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_EQDC_HPP
  #define BOOST_GEOMETRY_PROJECTIONS_EQDC_HPP
  
  #include <boost/geometry/util/math.hpp>
  #include <boost/math/special_functions/hypot.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_mlfn.hpp>
  #include <boost/geometry/srs/projections/impl/pj_msfn.hpp>
  
  namespace boost { namespace geometry
  {
  
  namespace projections
  {
      #ifndef DOXYGEN_NO_DETAIL
      namespace detail { namespace eqdc
      {
  
              static const double epsilon10 = 1.e-10;
  
              template <typename T>
              struct par_eqdc
              {
                  T    phi1;
                  T    phi2;
                  T    n;
                  T    rho0;
                  T    c;
                  detail::en<T> en;
                  bool ellips;
              };
  
              // template class, using CRTP to implement forward/inverse
              template <typename T, typename Parameters>
              struct base_eqdc_ellipsoid
                  : public base_t_fi<base_eqdc_ellipsoid<T, Parameters>, T, Parameters>
              {
                  par_eqdc<T> m_proj_parm;
  
                  inline base_eqdc_ellipsoid(const Parameters& par)
                      : base_t_fi<base_eqdc_ellipsoid<T, Parameters>, T, Parameters>(*this, par)
                  {}
  
                  // FORWARD(e_forward)  sphere & ellipsoid
                  // Project coordinates from geographic (lon, lat) to cartesian (x, y)
                  inline void fwd(T lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const
                  {
                      T rho = 0.0;
  
                      rho = this->m_proj_parm.c - (this->m_proj_parm.ellips ? pj_mlfn(lp_lat, sin(lp_lat),
                          cos(lp_lat), this->m_proj_parm.en) : lp_lat);
                      xy_x = rho * sin( lp_lon *= this->m_proj_parm.n );
                      xy_y = this->m_proj_parm.rho0 - rho * cos(lp_lon);
                  }
  
                  // INVERSE(e_inverse)  sphere & ellipsoid
                  // 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 T const half_pi = detail::half_pi<T>();
  
                      T rho = 0.0;
  
                      if ((rho = boost::math::hypot(xy_x, xy_y = this->m_proj_parm.rho0 - xy_y)) != 0.0 ) {
                          if (this->m_proj_parm.n < 0.) {
                              rho = -rho;
                              xy_x = -xy_x;
                              xy_y = -xy_y;
                          }
                          lp_lat = this->m_proj_parm.c - rho;
                          if (this->m_proj_parm.ellips)
                              lp_lat = pj_inv_mlfn(lp_lat, this->m_par.es, this->m_proj_parm.en);
                          lp_lon = atan2(xy_x, xy_y) / this->m_proj_parm.n;
                      } else {
                          lp_lon = 0.;
                          lp_lat = this->m_proj_parm.n > 0. ? half_pi : -half_pi;
                      }
                  }
  
                  static inline std::string get_name()
                  {
                      return "eqdc_ellipsoid";
                  }
  
              };
  
              // Equidistant Conic
              template <typename Params, typename Parameters, typename T>
              inline void setup_eqdc(Params const& params, Parameters& par, par_eqdc<T>& proj_parm)
              {
                  T cosphi, sinphi;
                  int secant;
  
                  proj_parm.phi1 = pj_get_param_r<T, srs::spar::lat_1>(params, "lat_1", srs::dpar::lat_1);
                  proj_parm.phi2 = pj_get_param_r<T, srs::spar::lat_2>(params, "lat_2", srs::dpar::lat_2);
  
                  if (fabs(proj_parm.phi1 + proj_parm.phi2) < epsilon10)
                      BOOST_THROW_EXCEPTION( projection_exception(error_conic_lat_equal) );
  
                  proj_parm.en = pj_enfn<T>(par.es);
  
                  proj_parm.n = sinphi = sin(proj_parm.phi1);
                  cosphi = cos(proj_parm.phi1);
                  secant = fabs(proj_parm.phi1 - proj_parm.phi2) >= epsilon10;
                  if( (proj_parm.ellips = (par.es > 0.)) ) {
                      double ml1, m1;
  
                      m1 = pj_msfn(sinphi, cosphi, par.es);
                      ml1 = pj_mlfn(proj_parm.phi1, sinphi, cosphi, proj_parm.en);
                      if (secant) { /* secant cone */
                          sinphi = sin(proj_parm.phi2);
                          cosphi = cos(proj_parm.phi2);
                          proj_parm.n = (m1 - pj_msfn(sinphi, cosphi, par.es)) /
                              (pj_mlfn(proj_parm.phi2, sinphi, cosphi, proj_parm.en) - ml1);
                      }
                      proj_parm.c = ml1 + m1 / proj_parm.n;
                      proj_parm.rho0 = proj_parm.c - pj_mlfn(par.phi0, sin(par.phi0),
                          cos(par.phi0), proj_parm.en);
                  } else {
                      if (secant)
                          proj_parm.n = (cosphi - cos(proj_parm.phi2)) / (proj_parm.phi2 - proj_parm.phi1);
                      proj_parm.c = proj_parm.phi1 + cos(proj_parm.phi1) / proj_parm.n;
                      proj_parm.rho0 = proj_parm.c - par.phi0;
                  }
              }
  
      }} // namespace detail::eqdc
      #endif // doxygen
  
      /*!
          \brief Equidistant Conic projection
          \ingroup projections
          \tparam Geographic latlong point type
          \tparam Cartesian xy point type
          \tparam Parameters parameter type
          \par Projection characteristics
           - Conic
           - Spheroid
           - Ellipsoid
          \par Projection parameters
           - lat_1: Latitude of first standard parallel (degrees)
           - lat_2: Latitude of second standard parallel (degrees)
          \par Example
          \image html ex_eqdc.gif
      */
      template <typename T, typename Parameters>
      struct eqdc_ellipsoid : public detail::eqdc::base_eqdc_ellipsoid<T, Parameters>
      {
          template <typename Params>
          inline eqdc_ellipsoid(Params const& params, Parameters const& par)
              : detail::eqdc::base_eqdc_ellipsoid<T, Parameters>(par)
          {
              detail::eqdc::setup_eqdc(params, this->m_par, this->m_proj_parm);
          }
      };
  
      #ifndef DOXYGEN_NO_DETAIL
      namespace detail
      {
  
          // Static projection
          BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION(srs::spar::proj_eqdc, eqdc_ellipsoid, eqdc_ellipsoid)
  
          // Factory entry(s)
          BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(eqdc_entry, eqdc_ellipsoid)
          
          BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(eqdc_init)
          {
              BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(eqdc, eqdc_entry);
          }
  
      } // namespace detail
      #endif // doxygen
  
  } // namespace projections
  
  }} // namespace boost::geometry
  
  #endif // BOOST_GEOMETRY_PROJECTIONS_EQDC_HPP
  
  