547 lines
22 KiB
C++
547 lines
22 KiB
C++
// 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, 2018, 2019.
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// Modifications copyright (c) 2017-2019, 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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// 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_STERE_HPP
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#define BOOST_GEOMETRY_PROJECTIONS_STERE_HPP
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#include <boost/config.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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#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_param.hpp>
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#include <boost/geometry/srs/projections/impl/pj_tsfn.hpp>
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#include <boost/geometry/srs/projections/impl/projects.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 stere
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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-8;
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static const int n_iter = 8;
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static const double conv_tolerance = 1.e-10;
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enum mode_type {
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s_pole = 0,
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n_pole = 1,
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obliq = 2,
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equit = 3
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};
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template <typename T>
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struct par_stere
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{
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T phits;
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T sinX1;
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T cosX1;
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T akm1;
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mode_type mode;
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bool variant_c;
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};
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template <typename T>
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inline T ssfn_(T const& phit, T sinphi, T const& eccen)
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{
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static const T half_pi = detail::half_pi<T>();
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sinphi *= eccen;
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return (tan (.5 * (half_pi + phit)) *
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math::pow((T(1) - sinphi) / (T(1) + sinphi), T(0.5) * eccen));
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}
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template <typename T, typename Parameters>
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struct base_stere_ellipsoid
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{
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par_stere<T> m_proj_parm;
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// FORWARD(e_forward) ellipsoid
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// Project coordinates from geographic (lon, lat) to cartesian (x, y)
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inline void fwd(Parameters const& par, T const& lp_lon, T lp_lat, T& xy_x, T& xy_y) const
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{
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static const T half_pi = detail::half_pi<T>();
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T coslam, sinlam, sinX=0.0, cosX=0.0, X, A = 0.0, sinphi;
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coslam = cos(lp_lon);
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sinlam = sin(lp_lon);
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sinphi = sin(lp_lat);
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if (this->m_proj_parm.mode == obliq || this->m_proj_parm.mode == equit) {
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sinX = sin(X = 2. * atan(ssfn_(lp_lat, sinphi, par.e)) - half_pi);
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cosX = cos(X);
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}
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switch (this->m_proj_parm.mode) {
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case obliq:
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A = this->m_proj_parm.akm1 / (this->m_proj_parm.cosX1 * (1. + this->m_proj_parm.sinX1 * sinX +
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this->m_proj_parm.cosX1 * cosX * coslam));
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xy_y = A * (this->m_proj_parm.cosX1 * sinX - this->m_proj_parm.sinX1 * cosX * coslam);
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goto xmul; /* but why not just xy.x = A * cosX; break; ? */
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case equit:
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// TODO: calculate denominator once
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/* avoid zero division */
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if (1. + cosX * coslam == 0.0) {
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xy_y = HUGE_VAL;
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} else {
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A = this->m_proj_parm.akm1 / (1. + cosX * coslam);
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xy_y = A * sinX;
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}
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xmul:
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xy_x = A * cosX;
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break;
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case s_pole:
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lp_lat = -lp_lat;
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coslam = - coslam;
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sinphi = -sinphi;
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BOOST_FALLTHROUGH;
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case n_pole:
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// see IOGP Publication 373-7-2 – Geomatics Guidance Note number 7, part 2
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// December 2021 pg. 82
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if( m_proj_parm.variant_c )
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{
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auto t = pj_tsfn(lp_lat, sinphi, par.e);
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auto tf = pj_tsfn(this->m_proj_parm.phits,
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sin(this->m_proj_parm.phits),
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par.e);
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xy_x = this->m_proj_parm.akm1 * t;
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auto mf = this->m_proj_parm.akm1 * tf;
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xy_y = - xy_x * coslam - mf;
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} else {
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xy_x = this->m_proj_parm.akm1 * pj_tsfn(lp_lat, sinphi, par.e);
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xy_y = - xy_x * coslam;
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}
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break;
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}
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xy_x = xy_x * sinlam;
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}
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// INVERSE(e_inverse) ellipsoid
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// Project coordinates from cartesian (x, y) to geographic (lon, lat)
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inline void inv(Parameters const& par, T xy_x, T xy_y, T& lp_lon, T& lp_lat) const
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{
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static const T half_pi = detail::half_pi<T>();
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T cosphi, sinphi, tp=0.0, phi_l=0.0, rho, halfe=0.0, halfpi=0.0;
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T mf = 0;
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int i;
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rho = boost::math::hypot(xy_x, xy_y);
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switch (this->m_proj_parm.mode) {
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case obliq:
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case equit:
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cosphi = cos( tp = 2. * atan2(rho * this->m_proj_parm.cosX1 , this->m_proj_parm.akm1) );
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sinphi = sin(tp);
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if( rho == 0.0 )
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phi_l = asin(cosphi * this->m_proj_parm.sinX1);
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else
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phi_l = asin(cosphi * this->m_proj_parm.sinX1 + (xy_y * sinphi * this->m_proj_parm.cosX1 / rho));
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tp = tan(.5 * (half_pi + phi_l));
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xy_x *= sinphi;
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xy_y = rho * this->m_proj_parm.cosX1 * cosphi - xy_y * this->m_proj_parm.sinX1* sinphi;
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halfpi = half_pi;
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halfe = .5 * par.e;
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break;
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case n_pole:
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xy_y = -xy_y;
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BOOST_FALLTHROUGH;
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case s_pole:
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// see IOGP Publication 373-7-2 – Geomatics Guidance Note number 7, part 2
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// December 2021 pg. 82
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if( m_proj_parm.variant_c )
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{
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auto tf = pj_tsfn(this->m_proj_parm.phits,
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sin(this->m_proj_parm.phits),
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par.e);
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mf = this->m_proj_parm.akm1 * tf;
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rho = boost::math::hypot(xy_x, xy_y + mf);
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}
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phi_l = half_pi - 2. * atan(tp = - rho / this->m_proj_parm.akm1);
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halfpi = -half_pi;
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halfe = -.5 * par.e;
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break;
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}
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for (i = n_iter; i--; phi_l = lp_lat) {
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sinphi = par.e * sin(phi_l);
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lp_lat = T(2) * atan(tp * math::pow((T(1)+sinphi)/(T(1)-sinphi), halfe)) - halfpi;
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if (fabs(phi_l - lp_lat) < conv_tolerance) {
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if (this->m_proj_parm.mode == s_pole)
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lp_lat = -lp_lat;
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lp_lon = (xy_x == 0. && xy_y == 0.) ? 0. : atan2(xy_x, xy_y + mf);
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return;
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}
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}
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BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
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}
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static inline std::string get_name()
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{
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return "stere_ellipsoid";
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}
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};
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template <typename T, typename Parameters>
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struct base_stere_spheroid
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{
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par_stere<T> m_proj_parm;
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// FORWARD(s_forward) spheroid
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// Project coordinates from geographic (lon, lat) to cartesian (x, y)
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inline void fwd(Parameters const& , T const& lp_lon, T lp_lat, T& xy_x, T& xy_y) const
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{
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static const T fourth_pi = detail::fourth_pi<T>();
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static const T half_pi = detail::half_pi<T>();
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T sinphi, cosphi, coslam, sinlam;
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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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sinlam = sin(lp_lon);
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switch (this->m_proj_parm.mode) {
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case equit:
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xy_y = 1. + cosphi * coslam;
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goto oblcon;
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case obliq:
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xy_y = 1. + this->m_proj_parm.sinX1 * sinphi + this->m_proj_parm.cosX1 * cosphi * coslam;
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oblcon:
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if (xy_y <= epsilon10) {
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BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
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}
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xy_x = (xy_y = this->m_proj_parm.akm1 / xy_y) * cosphi * sinlam;
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xy_y *= (this->m_proj_parm.mode == equit) ? sinphi :
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this->m_proj_parm.cosX1 * sinphi - this->m_proj_parm.sinX1 * cosphi * coslam;
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break;
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case n_pole:
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coslam = - coslam;
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lp_lat = - lp_lat;
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BOOST_FALLTHROUGH;
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case s_pole:
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if (fabs(lp_lat - half_pi) < tolerance) {
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BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
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}
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xy_x = sinlam * ( xy_y = this->m_proj_parm.akm1 * tan(fourth_pi + .5 * lp_lat) );
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xy_y *= coslam;
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break;
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}
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}
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// INVERSE(s_inverse) spheroid
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// Project coordinates from cartesian (x, y) to geographic (lon, lat)
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inline void inv(Parameters const& par, T const& xy_x, T xy_y, T& lp_lon, T& lp_lat) const
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{
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T c, rh, sinc, cosc;
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sinc = sin(c = 2. * atan((rh = boost::math::hypot(xy_x, xy_y)) / this->m_proj_parm.akm1));
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cosc = cos(c);
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lp_lon = 0.;
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switch (this->m_proj_parm.mode) {
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case equit:
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if (fabs(rh) <= epsilon10)
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lp_lat = 0.;
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else
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lp_lat = asin(xy_y * sinc / rh);
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if (cosc != 0. || xy_x != 0.)
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lp_lon = atan2(xy_x * sinc, cosc * rh);
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break;
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case obliq:
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if (fabs(rh) <= epsilon10)
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lp_lat = par.phi0;
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else
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lp_lat = asin(cosc * this->m_proj_parm.sinX1 + xy_y * sinc * this->m_proj_parm.cosX1 / rh);
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if ((c = cosc - this->m_proj_parm.sinX1 * sin(lp_lat)) != 0. || xy_x != 0.)
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lp_lon = atan2(xy_x * sinc * this->m_proj_parm.cosX1, c * rh);
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break;
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case n_pole:
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xy_y = -xy_y;
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BOOST_FALLTHROUGH;
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case s_pole:
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if (fabs(rh) <= epsilon10)
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lp_lat = par.phi0;
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else
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lp_lat = asin(this->m_proj_parm.mode == s_pole ? - cosc : cosc);
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lp_lon = (xy_x == 0. && xy_y == 0.) ? 0. : atan2(xy_x, xy_y);
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break;
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}
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}
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static inline std::string get_name()
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{
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return "stere_spheroid";
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}
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};
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template <typename Parameters, typename T>
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inline void setup(Parameters const& par, par_stere<T>& proj_parm) /* general initialization */
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{
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static const T fourth_pi = detail::fourth_pi<T>();
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static const T half_pi = detail::half_pi<T>();
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T t;
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if (fabs((t = fabs(par.phi0)) - half_pi) < epsilon10)
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proj_parm.mode = par.phi0 < 0. ? s_pole : n_pole;
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else
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proj_parm.mode = t > epsilon10 ? obliq : equit;
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proj_parm.phits = fabs(proj_parm.phits);
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if (par.es != 0.0) {
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T X;
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switch (proj_parm.mode) {
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case n_pole:
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case s_pole:
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if (fabs(proj_parm.phits - half_pi) < epsilon10)
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proj_parm.akm1 = 2. * par.k0 /
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sqrt(math::pow(T(1)+par.e,T(1)+par.e)*math::pow(T(1)-par.e,T(1)-par.e));
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else {
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proj_parm.akm1 = cos(proj_parm.phits) /
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pj_tsfn(proj_parm.phits, t = sin(proj_parm.phits), par.e);
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t *= par.e;
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proj_parm.akm1 /= sqrt(1. - t * t);
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}
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break;
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case equit:
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case obliq:
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t = sin(par.phi0);
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X = 2. * atan(ssfn_(par.phi0, t, par.e)) - half_pi;
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t *= par.e;
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proj_parm.akm1 = 2. * par.k0 * cos(par.phi0) / sqrt(1. - t * t);
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proj_parm.sinX1 = sin(X);
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proj_parm.cosX1 = cos(X);
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break;
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}
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} else {
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switch (proj_parm.mode) {
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case obliq:
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proj_parm.sinX1 = sin(par.phi0);
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proj_parm.cosX1 = cos(par.phi0);
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BOOST_FALLTHROUGH;
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case equit:
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proj_parm.akm1 = 2. * par.k0;
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break;
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case s_pole:
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case n_pole:
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proj_parm.akm1 = fabs(proj_parm.phits - half_pi) >= epsilon10 ?
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cos(proj_parm.phits) / tan(fourth_pi - .5 * proj_parm.phits) :
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2. * par.k0 ;
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break;
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}
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}
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}
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// Stereographic
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template <typename Params, typename Parameters, typename T>
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inline void setup_stere(Params const& params, Parameters const& par, par_stere<T>& proj_parm)
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{
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static const T half_pi = detail::half_pi<T>();
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if (! pj_param_r<srs::spar::lat_ts>(params, "lat_ts", srs::dpar::lat_ts, proj_parm.phits))
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proj_parm.phits = half_pi;
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proj_parm.variant_c = false;
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if (pj_param_exists<srs::spar::variant_c>(params, "variant_c", srs::dpar::variant_c))
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proj_parm.variant_c = true;
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setup(par, proj_parm);
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}
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// Universal Polar Stereographic
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template <typename Params, typename Parameters, typename T>
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inline void setup_ups(Params const& params, Parameters& par, par_stere<T>& proj_parm)
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{
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static const T half_pi = detail::half_pi<T>();
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/* International Ellipsoid */
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par.phi0 = pj_get_param_b<srs::spar::south>(params, "south", srs::dpar::south) ? -half_pi: half_pi;
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if (par.es == 0.0) {
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BOOST_THROW_EXCEPTION( projection_exception(error_ellipsoid_use_required) );
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}
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par.k0 = .994;
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par.x0 = 2000000.;
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par.y0 = 2000000.;
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proj_parm.phits = half_pi;
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par.lam0 = 0.;
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setup(par, proj_parm);
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}
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}} // namespace detail::stere
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#endif // doxygen
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/*!
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\brief Stereographic projection
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\ingroup projections
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\tparam Geographic latlong point type
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\tparam Cartesian xy point type
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\tparam Parameters parameter type
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\par Projection characteristics
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- Azimuthal
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- Spheroid
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- Ellipsoid
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\par Projection parameters
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- lat_ts: Latitude of true scale (degrees)
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\par Example
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\image html ex_stere.gif
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*/
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template <typename T, typename Parameters>
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struct stere_ellipsoid : public detail::stere::base_stere_ellipsoid<T, Parameters>
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{
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template <typename Params>
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inline stere_ellipsoid(Params const& params, Parameters const& par)
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{
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detail::stere::setup_stere(params, par, this->m_proj_parm);
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}
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};
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/*!
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\brief Stereographic projection
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\ingroup projections
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\tparam Geographic latlong point type
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\tparam Cartesian xy point type
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\tparam Parameters parameter type
|
||
\par Projection characteristics
|
||
- Azimuthal
|
||
- Spheroid
|
||
- Ellipsoid
|
||
\par Projection parameters
|
||
- lat_ts: Latitude of true scale (degrees)
|
||
\par Example
|
||
\image html ex_stere.gif
|
||
*/
|
||
template <typename T, typename Parameters>
|
||
struct stere_spheroid : public detail::stere::base_stere_spheroid<T, Parameters>
|
||
{
|
||
template <typename Params>
|
||
inline stere_spheroid(Params const& params, Parameters const& par)
|
||
{
|
||
detail::stere::setup_stere(params, par, this->m_proj_parm);
|
||
}
|
||
};
|
||
|
||
/*!
|
||
\brief Universal Polar Stereographic 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
|
||
- south: Denotes southern hemisphere UTM zone (boolean)
|
||
\par Example
|
||
\image html ex_ups.gif
|
||
*/
|
||
template <typename T, typename Parameters>
|
||
struct ups_ellipsoid : public detail::stere::base_stere_ellipsoid<T, Parameters>
|
||
{
|
||
template <typename Params>
|
||
inline ups_ellipsoid(Params const& params, Parameters & par)
|
||
{
|
||
detail::stere::setup_ups(params, par, this->m_proj_parm);
|
||
}
|
||
};
|
||
|
||
/*!
|
||
\brief Universal Polar Stereographic 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
|
||
- south: Denotes southern hemisphere UTM zone (boolean)
|
||
\par Example
|
||
\image html ex_ups.gif
|
||
*/
|
||
template <typename T, typename Parameters>
|
||
struct ups_spheroid : public detail::stere::base_stere_spheroid<T, Parameters>
|
||
{
|
||
template <typename Params>
|
||
inline ups_spheroid(Params const& params, Parameters & par)
|
||
{
|
||
detail::stere::setup_ups(params, par, this->m_proj_parm);
|
||
}
|
||
};
|
||
|
||
#ifndef DOXYGEN_NO_DETAIL
|
||
namespace detail
|
||
{
|
||
|
||
// Static projection
|
||
BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI2(srs::spar::proj_stere, stere_spheroid, stere_ellipsoid)
|
||
BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI2(srs::spar::proj_ups, ups_spheroid, ups_ellipsoid)
|
||
|
||
// Factory entry(s)
|
||
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI2(stere_entry, stere_spheroid, stere_ellipsoid)
|
||
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI2(ups_entry, ups_spheroid, ups_ellipsoid)
|
||
|
||
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(stere_init)
|
||
{
|
||
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(stere, stere_entry)
|
||
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(ups, ups_entry)
|
||
}
|
||
|
||
} // namespace detail
|
||
#endif // doxygen
|
||
|
||
} // namespace projections
|
||
|
||
}} // namespace boost::geometry
|
||
|
||
#endif // BOOST_GEOMETRY_PROJECTIONS_STERE_HPP
|
||
|