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, 2019, 2022.
  // Modifications copyright (c) 2017-2022, Oracle and/or its affiliates.
  // Contributed and/or modified by Vissarion Fysikopoulos, on behalf of Oracle.
  // 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_MERC_HPP
  #define BOOST_GEOMETRY_PROJECTIONS_MERC_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/factory_entry.hpp>
  #include <boost/geometry/srs/projections/impl/pj_msfn.hpp>
  #include <boost/geometry/srs/projections/impl/pj_param.hpp>
  #include <boost/geometry/srs/projections/impl/pj_phi2.hpp>
  #include <boost/geometry/srs/projections/impl/pj_tsfn.hpp>
  #include <boost/geometry/srs/projections/impl/projects.hpp>
  
  #include <boost/geometry/util/math.hpp>
  
  namespace boost { namespace geometry
  {
  
  namespace projections
  {
      #ifndef DOXYGEN_NO_DETAIL
      namespace detail { namespace merc
      {
  
              static const double epsilon10 = 1.e-10;
  
              template <typename T, typename Parameters>
              struct base_merc_ellipsoid
              {
                  // FORWARD(e_forward)  ellipsoid
                  // Project coordinates from geographic (lon, lat) to cartesian (x, y)
                  inline void fwd(Parameters const& par, T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const
                  {
                      static const T half_pi = detail::half_pi<T>();
  
                      if (fabs(fabs(lp_lat) - half_pi) <= epsilon10) {
                          BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
                      }
                      xy_x = par.k0 * lp_lon;
                      xy_y = - par.k0 * log(pj_tsfn(lp_lat, sin(lp_lat), par.e));
                  }
  
                  // INVERSE(e_inverse)  ellipsoid
                  // Project coordinates from cartesian (x, y) to geographic (lon, lat)
                  inline void inv(Parameters const& par, T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const
                  {
                      if ((lp_lat = pj_phi2(exp(- xy_y / par.k0), par.e)) == HUGE_VAL) {
                          BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
                      }
                      lp_lon = xy_x / par.k0;
                  }
  
                  static inline std::string get_name()
                  {
                      return "merc_ellipsoid";
                  }
  
              };
  
              template <typename T, typename Parameters>
              struct base_merc_spheroid
              {
                  // FORWARD(s_forward)  spheroid
                  // Project coordinates from geographic (lon, lat) to cartesian (x, y)
                  inline void fwd(Parameters const& par, T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const
                  {
                      static const T half_pi = detail::half_pi<T>();
                      static const T fourth_pi = detail::fourth_pi<T>();
  
                      if (fabs(fabs(lp_lat) - half_pi) <= epsilon10) {
                          BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
                      }
                      xy_x = par.k0 * lp_lon;
                      xy_y = par.k0 * log(tan(fourth_pi + .5 * lp_lat));
                  }
  
                  // INVERSE(s_inverse)  spheroid
                  // Project coordinates from cartesian (x, y) to geographic (lon, lat)
                  inline void inv(Parameters const& par, T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const
                  {
                      static const T half_pi = detail::half_pi<T>();
  
                      lp_lat = half_pi - 2. * atan(exp(-xy_y / par.k0));
                      lp_lon = xy_x / par.k0;
                  }
  
                  static inline std::string get_name()
                  {
                      return "merc_spheroid";
                  }
  
              };
  
              // Mercator
              template <typename Params, typename Parameters>
              inline void setup_merc(Params const& params, Parameters& par)
              {
                  typedef typename Parameters::type calc_t;
                  static const calc_t half_pi = detail::half_pi<calc_t>();
  
                  calc_t phits=0.0;
                  int is_phits;
  
                  if( (is_phits = pj_param_r<srs::spar::lat_ts>(params, "lat_ts", srs::dpar::lat_ts, phits)) ) {
                      phits = fabs(phits);
                      if (phits >= half_pi)
                          BOOST_THROW_EXCEPTION( projection_exception(error_lat_ts_larger_than_90) );
                  }
                  if (par.es != 0.0) { /* ellipsoid */
                      if (is_phits)
                          par.k0 = pj_msfn(sin(phits), cos(phits), par.es);
                  } else { /* sphere */
                      if (is_phits)
                          par.k0 = cos(phits);
                  }
              }
  
      }} // namespace detail::merc
      #endif // doxygen
  
      /*!
          \brief Mercator 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_merc.gif
      */
      template <typename T, typename Parameters>
      struct merc_ellipsoid : public detail::merc::base_merc_ellipsoid<T, Parameters>
      {
          template <typename Params>
          inline merc_ellipsoid(Params const& params, Parameters & par)
          {
              detail::merc::setup_merc(params, par);
          }
      };
  
      /*!
          \brief Mercator 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_merc.gif
      */
      template <typename T, typename Parameters>
      struct merc_spheroid : public detail::merc::base_merc_spheroid<T, Parameters>
      {
          template <typename Params>
          inline merc_spheroid(Params const& params, Parameters & par)
          {
              detail::merc::setup_merc(params, par);
          }
      };
  
      /*!
          \brief Web Mercator projection
          \ingroup projections
          \tparam Geographic latlong point type
          \tparam Cartesian xy point type
          \tparam Parameters parameter type
          \par Projection characteristics
           - Cylindrical
           - Spheroid
           - Ellipsoid
      */
      template <typename T, typename Parameters>
      struct webmerc_spheroid : public detail::merc::base_merc_spheroid<T, Parameters>
      {
          template <typename Params>
          inline webmerc_spheroid(Params const&, Parameters & par)
          {
              par.k0 = 1;
          }
      };
  
      #ifndef DOXYGEN_NO_DETAIL
      namespace detail
      {
  
          // Static projection
          BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI2(srs::spar::proj_merc, merc_spheroid, 
              merc_ellipsoid)
          BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_webmerc,
              webmerc_spheroid)
  
          // Factory entry(s)
          BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI2(merc_entry, merc_spheroid, 
              merc_ellipsoid)
          BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(webmerc_entry, webmerc_spheroid)
  
          BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(merc_init)
          {
              BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(merc, merc_entry)
              BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(webmerc, webmerc_entry)
          }
  
      } // namespace detail
      #endif // doxygen
  
  } // namespace projections
  
  }} // namespace boost::geometry
  
  #endif // BOOST_GEOMETRY_PROJECTIONS_MERC_HPP
  