ceph/src/boost/boost/geometry/srs/projections/proj/vandg.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_VANDG_HPP
  41 #define BOOST_GEOMETRY_PROJECTIONS_VANDG_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
  50 namespace boost { namespace geometry
  51 {
  52
  53 namespace projections
  54 {
  55     #ifndef DOXYGEN_NO_DETAIL
  56     namespace detail { namespace vandg
  57     {
  58
  59             static const double tolerance = 1.e-10;
  60
  61             template <typename T>
  62             inline T C2_27() { return .07407407407407407407407407407407; }
  63             template <typename T>
  64             inline T PI4_3() { return boost::math::constants::four_thirds_pi<T>(); }
  65             template <typename T>
  66             inline T TPISQ() { return 19.739208802178717237668981999752; }
  67             template <typename T>
  68             inline T HPISQ() { return 4.9348022005446793094172454999381; }
  69
  70             template <typename T, typename Parameters>
  71             struct base_vandg_spheroid
  72             {
  73                 // FORWARD(s_forward)  spheroid
  74                 // Project coordinates from geographic (lon, lat) to cartesian (x, y)
  75                 inline void fwd(Parameters const& , T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const
  76                 {
  77                     static const T half_pi = detail::half_pi<T>();
  78                     static const T pi = detail::pi<T>();
  79
  80                     T  al, al2, g, g2, p2;
  81
  82                     p2 = fabs(lp_lat / half_pi);
  83                     if ((p2 - tolerance) > 1.) {
  84                         BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
  85                     }
  86                     if (p2 > 1.)
  87                         p2 = 1.;
  88                     if (fabs(lp_lat) <= tolerance) {
  89                         xy_x = lp_lon;
  90                         xy_y = 0.;
  91                     } else if (fabs(lp_lon) <= tolerance || fabs(p2 - 1.) < tolerance) {
  92                         xy_x = 0.;
  93                         xy_y = pi * tan(.5 * asin(p2));
  94                         if (lp_lat < 0.) xy_y = -xy_y;
  95                     } else {
  96                         al = .5 * fabs(pi / lp_lon - lp_lon / pi);
  97                         al2 = al * al;
  98                         g = sqrt(1. - p2 * p2);
  99                         g = g / (p2 + g - 1.);
 100                         g2 = g * g;
 101                         p2 = g * (2. / p2 - 1.);
 102                         p2 = p2 * p2;
 103                         xy_x = g - p2; g = p2 + al2;
 104                         xy_x = pi * (al * xy_x + sqrt(al2 * xy_x * xy_x - g * (g2 - p2))) / g;
 105                         if (lp_lon < 0.) xy_x = -xy_x;
 106                         xy_y = fabs(xy_x / pi);
 107                         xy_y = 1. - xy_y * (xy_y + 2. * al);
 108                         if (xy_y < -tolerance) {
 109                             BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
 110                         }
 111                         if (xy_y < 0.)
 112                             xy_y = 0.;
 113                         else
 114                             xy_y = sqrt(xy_y) * (lp_lat < 0. ? -pi : pi);
 115                     }
 116                 }
 117
 118                 // INVERSE(s_inverse)  spheroid
 119                 // Project coordinates from cartesian (x, y) to geographic (lon, lat)
 120                 inline void inv(Parameters const& , 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                     static const T pi = detail::pi<T>();
 124                     static const T pi_sqr = detail::pi_sqr<T>();
 125                     static const T third = detail::third<T>();
 126                     static const T two_pi = detail::two_pi<T>();
 127
 128                     static const T C2_27 = vandg::C2_27<T>();
 129                     static const T PI4_3 = vandg::PI4_3<T>();
 130                     static const T TPISQ = vandg::TPISQ<T>();
 131                     static const T HPISQ = vandg::HPISQ<T>();
 132
 133                     T t, c0, c1, c2, c3, al, r2, r, m, d, ay, x2, y2;
 134
 135                     x2 = xy_x * xy_x;
 136                     if ((ay = fabs(xy_y)) < tolerance) {
 137                         lp_lat = 0.;
 138                         t = x2 * x2 + TPISQ * (x2 + HPISQ);
 139                         lp_lon = fabs(xy_x) <= tolerance ? 0. :
 140                            .5 * (x2 - pi_sqr + sqrt(t)) / xy_x;
 141                             return;
 142                     }
 143                     y2 = xy_y * xy_y;
 144                     r = x2 + y2;    r2 = r * r;
 145                     c1 = - pi * ay * (r + pi_sqr);
 146                     c3 = r2 + two_pi * (ay * r + pi * (y2 + pi * (ay + half_pi)));
 147                     c2 = c1 + pi_sqr * (r - 3. *  y2);
 148                     c0 = pi * ay;
 149                     c2 /= c3;
 150                     al = c1 / c3 - third * c2 * c2;
 151                     m = 2. * sqrt(-third * al);
 152                     d = C2_27 * c2 * c2 * c2 + (c0 * c0 - third * c2 * c1) / c3;
 153                     if (((t = fabs(d = 3. * d / (al * m))) - tolerance) <= 1.) {
 154                         d = t > 1. ? (d > 0. ? 0. : pi) : acos(d);
 155                         lp_lat = pi * (m * cos(d * third + PI4_3) - third * c2);
 156                         if (xy_y < 0.) lp_lat = -lp_lat;
 157                         t = r2 + TPISQ * (x2 - y2 + HPISQ);
 158                         lp_lon = fabs(xy_x) <= tolerance ? 0. :
 159                            .5 * (r - pi_sqr + (t <= 0. ? 0. : sqrt(t))) / xy_x;
 160                     } else {
 161                         BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
 162                     }
 163                 }
 164
 165                 static inline std::string get_name()
 166                 {
 167                     return "vandg_spheroid";
 168                 }
 169
 170             };
 171
 172             // van der Grinten (I)
 173             template <typename Parameters>
 174             inline void setup_vandg(Parameters& par)
 175             {
 176                 par.es = 0.;
 177             }
 178
 179     }} // namespace detail::vandg
 180     #endif // doxygen
 181
 182     /*!
 183         \brief van der Grinten (I) projection
 184         \ingroup projections
 185         \tparam Geographic latlong point type
 186         \tparam Cartesian xy point type
 187         \tparam Parameters parameter type
 188         \par Projection characteristics
 189          - Miscellaneous
 190          - Spheroid
 191         \par Example
 192         \image html ex_vandg.gif
 193     */
 194     template <typename T, typename Parameters>
 195     struct vandg_spheroid : public detail::vandg::base_vandg_spheroid<T, Parameters>
 196     {
 197         template <typename Params>
 198         inline vandg_spheroid(Params const& , Parameters & par)
 199         {
 200             detail::vandg::setup_vandg(par);
 201         }
 202     };
 203
 204     #ifndef DOXYGEN_NO_DETAIL
 205     namespace detail
 206     {
 207
 208         // Static projection
 209         BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_vandg, vandg_spheroid)
 210
 211         // Factory entry(s)
 212         BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(vandg_entry, vandg_spheroid)
 213
 214         BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(vandg_init)
 215         {
 216             BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(vandg, vandg_entry)
 217         }
 218
 219     } // namespace detail
 220     #endif // doxygen
 221
 222 } // namespace projections
 223
 224 }} // namespace boost::geometry
 225
 226 #endif // BOOST_GEOMETRY_PROJECTIONS_VANDG_HPP
 227