// 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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// Purpose: Implementation of the krovak (Krovak) projection.
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// Definition: http://www.ihsenergy.com/epsg/guid7.html#1.4.3
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// Author: Thomas Flemming, tf@ttqv.com
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// Copyright (c) 2001, Thomas Flemming, tf@ttqv.com
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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_KROVAK_HPP
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#define BOOST_GEOMETRY_PROJECTIONS_KROVAK_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 krovak
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{
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static double epsilon = 1e-15;
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static double S45 = 0.785398163397448; /* 45 deg */
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static double S90 = 1.570796326794896; /* 90 deg */
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static double UQ = 1.04216856380474; /* DU(2, 59, 42, 42.69689) */
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static double S0 = 1.37008346281555; /* Latitude of pseudo standard parallel 78deg 30'00" N */
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/* Not sure at all of the appropriate number for max_iter... */
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static int max_iter = 100;
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template <typename T>
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struct par_krovak
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{
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T alpha;
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T k;
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T n;
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T rho0;
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T ad;
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int czech;
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};
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/**
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NOTES: According to EPSG the full Krovak projection method should have
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the following parameters. Within PROJ.4 the azimuth, and pseudo
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standard parallel are hardcoded in the algorithm and can't be
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altered from outside. The others all have defaults to match the
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common usage with Krovak projection.
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lat_0 = latitude of centre of the projection
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lon_0 = longitude of centre of the projection
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** = azimuth (true) of the centre line passing through the centre of the projection
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** = latitude of pseudo standard parallel
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k = scale factor on the pseudo standard parallel
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x_0 = False Easting of the centre of the projection at the apex of the cone
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y_0 = False Northing of the centre of the projection at the apex of the cone
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**/
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template <typename T, typename Parameters>
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struct base_krovak_ellipsoid
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{
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par_krovak<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 const& lp_lat, T& xy_x, T& xy_y) const
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{
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T gfi, u, deltav, s, d, eps, rho;
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gfi = math::pow( (T(1) + par.e * sin(lp_lat)) / (T(1) - par.e * sin(lp_lat)), this->m_proj_parm.alpha * par.e / T(2));
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u = 2. * (atan(this->m_proj_parm.k * math::pow( tan(lp_lat / T(2) + S45), this->m_proj_parm.alpha) / gfi)-S45);
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deltav = -lp_lon * this->m_proj_parm.alpha;
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s = asin(cos(this->m_proj_parm.ad) * sin(u) + sin(this->m_proj_parm.ad) * cos(u) * cos(deltav));
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d = asin(cos(u) * sin(deltav) / cos(s));
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eps = this->m_proj_parm.n * d;
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rho = this->m_proj_parm.rho0 * math::pow(tan(S0 / T(2) + S45) , this->m_proj_parm.n) / math::pow(tan(s / T(2) + S45) , this->m_proj_parm.n);
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xy_y = rho * cos(eps);
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xy_x = rho * sin(eps);
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xy_y *= this->m_proj_parm.czech;
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xy_x *= this->m_proj_parm.czech;
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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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T u, deltav, s, d, eps, rho, fi1, xy0;
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int i;
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// TODO: replace with std::swap()
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xy0 = xy_x;
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xy_x = xy_y;
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xy_y = xy0;
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xy_x *= this->m_proj_parm.czech;
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xy_y *= this->m_proj_parm.czech;
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rho = sqrt(xy_x * xy_x + xy_y * xy_y);
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eps = atan2(xy_y, xy_x);
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d = eps / sin(S0);
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s = T(2) * (atan(math::pow(this->m_proj_parm.rho0 / rho, T(1) / this->m_proj_parm.n) * tan(S0 / T(2) + S45)) - S45);
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u = asin(cos(this->m_proj_parm.ad) * sin(s) - sin(this->m_proj_parm.ad) * cos(s) * cos(d));
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deltav = asin(cos(s) * sin(d) / cos(u));
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lp_lon = par.lam0 - deltav / this->m_proj_parm.alpha;
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/* ITERATION FOR lp_lat */
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fi1 = u;
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for (i = max_iter; i ; --i) {
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lp_lat = T(2) * ( atan( math::pow( this->m_proj_parm.k, T(-1) / this->m_proj_parm.alpha) *
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math::pow( tan(u / T(2) + S45) , T(1) / this->m_proj_parm.alpha) *
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math::pow( (T(1) + par.e * sin(fi1)) / (T(1) - par.e * sin(fi1)) , par.e / T(2))
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) - S45);
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if (fabs(fi1 - lp_lat) < epsilon)
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break;
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fi1 = lp_lat;
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}
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if( i == 0 )
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BOOST_THROW_EXCEPTION( projection_exception(error_non_convergent) );
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lp_lon -= par.lam0;
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}
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static inline std::string get_name()
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{
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return "krovak_ellipsoid";
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}
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};
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// Krovak
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template <typename Params, typename Parameters, typename T>
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inline void setup_krovak(Params const& params, Parameters& par, par_krovak<T>& proj_parm)
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{
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T u0, n0, g;
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/* we want Bessel as fixed ellipsoid */
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par.a = 6377397.155;
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par.es = 0.006674372230614;
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par.e = sqrt(par.es);
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/* if latitude of projection center is not set, use 49d30'N */
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if (!pj_param_exists<srs::spar::lat_0>(params, "lat_0", srs::dpar::lat_0))
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par.phi0 = 0.863937979737193;
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/* if center long is not set use 42d30'E of Ferro - 17d40' for Ferro */
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/* that will correspond to using longitudes relative to greenwich */
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/* as input and output, instead of lat/long relative to Ferro */
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if (!pj_param_exists<srs::spar::lon_0>(params, "lon_0", srs::dpar::lon_0))
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par.lam0 = 0.7417649320975901 - 0.308341501185665;
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/* if scale not set default to 0.9999 */
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if (!pj_param_exists<srs::spar::k>(params, "k", srs::dpar::k))
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par.k0 = 0.9999;
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proj_parm.czech = 1;
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if( !pj_param_exists<srs::spar::czech>(params, "czech", srs::dpar::czech) )
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proj_parm.czech = -1;
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/* Set up shared parameters between forward and inverse */
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proj_parm.alpha = sqrt(T(1) + (par.es * math::pow(cos(par.phi0), 4)) / (T(1) - par.es));
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u0 = asin(sin(par.phi0) / proj_parm.alpha);
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g = math::pow( (T(1) + par.e * sin(par.phi0)) / (T(1) - par.e * sin(par.phi0)) , proj_parm.alpha * par.e / T(2) );
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proj_parm.k = tan( u0 / 2. + S45) / math::pow(tan(par.phi0 / T(2) + S45) , proj_parm.alpha) * g;
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n0 = sqrt(T(1) - par.es) / (T(1) - par.es * math::pow(sin(par.phi0), 2));
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proj_parm.n = sin(S0);
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proj_parm.rho0 = par.k0 * n0 / tan(S0);
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proj_parm.ad = S90 - UQ;
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}
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}} // namespace detail::krovak
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#endif // doxygen
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/*!
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\brief Krovak 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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- Pseudocylindrical
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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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- lat_0: Latitude of origin
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- lon_0: Central meridian
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- k: Scale factor on the pseudo standard parallel
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\par Example
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\image html ex_krovak.gif
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*/
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template <typename T, typename Parameters>
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struct krovak_ellipsoid : public detail::krovak::base_krovak_ellipsoid<T, Parameters>
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{
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template <typename Params>
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inline krovak_ellipsoid(Params const& params, Parameters & par)
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{
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detail::krovak::setup_krovak(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_krovak, krovak_ellipsoid)
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// Factory entry(s)
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(krovak_entry, krovak_ellipsoid)
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(krovak_init)
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{
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(krovak, krovak_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_KROVAK_HPP
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