228 lines
9.2 KiB
C++
228 lines
9.2 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_VANDG_HPP
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#define BOOST_GEOMETRY_PROJECTIONS_VANDG_HPP
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#include <boost/geometry/util/math.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/projects.hpp>
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#include <boost/geometry/srs/projections/impl/factory_entry.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 vandg
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{
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static const double tolerance = 1.e-10;
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template <typename T>
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inline T C2_27() { return .07407407407407407407407407407407; }
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template <typename T>
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inline T PI4_3() { return boost::math::constants::four_thirds_pi<T>(); }
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template <typename T>
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inline T TPISQ() { return 19.739208802178717237668981999752; }
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template <typename T>
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inline T HPISQ() { return 4.9348022005446793094172454999381; }
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template <typename T, typename Parameters>
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struct base_vandg_spheroid
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{
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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 const& 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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static const T pi = detail::pi<T>();
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T al, al2, g, g2, p2;
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p2 = fabs(lp_lat / half_pi);
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if ((p2 - tolerance) > 1.) {
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BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
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}
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if (p2 > 1.)
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p2 = 1.;
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if (fabs(lp_lat) <= tolerance) {
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xy_x = lp_lon;
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xy_y = 0.;
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} else if (fabs(lp_lon) <= tolerance || fabs(p2 - 1.) < tolerance) {
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xy_x = 0.;
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xy_y = pi * tan(.5 * asin(p2));
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if (lp_lat < 0.) xy_y = -xy_y;
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} else {
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al = .5 * fabs(pi / lp_lon - lp_lon / pi);
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al2 = al * al;
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g = sqrt(1. - p2 * p2);
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g = g / (p2 + g - 1.);
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g2 = g * g;
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p2 = g * (2. / p2 - 1.);
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p2 = p2 * p2;
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xy_x = g - p2; g = p2 + al2;
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xy_x = pi * (al * xy_x + sqrt(al2 * xy_x * xy_x - g * (g2 - p2))) / g;
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if (lp_lon < 0.) xy_x = -xy_x;
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xy_y = fabs(xy_x / pi);
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xy_y = 1. - xy_y * (xy_y + 2. * al);
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if (xy_y < -tolerance) {
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BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
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}
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if (xy_y < 0.)
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xy_y = 0.;
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else
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xy_y = sqrt(xy_y) * (lp_lat < 0. ? -pi : pi);
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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& , T const& xy_x, T const& 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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static const T pi = detail::pi<T>();
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static const T pi_sqr = detail::pi_sqr<T>();
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static const T third = detail::third<T>();
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static const T two_pi = detail::two_pi<T>();
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static const T C2_27 = vandg::C2_27<T>();
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static const T PI4_3 = vandg::PI4_3<T>();
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static const T TPISQ = vandg::TPISQ<T>();
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static const T HPISQ = vandg::HPISQ<T>();
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T t, c0, c1, c2, c3, al, r2, r, m, d, ay, x2, y2;
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x2 = xy_x * xy_x;
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if ((ay = fabs(xy_y)) < tolerance) {
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lp_lat = 0.;
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t = x2 * x2 + TPISQ * (x2 + HPISQ);
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lp_lon = fabs(xy_x) <= tolerance ? 0. :
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.5 * (x2 - pi_sqr + sqrt(t)) / xy_x;
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return;
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}
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y2 = xy_y * xy_y;
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r = x2 + y2; r2 = r * r;
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c1 = - pi * ay * (r + pi_sqr);
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c3 = r2 + two_pi * (ay * r + pi * (y2 + pi * (ay + half_pi)));
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c2 = c1 + pi_sqr * (r - 3. * y2);
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c0 = pi * ay;
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c2 /= c3;
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al = c1 / c3 - third * c2 * c2;
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m = 2. * sqrt(-third * al);
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d = C2_27 * c2 * c2 * c2 + (c0 * c0 - third * c2 * c1) / c3;
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if (((t = fabs(d = 3. * d / (al * m))) - tolerance) <= 1.) {
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d = t > 1. ? (d > 0. ? 0. : pi) : acos(d);
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lp_lat = pi * (m * cos(d * third + PI4_3) - third * c2);
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if (xy_y < 0.) lp_lat = -lp_lat;
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t = r2 + TPISQ * (x2 - y2 + HPISQ);
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lp_lon = fabs(xy_x) <= tolerance ? 0. :
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.5 * (r - pi_sqr + (t <= 0. ? 0. : sqrt(t))) / xy_x;
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} else {
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BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
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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 "vandg_spheroid";
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}
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};
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// van der Grinten (I)
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template <typename Parameters>
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inline void setup_vandg(Parameters& par)
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{
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par.es = 0.;
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}
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}} // namespace detail::vandg
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#endif // doxygen
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/*!
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\brief van der Grinten (I) 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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- Miscellaneous
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- Spheroid
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\par Example
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\image html ex_vandg.gif
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*/
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template <typename T, typename Parameters>
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struct vandg_spheroid : public detail::vandg::base_vandg_spheroid<T, Parameters>
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{
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template <typename Params>
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inline vandg_spheroid(Params const& , Parameters & par)
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{
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detail::vandg::setup_vandg(par);
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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_vandg, vandg_spheroid)
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// Factory entry(s)
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(vandg_entry, vandg_spheroid)
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(vandg_init)
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{
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(vandg, vandg_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_VANDG_HPP
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