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_BIPC_HPP 41 #define BOOST_GEOMETRY_PROJECTIONS_BIPC_HPP 42 43 #include <boost/geometry/srs/projections/impl/base_static.hpp> 44 #include <boost/geometry/srs/projections/impl/base_dynamic.hpp> 45 #include <boost/geometry/srs/projections/impl/factory_entry.hpp> 46 #include <boost/geometry/srs/projections/impl/pj_param.hpp> 47 #include <boost/geometry/srs/projections/impl/projects.hpp> 48 49 #include <boost/geometry/util/math.hpp> 50 51 #include <boost/math/special_functions/hypot.hpp> 52 53 namespace boost { namespace geometry 54 { 55 56 namespace projections 57 { 58 #ifndef DOXYGEN_NO_DETAIL 59 namespace detail { namespace bipc 60 { 61 62 static const double epsilon = 1e-10; 63 static const double epsilon10 = 1e-10; 64 static const double one_plus_eps = 1.000000001; 65 static const int n_iter = 10; 66 static const double lamB = -.34894976726250681539; 67 static const double n = .63055844881274687180; 68 static const double F = 1.89724742567461030582; 69 static const double Azab = .81650043674686363166; 70 static const double Azba = 1.82261843856185925133; 71 static const double const_T = 1.27246578267089012270; 72 static const double rhoc = 1.20709121521568721927; 73 static const double cAzc = .69691523038678375519; 74 static const double sAzc = .71715351331143607555; 75 static const double C45 = .70710678118654752469; 76 static const double S45 = .70710678118654752410; 77 static const double C20 = .93969262078590838411; 78 static const double S20 = -.34202014332566873287; 79 static const double R110 = 1.91986217719376253360; 80 static const double R104 = 1.81514242207410275904; 81 82 struct par_bipc 83 { 84 bool noskew; 85 }; 86 87 template <typename T, typename Parameters> 88 struct base_bipc_spheroid 89 { 90 par_bipc m_proj_parm; 91 92 // FORWARD(s_forward) spheroid 93 // Project coordinates from geographic (lon, lat) to cartesian (x, y) fwdboost::geometry::projections::detail::bipc::base_bipc_spheroid94 inline void fwd(Parameters const& , T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const 95 { 96 static const T half_pi = detail::half_pi<T>(); 97 static const T pi = detail::pi<T>(); 98 99 T cphi, sphi, tphi, t, al, Az, z, Av, cdlam, sdlam, r; 100 int tag; 101 102 cphi = cos(lp_lat); 103 sphi = sin(lp_lat); 104 cdlam = cos(sdlam = lamB - lp_lon); 105 sdlam = sin(sdlam); 106 if (fabs(fabs(lp_lat) - half_pi) < epsilon10) { 107 Az = lp_lat < 0. ? pi : 0.; 108 tphi = HUGE_VAL; 109 } else { 110 tphi = sphi / cphi; 111 Az = atan2(sdlam , C45 * (tphi - cdlam)); 112 } 113 if( (tag = (Az > Azba)) ) { 114 cdlam = cos(sdlam = lp_lon + R110); 115 sdlam = sin(sdlam); 116 z = S20 * sphi + C20 * cphi * cdlam; 117 if (fabs(z) > 1.) { 118 if (fabs(z) > one_plus_eps) 119 BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) ); 120 else 121 z = z < 0. ? -1. : 1.; 122 } else 123 z = acos(z); 124 if (tphi != HUGE_VAL) 125 Az = atan2(sdlam, (C20 * tphi - S20 * cdlam)); 126 Av = Azab; 127 xy_y = rhoc; 128 } else { 129 z = S45 * (sphi + cphi * cdlam); 130 if (fabs(z) > 1.) { 131 if (fabs(z) > one_plus_eps) 132 BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) ); 133 else 134 z = z < 0. ? -1. : 1.; 135 } else 136 z = acos(z); 137 Av = Azba; 138 xy_y = -rhoc; 139 } 140 if (z < 0.) { 141 BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) ); 142 } 143 r = F * (t = math::pow(tan(T(0.5) * z), n)); 144 if ((al = .5 * (R104 - z)) < 0.) { 145 BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) ); 146 } 147 al = (t + math::pow(al, n)) / const_T; 148 if (fabs(al) > 1.) { 149 if (fabs(al) > one_plus_eps) 150 BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) ); 151 else 152 al = al < 0. ? -1. : 1.; 153 } else 154 al = acos(al); 155 if (fabs(t = n * (Av - Az)) < al) 156 r /= cos(al + (tag ? t : -t)); 157 xy_x = r * sin(t); 158 xy_y += (tag ? -r : r) * cos(t); 159 if (this->m_proj_parm.noskew) { 160 t = xy_x; 161 xy_x = -xy_x * cAzc - xy_y * sAzc; 162 xy_y = -xy_y * cAzc + t * sAzc; 163 } 164 } 165 166 // INVERSE(s_inverse) spheroid 167 // Project coordinates from cartesian (x, y) to geographic (lon, lat) invboost::geometry::projections::detail::bipc::base_bipc_spheroid168 inline void inv(Parameters const& , T xy_x, T xy_y, T& lp_lon, T& lp_lat) const 169 { 170 T t, r, rp, rl, al, z, fAz, Az, s, c, Av; 171 int neg, i; 172 173 if (this->m_proj_parm.noskew) { 174 t = xy_x; 175 xy_x = -xy_x * cAzc + xy_y * sAzc; 176 xy_y = -xy_y * cAzc - t * sAzc; 177 } 178 if( (neg = (xy_x < 0.)) ) { 179 xy_y = rhoc - xy_y; 180 s = S20; 181 c = C20; 182 Av = Azab; 183 } else { 184 xy_y += rhoc; 185 s = S45; 186 c = C45; 187 Av = Azba; 188 } 189 rl = rp = r = boost::math::hypot(xy_x, xy_y); 190 fAz = fabs(Az = atan2(xy_x, xy_y)); 191 for (i = n_iter; i ; --i) { 192 z = 2. * atan(math::pow(r / F,T(1) / n)); 193 al = acos((math::pow(tan(T(0.5) * z), n) + 194 math::pow(tan(T(0.5) * (R104 - z)), n)) / const_T); 195 if (fAz < al) 196 r = rp * cos(al + (neg ? Az : -Az)); 197 if (fabs(rl - r) < epsilon) 198 break; 199 rl = r; 200 } 201 if (! i) 202 BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) ); 203 Az = Av - Az / n; 204 lp_lat = asin(s * cos(z) + c * sin(z) * cos(Az)); 205 lp_lon = atan2(sin(Az), c / tan(z) - s * cos(Az)); 206 if (neg) 207 lp_lon -= R110; 208 else 209 lp_lon = lamB - lp_lon; 210 } 211 get_nameboost::geometry::projections::detail::bipc::base_bipc_spheroid212 static inline std::string get_name() 213 { 214 return "bipc_spheroid"; 215 } 216 217 }; 218 219 // Bipolar conic of western hemisphere 220 template <typename Params, typename Parameters> setup_bipc(Params const & params,Parameters & par,par_bipc & proj_parm)221 inline void setup_bipc(Params const& params, Parameters& par, par_bipc& proj_parm) 222 { 223 proj_parm.noskew = pj_get_param_b<srs::spar::ns>(params, "ns", srs::dpar::ns); 224 par.es = 0.; 225 } 226 227 }} // namespace detail::bipc 228 #endif // doxygen 229 230 /*! 231 \brief Bipolar conic of western hemisphere projection 232 \ingroup projections 233 \tparam Geographic latlong point type 234 \tparam Cartesian xy point type 235 \tparam Parameters parameter type 236 \par Projection characteristics 237 - Conic 238 - Spheroid 239 \par Projection parameters 240 - ns (boolean) 241 \par Example 242 \image html ex_bipc.gif 243 */ 244 template <typename T, typename Parameters> 245 struct bipc_spheroid : public detail::bipc::base_bipc_spheroid<T, Parameters> 246 { 247 template <typename Params> bipc_spheroidboost::geometry::projections::bipc_spheroid248 inline bipc_spheroid(Params const& params, Parameters & par) 249 { 250 detail::bipc::setup_bipc(params, par, this->m_proj_parm); 251 } 252 }; 253 254 #ifndef DOXYGEN_NO_DETAIL 255 namespace detail 256 { 257 258 // Static projection BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_bipc,bipc_spheroid)259 BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_bipc, bipc_spheroid) 260 261 // Factory entry(s) 262 BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(bipc_entry, bipc_spheroid) 263 264 BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(bipc_init) 265 { 266 BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(bipc, bipc_entry) 267 } 268 269 } // namespace detail 270 #endif // doxygen 271 272 } // namespace projections 273 274 }} // namespace boost::geometry 275 276 #endif // BOOST_GEOMETRY_PROJECTIONS_BIPC_HPP 277 278