
                          }
                       // if (!z) pj_errno = -15; // invalid x or y
                          if (!z) lp_lon = HUGE_VAL;
                          if (!z) lp_lat = HUGE_VAL;
                  }
  
                  static inline std::string get_name()
                  {
                      return "igh_spheroid";
                  }
  
              };
  
              // Interrupted Goode Homolosine
              template <typename T, typename Parameters>
              inline void setup_igh(Parameters& par, par_igh<T, Parameters>& proj_parm)
              {
                  static const T d0   =  0;
                  static const T d4044118 = igh::d4044118<T>();
                  static const T d20  =  igh::d20<T>();
                  static const T d30  =  igh::d30<T>();
                  static const T d60  =  igh::d60<T>();
                  static const T d100 = igh::d100<T>();
                  static const T d140 = igh::d140<T>();
                  static const T d160 = igh::d160<T>();
  
              /*
                Zones:
  
                  -180            -40                       180
                    +--------------+-------------------------+    Zones 1,2,9,10,11 & 12:
                    |1             |2                        |      Mollweide projection
                    |              |                         |
                    +--------------+-------------------------+    Zones 3,4,5,6,7 & 8:
                    |3             |4                        |      Sinusoidal projection
                    |              |                         |
                  0 +-------+------+-+-----------+-----------+
                    |5      |6       |7          |8          |
                    |       |        |           |           |
                    +-------+--------+-----------+-----------+
                    |9      |10      |11         |12         |
                    |       |        |           |           |
                    +-------+--------+-----------+-----------+
                  -180    -100      -20         80          180
              */
                  
                      T lp_lam = 0, lp_phi = d4044118;
                      T xy1_x, xy1_y;
                      T xy3_x, xy3_y;
  
                      // IMPORTANT: Force spherical sinu projection
                      // This is required because unlike in the original proj4 here
                      // parameters are used to initialize underlying projections.
                      // In the original code zeroed parameters are passed which
                      // could be done here as well though.
                      par.es = 0.;
  
                      // sinusoidal zones
                      do_setup<sinu_entry>(3, par, proj_parm, -d100, d0, -d100);
                      do_setup<sinu_entry>(4, par, proj_parm,   d30, d0,   d30);
                      do_setup<sinu_entry>(5, par, proj_parm, -d160, d0, -d160);
                      do_setup<sinu_entry>(6, par, proj_parm,  -d60, d0,  -d60);
                      do_setup<sinu_entry>(7, par, proj_parm,   d20, d0,   d20);
                      do_setup<sinu_entry>(8, par, proj_parm,  d140, d0,  d140);
  
                      // mollweide zones
                      do_setup<moll_entry>(1, par, proj_parm, -d100, d0, -d100);
  
                      // y0 ?
                       proj_parm.pj[0]->fwd(lp_lam, lp_phi, xy1_x, xy1_y); // zone 1
                       proj_parm.pj[2]->fwd(lp_lam, lp_phi, xy3_x, xy3_y); // zone 3
                      // y0 + xy1_y = xy3_y for lt = 40d44'11.8"
                      proj_parm.dy0 = xy3_y - xy1_y;
  
                      proj_parm.pj[0]->mutable_params().y0 = proj_parm.dy0;
  
                      // mollweide zones (cont'd)
                      do_setup<moll_entry>( 2, par, proj_parm,   d30,  proj_parm.dy0,   d30);
                      do_setup<moll_entry>( 9, par, proj_parm, -d160, -proj_parm.dy0, -d160);
                      do_setup<moll_entry>(10, par, proj_parm,  -d60, -proj_parm.dy0,  -d60);
                      do_setup<moll_entry>(11, par, proj_parm,   d20, -proj_parm.dy0,   d20);
                      do_setup<moll_entry>(12, par, proj_parm,  d140, -proj_parm.dy0,  d140);
  
                      // Already done before
                      //par.es = 0.;
              }
  
      }} // namespace detail::igh
      #endif // doxygen
  
      /*!
          \brief Interrupted Goode Homolosine projection
          \ingroup projections
          \tparam Geographic latlong point type
          \tparam Cartesian xy point type
          \tparam Parameters parameter type
          \par Projection characteristics
           - Pseudocylindrical
           - Spheroid
          \par Example
          \image html ex_igh.gif
      */
      template <typename T, typename Parameters>
      struct igh_spheroid : public detail::igh::base_igh_spheroid<T, Parameters>
      {
          inline igh_spheroid(const Parameters& par) : detail::igh::base_igh_spheroid<T, Parameters>(par)
          {
              detail::igh::setup_igh(this->m_par, this->m_proj_parm);
          }
      };
  
      #ifndef DOXYGEN_NO_DETAIL
      namespace detail
      {
  
          // Static projection
          BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION(srs::par4::igh, igh_spheroid, igh_spheroid)
  
          // Factory entry(s)
          template <typename T, typename Parameters>
          class igh_entry : public detail::factory_entry<T, Parameters>
          {
              public :
                  virtual base_v<T, Parameters>* create_new(const Parameters& par) const
                  {
                      return new base_v_fi<igh_spheroid<T, Parameters>, T, Parameters>(par);
                  }
          };
  
          template <typename T, typename Parameters>
          inline void igh_init(detail::base_factory<T, Parameters>& factory)
          {
              factory.add_to_factory("igh", new igh_entry<T, Parameters>);
          }
  
      } // namespace detail
      #endif // doxygen
  
  } // namespace projections
  
  }} // namespace boost::geometry
  
  #endif // BOOST_GEOMETRY_PROJECTIONS_IGH_HPP
  
  