552 lines
22 KiB
C++
552 lines
22 KiB
C++
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// Boost.Geometry - gis-projections (based on PROJ4)
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// Copyright (c) 2008-2015 Barend Gehrels, Amsterdam, the Netherlands.
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// This file was modified by Oracle on 2017-2020.
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// Modifications copyright (c) 2017-2020, Oracle and/or its affiliates.
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// Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle.
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// Use, modification and distribution is subject to the Boost Software License,
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// Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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// This file is converted from PROJ4, http://trac.osgeo.org/proj
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// PROJ4 is originally written by Gerald Evenden (then of the USGS)
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// PROJ4 is maintained by Frank Warmerdam
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// PROJ4 is converted to Boost.Geometry by Barend Gehrels
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// Last updated version of proj: 5.0.0
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// Original copyright notice:
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// Purpose: Implementation of the aeqd (Azimuthal Equidistant) projection.
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// Author: Gerald Evenden
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// Copyright (c) 1995, Gerald Evenden
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// Permission is hereby granted, free of charge, to any person obtaining a
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// copy of this software and associated documentation files (the "Software"),
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// to deal in the Software without restriction, including without limitation
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// the rights to use, copy, modify, merge, publish, distribute, sublicense,
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// and/or sell copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following conditions:
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// The above copyright notice and this permission notice shall be included
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// in all copies or substantial portions of the Software.
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
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// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
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// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
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// DEALINGS IN THE SOFTWARE.
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#ifndef BOOST_GEOMETRY_PROJECTIONS_AEQD_HPP
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#define BOOST_GEOMETRY_PROJECTIONS_AEQD_HPP
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#include <type_traits>
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#include <boost/config.hpp>
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#include <boost/geometry/formulas/vincenty_direct.hpp>
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#include <boost/geometry/formulas/vincenty_inverse.hpp>
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#include <boost/geometry/srs/projections/impl/aasincos.hpp>
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#include <boost/geometry/srs/projections/impl/base_static.hpp>
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#include <boost/geometry/srs/projections/impl/base_dynamic.hpp>
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#include <boost/geometry/srs/projections/impl/factory_entry.hpp>
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#include <boost/geometry/srs/projections/impl/pj_mlfn.hpp>
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#include <boost/geometry/srs/projections/impl/pj_param.hpp>
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#include <boost/geometry/srs/projections/impl/projects.hpp>
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#include <boost/geometry/util/math.hpp>
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#include <boost/math/special_functions/hypot.hpp>
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namespace boost { namespace geometry
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{
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namespace projections
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{
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#ifndef DOXYGEN_NO_DETAIL
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namespace detail { namespace aeqd
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{
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static const double epsilon10 = 1.e-10;
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static const double tolerance = 1.e-14;
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enum mode_type {
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n_pole = 0,
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s_pole = 1,
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equit = 2,
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obliq = 3
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};
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template <typename T>
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struct par_aeqd
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{
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T sinph0;
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T cosph0;
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detail::en<T> en;
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T M1;
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//T N1;
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T Mp;
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//T He;
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//T G;
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T b;
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mode_type mode;
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};
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template <typename T, typename Par, typename ProjParm>
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inline void e_forward(T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y, Par const& par, ProjParm const& proj_parm)
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{
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T coslam, cosphi, sinphi, rho;
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//T azi1, s12;
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//T lam1, phi1, lam2, phi2;
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coslam = cos(lp_lon);
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cosphi = cos(lp_lat);
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sinphi = sin(lp_lat);
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switch (proj_parm.mode) {
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case n_pole:
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coslam = - coslam;
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BOOST_FALLTHROUGH;
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case s_pole:
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xy_x = (rho = fabs(proj_parm.Mp - pj_mlfn(lp_lat, sinphi, cosphi, proj_parm.en))) *
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sin(lp_lon);
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xy_y = rho * coslam;
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break;
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case equit:
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case obliq:
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if (fabs(lp_lon) < epsilon10 && fabs(lp_lat - par.phi0) < epsilon10) {
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xy_x = xy_y = 0.;
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break;
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}
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//phi1 = par.phi0; lam1 = par.lam0;
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//phi2 = lp_lat; lam2 = lp_lon + par.lam0;
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formula::result_inverse<T> const inv =
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formula::vincenty_inverse
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<
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T, true, true
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>::apply(par.lam0, par.phi0, lp_lon + par.lam0, lp_lat, srs::spheroid<T>(par.a, proj_parm.b));
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//azi1 = inv.azimuth; s12 = inv.distance;
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xy_x = inv.distance * sin(inv.azimuth) / par.a;
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xy_y = inv.distance * cos(inv.azimuth) / par.a;
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break;
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}
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}
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template <typename T, typename Par, typename ProjParm>
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inline void e_inverse(T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat, Par const& par, ProjParm const& proj_parm)
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{
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T c;
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if ((c = boost::math::hypot(xy_x, xy_y)) < epsilon10) {
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lp_lat = par.phi0;
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lp_lon = 0.;
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return;
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}
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if (proj_parm.mode == obliq || proj_parm.mode == equit) {
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T const x2 = xy_x * par.a;
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T const y2 = xy_y * par.a;
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//T const lat1 = par.phi0;
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//T const lon1 = par.lam0;
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T const azi1 = atan2(x2, y2);
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T const s12 = sqrt(x2 * x2 + y2 * y2);
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formula::result_direct<T> const dir =
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formula::vincenty_direct
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<
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T, true
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>::apply(par.lam0, par.phi0, s12, azi1, srs::spheroid<T>(par.a, proj_parm.b));
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lp_lat = dir.lat2;
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lp_lon = dir.lon2;
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lp_lon -= par.lam0;
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} else { /* Polar */
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lp_lat = pj_inv_mlfn(proj_parm.mode == n_pole ? proj_parm.Mp - c : proj_parm.Mp + c,
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par.es, proj_parm.en);
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lp_lon = atan2(xy_x, proj_parm.mode == n_pole ? -xy_y : xy_y);
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}
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}
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template <typename T, typename Par, typename ProjParm>
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inline void e_guam_fwd(T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y, Par const& par, ProjParm const& proj_parm)
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{
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T cosphi, sinphi, t;
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cosphi = cos(lp_lat);
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sinphi = sin(lp_lat);
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t = 1. / sqrt(1. - par.es * sinphi * sinphi);
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xy_x = lp_lon * cosphi * t;
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xy_y = pj_mlfn(lp_lat, sinphi, cosphi, proj_parm.en) - proj_parm.M1 +
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.5 * lp_lon * lp_lon * cosphi * sinphi * t;
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}
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template <typename T, typename Par, typename ProjParm>
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inline void e_guam_inv(T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat, Par const& par, ProjParm const& proj_parm)
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{
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T x2, t = 0.0;
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int i;
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x2 = 0.5 * xy_x * xy_x;
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lp_lat = par.phi0;
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for (i = 0; i < 3; ++i) {
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t = par.e * sin(lp_lat);
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lp_lat = pj_inv_mlfn(proj_parm.M1 + xy_y -
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x2 * tan(lp_lat) * (t = sqrt(1. - t * t)), par.es, proj_parm.en);
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}
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lp_lon = xy_x * t / cos(lp_lat);
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}
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template <typename T, typename Par, typename ProjParm>
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inline void s_forward(T const& lp_lon, T lp_lat, T& xy_x, T& xy_y, Par const& /*par*/, ProjParm const& proj_parm)
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{
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static const T half_pi = detail::half_pi<T>();
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T coslam, cosphi, sinphi;
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sinphi = sin(lp_lat);
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cosphi = cos(lp_lat);
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coslam = cos(lp_lon);
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switch (proj_parm.mode) {
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case equit:
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xy_y = cosphi * coslam;
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goto oblcon;
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case obliq:
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xy_y = proj_parm.sinph0 * sinphi + proj_parm.cosph0 * cosphi * coslam;
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oblcon:
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if (fabs(fabs(xy_y) - 1.) < tolerance)
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if (xy_y < 0.)
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BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
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else
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xy_x = xy_y = 0.;
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else {
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xy_y = acos(xy_y);
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xy_y /= sin(xy_y);
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xy_x = xy_y * cosphi * sin(lp_lon);
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xy_y *= (proj_parm.mode == equit) ? sinphi :
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proj_parm.cosph0 * sinphi - proj_parm.sinph0 * cosphi * coslam;
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}
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break;
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case n_pole:
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lp_lat = -lp_lat;
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coslam = -coslam;
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BOOST_FALLTHROUGH;
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case s_pole:
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if (fabs(lp_lat - half_pi) < epsilon10)
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BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
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xy_x = (xy_y = (half_pi + lp_lat)) * sin(lp_lon);
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xy_y *= coslam;
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break;
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}
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}
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template <typename T, typename Par, typename ProjParm>
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inline void s_inverse(T xy_x, T xy_y, T& lp_lon, T& lp_lat, Par const& par, ProjParm const& proj_parm)
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{
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static const T pi = detail::pi<T>();
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static const T half_pi = detail::half_pi<T>();
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T cosc, c_rh, sinc;
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if ((c_rh = boost::math::hypot(xy_x, xy_y)) > pi) {
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if (c_rh - epsilon10 > pi)
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BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
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c_rh = pi;
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} else if (c_rh < epsilon10) {
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lp_lat = par.phi0;
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lp_lon = 0.;
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return;
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}
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if (proj_parm.mode == obliq || proj_parm.mode == equit) {
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sinc = sin(c_rh);
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cosc = cos(c_rh);
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if (proj_parm.mode == equit) {
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lp_lat = aasin(xy_y * sinc / c_rh);
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xy_x *= sinc;
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xy_y = cosc * c_rh;
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} else {
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lp_lat = aasin(cosc * proj_parm.sinph0 + xy_y * sinc * proj_parm.cosph0 /
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c_rh);
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xy_y = (cosc - proj_parm.sinph0 * sin(lp_lat)) * c_rh;
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xy_x *= sinc * proj_parm.cosph0;
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}
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lp_lon = xy_y == 0. ? 0. : atan2(xy_x, xy_y);
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} else if (proj_parm.mode == n_pole) {
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lp_lat = half_pi - c_rh;
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lp_lon = atan2(xy_x, -xy_y);
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} else {
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lp_lat = c_rh - half_pi;
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lp_lon = atan2(xy_x, xy_y);
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}
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}
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// Azimuthal Equidistant
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template <typename Params, typename Parameters, typename T>
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inline void setup_aeqd(Params const& params, Parameters& par, par_aeqd<T>& proj_parm, bool is_sphere, bool is_guam)
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{
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static const T half_pi = detail::half_pi<T>();
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par.phi0 = pj_get_param_r<T, srs::spar::lat_0>(params, "lat_0", srs::dpar::lat_0);
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if (fabs(fabs(par.phi0) - half_pi) < epsilon10) {
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proj_parm.mode = par.phi0 < 0. ? s_pole : n_pole;
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proj_parm.sinph0 = par.phi0 < 0. ? -1. : 1.;
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proj_parm.cosph0 = 0.;
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} else if (fabs(par.phi0) < epsilon10) {
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proj_parm.mode = equit;
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proj_parm.sinph0 = 0.;
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proj_parm.cosph0 = 1.;
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} else {
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proj_parm.mode = obliq;
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proj_parm.sinph0 = sin(par.phi0);
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proj_parm.cosph0 = cos(par.phi0);
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}
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if (is_sphere) {
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/* empty */
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} else {
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proj_parm.en = pj_enfn<T>(par.es);
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if (is_guam) {
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proj_parm.M1 = pj_mlfn(par.phi0, proj_parm.sinph0, proj_parm.cosph0, proj_parm.en);
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} else {
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switch (proj_parm.mode) {
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case n_pole:
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proj_parm.Mp = pj_mlfn<T>(half_pi, 1., 0., proj_parm.en);
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break;
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case s_pole:
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proj_parm.Mp = pj_mlfn<T>(-half_pi, -1., 0., proj_parm.en);
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break;
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case equit:
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case obliq:
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//proj_parm.N1 = 1. / sqrt(1. - par.es * proj_parm.sinph0 * proj_parm.sinph0);
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//proj_parm.G = proj_parm.sinph0 * (proj_parm.He = par.e / sqrt(par.one_es));
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//proj_parm.He *= proj_parm.cosph0;
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break;
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}
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// Boost.Geometry specific, in proj4 geodesic is initialized at the beginning
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||
|
|
proj_parm.b = math::sqrt(math::sqr(par.a) * (1. - par.es));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename T, typename Parameters>
|
||
|
|
struct base_aeqd_e
|
||
|
|
{
|
||
|
|
par_aeqd<T> m_proj_parm;
|
||
|
|
|
||
|
|
// FORWARD(e_forward) elliptical
|
||
|
|
// 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
|
||
|
|
{
|
||
|
|
e_forward(lp_lon, lp_lat, xy_x, xy_y, par, this->m_proj_parm);
|
||
|
|
}
|
||
|
|
|
||
|
|
// INVERSE(e_inverse) elliptical
|
||
|
|
// Project coordinates from cartesian (x, y) to geographic (lon, lat)
|
||
|
|
inline void inv(Parameters const& par, T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const
|
||
|
|
{
|
||
|
|
e_inverse(xy_x, xy_y, lp_lon, lp_lat, par, this->m_proj_parm);
|
||
|
|
}
|
||
|
|
|
||
|
|
static inline std::string get_name()
|
||
|
|
{
|
||
|
|
return "aeqd_e";
|
||
|
|
}
|
||
|
|
|
||
|
|
};
|
||
|
|
|
||
|
|
template <typename T, typename Parameters>
|
||
|
|
struct base_aeqd_e_guam
|
||
|
|
{
|
||
|
|
par_aeqd<T> m_proj_parm;
|
||
|
|
|
||
|
|
// FORWARD(e_guam_fwd) Guam elliptical
|
||
|
|
// 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
|
||
|
|
{
|
||
|
|
e_guam_fwd(lp_lon, lp_lat, xy_x, xy_y, par, this->m_proj_parm);
|
||
|
|
}
|
||
|
|
|
||
|
|
// INVERSE(e_guam_inv) Guam elliptical
|
||
|
|
// Project coordinates from cartesian (x, y) to geographic (lon, lat)
|
||
|
|
inline void inv(Parameters const& par, T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const
|
||
|
|
{
|
||
|
|
e_guam_inv(xy_x, xy_y, lp_lon, lp_lat, par, this->m_proj_parm);
|
||
|
|
}
|
||
|
|
|
||
|
|
static inline std::string get_name()
|
||
|
|
{
|
||
|
|
return "aeqd_e_guam";
|
||
|
|
}
|
||
|
|
|
||
|
|
};
|
||
|
|
|
||
|
|
template <typename T, typename Parameters>
|
||
|
|
struct base_aeqd_s
|
||
|
|
{
|
||
|
|
par_aeqd<T> m_proj_parm;
|
||
|
|
|
||
|
|
// FORWARD(s_forward) spherical
|
||
|
|
// 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
|
||
|
|
{
|
||
|
|
s_forward(lp_lon, lp_lat, xy_x, xy_y, par, this->m_proj_parm);
|
||
|
|
}
|
||
|
|
|
||
|
|
// INVERSE(s_inverse) spherical
|
||
|
|
// Project coordinates from cartesian (x, y) to geographic (lon, lat)
|
||
|
|
inline void inv(Parameters const& par, T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const
|
||
|
|
{
|
||
|
|
s_inverse(xy_x, xy_y, lp_lon, lp_lat, par, this->m_proj_parm);
|
||
|
|
}
|
||
|
|
|
||
|
|
static inline std::string get_name()
|
||
|
|
{
|
||
|
|
return "aeqd_s";
|
||
|
|
}
|
||
|
|
|
||
|
|
};
|
||
|
|
|
||
|
|
}} // namespace detail::aeqd
|
||
|
|
#endif // doxygen
|
||
|
|
|
||
|
|
/*!
|
||
|
|
\brief Azimuthal Equidistant projection
|
||
|
|
\ingroup projections
|
||
|
|
\tparam Geographic latlong point type
|
||
|
|
\tparam Cartesian xy point type
|
||
|
|
\tparam Parameters parameter type
|
||
|
|
\par Projection characteristics
|
||
|
|
- Azimuthal
|
||
|
|
- Spheroid
|
||
|
|
- Ellipsoid
|
||
|
|
\par Projection parameters
|
||
|
|
- lat_0: Latitude of origin (degrees)
|
||
|
|
- guam (boolean)
|
||
|
|
\par Example
|
||
|
|
\image html ex_aeqd.gif
|
||
|
|
*/
|
||
|
|
template <typename T, typename Parameters>
|
||
|
|
struct aeqd_e : public detail::aeqd::base_aeqd_e<T, Parameters>
|
||
|
|
{
|
||
|
|
template <typename Params>
|
||
|
|
inline aeqd_e(Params const& params, Parameters & par)
|
||
|
|
{
|
||
|
|
detail::aeqd::setup_aeqd(params, par, this->m_proj_parm, false, false);
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
/*!
|
||
|
|
\brief Azimuthal Equidistant projection
|
||
|
|
\ingroup projections
|
||
|
|
\tparam Geographic latlong point type
|
||
|
|
\tparam Cartesian xy point type
|
||
|
|
\tparam Parameters parameter type
|
||
|
|
\par Projection characteristics
|
||
|
|
- Azimuthal
|
||
|
|
- Spheroid
|
||
|
|
- Ellipsoid
|
||
|
|
\par Projection parameters
|
||
|
|
- lat_0: Latitude of origin (degrees)
|
||
|
|
- guam (boolean)
|
||
|
|
\par Example
|
||
|
|
\image html ex_aeqd.gif
|
||
|
|
*/
|
||
|
|
template <typename T, typename Parameters>
|
||
|
|
struct aeqd_e_guam : public detail::aeqd::base_aeqd_e_guam<T, Parameters>
|
||
|
|
{
|
||
|
|
template <typename Params>
|
||
|
|
inline aeqd_e_guam(Params const& params, Parameters & par)
|
||
|
|
{
|
||
|
|
detail::aeqd::setup_aeqd(params, par, this->m_proj_parm, false, true);
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
/*!
|
||
|
|
\brief Azimuthal Equidistant projection
|
||
|
|
\ingroup projections
|
||
|
|
\tparam Geographic latlong point type
|
||
|
|
\tparam Cartesian xy point type
|
||
|
|
\tparam Parameters parameter type
|
||
|
|
\par Projection characteristics
|
||
|
|
- Azimuthal
|
||
|
|
- Spheroid
|
||
|
|
- Ellipsoid
|
||
|
|
\par Projection parameters
|
||
|
|
- lat_0: Latitude of origin (degrees)
|
||
|
|
- guam (boolean)
|
||
|
|
\par Example
|
||
|
|
\image html ex_aeqd.gif
|
||
|
|
*/
|
||
|
|
template <typename T, typename Parameters>
|
||
|
|
struct aeqd_s : public detail::aeqd::base_aeqd_s<T, Parameters>
|
||
|
|
{
|
||
|
|
template <typename Params>
|
||
|
|
inline aeqd_s(Params const& params, Parameters & par)
|
||
|
|
{
|
||
|
|
detail::aeqd::setup_aeqd(params, par, this->m_proj_parm, true, false);
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
#ifndef DOXYGEN_NO_DETAIL
|
||
|
|
namespace detail
|
||
|
|
{
|
||
|
|
|
||
|
|
// Static projection
|
||
|
|
template <typename BGP, typename CT, typename P>
|
||
|
|
struct static_projection_type<srs::spar::proj_aeqd, srs_sphere_tag, BGP, CT, P>
|
||
|
|
{
|
||
|
|
typedef static_wrapper_fi<aeqd_s<CT, P>, P> type;
|
||
|
|
};
|
||
|
|
template <typename BGP, typename CT, typename P>
|
||
|
|
struct static_projection_type<srs::spar::proj_aeqd, srs_spheroid_tag, BGP, CT, P>
|
||
|
|
{
|
||
|
|
typedef static_wrapper_fi
|
||
|
|
<
|
||
|
|
std::conditional_t
|
||
|
|
<
|
||
|
|
std::is_void
|
||
|
|
<
|
||
|
|
typename geometry::tuples::find_if
|
||
|
|
<
|
||
|
|
BGP,
|
||
|
|
//srs::par4::detail::is_guam
|
||
|
|
srs::spar::detail::is_param<srs::spar::guam>::pred
|
||
|
|
>::type
|
||
|
|
>::value,
|
||
|
|
aeqd_e<CT, P>,
|
||
|
|
aeqd_e_guam<CT, P>
|
||
|
|
>
|
||
|
|
, P
|
||
|
|
> type;
|
||
|
|
};
|
||
|
|
|
||
|
|
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_BEGIN(aeqd_entry)
|
||
|
|
{
|
||
|
|
bool const guam = pj_get_param_b<srs::spar::guam>(params, "guam", srs::dpar::guam);
|
||
|
|
|
||
|
|
if (parameters.es && ! guam)
|
||
|
|
return new dynamic_wrapper_fi<aeqd_e<T, Parameters>, T, Parameters>(params, parameters);
|
||
|
|
else if (parameters.es && guam)
|
||
|
|
return new dynamic_wrapper_fi<aeqd_e_guam<T, Parameters>, T, Parameters>(params, parameters);
|
||
|
|
else
|
||
|
|
return new dynamic_wrapper_fi<aeqd_s<T, Parameters>, T, Parameters>(params, parameters);
|
||
|
|
}
|
||
|
|
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_END
|
||
|
|
|
||
|
|
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(aeqd_init)
|
||
|
|
{
|
||
|
|
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(aeqd, aeqd_entry)
|
||
|
|
}
|
||
|
|
|
||
|
|
} // namespace detail
|
||
|
|
#endif // doxygen
|
||
|
|
|
||
|
|
} // namespace projections
|
||
|
|
|
||
|
|
}} // namespace boost::geometry
|
||
|
|
|
||
|
|
#endif // BOOST_GEOMETRY_PROJECTIONS_AEQD_HPP
|
||
|
|
|