// Boost.Geometry - gis-projections (based on PROJ4) // Copyright (c) 2008-2015 Barend Gehrels, Amsterdam, the Netherlands. // This file was modified by Oracle on 2017, 2018, 2019. // Modifications copyright (c) 2017-2019, Oracle and/or its affiliates. // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle. // Use, modification and distribution is subject to the Boost Software License, // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at // http://www.boost.org/LICENSE_1_0.txt) // This file is converted from PROJ4, http://trac.osgeo.org/proj // PROJ4 is originally written by Gerald Evenden (then of the USGS) // PROJ4 is maintained by Frank Warmerdam // PROJ4 is converted to Boost.Geometry by Barend Gehrels // Last updated version of proj: 5.0.0 // Original copyright notice: // Permission is hereby granted, free of charge, to any person obtaining a // copy of this software and associated documentation files (the "Software"), // to deal in the Software without restriction, including without limitation // the rights to use, copy, modify, merge, publish, distribute, sublicense, // and/or sell copies of the Software, and to permit persons to whom the // Software is furnished to do so, subject to the following conditions: // The above copyright notice and this permission notice shall be included // in all copies or substantial portions of the Software. // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS // OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL // THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING // FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER // DEALINGS IN THE SOFTWARE. #ifndef BOOST_GEOMETRY_PROJECTIONS_VANDG_HPP #define BOOST_GEOMETRY_PROJECTIONS_VANDG_HPP #include #include #include #include #include namespace boost { namespace geometry { namespace projections { #ifndef DOXYGEN_NO_DETAIL namespace detail { namespace vandg { static const double tolerance = 1.e-10; template inline T C2_27() { return .07407407407407407407407407407407; } template inline T PI4_3() { return boost::math::constants::four_thirds_pi(); } template inline T TPISQ() { return 19.739208802178717237668981999752; } template inline T HPISQ() { return 4.9348022005446793094172454999381; } template struct base_vandg_spheroid { // FORWARD(s_forward) spheroid // Project coordinates from geographic (lon, lat) to cartesian (x, y) inline void fwd(Parameters const& , T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const { static const T half_pi = detail::half_pi(); static const T pi = detail::pi(); T al, al2, g, g2, p2; p2 = fabs(lp_lat / half_pi); if ((p2 - tolerance) > 1.) { BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) ); } if (p2 > 1.) p2 = 1.; if (fabs(lp_lat) <= tolerance) { xy_x = lp_lon; xy_y = 0.; } else if (fabs(lp_lon) <= tolerance || fabs(p2 - 1.) < tolerance) { xy_x = 0.; xy_y = pi * tan(.5 * asin(p2)); if (lp_lat < 0.) xy_y = -xy_y; } else { al = .5 * fabs(pi / lp_lon - lp_lon / pi); al2 = al * al; g = sqrt(1. - p2 * p2); g = g / (p2 + g - 1.); g2 = g * g; p2 = g * (2. / p2 - 1.); p2 = p2 * p2; xy_x = g - p2; g = p2 + al2; xy_x = pi * (al * xy_x + sqrt(al2 * xy_x * xy_x - g * (g2 - p2))) / g; if (lp_lon < 0.) xy_x = -xy_x; xy_y = fabs(xy_x / pi); xy_y = 1. - xy_y * (xy_y + 2. * al); if (xy_y < -tolerance) { BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) ); } if (xy_y < 0.) xy_y = 0.; else xy_y = sqrt(xy_y) * (lp_lat < 0. ? -pi : pi); } } // INVERSE(s_inverse) spheroid // Project coordinates from cartesian (x, y) to geographic (lon, lat) inline void inv(Parameters const& , T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const { static const T half_pi = detail::half_pi(); static const T pi = detail::pi(); static const T pi_sqr = detail::pi_sqr(); static const T third = detail::third(); static const T two_pi = detail::two_pi(); static const T C2_27 = vandg::C2_27(); static const T PI4_3 = vandg::PI4_3(); static const T TPISQ = vandg::TPISQ(); static const T HPISQ = vandg::HPISQ(); T t, c0, c1, c2, c3, al, r2, r, m, d, ay, x2, y2; x2 = xy_x * xy_x; if ((ay = fabs(xy_y)) < tolerance) { lp_lat = 0.; t = x2 * x2 + TPISQ * (x2 + HPISQ); lp_lon = fabs(xy_x) <= tolerance ? 0. : .5 * (x2 - pi_sqr + sqrt(t)) / xy_x; return; } y2 = xy_y * xy_y; r = x2 + y2; r2 = r * r; c1 = - pi * ay * (r + pi_sqr); c3 = r2 + two_pi * (ay * r + pi * (y2 + pi * (ay + half_pi))); c2 = c1 + pi_sqr * (r - 3. * y2); c0 = pi * ay; c2 /= c3; al = c1 / c3 - third * c2 * c2; m = 2. * sqrt(-third * al); d = C2_27 * c2 * c2 * c2 + (c0 * c0 - third * c2 * c1) / c3; if (((t = fabs(d = 3. * d / (al * m))) - tolerance) <= 1.) { d = t > 1. ? (d > 0. ? 0. : pi) : acos(d); lp_lat = pi * (m * cos(d * third + PI4_3) - third * c2); if (xy_y < 0.) lp_lat = -lp_lat; t = r2 + TPISQ * (x2 - y2 + HPISQ); lp_lon = fabs(xy_x) <= tolerance ? 0. : .5 * (r - pi_sqr + (t <= 0. ? 0. : sqrt(t))) / xy_x; } else { BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) ); } } static inline std::string get_name() { return "vandg_spheroid"; } }; // van der Grinten (I) template inline void setup_vandg(Parameters& par) { par.es = 0.; } }} // namespace detail::vandg #endif // doxygen /*! \brief van der Grinten (I) projection \ingroup projections \tparam Geographic latlong point type \tparam Cartesian xy point type \tparam Parameters parameter type \par Projection characteristics - Miscellaneous - Spheroid \par Example \image html ex_vandg.gif */ template struct vandg_spheroid : public detail::vandg::base_vandg_spheroid { template inline vandg_spheroid(Params const& , Parameters & par) { detail::vandg::setup_vandg(par); } }; #ifndef DOXYGEN_NO_DETAIL namespace detail { // Static projection BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_vandg, vandg_spheroid) // Factory entry(s) BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(vandg_entry, vandg_spheroid) BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(vandg_init) { BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(vandg, vandg_entry) } } // namespace detail #endif // doxygen } // namespace projections }} // namespace boost::geometry #endif // BOOST_GEOMETRY_PROJECTIONS_VANDG_HPP