244 lines
10 KiB
C++
244 lines
10 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, 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_LABRD_HPP
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#define BOOST_GEOMETRY_PROJECTIONS_LABRD_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/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 labrd
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{
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static const double epsilon = 1.e-10;
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template <typename T>
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struct par_labrd
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{
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T Az, kRg, p0s, A, C, Ca, Cb, Cc, Cd;
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};
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template <typename T, typename Parameters>
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struct base_labrd_ellipsoid
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{
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par_labrd<T> m_proj_parm;
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// FORWARD(e_forward)
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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 const& 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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T V1, V2, ps, sinps, cosps, sinps2, cosps2;
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T I1, I2, I3, I4, I5, I6, x2, y2, t;
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V1 = this->m_proj_parm.A * log( tan(fourth_pi + .5 * lp_lat) );
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t = par.e * sin(lp_lat);
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V2 = .5 * par.e * this->m_proj_parm.A * log ((1. + t)/(1. - t));
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ps = 2. * (atan(exp(V1 - V2 + this->m_proj_parm.C)) - fourth_pi);
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I1 = ps - this->m_proj_parm.p0s;
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cosps = cos(ps); cosps2 = cosps * cosps;
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sinps = sin(ps); sinps2 = sinps * sinps;
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I4 = this->m_proj_parm.A * cosps;
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I2 = .5 * this->m_proj_parm.A * I4 * sinps;
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I3 = I2 * this->m_proj_parm.A * this->m_proj_parm.A * (5. * cosps2 - sinps2) / 12.;
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I6 = I4 * this->m_proj_parm.A * this->m_proj_parm.A;
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I5 = I6 * (cosps2 - sinps2) / 6.;
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I6 *= this->m_proj_parm.A * this->m_proj_parm.A *
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(5. * cosps2 * cosps2 + sinps2 * (sinps2 - 18. * cosps2)) / 120.;
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t = lp_lon * lp_lon;
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xy_x = this->m_proj_parm.kRg * lp_lon * (I4 + t * (I5 + t * I6));
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xy_y = this->m_proj_parm.kRg * (I1 + t * (I2 + t * I3));
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x2 = xy_x * xy_x;
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y2 = xy_y * xy_y;
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V1 = 3. * xy_x * y2 - xy_x * x2;
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V2 = xy_y * y2 - 3. * x2 * xy_y;
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xy_x += this->m_proj_parm.Ca * V1 + this->m_proj_parm.Cb * V2;
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xy_y += this->m_proj_parm.Ca * V2 - this->m_proj_parm.Cb * V1;
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}
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// INVERSE(e_inverse) ellipsoid & 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 xy_x, T xy_y, T& lp_lon, T& lp_lat) const
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{
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static const T fourth_pi = detail::fourth_pi<T>();
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/* t = 0.0 optimization is to avoid a false positive cppcheck warning */
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/* (cppcheck git beaf29c15867984aa3c2a15cf15bd7576ccde2b3). Might no */
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/* longer be necessary with later versions. */
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T x2, y2, V1, V2, V3, V4, t = 0.0, t2, ps, pe, tpe, s;
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T I7, I8, I9, I10, I11, d, Re;
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int i;
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x2 = xy_x * xy_x;
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y2 = xy_y * xy_y;
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V1 = 3. * xy_x * y2 - xy_x * x2;
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V2 = xy_y * y2 - 3. * x2 * xy_y;
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V3 = xy_x * (5. * y2 * y2 + x2 * (-10. * y2 + x2 ));
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V4 = xy_y * (5. * x2 * x2 + y2 * (-10. * x2 + y2 ));
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xy_x += - this->m_proj_parm.Ca * V1 - this->m_proj_parm.Cb * V2 + this->m_proj_parm.Cc * V3 + this->m_proj_parm.Cd * V4;
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xy_y += this->m_proj_parm.Cb * V1 - this->m_proj_parm.Ca * V2 - this->m_proj_parm.Cd * V3 + this->m_proj_parm.Cc * V4;
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ps = this->m_proj_parm.p0s + xy_y / this->m_proj_parm.kRg;
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pe = ps + par.phi0 - this->m_proj_parm.p0s;
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for ( i = 20; i; --i) {
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V1 = this->m_proj_parm.A * log(tan(fourth_pi + .5 * pe));
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tpe = par.e * sin(pe);
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V2 = .5 * par.e * this->m_proj_parm.A * log((1. + tpe)/(1. - tpe));
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t = ps - 2. * (atan(exp(V1 - V2 + this->m_proj_parm.C)) - fourth_pi);
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pe += t;
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if (fabs(t) < epsilon)
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break;
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}
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t = par.e * sin(pe);
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t = 1. - t * t;
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Re = par.one_es / ( t * sqrt(t) );
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t = tan(ps);
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t2 = t * t;
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s = this->m_proj_parm.kRg * this->m_proj_parm.kRg;
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d = Re * par.k0 * this->m_proj_parm.kRg;
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I7 = t / (2. * d);
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I8 = t * (5. + 3. * t2) / (24. * d * s);
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d = cos(ps) * this->m_proj_parm.kRg * this->m_proj_parm.A;
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I9 = 1. / d;
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d *= s;
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I10 = (1. + 2. * t2) / (6. * d);
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I11 = (5. + t2 * (28. + 24. * t2)) / (120. * d * s);
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x2 = xy_x * xy_x;
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lp_lat = pe + x2 * (-I7 + I8 * x2);
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lp_lon = xy_x * (I9 + x2 * (-I10 + x2 * I11));
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}
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static inline std::string get_name()
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{
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return "labrd_ellipsoid";
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}
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};
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// Laborde
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template <typename Params, typename Parameters, typename T>
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inline void setup_labrd(Params const& params, Parameters const& par, par_labrd<T>& proj_parm)
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{
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static const T fourth_pi = detail::fourth_pi<T>();
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T Az, sinp, R, N, t;
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Az = pj_get_param_r<T, srs::spar::azi>(params, "azi", srs::dpar::azi);
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sinp = sin(par.phi0);
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t = 1. - par.es * sinp * sinp;
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N = 1. / sqrt(t);
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R = par.one_es * N / t;
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proj_parm.kRg = par.k0 * sqrt( N * R );
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proj_parm.p0s = atan( sqrt(R / N) * tan(par.phi0) );
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proj_parm.A = sinp / sin(proj_parm.p0s);
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t = par.e * sinp;
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proj_parm.C = .5 * par.e * proj_parm.A * log((1. + t)/(1. - t)) +
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- proj_parm.A * log( tan(fourth_pi + .5 * par.phi0))
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+ log( tan(fourth_pi + .5 * proj_parm.p0s));
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t = Az + Az;
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proj_parm.Ca = (1. - cos(t)) * ( proj_parm.Cb = 1. / (12. * proj_parm.kRg * proj_parm.kRg) );
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proj_parm.Cb *= sin(t);
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proj_parm.Cc = 3. * (proj_parm.Ca * proj_parm.Ca - proj_parm.Cb * proj_parm.Cb);
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proj_parm.Cd = 6. * proj_parm.Ca * proj_parm.Cb;
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}
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}} // namespace detail::labrd
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#endif // doxygen
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/*!
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\brief Laborde 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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- Cylindrical
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- Spheroid
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- Special for Madagascar
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\par Projection parameters
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- no_rot: No rotation (boolean)
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- azi: Azimuth (or Gamma) (degrees)
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\par Example
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\image html ex_labrd.gif
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*/
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template <typename T, typename Parameters>
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struct labrd_ellipsoid : public detail::labrd::base_labrd_ellipsoid<T, Parameters>
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{
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template <typename Params>
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inline labrd_ellipsoid(Params const& params, Parameters const& par)
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{
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detail::labrd::setup_labrd(params, par, this->m_proj_parm);
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}
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};
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#ifndef DOXYGEN_NO_DETAIL
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namespace detail
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{
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// Static projection
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_labrd, labrd_ellipsoid)
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// Factory entry(s)
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(labrd_entry, labrd_ellipsoid)
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(labrd_init)
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{
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(labrd, labrd_entry)
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}
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} // namespace detail
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#endif // doxygen
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} // namespace projections
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}} // namespace boost::geometry
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#endif // BOOST_GEOMETRY_PROJECTIONS_LABRD_HPP
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