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+// Boost.Geometry (aka GGL, Generic Geometry Library)
+// This file is manually converted from PROJ4
+
+// Copyright (c) 2008-2012 Barend Gehrels, Amsterdam, the Netherlands.
+
+// This file was modified by Oracle on 2017.
+// Modifications copyright (c) 2017, Oracle and/or its affiliates.
+// Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
+
+// Use, modification and distribution is subject to the Boost Software License,
+// Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt)
+
+// This file is converted from PROJ4, http://trac.osgeo.org/proj
+// PROJ4 is originally written by Gerald Evenden (then of the USGS)
+// PROJ4 is maintained by Frank Warmerdam
+// PROJ4 is converted to Geometry Library by Barend Gehrels (Geodan, Amsterdam)
+
+// Original copyright notice:
+
+// Permission is hereby granted, free of charge, to any person obtaining a
+// copy of this software and associated documentation files (the "Software"),
+// to deal in the Software without restriction, including without limitation
+// the rights to use, copy, modify, merge, publish, distribute, sublicense,
+// and/or sell copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included
+// in all copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+// DEALINGS IN THE SOFTWARE.
+
+#ifndef BOOST_GEOMETRY_PROJECTIONS_IMPL_PJ_GAUSS_HPP
+#define BOOST_GEOMETRY_PROJECTIONS_IMPL_PJ_GAUSS_HPP
+
+
+#include <boost/geometry/util/math.hpp>
+
+
+namespace boost { namespace geometry { namespace projections {
+
+namespace detail { namespace gauss {
+
+
+static const int MAX_ITER = 20;
+
+template <typename T>
+struct GAUSS
+{
+ T C;
+ T K;
+ T e;
+ T ratexp;
+};
+
+template <typename T>
+inline T srat(T const& esinp, T const& exp)
+{
+ return (pow((1.0 - esinp) / (1.0 + esinp), exp));
+}
+
+template <typename T>
+inline GAUSS<T> gauss_ini(T const& e, T const& phi0, T& chi, T& rc)
+{
+ static const T FORTPI = detail::FORTPI<T>();
+
+ using std::asin;
+ using std::cos;
+ using std::sin;
+ using std::sqrt;
+ using std::tan;
+
+ T sphi = 0;
+ T cphi = 0;
+ T es = 0;
+
+ GAUSS<T> en;
+ es = e * e;
+ en.e = e;
+ sphi = sin(phi0);
+ cphi = cos(phi0);
+ cphi *= cphi;
+
+ rc = sqrt(1.0 - es) / (1.0 - es * sphi * sphi);
+ en.C = sqrt(1.0 + es * cphi * cphi / (1.0 - es));
+ chi = asin(sphi / en.C);
+ en.ratexp = 0.5 * en.C * e;
+ en.K = tan(0.5 * chi + FORTPI)
+ / (pow(tan(0.5 * phi0 + FORTPI), en.C) * srat(en.e * sphi, en.ratexp));
+
+ return en;
+}
+
+template <typename T>
+inline void gauss(GAUSS<T> const& en, T& lam, T& phi)
+{
+ static const T FORTPI = detail::FORTPI<T>();
+
+ phi = 2.0 * atan(en.K * pow(tan(0.5 * phi + FORTPI), en.C)
+ * srat(en.e * sin(phi), en.ratexp) ) - geometry::math::half_pi<T>();
+
+ lam *= en.C;
+}
+
+template <typename T>
+inline void inv_gauss(GAUSS<T> const& en, T& lam, T& phi)
+{
+ static const T FORTPI = detail::FORTPI<T>();
+ static const T DEL_TOL = 1e-14;
+
+ lam /= en.C;
+ const T num = pow(tan(0.5 * phi + FORTPI) / en.K, 1.0 / en.C);
+
+ int i = 0;
+ for (i = MAX_ITER; i; --i)
+ {
+ const T elp_phi = 2.0 * atan(num * srat(en.e * sin(phi), - 0.5 * en.e)) - geometry::math::half_pi<T>();
+
+ if (geometry::math::abs(elp_phi - phi) < DEL_TOL)
+ {
+ break;
+ }
+ phi = elp_phi;
+ }
+
+ /* convergence failed */
+ if (!i)
+ {
+ BOOST_THROW_EXCEPTION( projection_exception(-17) );
+ }
+}
+
+}} // namespace detail::gauss
+}}} // namespace boost::geometry::projections
+
+#endif // BOOST_GEOMETRY_PROJECTIONS_IMPL_PJ_GAUSS_HPP