boost/geometry/srs/projections/proj/omerc.hpp

   1 // Boost.Geometry - gis-projections (based on PROJ4)
   2
   3 // Copyright (c) 2008-2015 Barend Gehrels, Amsterdam, the Netherlands.
   4
   5 // This file was modified by Oracle on 2017, 2018, 2019.
   6 // Modifications copyright (c) 2017-2019, Oracle and/or its affiliates.
   7 // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle.
   8
   9 // Use, modification and distribution is subject to the Boost Software License,
  10 // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
  11 // http://www.boost.org/LICENSE_1_0.txt)
  12
  13 // This file is converted from PROJ4, http://trac.osgeo.org/proj
  14 // PROJ4 is originally written by Gerald Evenden (then of the USGS)
  15 // PROJ4 is maintained by Frank Warmerdam
  16 // PROJ4 is converted to Boost.Geometry by Barend Gehrels
  17
  18 // Last updated version of proj: 5.0.0
  19
  20 // Original copyright notice:
  21
  22 // Copyright (c) 2003, 2006   Gerald I. Evenden
  23
  24 // Permission is hereby granted, free of charge, to any person obtaining a
  25 // copy of this software and associated documentation files (the "Software"),
  26 // to deal in the Software without restriction, including without limitation
  27 // the rights to use, copy, modify, merge, publish, distribute, sublicense,
  28 // and/or sell copies of the Software, and to permit persons to whom the
  29 // Software is furnished to do so, subject to the following conditions:
  30
  31 // The above copyright notice and this permission notice shall be included
  32 // in all copies or substantial portions of the Software.
  33
  34 // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
  35 // OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  36 // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
  37 // THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  38 // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
  39 // FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
  40 // DEALINGS IN THE SOFTWARE.
  41
  42 #ifndef BOOST_GEOMETRY_PROJECTIONS_OMERC_HPP
  43 #define BOOST_GEOMETRY_PROJECTIONS_OMERC_HPP
  44
  45 #include <boost/geometry/util/math.hpp>
  46
  47 #include <boost/geometry/srs/projections/impl/base_static.hpp>
  48 #include <boost/geometry/srs/projections/impl/base_dynamic.hpp>
  49 #include <boost/geometry/srs/projections/impl/factory_entry.hpp>
  50 #include <boost/geometry/srs/projections/impl/pj_param.hpp>
  51 #include <boost/geometry/srs/projections/impl/pj_phi2.hpp>
  52 #include <boost/geometry/srs/projections/impl/pj_tsfn.hpp>
  53 #include <boost/geometry/srs/projections/impl/projects.hpp>
  54
  55 namespace boost { namespace geometry
  56 {
  57
  58 namespace projections
  59 {
  60     #ifndef DOXYGEN_NO_DETAIL
  61     namespace detail { namespace omerc
  62     {
  63             template <typename T>
  64             struct par_omerc
  65             {
  66                 T    A, B, E, AB, ArB, BrA, rB, singam, cosgam, sinrot, cosrot;
  67                 T    v_pole_n, v_pole_s, u_0;
  68                 bool no_rot;
  69             };
  70
  71             static const double tolerance = 1.e-7;
  72             static const double epsilon = 1.e-10;
  73
  74             template <typename T, typename Parameters>
  75             struct base_omerc_ellipsoid
  76             {
  77                 par_omerc<T> m_proj_parm;
  78
  79                 // FORWARD(e_forward)  ellipsoid
  80                 // Project coordinates from geographic (lon, lat) to cartesian (x, y)
  81                 inline void fwd(Parameters const& par, T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const
  82                 {
  83                     static const T half_pi = detail::half_pi<T>();
  84
  85                     T  s, t, U, V, W, temp, u, v;
  86
  87                     if (fabs(fabs(lp_lat) - half_pi) > epsilon) {
  88                         W = this->m_proj_parm.E / math::pow(pj_tsfn(lp_lat, sin(lp_lat), par.e), this->m_proj_parm.B);
  89                         temp = 1. / W;
  90                         s = .5 * (W - temp);
  91                         t = .5 * (W + temp);
  92                         V = sin(this->m_proj_parm.B * lp_lon);
  93                         U = (s * this->m_proj_parm.singam - V * this->m_proj_parm.cosgam) / t;
  94                         if (fabs(fabs(U) - 1.0) < epsilon) {
  95                             BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
  96                         }
  97                         v = 0.5 * this->m_proj_parm.ArB * log((1. - U)/(1. + U));
  98                         temp = cos(this->m_proj_parm.B * lp_lon);
  99                         if(fabs(temp) < tolerance) {
 100                             u = this->m_proj_parm.A * lp_lon;
 101                         } else {
 102                             u = this->m_proj_parm.ArB * atan2((s * this->m_proj_parm.cosgam + V * this->m_proj_parm.singam), temp);
 103                         }
 104                     } else {
 105                         v = lp_lat > 0 ? this->m_proj_parm.v_pole_n : this->m_proj_parm.v_pole_s;
 106                         u = this->m_proj_parm.ArB * lp_lat;
 107                     }
 108                     if (this->m_proj_parm.no_rot) {
 109                         xy_x = u;
 110                         xy_y = v;
 111                     } else {
 112                         u -= this->m_proj_parm.u_0;
 113                         xy_x = v * this->m_proj_parm.cosrot + u * this->m_proj_parm.sinrot;
 114                         xy_y = u * this->m_proj_parm.cosrot - v * this->m_proj_parm.sinrot;
 115                     }
 116                 }
 117
 118                 // INVERSE(e_inverse)  ellipsoid
 119                 // Project coordinates from cartesian (x, y) to geographic (lon, lat)
 120                 inline void inv(Parameters const& par, T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const
 121                 {
 122                     static const T half_pi = detail::half_pi<T>();
 123
 124                     T  u, v, Qp, Sp, Tp, Vp, Up;
 125
 126                     if (this->m_proj_parm.no_rot) {
 127                         v = xy_y;
 128                         u = xy_x;
 129                     } else {
 130                         v = xy_x * this->m_proj_parm.cosrot - xy_y * this->m_proj_parm.sinrot;
 131                         u = xy_y * this->m_proj_parm.cosrot + xy_x * this->m_proj_parm.sinrot + this->m_proj_parm.u_0;
 132                     }
 133                     Qp = exp(- this->m_proj_parm.BrA * v);
 134                     Sp = .5 * (Qp - 1. / Qp);
 135                     Tp = .5 * (Qp + 1. / Qp);
 136                     Vp = sin(this->m_proj_parm.BrA * u);
 137                     Up = (Vp * this->m_proj_parm.cosgam + Sp * this->m_proj_parm.singam) / Tp;
 138                     if (fabs(fabs(Up) - 1.) < epsilon) {
 139                         lp_lon = 0.;
 140                         lp_lat = Up < 0. ? -half_pi : half_pi;
 141                     } else {
 142                         lp_lat = this->m_proj_parm.E / sqrt((1. + Up) / (1. - Up));
 143                         if ((lp_lat = pj_phi2(math::pow(lp_lat, T(1) / this->m_proj_parm.B), par.e)) == HUGE_VAL) {
 144                             BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
 145                         }
 146                         lp_lon = - this->m_proj_parm.rB * atan2((Sp * this->m_proj_parm.cosgam -
 147                             Vp * this->m_proj_parm.singam), cos(this->m_proj_parm.BrA * u));
 148                     }
 149                 }
 150
 151                 static inline std::string get_name()
 152                 {
 153                     return "omerc_ellipsoid";
 154                 }
 155
 156             };
 157
 158             // Oblique Mercator
 159             template <typename Params, typename Parameters, typename T>
 160             inline void setup_omerc(Params const& params, Parameters & par, par_omerc<T>& proj_parm)
 161             {
 162                 static const T fourth_pi = detail::fourth_pi<T>();
 163                 static const T half_pi = detail::half_pi<T>();
 164                 static const T pi = detail::pi<T>();
 165                 static const T two_pi = detail::two_pi<T>();
 166
 167                 T con, com, cosph0, D, F, H, L, sinph0, p, J, gamma=0,
 168                   gamma0, lamc=0, lam1=0, lam2=0, phi1=0, phi2=0, alpha_c=0;
 169                 int alp, gam, no_off = 0;
 170
 171                 proj_parm.no_rot = pj_get_param_b<srs::spar::no_rot>(params, "no_rot", srs::dpar::no_rot);
 172                 alp = pj_param_r<srs::spar::alpha>(params, "alpha", srs::dpar::alpha, alpha_c);
 173                 gam = pj_param_r<srs::spar::gamma>(params, "gamma", srs::dpar::gamma, gamma);
 174                 if (alp || gam) {
 175                     lamc = pj_get_param_r<T, srs::spar::lonc>(params, "lonc", srs::dpar::lonc);
 176                     // NOTE: This is not needed in Boost.Geometry
 177                     //no_off =
 178                     //            /* For libproj4 compatability */
 179                     //            pj_param_exists(par.params, "no_off")
 180                     //            /* for backward compatibility */
 181                     //            || pj_param_exists(par.params, "no_uoff");
 182                     //if( no_off )
 183                     //{
 184                     //    /* Mark the parameter as used, so that the pj_get_def() return them */
 185                     //    pj_get_param_s(par.params, "no_uoff");
 186                     //    pj_get_param_s(par.params, "no_off");
 187                     //}
 188                 } else {
 189                     lam1 = pj_get_param_r<T, srs::spar::lon_1>(params, "lon_1", srs::dpar::lon_1);
 190                     phi1 = pj_get_param_r<T, srs::spar::lat_1>(params, "lat_1", srs::dpar::lat_1);
 191                     lam2 = pj_get_param_r<T, srs::spar::lon_2>(params, "lon_2", srs::dpar::lon_2);
 192                     phi2 = pj_get_param_r<T, srs::spar::lat_2>(params, "lat_2", srs::dpar::lat_2);
 193                     if (fabs(phi1 - phi2) <= tolerance ||
 194                         (con = fabs(phi1)) <= tolerance ||
 195                         fabs(con - half_pi) <= tolerance ||
 196                         fabs(fabs(par.phi0) - half_pi) <= tolerance ||
 197                         fabs(fabs(phi2) - half_pi) <= tolerance)
 198                         BOOST_THROW_EXCEPTION( projection_exception(error_lat_0_or_alpha_eq_90) );
 199                 }
 200                 com = sqrt(par.one_es);
 201                 if (fabs(par.phi0) > epsilon) {
 202                     sinph0 = sin(par.phi0);
 203                     cosph0 = cos(par.phi0);
 204                     con = 1. - par.es * sinph0 * sinph0;
 205                     proj_parm.B = cosph0 * cosph0;
 206                     proj_parm.B = sqrt(1. + par.es * proj_parm.B * proj_parm.B / par.one_es);
 207                     proj_parm.A = proj_parm.B * par.k0 * com / con;
 208                     D = proj_parm.B * com / (cosph0 * sqrt(con));
 209                     if ((F = D * D - 1.) <= 0.)
 210                         F = 0.;
 211                     else {
 212                         F = sqrt(F);
 213                         if (par.phi0 < 0.)
 214                             F = -F;
 215                     }
 216                     proj_parm.E = F += D;
 217                     proj_parm.E *= math::pow(pj_tsfn(par.phi0, sinph0, par.e), proj_parm.B);
 218                 } else {
 219                     proj_parm.B = 1. / com;
 220                     proj_parm.A = par.k0;
 221                     proj_parm.E = D = F = 1.;
 222                 }
 223                 if (alp || gam) {
 224                     if (alp) {
 225                         gamma0 = aasin(sin(alpha_c) / D);
 226                         if (!gam)
 227                             gamma = alpha_c;
 228                     } else
 229                         alpha_c = aasin(D*sin(gamma0 = gamma));
 230                     par.lam0 = lamc - aasin(.5 * (F - 1. / F) *
 231                        tan(gamma0)) / proj_parm.B;
 232                 } else {
 233                     H = math::pow(pj_tsfn(phi1, sin(phi1), par.e), proj_parm.B);
 234                     L = math::pow(pj_tsfn(phi2, sin(phi2), par.e), proj_parm.B);
 235                     F = proj_parm.E / H;
 236                     p = (L - H) / (L + H);
 237                     J = proj_parm.E * proj_parm.E;
 238                     J = (J - L * H) / (J + L * H);
 239                     if ((con = lam1 - lam2) < -pi)
 240                         lam2 -= two_pi;
 241                     else if (con > pi)
 242                         lam2 += two_pi;
 243                     par.lam0 = adjlon(.5 * (lam1 + lam2) - atan(
 244                        J * tan(.5 * proj_parm.B * (lam1 - lam2)) / p) / proj_parm.B);
 245                     gamma0 = atan(2. * sin(proj_parm.B * adjlon(lam1 - par.lam0)) /
 246                        (F - 1. / F));
 247                     gamma = alpha_c = aasin(D * sin(gamma0));
 248                 }
 249                 proj_parm.singam = sin(gamma0);
 250                 proj_parm.cosgam = cos(gamma0);
 251                 proj_parm.sinrot = sin(gamma);
 252                 proj_parm.cosrot = cos(gamma);
 253                 proj_parm.BrA = 1. / (proj_parm.ArB = proj_parm.A * (proj_parm.rB = 1. / proj_parm.B));
 254                 proj_parm.AB = proj_parm.A * proj_parm.B;
 255                 if (no_off)
 256                     proj_parm.u_0 = 0;
 257                 else {
 258                     proj_parm.u_0 = fabs(proj_parm.ArB * atan(sqrt(D * D - 1.) / cos(alpha_c)));
 259                     if (par.phi0 < 0.)
 260                         proj_parm.u_0 = - proj_parm.u_0;
 261                 }
 262                 F = 0.5 * gamma0;
 263                 proj_parm.v_pole_n = proj_parm.ArB * log(tan(fourth_pi - F));
 264                 proj_parm.v_pole_s = proj_parm.ArB * log(tan(fourth_pi + F));
 265             }
 266
 267     }} // namespace detail::omerc
 268     #endif // doxygen
 269
 270     /*!
 271         \brief Oblique Mercator projection
 272         \ingroup projections
 273         \tparam Geographic latlong point type
 274         \tparam Cartesian xy point type
 275         \tparam Parameters parameter type
 276         \par Projection characteristics
 277          - Cylindrical
 278          - Spheroid
 279          - Ellipsoid
 280         \par Projection parameters
 281          - no_rot: No rotation
 282          - alpha: Alpha (degrees)
 283          - gamma: Gamma (degrees)
 284          - no_off: Only for compatibility with libproj, proj4 (string)
 285          - lonc: Longitude (only used if alpha (or gamma) is specified) (degrees)
 286          - lon_1 (degrees)
 287          - lat_1: Latitude of first standard parallel (degrees)
 288          - lon_2 (degrees)
 289          - lat_2: Latitude of second standard parallel (degrees)
 290          - no_uoff (string)
 291         \par Example
 292         \image html ex_omerc.gif
 293     */
 294     template <typename T, typename Parameters>
 295     struct omerc_ellipsoid : public detail::omerc::base_omerc_ellipsoid<T, Parameters>
 296     {
 297         template <typename Params>
 298         inline omerc_ellipsoid(Params const& params, Parameters & par)
 299         {
 300             detail::omerc::setup_omerc(params, par, this->m_proj_parm);
 301         }
 302     };
 303
 304     #ifndef DOXYGEN_NO_DETAIL
 305     namespace detail
 306     {
 307
 308         // Static projection
 309         BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_omerc, omerc_ellipsoid)
 310
 311         // Factory entry(s)
 312         BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(omerc_entry, omerc_ellipsoid)
 313
 314         BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(omerc_init)
 315         {
 316             BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(omerc, omerc_entry)
 317         }
 318
 319     } // namespace detail
 320     #endif // doxygen
 321
 322 } // namespace projections
 323
 324 }} // namespace boost::geometry
 325
 326 #endif // BOOST_GEOMETRY_PROJECTIONS_OMERC_HPP
 327