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
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  // Software is furnished to do so, subject to the following conditions:
  
  // The above copyright notice and this permission notice shall be included
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  // OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
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  /*****************************************************************************
  
                 Lambert Conformal Conic Alternative
                 -----------------------------------
  
      This is Gerald Evenden's 2003 implementation of an alternative
      "almost" LCC, which has been in use historically, but which
      should NOT be used for new projects - i.e: use this implementation
      if you need interoperability with old data represented in this
      projection, but not in any other case.
  
      The code was originally discussed on the PROJ.4 mailing list in
      a thread archived over at
  
      http://lists.maptools.org/pipermail/proj/2003-March/000644.html
  
      It was discussed again in the thread starting at
  
      http://lists.maptools.org/pipermail/proj/2017-October/007828.html
          and continuing at
      http://lists.maptools.org/pipermail/proj/2017-November/007831.html
  
      which prompted Clifford J. Mugnier to add these clarifying notes:
  
      The French Army Truncated Cubic Lambert (partially conformal) Conic
      projection is the Legal system for the projection in France between
      the late 1800s and 1948 when the French Legislature changed the law
      to recognize the fully conformal version.
  
      It was (might still be in one or two North African prior French
      Colonies) used in North Africa in Algeria, Tunisia, & Morocco, as
      well as in Syria during the Levant.
  
      Last time I have seen it used was about 30+ years ago in
      Algeria when it was used to define Lease Block boundaries for
      Petroleum Exploration & Production.
  
      (signed)
  
      Clifford J. Mugnier, c.p., c.m.s.
      Chief of Geodesy
      LSU Center for GeoInformatics
      Dept. of Civil Engineering
      LOUISIANA STATE UNIVERSITY
  
  *****************************************************************************/
  
  #ifndef BOOST_GEOMETRY_PROJECTIONS_LCCA_HPP
  #define BOOST_GEOMETRY_PROJECTIONS_LCCA_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>
  
  namespace boost { namespace geometry
  {
  
  namespace srs { namespace par4
  {
      struct lcca {};
  
  }} //namespace srs::par4
  
  namespace projections
  {
      #ifndef DOXYGEN_NO_DETAIL
      namespace detail { namespace lcca
      {
  
              static const int max_iter = 10;
              static const double del_tol = 1e-12;
  
              template <typename T>
              struct par_lcca
              {
                  detail::en<T> en;
                  T    r0, l, M0;
                  T    C;
              };
  
              template <typename T> /* func to compute dr */
              inline T fS(T const& S, T const& C)
              {
                  return(S * ( 1. + S * S * C));
              }
  
              template <typename T> /* deriv of fs */
              inline T fSp(T const& S, T const& C)
              {
                  return(1. + 3.* S * S * C);
              }
  
              // template class, using CRTP to implement forward/inverse
              template <typename T, typename Parameters>
              struct base_lcca_ellipsoid
                  : public base_t_fi<base_lcca_ellipsoid<T, Parameters>, T, Parameters>
              {
                  par_lcca<T> m_proj_parm;
  
                  inline base_lcca_ellipsoid(const Parameters& par)
                      : base_t_fi<base_lcca_ellipsoid<T, Parameters>, T, Parameters>(*this, par)
                  {}
  
                  // FORWARD(e_forward)  ellipsoid
                  // 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
                  {
                      T S, r, dr;
  
                      S = pj_mlfn(lp_lat, sin(lp_lat), cos(lp_lat), this->m_proj_parm.en) - this->m_proj_parm.M0;
                      dr = fS(S, this->m_proj_parm.C);
                      r = this->m_proj_parm.r0 - dr;
                      xy_x = this->m_par.k0 * (r * sin( lp_lon *= this->m_proj_parm.l ) );
                      xy_y = this->m_par.k0 * (this->m_proj_parm.r0 - r * cos(lp_lon) );
                  }
  
                  // INVERSE(e_inverse)  ellipsoid & 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
                  {
                      T theta, dr, S, dif;
                      int i;
  
                      xy_x /= this->m_par.k0;
                      xy_y /= this->m_par.k0;
                      theta = atan2(xy_x , this->m_proj_parm.r0 - xy_y);
                      dr = xy_y - xy_x * tan(0.5 * theta);
                      lp_lon = theta / this->m_proj_parm.l;
                      S = dr;
                      for (i = max_iter; i ; --i) {
                          S -= (dif = (fS(S, this->m_proj_parm.C) - dr) / fSp(S, this->m_proj_parm.C));
                          if (fabs(dif) < del_tol) break;
                      }
                      if (!i) {
                          BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
                      }
                      lp_lat = pj_inv_mlfn(S + this->m_proj_parm.M0, this->m_par.es, this->m_proj_parm.en);
                  }
  
                  static inline std::string get_name()
                  {
                      return "lcca_ellipsoid";
                  }
  
              };
  
              // Lambert Conformal Conic Alternative
              template <typename Parameters, typename T>
              inline void setup_lcca(Parameters& par, par_lcca<T>& proj_parm)
              {
                  T s2p0, N0, R0, tan0;
  
                  proj_parm.en = pj_enfn<T>(par.es);
  
                  if (par.phi0 == 0.) {
                      BOOST_THROW_EXCEPTION( projection_exception(error_lat_0_is_zero) );
                  }
                  proj_parm.l = sin(par.phi0);
                  proj_parm.M0 = pj_mlfn(par.phi0, proj_parm.l, cos(par.phi0), proj_parm.en);
                  s2p0 = proj_parm.l * proj_parm.l;
                  R0 = 1. / (1. - par.es * s2p0);
                  N0 = sqrt(R0);
                  R0 *= par.one_es * N0;
                  tan0 = tan(par.phi0);
                  proj_parm.r0 = N0 / tan0;
                  proj_parm.C = 1. / (6. * R0 * N0);
              }
  
      }} // namespace detail::lcca
      #endif // doxygen
  
      /*!
          \brief Lambert Conformal Conic Alternative 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_0: Latitude of origin
          \par Example
          \image html ex_lcca.gif
      */
      template <typename T, typename Parameters>
      struct lcca_ellipsoid : public detail::lcca::base_lcca_ellipsoid<T, Parameters>
      {
          inline lcca_ellipsoid(const Parameters& par) : detail::lcca::base_lcca_ellipsoid<T, Parameters>(par)
          {
              detail::lcca::setup_lcca(this->m_par, this->m_proj_parm);
          }
      };
  
      #ifndef DOXYGEN_NO_DETAIL
      namespace detail
      {
  
          // Static projection
          BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION(srs::par4::lcca, lcca_ellipsoid, lcca_ellipsoid)
  
          // Factory entry(s)
          template <typename T, typename Parameters>
          class lcca_entry : public detail::factory_entry<T, Parameters>
          {
              public :
                  virtual base_v<T, Parameters>* create_new(const Parameters& par) const
                  {
                      return new base_v_fi<lcca_ellipsoid<T, Parameters>, T, Parameters>(par);
                  }
          };
  
          template <typename T, typename Parameters>
          inline void lcca_init(detail::base_factory<T, Parameters>& factory)
          {
              factory.add_to_factory("lcca", new lcca_entry<T, Parameters>);
          }
  
      } // namespace detail
      #endif // doxygen
  
  } // namespace projections
  
  }} // namespace boost::geometry
  
  #endif // BOOST_GEOMETRY_PROJECTIONS_LCCA_HPP
  