boost/geometry/srs/projections/proj/robin.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 // Permission is hereby granted, free of charge, to any person obtaining a
  23 // copy of this software and associated documentation files (the "Software"),
  24 // to deal in the Software without restriction, including without limitation
  25 // the rights to use, copy, modify, merge, publish, distribute, sublicense,
  26 // and/or sell copies of the Software, and to permit persons to whom the
  27 // Software is furnished to do so, subject to the following conditions:
  28
  29 // The above copyright notice and this permission notice shall be included
  30 // in all copies or substantial portions of the Software.
  31
  32 // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
  33 // OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  34 // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
  35 // THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  36 // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
  37 // FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
  38 // DEALINGS IN THE SOFTWARE.
  39
  40 #ifndef BOOST_GEOMETRY_PROJECTIONS_ROBIN_HPP
  41 #define BOOST_GEOMETRY_PROJECTIONS_ROBIN_HPP
  42
  43 #include <boost/geometry/util/math.hpp>
  44
  45 #include <boost/geometry/srs/projections/impl/base_static.hpp>
  46 #include <boost/geometry/srs/projections/impl/base_dynamic.hpp>
  47 #include <boost/geometry/srs/projections/impl/projects.hpp>
  48 #include <boost/geometry/srs/projections/impl/factory_entry.hpp>
  49 #include <boost/geometry/srs/projections/impl/function_overloads.hpp>
  50
  51 namespace boost { namespace geometry
  52 {
  53
  54 namespace projections
  55 {
  56     #ifndef DOXYGEN_NO_DETAIL
  57     namespace detail { namespace robin
  58     {
  59
  60             static const double FXC = 0.8487;
  61             static const double FYC = 1.3523;
  62             static const double C1 = 11.45915590261646417544;
  63             static const double RC1 = 0.08726646259971647884;
  64             static const int n_nodes = 18;
  65             static const double one_plus_eps = 1.000001;
  66             static const double epsilon = 1e-8;
  67             /* Not sure at all of the appropriate number for max_iter... */
  68             static const int max_iter = 100;
  69
  70             /*
  71             note: following terms based upon 5 deg. intervals in degrees.
  72
  73             Some background on these coefficients is available at:
  74
  75             http://article.gmane.org/gmane.comp.gis.proj-4.devel/6039
  76             http://trac.osgeo.org/proj/ticket/113
  77             */
  78
  79             template <typename T>
  80             struct coefs {
  81                 T c0, c1, c2, c3;
  82             };
  83
  84             template <typename T>
  85             inline const coefs<T> * coefs_x()
  86             {
  87                 static const coefs<T> result[] = {
  88                     {1.0, 2.2199e-17, -7.15515e-05, 3.1103e-06},
  89                     {0.9986, -0.000482243, -2.4897e-05, -1.3309e-06},
  90                     {0.9954, -0.00083103, -4.48605e-05, -9.86701e-07},
  91                     {0.99, -0.00135364, -5.9661e-05, 3.6777e-06},
  92                     {0.9822, -0.00167442, -4.49547e-06, -5.72411e-06},
  93                     {0.973, -0.00214868, -9.03571e-05, 1.8736e-08},
  94                     {0.96, -0.00305085, -9.00761e-05, 1.64917e-06},
  95                     {0.9427, -0.00382792, -6.53386e-05, -2.6154e-06},
  96                     {0.9216, -0.00467746, -0.00010457, 4.81243e-06},
  97                     {0.8962, -0.00536223, -3.23831e-05, -5.43432e-06},
  98                     {0.8679, -0.00609363, -0.000113898, 3.32484e-06},
  99                     {0.835, -0.00698325, -6.40253e-05, 9.34959e-07},
 100                     {0.7986, -0.00755338, -5.00009e-05, 9.35324e-07},
 101                     {0.7597, -0.00798324, -3.5971e-05, -2.27626e-06},
 102                     {0.7186, -0.00851367, -7.01149e-05, -8.6303e-06},
 103                     {0.6732, -0.00986209, -0.000199569, 1.91974e-05},
 104                     {0.6213, -0.010418, 8.83923e-05, 6.24051e-06},
 105                     {0.5722, -0.00906601, 0.000182, 6.24051e-06},
 106                     {0.5322, -0.00677797, 0.000275608, 6.24051e-06}
 107                 };
 108                 return result;
 109             }
 110
 111             template <typename T>
 112             inline const coefs<T> * coefs_y()
 113             {
 114                 static const coefs<T> result[] = {
 115                     {-5.20417e-18, 0.0124, 1.21431e-18, -8.45284e-11},
 116                     {0.062, 0.0124, -1.26793e-09, 4.22642e-10},
 117                     {0.124, 0.0124, 5.07171e-09, -1.60604e-09},
 118                     {0.186, 0.0123999, -1.90189e-08, 6.00152e-09},
 119                     {0.248, 0.0124002, 7.10039e-08, -2.24e-08},
 120                     {0.31, 0.0123992, -2.64997e-07, 8.35986e-08},
 121                     {0.372, 0.0124029, 9.88983e-07, -3.11994e-07},
 122                     {0.434, 0.0123893, -3.69093e-06, -4.35621e-07},
 123                     {0.4958, 0.0123198, -1.02252e-05, -3.45523e-07},
 124                     {0.5571, 0.0121916, -1.54081e-05, -5.82288e-07},
 125                     {0.6176, 0.0119938, -2.41424e-05, -5.25327e-07},
 126                     {0.6769, 0.011713, -3.20223e-05, -5.16405e-07},
 127                     {0.7346, 0.0113541, -3.97684e-05, -6.09052e-07},
 128                     {0.7903, 0.0109107, -4.89042e-05, -1.04739e-06},
 129                     {0.8435, 0.0103431, -6.4615e-05, -1.40374e-09},
 130                     {0.8936, 0.00969686, -6.4636e-05, -8.547e-06},
 131                     {0.9394, 0.00840947, -0.000192841, -4.2106e-06},
 132                     {0.9761, 0.00616527, -0.000256, -4.2106e-06},
 133                     {1.0, 0.00328947, -0.000319159, -4.2106e-06}
 134                 };
 135                 return result;
 136             }
 137
 138             template <typename T, typename Parameters>
 139             struct base_robin_spheroid
 140             {
 141                 inline T v(coefs<T> const& c, T const& z) const
 142                 { return (c.c0 + z * (c.c1 + z * (c.c2 + z * c.c3))); }
 143                 inline T dv(coefs<T> const& c, T const&  z) const
 144                 { return (c.c1 + z * (c.c2 + c.c2 + z * 3. * c.c3)); }
 145
 146                 // FORWARD(s_forward)  spheroid
 147                 // Project coordinates from geographic (lon, lat) to cartesian (x, y)
 148                 inline void fwd(Parameters const& , T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const
 149                 {
 150                     int i;
 151                     T dphi;
 152
 153                     i = int_floor((dphi = fabs(lp_lat)) * C1);
 154                     if (i < 0) {
 155                         BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
 156                     }
 157                     if (i >= n_nodes) i = n_nodes - 1;
 158                     dphi = geometry::math::r2d<T>() * (dphi - RC1 * i);
 159                     xy_x = v(coefs_x<T>()[i], dphi) * FXC * lp_lon;
 160                     xy_y = v(coefs_y<T>()[i], dphi) * FYC;
 161                     if (lp_lat < 0.) xy_y = -xy_y;
 162                 }
 163
 164                 // INVERSE(s_inverse)  spheroid
 165                 // Project coordinates from cartesian (x, y) to geographic (lon, lat)
 166                 inline void inv(Parameters const& , T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const
 167                 {
 168                     static const T half_pi = detail::half_pi<T>();
 169                     const coefs<T> * coefs_x = robin::coefs_x<T>();
 170                     const coefs<T> * coefs_y = robin::coefs_y<T>();
 171
 172                     int i;
 173                     T t, t1;
 174                     coefs<T> coefs_t;
 175                     int iters;
 176
 177                     lp_lon = xy_x / FXC;
 178                     lp_lat = fabs(xy_y / FYC);
 179                     if (lp_lat >= 1.) { /* simple pathologic cases */
 180                         if (lp_lat > one_plus_eps) {
 181                             BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
 182                         } else {
 183                             lp_lat = xy_y < 0. ? -half_pi : half_pi;
 184                             lp_lon /= coefs_x[n_nodes].c0;
 185                         }
 186                     } else { /* general problem */
 187                         /* in Y space, reduce to table interval */
 188                         i = int_floor(lp_lat * n_nodes);
 189                         if( i < 0 || i >= n_nodes ) {
 190                             BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
 191                         }
 192                         for (;;) {
 193                             if (coefs_y[i].c0 > lp_lat) --i;
 194                             else if (coefs_y[i+1].c0 <= lp_lat) ++i;
 195                             else break;
 196                         }
 197                         coefs_t = coefs_y[i];
 198                         /* first guess, linear interp */
 199                         t = 5. * (lp_lat - coefs_t.c0)/(coefs_y[i+1].c0 - coefs_t.c0);
 200                         /* make into root */
 201                         coefs_t.c0 = (T)(coefs_t.c0 - lp_lat);
 202                         for (iters = max_iter; iters ; --iters) { /* Newton-Raphson */
 203                             t -= t1 = v(coefs_t,t) / dv(coefs_t,t);
 204                             if (fabs(t1) < epsilon)
 205                                 break;
 206                         }
 207                         if( iters == 0 )
 208                             BOOST_THROW_EXCEPTION( projection_exception(error_non_convergent) );
 209                         lp_lat = (5 * i + t) * geometry::math::d2r<T>();
 210                         if (xy_y < 0.) lp_lat = -lp_lat;
 211                         lp_lon /= v(coefs_x[i], t);
 212                     }
 213                 }
 214
 215                 static inline std::string get_name()
 216                 {
 217                     return "robin_spheroid";
 218                 }
 219
 220             };
 221
 222             // Robinson
 223             template <typename Parameters>
 224             inline void setup_robin(Parameters& par)
 225             {
 226                 par.es = 0.;
 227             }
 228
 229     }} // namespace detail::robin
 230     #endif // doxygen
 231
 232     /*!
 233         \brief Robinson projection
 234         \ingroup projections
 235         \tparam Geographic latlong point type
 236         \tparam Cartesian xy point type
 237         \tparam Parameters parameter type
 238         \par Projection characteristics
 239          - Pseudocylindrical
 240          - Spheroid
 241         \par Example
 242         \image html ex_robin.gif
 243     */
 244     template <typename T, typename Parameters>
 245     struct robin_spheroid : public detail::robin::base_robin_spheroid<T, Parameters>
 246     {
 247         template <typename Params>
 248         inline robin_spheroid(Params const& , Parameters & par)
 249         {
 250             detail::robin::setup_robin(par);
 251         }
 252     };
 253
 254     #ifndef DOXYGEN_NO_DETAIL
 255     namespace detail
 256     {
 257
 258         // Static projection
 259         BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_robin, robin_spheroid)
 260
 261         // Factory entry(s)
 262         BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(robin_entry, robin_spheroid)
 263
 264         BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(robin_init)
 265         {
 266             BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(robin, robin_entry)
 267         }
 268
 269     } // namespace detail
 270     #endif // doxygen
 271
 272 } // namespace projections
 273
 274 }} // namespace boost::geometry
 275
 276 #endif // BOOST_GEOMETRY_PROJECTIONS_ROBIN_HPP
 277