146 lines
4.3 KiB
C++
146 lines
4.3 KiB
C++
// Boost.Geometry (aka GGL, Generic Geometry Library)
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// This file is manually converted from PROJ4
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// Copyright (c) 2008-2012 Barend Gehrels, Amsterdam, the Netherlands.
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// This file was modified by Oracle on 2017, 2018.
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// Modifications copyright (c) 2017-2018, 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 Geometry Library by Barend Gehrels (Geodan, Amsterdam)
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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_IMPL_PJ_GAUSS_HPP
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#define BOOST_GEOMETRY_PROJECTIONS_IMPL_PJ_GAUSS_HPP
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#include <boost/geometry/srs/projections/constants.hpp>
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#include <boost/geometry/srs/projections/exception.hpp>
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namespace boost { namespace geometry { namespace projections {
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namespace detail {
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template <typename T>
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struct gauss
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{
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T C;
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T K;
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T e;
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T ratexp;
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};
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template <typename T>
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inline T srat(T const& esinp, T const& exp)
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{
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return (math::pow((T(1) - esinp) / (T(1) + esinp), exp));
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}
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template <typename T>
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inline gauss<T> gauss_ini(T const& e, T const& phi0, T& chi, T& rc)
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{
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static const T fourth_pi = detail::fourth_pi<T>();
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using std::asin;
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using std::cos;
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using std::sin;
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using std::sqrt;
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using std::tan;
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T sphi = 0;
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T cphi = 0;
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T es = 0;
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gauss<T> en;
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es = e * e;
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en.e = e;
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sphi = sin(phi0);
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cphi = cos(phi0);
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cphi *= cphi;
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rc = sqrt(1.0 - es) / (1.0 - es * sphi * sphi);
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en.C = sqrt(1.0 + es * cphi * cphi / (1.0 - es));
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chi = asin(sphi / en.C);
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en.ratexp = 0.5 * en.C * e;
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en.K = tan(0.5 * chi + fourth_pi)
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/ (math::pow(tan(T(0.5) * phi0 + fourth_pi), en.C) * srat(en.e * sphi, en.ratexp));
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return en;
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}
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template <typename T>
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inline void gauss_fwd(gauss<T> const& en, T& lam, T& phi)
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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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phi = T(2) * atan(en.K * math::pow(tan(T(0.5) * phi + fourth_pi), en.C)
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* srat(en.e * sin(phi), en.ratexp) ) - half_pi;
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lam *= en.C;
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}
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template <typename T>
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inline void gauss_inv(gauss<T> const& en, T& lam, T& phi)
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{
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static const int max_iter = 20;
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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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static const T del_tol = 1e-14;
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lam /= en.C;
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const T num = math::pow(tan(T(0.5) * phi + fourth_pi) / en.K, T(1) / en.C);
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int i = 0;
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for (i = max_iter; i; --i)
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{
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const T elp_phi = 2.0 * atan(num * srat(en.e * sin(phi), - 0.5 * en.e)) - half_pi;
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if (geometry::math::abs(elp_phi - phi) < del_tol)
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{
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break;
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}
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phi = elp_phi;
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}
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/* convergence failed */
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if (!i)
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{
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BOOST_THROW_EXCEPTION( projection_exception(error_non_conv_inv_meri_dist) );
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}
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}
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} // namespace detail
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}}} // namespace boost::geometry::projections
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#endif // BOOST_GEOMETRY_PROJECTIONS_IMPL_PJ_GAUSS_HPP
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