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.
  // Modifications copyright (c) 2017-2019, 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_FOUC_S_HPP
  #define BOOST_GEOMETRY_PROJECTIONS_FOUC_S_HPP
  
  #include <boost/geometry/srs/projections/impl/aasincos.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_param.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 fouc_s
      {
  
              static const int max_iter = 10;
              static const double loop_tol = 1e-7;
  
              template <typename T>
              struct par_fouc_s
              {
                  T n, n1;
              };
  
              template <typename T, typename Parameters>
              struct base_fouc_s_spheroid
              {
                  par_fouc_s<T> m_proj_parm;
  
                  // FORWARD(s_forward)  spheroid
                  // Project coordinates from geographic (lon, lat) to cartesian (x, y)
                  inline void fwd(Parameters const& , T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const
                  {
                      T t;
  
                      t = cos(lp_lat);
                      xy_x = lp_lon * t / (this->m_proj_parm.n + this->m_proj_parm.n1 * t);
                      xy_y = this->m_proj_parm.n * lp_lat + this->m_proj_parm.n1 * sin(lp_lat);
                  }
  
                  // INVERSE(s_inverse)  spheroid
                  // Project coordinates from cartesian (x, y) to geographic (lon, lat)
                  inline void inv(Parameters const& , T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const
                  {
                      static T const half_pi = detail::half_pi<T>();
  
                      T V;
                      int i;
  
                      if (this->m_proj_parm.n != 0.0) {
                          lp_lat = xy_y;
                          for (i = max_iter; i ; --i) {
                              lp_lat -= V = (this->m_proj_parm.n * lp_lat + this->m_proj_parm.n1 * sin(lp_lat) - xy_y ) /
                                  (this->m_proj_parm.n + this->m_proj_parm.n1 * cos(lp_lat));
                              if (fabs(V) < loop_tol)
                                  break;
                          }
                          if (!i)
                              lp_lat = xy_y < 0. ? -half_pi : half_pi;
                      } else
                          lp_lat = aasin(xy_y);
                      V = cos(lp_lat);
                      lp_lon = xy_x * (this->m_proj_parm.n + this->m_proj_parm.n1 * V) / V;
                  }
  
                  static inline std::string get_name()
                  {
                      return "fouc_s_spheroid";
                  }
  
              };
  
              // Foucaut Sinusoidal
              template <typename Params, typename Parameters, typename T>
              inline void setup_fouc_s(Params const& params, Parameters& par, par_fouc_s<T>& proj_parm)
              {
                  proj_parm.n = pj_get_param_f<T, srs::spar::n>(params, "n", srs::dpar::n);
                  if ((proj_parm.n < 0.) || (proj_parm.n > 1.))
                      BOOST_THROW_EXCEPTION( projection_exception(error_n_out_of_range) );
  
                  proj_parm.n1 = 1. - proj_parm.n;
                  par.es = 0;
              }
  
      }} // namespace detail::fouc_s
      #endif // doxygen
  
      /*!
          \brief Foucaut Sinusoidal projection
          \ingroup projections
          \tparam Geographic latlong point type
          \tparam Cartesian xy point type
          \tparam Parameters parameter type
          \par Projection characteristics
           - Pseudocylindrical
           - Spheroid
          \par Projection parameters
           - n (real)
          \par Example
          \image html ex_fouc_s.gif
      */
      template <typename T, typename Parameters>
      struct fouc_s_spheroid : public detail::fouc_s::base_fouc_s_spheroid<T, Parameters>
      {
          template <typename Params>
          inline fouc_s_spheroid(Params const& params, Parameters & par)
          {
              detail::fouc_s::setup_fouc_s(params, par, this->m_proj_parm);
          }
      };
  
      #ifndef DOXYGEN_NO_DETAIL
      namespace detail
      {
  
          // Static projection
          BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_fouc_s, fouc_s_spheroid)
  
          // Factory entry(s)
          BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(fouc_s_entry, fouc_s_spheroid)
          
          BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(fouc_s_init)
          {
              BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(fouc_s, fouc_s_entry);
          }
  
      } // namespace detail
      #endif // doxygen
  
  } // namespace projections
  
  }} // namespace boost::geometry
  
  #endif // BOOST_GEOMETRY_PROJECTIONS_FOUC_S_HPP
  
  