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_BIPC_HPP
  #define BOOST_GEOMETRY_PROJECTIONS_BIPC_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>
  
  namespace boost { namespace geometry
  {
  
  namespace projections
  {
      #ifndef DOXYGEN_NO_DETAIL
      namespace detail { namespace bipc
      {
  
              static const double epsilon = 1e-10;
              static const double epsilon10 = 1e-10;
              static const double one_plus_eps = 1.000000001;
              static const int n_iter = 10;
              static const double lamB = -.34894976726250681539;
              static const double n = .63055844881274687180;
              static const double F = 1.89724742567461030582;
              static const double Azab = .81650043674686363166;
              static const double Azba = 1.82261843856185925133;
              static const double const_T = 1.27246578267089012270;
              static const double rhoc = 1.20709121521568721927;
              static const double cAzc = .69691523038678375519;
              static const double sAzc = .71715351331143607555;
              static const double C45 = .70710678118654752469;
              static const double S45 = .70710678118654752410;
              static const double C20 = .93969262078590838411;
              static const double S20 = -.34202014332566873287;
              static const double R110 = 1.91986217719376253360;
              static const double R104 = 1.81514242207410275904;
  
              struct par_bipc
              {
                  int    noskew;
              };
  
              // template class, using CRTP to implement forward/inverse
              template <typename T, typename Parameters>
              struct base_bipc_spheroid
                  : public base_t_fi<base_bipc_spheroid<T, Parameters>, T, Parameters>
              {
                  par_bipc m_proj_parm;
  
                  inline base_bipc_spheroid(const Parameters& par)
                      : base_t_fi<base_bipc_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 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 pi = detail::pi<T>();
  
                      T cphi, sphi, tphi, t, al, Az, z, Av, cdlam, sdlam, r;
                      int tag;
  
                      cphi = cos(lp_lat);
                      sphi = sin(lp_lat);
                      cdlam = cos(sdlam = lamB - lp_lon);
                      sdlam = sin(sdlam);
                      if (fabs(fabs(lp_lat) - half_pi) < epsilon10) {
                          Az = lp_lat < 0. ? pi : 0.;
                          tphi = HUGE_VAL;
                      } else {
                          tphi = sphi / cphi;
                          Az = atan2(sdlam , C45 * (tphi - cdlam));
                      }
                      if( (tag = (Az > Azba)) ) {
                          cdlam = cos(sdlam = lp_lon + R110);
                          sdlam = sin(sdlam);
                          z = S20 * sphi + C20 * cphi * cdlam;
                          if (fabs(z) > 1.) {
                              if (fabs(z) > one_plus_eps)
                                  BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
                              else
                                  z = z < 0. ? -1. : 1.;
                          } else
                              z = acos(z);
                          if (tphi != HUGE_VAL)
                              Az = atan2(sdlam, (C20 * tphi - S20 * cdlam));
                          Av = Azab;
                          xy_y = rhoc;
                      } else {
                          z = S45 * (sphi + cphi * cdlam);
                          if (fabs(z) > 1.) {
                              if (fabs(z) > one_plus_eps)
                                  BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
                              else
                                  z = z < 0. ? -1. : 1.;
                          } else
                              z = acos(z);
                          Av = Azba;
                          xy_y = -rhoc;
                      }
                      if (z < 0.) {
                          BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
                      }
                      r = F * (t = math::pow(tan(T(0.5) * z), n));
                      if ((al = .5 * (R104 - z)) < 0.) {
                          BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
                      }
                      al = (t + math::pow(al, n)) / const_T;
                      if (fabs(al) > 1.) {
                          if (fabs(al) > one_plus_eps)
                              BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
                          else
                              al = al < 0. ? -1. : 1.;
                      } else
                          al = acos(al);
                      if (fabs(t = n * (Av - Az)) < al)
                          r /= cos(al + (tag ? t : -t));
                      xy_x = r * sin(t);
                      xy_y += (tag ? -r : r) * cos(t);
                      if (this->m_proj_parm.noskew) {
                          t = xy_x;
                          xy_x = -xy_x * cAzc - xy_y * sAzc;
                          xy_y = -xy_y * cAzc + t * sAzc;
                      }
                  }
  
                  // 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
                  {
                      T t, r, rp, rl, al, z, fAz, Az, s, c, Av;
                      int neg, i;
  
                      if (this->m_proj_parm.noskew) {
                          t = xy_x;
                          xy_x = -xy_x * cAzc + xy_y * sAzc;
                          xy_y = -xy_y * cAzc - t * sAzc;
                      }
                      if( (neg = (xy_x < 0.)) ) {
                          xy_y = rhoc - xy_y;
                          s = S20;
                          c = C20;
                          Av = Azab;
                      } else {
                          xy_y += rhoc;
                          s = S45;
                          c = C45;
                          Av = Azba;
                      }
                      rl = rp = r = boost::math::hypot(xy_x, xy_y);
                      fAz = fabs(Az = atan2(xy_x, xy_y));
                      for (i = n_iter; i ; --i) {
                          z = 2. * atan(math::pow(r / F,T(1) / n));
                          al = acos((math::pow(tan(T(0.5) * z), n) +
                             math::pow(tan(T(0.5) * (R104 - z)), n)) / const_T);
                          if (fAz < al)
                              r = rp * cos(al + (neg ? Az : -Az));
                          if (fabs(rl - r) < epsilon)
                              break;
                          rl = r;
                      }
                      if (! i)
                          BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
                      Az = Av - Az / n;
                      lp_lat = asin(s * cos(z) + c * sin(z) * cos(Az));
                      lp_lon = atan2(sin(Az), c / tan(z) - s * cos(Az));
                      if (neg)
                          lp_lon -= R110;
                      else
                          lp_lon = lamB - lp_lon;
                  }
  
                  static inline std::string get_name()
                  {
                      return "bipc_spheroid";
                  }
  
              };
  
              // Bipolar conic of western hemisphere
              template <typename Params, typename Parameters>
              inline void setup_bipc(Params const& params, Parameters& par, par_bipc& proj_parm)
              {
                  proj_parm.noskew = pj_get_param_b<srs::spar::ns>(params, "ns", srs::dpar::ns);
                  par.es = 0.;
              }
  
      }} // namespace detail::bipc
      #endif // doxygen
  
      /*!
          \brief Bipolar conic of western hemisphere projection
          \ingroup projections
          \tparam Geographic latlong point type
          \tparam Cartesian xy point type
          \tparam Parameters parameter type
          \par Projection characteristics
           - Conic
           - Spheroid
          \par Projection parameters
           - ns (boolean)
          \par Example
          \image html ex_bipc.gif
      */
      template <typename T, typename Parameters>
      struct bipc_spheroid : public detail::bipc::base_bipc_spheroid<T, Parameters>
      {
          template <typename Params>
          inline bipc_spheroid(Params const& params, Parameters const& par)
              : detail::bipc::base_bipc_spheroid<T, Parameters>(par)
          {
              detail::bipc::setup_bipc(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_bipc, bipc_spheroid, bipc_spheroid)
  
          // Factory entry(s)
          BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(bipc_entry, bipc_spheroid)
          
          BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(bipc_init)
          {
              BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(bipc, bipc_entry)
          }
  
      } // namespace detail
      #endif // doxygen
  
  } // namespace projections
  
  }} // namespace boost::geometry
  
  #endif // BOOST_GEOMETRY_PROJECTIONS_BIPC_HPP
  
  