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_CEA_HPP
  #define BOOST_GEOMETRY_PROJECTIONS_CEA_HPP
  
  #include <boost/geometry/util/math.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/impl/pj_auth.hpp>
  #include <boost/geometry/srs/projections/impl/pj_qsfn.hpp>
  
  namespace boost { namespace geometry
  {
  
  namespace srs { namespace par4
  {
      struct cea {};
  
  }} //namespace srs::par4
  
  namespace projections
  {
      #ifndef DOXYGEN_NO_DETAIL
      namespace detail { namespace cea
      {
  
              static const double epsilon = 1e-10;
  
              template <typename T>
              struct par_cea
              {
                  T qp;
                  detail::apa<T> apa;
              };
  
              // template class, using CRTP to implement forward/inverse
              template <typename T, typename Parameters>
              struct base_cea_ellipsoid
                  : public base_t_fi<base_cea_ellipsoid<T, Parameters>, T, Parameters>
              {
                  par_cea<T> m_proj_parm;
  
                  inline base_cea_ellipsoid(const Parameters& par)
                      : base_t_fi<base_cea_ellipsoid<T, Parameters>, T, Parameters>(*this, par)
                  {}
  
                  // FORWARD(e_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
                  {
                      xy_x = this->m_par.k0 * lp_lon;
                      xy_y = .5 * pj_qsfn(sin(lp_lat), this->m_par.e, this->m_par.one_es) / this->m_par.k0;
                  }
  
                  // INVERSE(e_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
                  {
                      lp_lat = pj_authlat(asin( 2. * xy_y * this->m_par.k0 / this->m_proj_parm.qp), this->m_proj_parm.apa);
                      lp_lon = xy_x / this->m_par.k0;
                  }
  
                  static inline std::string get_name()
                  {
                      return "cea_ellipsoid";
                  }
  
              };
  
              // template class, using CRTP to implement forward/inverse
              template <typename T, typename Parameters>
              struct base_cea_spheroid
                  : public base_t_fi<base_cea_spheroid<T, Parameters>, T, Parameters>
              {
                  par_cea<T> m_proj_parm;
  
                  inline base_cea_spheroid(const Parameters& par)
                      : base_t_fi<base_cea_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
                  {
                      xy_x = this->m_par.k0 * lp_lon;
                      xy_y = sin(lp_lat) / this->m_par.k0;
                  }
  
                  // 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 half_pi = detail::half_pi<T>();
  
                      T t;
  
                      if ((t = fabs(xy_y *= this->m_par.k0)) - epsilon <= 1.) {
                          if (t >= 1.)
                              lp_lat = xy_y < 0. ? -half_pi : half_pi;
                          else
                              lp_lat = asin(xy_y);
                          lp_lon = xy_x / this->m_par.k0;
                      } else
                          BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
                  }
  
                  static inline std::string get_name()
                  {
                      return "cea_spheroid";
                  }
  
              };
  
              // Equal Area Cylindrical
              template <typename Parameters, typename T>
              inline void setup_cea(Parameters& par, par_cea<T>& proj_parm)
              {
                  T t = 0;
  
                  if (pj_param_r(par.params, "lat_ts", t)) {
                      par.k0 = cos(t);
                      if (par.k0 < 0.) {
                          BOOST_THROW_EXCEPTION( projection_exception(error_lat_ts_larger_than_90) );
                      }
                  }
                  if (par.es != 0.0) {
                      t = sin(t);
                      par.k0 /= sqrt(1. - par.es * t * t);
                      par.e = sqrt(par.es);
                      proj_parm.apa = pj_authset<T>(par.es);
  
                      proj_parm.qp = pj_qsfn(1., par.e, par.one_es);
                  }
              }
  
      }} // namespace detail::cea
      #endif // doxygen
  
      /*!
          \brief Equal Area Cylindrical projection
          \ingroup projections
          \tparam Geographic latlong point type
          \tparam Cartesian xy point type
          \tparam Parameters parameter type
          \par Projection characteristics
           - Cylindrical
           - Spheroid
           - Ellipsoid
          \par Projection parameters
           - lat_ts: Latitude of true scale (degrees)
          \par Example
          \image html ex_cea.gif
      */
      template <typename T, typename Parameters>
      struct cea_ellipsoid : public detail::cea::base_cea_ellipsoid<T, Parameters>
      {
          inline cea_ellipsoid(const Parameters& par) : detail::cea::base_cea_ellipsoid<T, Parameters>(par)
          {
              detail::cea::setup_cea(this->m_par, this->m_proj_parm);
          }
      };
  
      /*!
          \brief Equal Area Cylindrical projection
          \ingroup projections
          \tparam Geographic latlong point type
          \tparam Cartesian xy point type
          \tparam Parameters parameter type
          \par Projection characteristics
           - Cylindrical
           - Spheroid
           - Ellipsoid
          \par Projection parameters
           - lat_ts: Latitude of true scale (degrees)
          \par Example
          \image html ex_cea.gif
      */
      template <typename T, typename Parameters>
      struct cea_spheroid : public detail::cea::base_cea_spheroid<T, Parameters>
      {
          inline cea_spheroid(const Parameters& par) : detail::cea::base_cea_spheroid<T, Parameters>(par)
          {
              detail::cea::setup_cea(this->m_par, this->m_proj_parm);
          }
      };
  
      #ifndef DOXYGEN_NO_DETAIL
      namespace detail
      {
  
          // Static projection
          BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION(srs::par4::cea, cea_spheroid, cea_ellipsoid)
  
          // Factory entry(s)
          template <typename T, typename Parameters>
          class cea_entry : public detail::factory_entry<T, Parameters>
          {
              public :
                  virtual base_v<T, Parameters>* create_new(const Parameters& par) const
                  {
                      if (par.es)
                          return new base_v_fi<cea_ellipsoid<T, Parameters>, T, Parameters>(par);
                      else
                          return new base_v_fi<cea_spheroid<T, Parameters>, T, Parameters>(par);
                  }
          };
  
          template <typename T, typename Parameters>
          inline void cea_init(detail::base_factory<T, Parameters>& factory)
          {
              factory.add_to_factory("cea", new cea_entry<T, Parameters>);
          }
  
      } // namespace detail
      #endif // doxygen
  
  } // namespace projections
  
  }} // namespace boost::geometry
  
  #endif // BOOST_GEOMETRY_PROJECTIONS_CEA_HPP
  
  