projections/proj/robin.hpp

0001 // Boost.Geometry - gis-projections (based on PROJ4)
0002
0003 // Copyright (c) 2008-2015 Barend Gehrels, Amsterdam, the Netherlands.
0004
0005 // This file was modified by Oracle on 2017, 2018, 2019.
0006 // Modifications copyright (c) 2017-2019, Oracle and/or its affiliates.
0007 // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle.
0008
0009 // Use, modification and distribution is subject to the Boost Software License,
0010 // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
0011 // http://www.boost.org/LICENSE_1_0.txt)
0012
0013 // This file is converted from PROJ4, http://trac.osgeo.org/proj
0014 // PROJ4 is originally written by Gerald Evenden (then of the USGS)
0015 // PROJ4 is maintained by Frank Warmerdam
0016 // PROJ4 is converted to Boost.Geometry by Barend Gehrels
0017
0018 // Last updated version of proj: 5.0.0
0019
0020 // Original copyright notice:
0021
0022 // Permission is hereby granted, free of charge, to any person obtaining a
0023 // copy of this software and associated documentation files (the "Software"),
0024 // to deal in the Software without restriction, including without limitation
0025 // the rights to use, copy, modify, merge, publish, distribute, sublicense,
0026 // and/or sell copies of the Software, and to permit persons to whom the
0027 // Software is furnished to do so, subject to the following conditions:
0028
0029 // The above copyright notice and this permission notice shall be included
0030 // in all copies or substantial portions of the Software.
0031
0032 // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
0033 // OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
0034 // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
0035 // THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
0036 // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
0037 // FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
0038 // DEALINGS IN THE SOFTWARE.
0039
0040 #ifndef BOOST_GEOMETRY_PROJECTIONS_ROBIN_HPP
0041 #define BOOST_GEOMETRY_PROJECTIONS_ROBIN_HPP
0042
0043 #include <boost/geometry/util/math.hpp>
0044
0045 #include <boost/geometry/srs/projections/impl/base_static.hpp>
0046 #include <boost/geometry/srs/projections/impl/base_dynamic.hpp>
0047 #include <boost/geometry/srs/projections/impl/projects.hpp>
0048 #include <boost/geometry/srs/projections/impl/factory_entry.hpp>
0049 #include <boost/geometry/srs/projections/impl/function_overloads.hpp>
0050
0051 namespace boost { namespace geometry
0052 {
0053
0054 namespace projections
0055 {
0056     #ifndef DOXYGEN_NO_DETAIL
0057     namespace detail { namespace robin
0058     {
0059
0060             static const double FXC = 0.8487;
0061             static const double FYC = 1.3523;
0062             static const double C1 = 11.45915590261646417544;
0063             static const double RC1 = 0.08726646259971647884;
0064             static const int n_nodes = 18;
0065             static const double one_plus_eps = 1.000001;
0066             static const double epsilon = 1e-8;
0067             /* Not sure at all of the appropriate number for max_iter... */
0068             static const int max_iter = 100;
0069
0070             /*
0071             note: following terms based upon 5 deg. intervals in degrees.
0072
0073             Some background on these coefficients is available at:
0074
0075             http://article.gmane.org/gmane.comp.gis.proj-4.devel/6039
0076             http://trac.osgeo.org/proj/ticket/113
0077             */
0078
0079             template <typename T>
0080             struct coefs {
0081                 T c0, c1, c2, c3;
0082             };
0083
0084             template <typename T>
0085             inline const coefs<T> * coefs_x()
0086             {
0087                 static const coefs<T> result[] = {
0088                     {1.0, 2.2199e-17, -7.15515e-05, 3.1103e-06},
0089                     {0.9986, -0.000482243, -2.4897e-05, -1.3309e-06},
0090                     {0.9954, -0.00083103, -4.48605e-05, -9.86701e-07},
0091                     {0.99, -0.00135364, -5.9661e-05, 3.6777e-06},
0092                     {0.9822, -0.00167442, -4.49547e-06, -5.72411e-06},
0093                     {0.973, -0.00214868, -9.03571e-05, 1.8736e-08},
0094                     {0.96, -0.00305085, -9.00761e-05, 1.64917e-06},
0095                     {0.9427, -0.00382792, -6.53386e-05, -2.6154e-06},
0096                     {0.9216, -0.00467746, -0.00010457, 4.81243e-06},
0097                     {0.8962, -0.00536223, -3.23831e-05, -5.43432e-06},
0098                     {0.8679, -0.00609363, -0.000113898, 3.32484e-06},
0099                     {0.835, -0.00698325, -6.40253e-05, 9.34959e-07},
0100                     {0.7986, -0.00755338, -5.00009e-05, 9.35324e-07},
0101                     {0.7597, -0.00798324, -3.5971e-05, -2.27626e-06},
0102                     {0.7186, -0.00851367, -7.01149e-05, -8.6303e-06},
0103                     {0.6732, -0.00986209, -0.000199569, 1.91974e-05},
0104                     {0.6213, -0.010418, 8.83923e-05, 6.24051e-06},
0105                     {0.5722, -0.00906601, 0.000182, 6.24051e-06},
0106                     {0.5322, -0.00677797, 0.000275608, 6.24051e-06}
0107                 };
0108                 return result;
0109             }
0110
0111             template <typename T>
0112             inline const coefs<T> * coefs_y()
0113             {
0114                 static const coefs<T> result[] = {
0115                     {-5.20417e-18, 0.0124, 1.21431e-18, -8.45284e-11},
0116                     {0.062, 0.0124, -1.26793e-09, 4.22642e-10},
0117                     {0.124, 0.0124, 5.07171e-09, -1.60604e-09},
0118                     {0.186, 0.0123999, -1.90189e-08, 6.00152e-09},
0119                     {0.248, 0.0124002, 7.10039e-08, -2.24e-08},
0120                     {0.31, 0.0123992, -2.64997e-07, 8.35986e-08},
0121                     {0.372, 0.0124029, 9.88983e-07, -3.11994e-07},
0122                     {0.434, 0.0123893, -3.69093e-06, -4.35621e-07},
0123                     {0.4958, 0.0123198, -1.02252e-05, -3.45523e-07},
0124                     {0.5571, 0.0121916, -1.54081e-05, -5.82288e-07},
0125                     {0.6176, 0.0119938, -2.41424e-05, -5.25327e-07},
0126                     {0.6769, 0.011713, -3.20223e-05, -5.16405e-07},
0127                     {0.7346, 0.0113541, -3.97684e-05, -6.09052e-07},
0128                     {0.7903, 0.0109107, -4.89042e-05, -1.04739e-06},
0129                     {0.8435, 0.0103431, -6.4615e-05, -1.40374e-09},
0130                     {0.8936, 0.00969686, -6.4636e-05, -8.547e-06},
0131                     {0.9394, 0.00840947, -0.000192841, -4.2106e-06},
0132                     {0.9761, 0.00616527, -0.000256, -4.2106e-06},
0133                     {1.0, 0.00328947, -0.000319159, -4.2106e-06}
0134                 };
0135                 return result;
0136             }
0137
0138             template <typename T, typename Parameters>
0139             struct base_robin_spheroid
0140             {
0141                 inline T v(coefs<T> const& c, T const& z) const
0142                 { return (c.c0 + z * (c.c1 + z * (c.c2 + z * c.c3))); }
0143                 inline T dv(coefs<T> const& c, T const&  z) const
0144                 { return (c.c1 + z * (c.c2 + c.c2 + z * 3. * c.c3)); }
0145
0146                 // FORWARD(s_forward)  spheroid
0147                 // Project coordinates from geographic (lon, lat) to cartesian (x, y)
0148                 inline void fwd(Parameters const& , T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const
0149                 {
0150                     int i;
0151                     T dphi;
0152
0153                     i = int_floor((dphi = fabs(lp_lat)) * C1);
0154                     if (i < 0) {
0155                         BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
0156                     }
0157                     if (i >= n_nodes) i = n_nodes - 1;
0158                     dphi = geometry::math::r2d<T>() * (dphi - RC1 * i);
0159                     xy_x = v(coefs_x<T>()[i], dphi) * FXC * lp_lon;
0160                     xy_y = v(coefs_y<T>()[i], dphi) * FYC;
0161                     if (lp_lat < 0.) xy_y = -xy_y;
0162                 }
0163
0164                 // INVERSE(s_inverse)  spheroid
0165                 // Project coordinates from cartesian (x, y) to geographic (lon, lat)
0166                 inline void inv(Parameters const& , T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const
0167                 {
0168                     static const T half_pi = detail::half_pi<T>();
0169                     const coefs<T> * coefs_x = robin::coefs_x<T>();
0170                     const coefs<T> * coefs_y = robin::coefs_y<T>();
0171
0172                     int i;
0173                     T t, t1;
0174                     coefs<T> coefs_t;
0175                     int iters;
0176
0177                     lp_lon = xy_x / FXC;
0178                     lp_lat = fabs(xy_y / FYC);
0179                     if (lp_lat >= 1.) { /* simple pathologic cases */
0180                         if (lp_lat > one_plus_eps) {
0181                             BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
0182                         } else {
0183                             lp_lat = xy_y < 0. ? -half_pi : half_pi;
0184                             lp_lon /= coefs_x[n_nodes].c0;
0185                         }
0186                     } else { /* general problem */
0187                         /* in Y space, reduce to table interval */
0188                         i = int_floor(lp_lat * n_nodes);
0189                         if( i < 0 || i >= n_nodes ) {
0190                             BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
0191                         }
0192                         for (;;) {
0193                             if (coefs_y[i].c0 > lp_lat) --i;
0194                             else if (coefs_y[i+1].c0 <= lp_lat) ++i;
0195                             else break;
0196                         }
0197                         coefs_t = coefs_y[i];
0198                         /* first guess, linear interp */
0199                         t = 5. * (lp_lat - coefs_t.c0)/(coefs_y[i+1].c0 - coefs_t.c0);
0200                         /* make into root */
0201                         coefs_t.c0 = (T)(coefs_t.c0 - lp_lat);
0202                         for (iters = max_iter; iters ; --iters) { /* Newton-Raphson */
0203                             t -= t1 = v(coefs_t,t) / dv(coefs_t,t);
0204                             if (fabs(t1) < epsilon)
0205                                 break;
0206                         }
0207                         if( iters == 0 )
0208                             BOOST_THROW_EXCEPTION( projection_exception(error_non_convergent) );
0209                         lp_lat = (5 * i + t) * geometry::math::d2r<T>();
0210                         if (xy_y < 0.) lp_lat = -lp_lat;
0211                         lp_lon /= v(coefs_x[i], t);
0212                     }
0213                 }
0214
0215                 static inline std::string get_name()
0216                 {
0217                     return "robin_spheroid";
0218                 }
0219
0220             };
0221
0222             // Robinson
0223             template <typename Parameters>
0224             inline void setup_robin(Parameters& par)
0225             {
0226                 par.es = 0.;
0227             }
0228
0229     }} // namespace detail::robin
0230     #endif // doxygen
0231
0232     /*!
0233         \brief Robinson projection
0234         \ingroup projections
0235         \tparam Geographic latlong point type
0236         \tparam Cartesian xy point type
0237         \tparam Parameters parameter type
0238         \par Projection characteristics
0239          - Pseudocylindrical
0240          - Spheroid
0241         \par Example
0242         \image html ex_robin.gif
0243     */
0244     template <typename T, typename Parameters>
0245     struct robin_spheroid : public detail::robin::base_robin_spheroid<T, Parameters>
0246     {
0247         template <typename Params>
0248         inline robin_spheroid(Params const& , Parameters & par)
0249         {
0250             detail::robin::setup_robin(par);
0251         }
0252     };
0253
0254     #ifndef DOXYGEN_NO_DETAIL
0255     namespace detail
0256     {
0257
0258         // Static projection
0259         BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_robin, robin_spheroid)
0260
0261         // Factory entry(s)
0262         BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(robin_entry, robin_spheroid)
0263
0264         BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(robin_init)
0265         {
0266             BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(robin, robin_entry)
0267         }
0268
0269     } // namespace detail
0270     #endif // doxygen
0271
0272 } // namespace projections
0273
0274 }} // namespace boost::geometry
0275
0276 #endif // BOOST_GEOMETRY_PROJECTIONS_ROBIN_HPP
0277