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// 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_LAEA_HPP #define BOOST_GEOMETRY_PROJECTIONS_LAEA_HPP #include #include #include #include #include #include #include #include #include namespace boost { namespace geometry { namespace projections { #ifndef DOXYGEN_NO_DETAIL namespace detail { namespace laea { static const double epsilon10 = 1.e-10; enum mode_type { n_pole = 0, s_pole = 1, equit = 2, obliq = 3 }; template struct par_laea { T sinb1; T cosb1; T xmf; T ymf; T mmf; T qp; T dd; T rq; detail::apa apa; mode_type mode; }; template struct base_laea_ellipsoid { par_laea m_proj_parm; // FORWARD(e_forward) ellipsoid // Project coordinates from geographic (lon, lat) to cartesian (x, y) inline void fwd(Parameters const& par, T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const { static const T half_pi = detail::half_pi(); T coslam, sinlam, sinphi, q, sinb=0.0, cosb=0.0, b=0.0; coslam = cos(lp_lon); sinlam = sin(lp_lon); sinphi = sin(lp_lat); q = pj_qsfn(sinphi, par.e, par.one_es); if (this->m_proj_parm.mode == obliq || this->m_proj_parm.mode == equit) { sinb = q / this->m_proj_parm.qp; cosb = sqrt(1. - sinb * sinb); } switch (this->m_proj_parm.mode) { case obliq: b = 1. + this->m_proj_parm.sinb1 * sinb + this->m_proj_parm.cosb1 * cosb * coslam; break; case equit: b = 1. + cosb * coslam; break; case n_pole: b = half_pi + lp_lat; q = this->m_proj_parm.qp - q; break; case s_pole: b = lp_lat - half_pi; q = this->m_proj_parm.qp + q; break; } if (fabs(b) < epsilon10) { BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) ); } switch (this->m_proj_parm.mode) { case obliq: b = sqrt(2. / b); xy_y = this->m_proj_parm.ymf * b * (this->m_proj_parm.cosb1 * sinb - this->m_proj_parm.sinb1 * cosb * coslam); goto eqcon; break; case equit: b = sqrt(2. / (1. + cosb * coslam)); xy_y = b * sinb * this->m_proj_parm.ymf; eqcon: xy_x = this->m_proj_parm.xmf * b * cosb * sinlam; break; case n_pole: case s_pole: if (q >= 0.) { b = sqrt(q); xy_x = b * sinlam; xy_y = coslam * (this->m_proj_parm.mode == s_pole ? b : -b); } else xy_x = xy_y = 0.; break; } } // INVERSE(e_inverse) ellipsoid // Project coordinates from cartesian (x, y) to geographic (lon, lat) inline void inv(Parameters const& par, T xy_x, T xy_y, T& lp_lon, T& lp_lat) const { T cCe, sCe, q, rho, ab=0.0; switch (this->m_proj_parm.mode) { case equit: case obliq: xy_x /= this->m_proj_parm.dd; xy_y *= this->m_proj_parm.dd; rho = boost::math::hypot(xy_x, xy_y); if (rho < epsilon10) { lp_lon = 0.; lp_lat = par.phi0; return; } sCe = 2. * asin(.5 * rho / this->m_proj_parm.rq); cCe = cos(sCe); sCe = sin(sCe); xy_x *= sCe; if (this->m_proj_parm.mode == obliq) { ab = cCe * this->m_proj_parm.sinb1 + xy_y * sCe * this->m_proj_parm.cosb1 / rho; xy_y = rho * this->m_proj_parm.cosb1 * cCe - xy_y * this->m_proj_parm.sinb1 * sCe; } else { ab = xy_y * sCe / rho; xy_y = rho * cCe; } break; case n_pole: xy_y = -xy_y; BOOST_FALLTHROUGH; case s_pole: q = (xy_x * xy_x + xy_y * xy_y); if (q == 0.0) { lp_lon = 0.; lp_lat = par.phi0; return; } ab = 1. - q / this->m_proj_parm.qp; if (this->m_proj_parm.mode == s_pole) ab = - ab; break; } lp_lon = atan2(xy_x, xy_y); lp_lat = pj_authlat(asin(ab), this->m_proj_parm.apa); } static inline std::string get_name() { return "laea_ellipsoid"; } }; template struct base_laea_spheroid { par_laea m_proj_parm; // FORWARD(s_forward) spheroid // Project coordinates from geographic (lon, lat) to cartesian (x, y) inline void fwd(Parameters const& par, T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const { static const T fourth_pi = detail::fourth_pi(); T coslam, cosphi, sinphi; sinphi = sin(lp_lat); cosphi = cos(lp_lat); coslam = cos(lp_lon); switch (this->m_proj_parm.mode) { case equit: xy_y = 1. + cosphi * coslam; goto oblcon; case obliq: xy_y = 1. + this->m_proj_parm.sinb1 * sinphi + this->m_proj_parm.cosb1 * cosphi * coslam; oblcon: if (xy_y <= epsilon10) { BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) ); } xy_y = sqrt(2. / xy_y); xy_x = xy_y * cosphi * sin(lp_lon); xy_y *= this->m_proj_parm.mode == equit ? sinphi : this->m_proj_parm.cosb1 * sinphi - this->m_proj_parm.sinb1 * cosphi * coslam; break; case n_pole: coslam = -coslam; BOOST_FALLTHROUGH; case s_pole: if (fabs(lp_lat + par.phi0) < epsilon10) { BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) ); } xy_y = fourth_pi - lp_lat * .5; xy_y = 2. * (this->m_proj_parm.mode == s_pole ? cos(xy_y) : sin(xy_y)); xy_x = xy_y * sin(lp_lon); xy_y *= coslam; break; } } // INVERSE(s_inverse) spheroid // Project coordinates from cartesian (x, y) to geographic (lon, lat) inline void inv(Parameters const& par, T xy_x, T xy_y, T& lp_lon, T& lp_lat) const { static const T half_pi = detail::half_pi(); T cosz=0.0, rh, sinz=0.0; rh = boost::math::hypot(xy_x, xy_y); if ((lp_lat = rh * .5 ) > 1.) { BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) ); } lp_lat = 2. * asin(lp_lat); if (this->m_proj_parm.mode == obliq || this->m_proj_parm.mode == equit) { sinz = sin(lp_lat); cosz = cos(lp_lat); } switch (this->m_proj_parm.mode) { case equit: lp_lat = fabs(rh) <= epsilon10 ? 0. : asin(xy_y * sinz / rh); xy_x *= sinz; xy_y = cosz * rh; break; case obliq: lp_lat = fabs(rh) <= epsilon10 ? par.phi0 : asin(cosz * this->m_proj_parm.sinb1 + xy_y * sinz * this->m_proj_parm.cosb1 / rh); xy_x *= sinz * this->m_proj_parm.cosb1; xy_y = (cosz - sin(lp_lat) * this->m_proj_parm.sinb1) * rh; break; case n_pole: xy_y = -xy_y; lp_lat = half_pi - lp_lat; break; case s_pole: lp_lat -= half_pi; break; } lp_lon = (xy_y == 0. && (this->m_proj_parm.mode == equit || this->m_proj_parm.mode == obliq)) ? 0. : atan2(xy_x, xy_y); } static inline std::string get_name() { return "laea_spheroid"; } }; // Lambert Azimuthal Equal Area template inline void setup_laea(Parameters& par, par_laea& proj_parm) { static const T half_pi = detail::half_pi(); T t; t = fabs(par.phi0); if (fabs(t - half_pi) < epsilon10) proj_parm.mode = par.phi0 < 0. ? s_pole : n_pole; else if (fabs(t) < epsilon10) proj_parm.mode = equit; else proj_parm.mode = obliq; if (par.es != 0.0) { double sinphi; par.e = sqrt(par.es); // TODO : Isn't it already set? proj_parm.qp = pj_qsfn(1., par.e, par.one_es); proj_parm.mmf = .5 / (1. - par.es); proj_parm.apa = pj_authset(par.es); switch (proj_parm.mode) { case n_pole: case s_pole: proj_parm.dd = 1.; break; case equit: proj_parm.dd = 1. / (proj_parm.rq = sqrt(.5 * proj_parm.qp)); proj_parm.xmf = 1.; proj_parm.ymf = .5 * proj_parm.qp; break; case obliq: proj_parm.rq = sqrt(.5 * proj_parm.qp); sinphi = sin(par.phi0); proj_parm.sinb1 = pj_qsfn(sinphi, par.e, par.one_es) / proj_parm.qp; proj_parm.cosb1 = sqrt(1. - proj_parm.sinb1 * proj_parm.sinb1); proj_parm.dd = cos(par.phi0) / (sqrt(1. - par.es * sinphi * sinphi) * proj_parm.rq * proj_parm.cosb1); proj_parm.ymf = (proj_parm.xmf = proj_parm.rq) / proj_parm.dd; proj_parm.xmf *= proj_parm.dd; break; } } else { if (proj_parm.mode == obliq) { proj_parm.sinb1 = sin(par.phi0); proj_parm.cosb1 = cos(par.phi0); } } } }} // namespace laea #endif // doxygen /*! \brief Lambert Azimuthal Equal Area projection \ingroup projections \tparam Geographic latlong point type \tparam Cartesian xy point type \tparam Parameters parameter type \par Projection characteristics - Azimuthal - Spheroid - Ellipsoid \par Example \image html ex_laea.gif */ template struct laea_ellipsoid : public detail::laea::base_laea_ellipsoid { template inline laea_ellipsoid(Params const& , Parameters & par) { detail::laea::setup_laea(par, this->m_proj_parm); } }; /*! \brief Lambert Azimuthal Equal Area projection \ingroup projections \tparam Geographic latlong point type \tparam Cartesian xy point type \tparam Parameters parameter type \par Projection characteristics - Azimuthal - Spheroid - Ellipsoid \par Example \image html ex_laea.gif */ template struct laea_spheroid : public detail::laea::base_laea_spheroid { template inline laea_spheroid(Params const& , Parameters & par) { detail::laea::setup_laea(par, this->m_proj_parm); } }; #ifndef DOXYGEN_NO_DETAIL namespace detail { // Static projection BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI2(srs::spar::proj_laea, laea_spheroid, laea_ellipsoid) // Factory entry(s) BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI2(laea_entry, laea_spheroid, laea_ellipsoid) BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(laea_init) { BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(laea, laea_entry) } } // namespace detail #endif // doxygen } // namespace projections }} // namespace boost::geometry #endif // BOOST_GEOMETRY_PROJECTIONS_LAEA_HPP