716 lines
29 KiB
C++
716 lines
29 KiB
C++
// 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, 2022.
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// Modifications copyright (c) 2017-2022, Oracle and/or its affiliates.
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// Contributed and/or modified by Vissarion Fysikopoulos, on behalf of Oracle.
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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: 8.2.1
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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_TMERC_HPP
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#define BOOST_GEOMETRY_PROJECTIONS_TMERC_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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#include <boost/geometry/srs/projections/impl/function_overloads.hpp>
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#include <boost/geometry/srs/projections/impl/pj_mlfn.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 tmerc
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{
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static const double epsilon10 = 1.e-10;
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/* Constant for "exact" transverse mercator */
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static const int proj_etmerc_order = 6;
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template <typename T>
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inline T FC1() { return 1.; }
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template <typename T>
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inline T FC2() { return .5; }
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template <typename T>
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inline T FC3() { return .16666666666666666666666666666666666666; }
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template <typename T>
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inline T FC4() { return .08333333333333333333333333333333333333; }
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template <typename T>
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inline T FC5() { return .05; }
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template <typename T>
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inline T FC6() { return .03333333333333333333333333333333333333; }
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template <typename T>
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inline T FC7() { return .02380952380952380952380952380952380952; }
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template <typename T>
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inline T FC8() { return .01785714285714285714285714285714285714; }
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template <typename T>
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struct par_tmerc
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{
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T esp;
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T ml0;
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detail::en<T> en;
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};
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// More exact: Poder/Engsager
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template <typename T>
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struct par_tmerc_exact
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{
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T Qn; /* Merid. quad., scaled to the projection */
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T Zb; /* Radius vector in polar coord. systems */
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T cgb[6]; /* Constants for Gauss -> Geo lat */
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T cbg[6]; /* Constants for Geo lat -> Gauss */
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T utg[6]; /* Constants for transv. merc. -> geo */
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T gtu[6]; /* Constants for geo -> transv. merc. */
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};
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template <typename T, typename Parameters>
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struct base_tmerc_ellipsoid
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{
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par_tmerc<T> m_proj_parm;
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// FORWARD(e_forward) ellipse
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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 half_pi = detail::half_pi<T>();
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static const T FC1 = tmerc::FC1<T>();
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static const T FC2 = tmerc::FC2<T>();
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static const T FC3 = tmerc::FC3<T>();
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static const T FC4 = tmerc::FC4<T>();
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static const T FC5 = tmerc::FC5<T>();
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static const T FC6 = tmerc::FC6<T>();
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static const T FC7 = tmerc::FC7<T>();
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static const T FC8 = tmerc::FC8<T>();
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T al, als, n, cosphi, sinphi, t;
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/*
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* Fail if our longitude is more than 90 degrees from the
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* central meridian since the results are essentially garbage.
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* Is error -20 really an appropriate return value?
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*
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* http://trac.osgeo.org/proj/ticket/5
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*/
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if( lp_lon < -half_pi || lp_lon > half_pi )
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{
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xy_x = HUGE_VAL;
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xy_y = HUGE_VAL;
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BOOST_THROW_EXCEPTION( projection_exception(error_lat_or_lon_exceed_limit) );
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return;
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}
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sinphi = sin(lp_lat);
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cosphi = cos(lp_lat);
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t = fabs(cosphi) > 1e-10 ? sinphi/cosphi : 0.;
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t *= t;
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al = cosphi * lp_lon;
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als = al * al;
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al /= sqrt(1. - par.es * sinphi * sinphi);
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n = this->m_proj_parm.esp * cosphi * cosphi;
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xy_x = par.k0 * al * (FC1 +
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FC3 * als * (1. - t + n +
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FC5 * als * (5. + t * (t - 18.) + n * (14. - 58. * t)
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+ FC7 * als * (61. + t * ( t * (179. - t) - 479. ) )
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)));
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xy_y = par.k0 * (pj_mlfn(lp_lat, sinphi, cosphi, this->m_proj_parm.en) - this->m_proj_parm.ml0 +
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sinphi * al * lp_lon * FC2 * ( 1. +
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FC4 * als * (5. - t + n * (9. + 4. * n) +
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FC6 * als * (61. + t * (t - 58.) + n * (270. - 330 * t)
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+ FC8 * als * (1385. + t * ( t * (543. - t) - 3111.) )
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))));
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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 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 FC1 = tmerc::FC1<T>();
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static const T FC2 = tmerc::FC2<T>();
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static const T FC3 = tmerc::FC3<T>();
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static const T FC4 = tmerc::FC4<T>();
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static const T FC5 = tmerc::FC5<T>();
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static const T FC6 = tmerc::FC6<T>();
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static const T FC7 = tmerc::FC7<T>();
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static const T FC8 = tmerc::FC8<T>();
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T n, con, cosphi, d, ds, sinphi, t;
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lp_lat = pj_inv_mlfn(this->m_proj_parm.ml0 + xy_y / par.k0, par.es, this->m_proj_parm.en);
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if (fabs(lp_lat) >= half_pi) {
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lp_lat = xy_y < 0. ? -half_pi : half_pi;
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lp_lon = 0.;
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} else {
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sinphi = sin(lp_lat);
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cosphi = cos(lp_lat);
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t = fabs(cosphi) > 1e-10 ? sinphi/cosphi : 0.;
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n = this->m_proj_parm.esp * cosphi * cosphi;
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d = xy_x * sqrt(con = 1. - par.es * sinphi * sinphi) / par.k0;
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con *= t;
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t *= t;
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ds = d * d;
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lp_lat -= (con * ds / (1.-par.es)) * FC2 * (1. -
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ds * FC4 * (5. + t * (3. - 9. * n) + n * (1. - 4 * n) -
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ds * FC6 * (61. + t * (90. - 252. * n +
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45. * t) + 46. * n
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- ds * FC8 * (1385. + t * (3633. + t * (4095. + 1574. * t)) )
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)));
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lp_lon = d*(FC1 -
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ds*FC3*( 1. + 2.*t + n -
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ds*FC5*(5. + t*(28. + 24.*t + 8.*n) + 6.*n
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- ds * FC7 * (61. + t * (662. + t * (1320. + 720. * t)) )
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))) / cosphi;
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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 "tmerc_ellipsoid";
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}
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};
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template <typename T, typename Parameters>
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struct base_tmerc_ellipsoid_exact
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{
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par_tmerc_exact<T> m_proj_parm;
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static inline std::string get_name()
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{
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return "tmerc_ellipsoid";
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}
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/* Helper functions for "exact" transverse mercator */
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inline
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static T gatg(const T *p1, int len_p1, T B, T cos_2B, T sin_2B)
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{
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T h = 0, h1, h2 = 0;
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const T two_cos_2B = 2*cos_2B;
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const T* p = p1 + len_p1;
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h1 = *--p;
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while (p - p1) {
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h = -h2 + two_cos_2B*h1 + *--p;
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h2 = h1;
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h1 = h;
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}
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return (B + h*sin_2B);
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}
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/* Complex Clenshaw summation */
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inline
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static T clenS(const T *a, int size,
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T sin_arg_r, T cos_arg_r,
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T sinh_arg_i, T cosh_arg_i,
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T *R, T *I)
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{
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T r, i, hr, hr1, hr2, hi, hi1, hi2;
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/* arguments */
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const T* p = a + size;
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r = 2*cos_arg_r*cosh_arg_i;
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i = -2*sin_arg_r*sinh_arg_i;
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/* summation loop */
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hi1 = hr1 = hi = 0;
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hr = *--p;
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for (; a - p;) {
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hr2 = hr1;
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hi2 = hi1;
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hr1 = hr;
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hi1 = hi;
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hr = -hr2 + r*hr1 - i*hi1 + *--p;
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hi = -hi2 + i*hr1 + r*hi1;
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}
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r = sin_arg_r*cosh_arg_i;
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i = cos_arg_r*sinh_arg_i;
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*R = r*hr - i*hi;
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*I = r*hi + i*hr;
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return *R;
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}
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/* Real Clenshaw summation */
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static T clens(const T *a, int size, T arg_r)
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{
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T r, hr, hr1, hr2, cos_arg_r;
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const T* p = a + size;
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cos_arg_r = cos(arg_r);
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r = 2*cos_arg_r;
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/* summation loop */
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hr1 = 0;
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hr = *--p;
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for (; a - p;) {
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hr2 = hr1;
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hr1 = hr;
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hr = -hr2 + r*hr1 + *--p;
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}
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return sin(arg_r)*hr;
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}
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/* Ellipsoidal, forward */
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//static PJ_XY exact_e_fwd (PJ_LP lp, PJ *P)
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inline void fwd(Parameters const& par,
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T const& lp_lon,
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T const& lp_lat,
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T& xy_x, T& xy_y) const
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{
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//PJ_XY xy = {0.0,0.0};
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//const auto *Q = &(static_cast<struct tmerc_data*>(par.opaque)->exact);
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/* ell. LAT, LNG -> Gaussian LAT, LNG */
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T Cn = gatg (this->m_proj_parm.cbg, proj_etmerc_order, lp_lat,
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cos(2*lp_lat), sin(2*lp_lat));
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/* Gaussian LAT, LNG -> compl. sph. LAT */
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const T sin_Cn = sin (Cn);
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const T cos_Cn = cos (Cn);
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const T sin_Ce = sin (lp_lon);
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const T cos_Ce = cos (lp_lon);
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const T cos_Cn_cos_Ce = cos_Cn*cos_Ce;
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Cn = atan2 (sin_Cn, cos_Cn_cos_Ce);
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const T inv_denom_tan_Ce = 1. / hypot (sin_Cn, cos_Cn_cos_Ce);
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const T tan_Ce = sin_Ce*cos_Cn * inv_denom_tan_Ce;
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#if 0
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// Variant of the above: found not to be measurably faster
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const T sin_Ce_cos_Cn = sin_Ce*cos_Cn;
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const T denom = sqrt(1 - sin_Ce_cos_Cn * sin_Ce_cos_Cn);
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const T tan_Ce = sin_Ce_cos_Cn / denom;
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#endif
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/* compl. sph. N, E -> ell. norm. N, E */
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T Ce = asinh ( tan_Ce ); /* Replaces: Ce = log(tan(FORTPI + Ce*0.5)); */
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/*
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* Non-optimized version:
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* const T sin_arg_r = sin(2*Cn);
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* const T cos_arg_r = cos(2*Cn);
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*
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* Given:
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* sin(2 * Cn) = 2 sin(Cn) cos(Cn)
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* sin(atan(y)) = y / sqrt(1 + y^2)
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* cos(atan(y)) = 1 / sqrt(1 + y^2)
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* ==> sin(2 * Cn) = 2 tan_Cn / (1 + tan_Cn^2)
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*
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* cos(2 * Cn) = 2cos^2(Cn) - 1
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* = 2 / (1 + tan_Cn^2) - 1
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*/
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const T two_inv_denom_tan_Ce = 2 * inv_denom_tan_Ce;
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const T two_inv_denom_tan_Ce_square = two_inv_denom_tan_Ce * inv_denom_tan_Ce;
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const T tmp_r = cos_Cn_cos_Ce * two_inv_denom_tan_Ce_square;
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const T sin_arg_r = sin_Cn * tmp_r;
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const T cos_arg_r = cos_Cn_cos_Ce * tmp_r - 1;
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/*
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* Non-optimized version:
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* const T sinh_arg_i = sinh(2*Ce);
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* const T cosh_arg_i = cosh(2*Ce);
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*
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* Given
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* sinh(2 * Ce) = 2 sinh(Ce) cosh(Ce)
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* sinh(asinh(y)) = y
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* cosh(asinh(y)) = sqrt(1 + y^2)
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* ==> sinh(2 * Ce) = 2 tan_Ce sqrt(1 + tan_Ce^2)
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*
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* cosh(2 * Ce) = 2cosh^2(Ce) - 1
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* = 2 * (1 + tan_Ce^2) - 1
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*
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* and 1+tan_Ce^2 = 1 + sin_Ce^2 * cos_Cn^2 / (sin_Cn^2 + cos_Cn^2 * cos_Ce^2)
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* = (sin_Cn^2 + cos_Cn^2 * cos_Ce^2 + sin_Ce^2 * cos_Cn^2) / (sin_Cn^2 + cos_Cn^2 * cos_Ce^2)
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* = 1. / (sin_Cn^2 + cos_Cn^2 * cos_Ce^2)
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* = inv_denom_tan_Ce^2
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*
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*/
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const T sinh_arg_i = tan_Ce * two_inv_denom_tan_Ce;
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const T cosh_arg_i = two_inv_denom_tan_Ce_square - 1;
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T dCn, dCe;
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Cn += clenS (this->m_proj_parm.gtu, proj_etmerc_order,
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sin_arg_r, cos_arg_r, sinh_arg_i, cosh_arg_i,
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&dCn, &dCe);
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Ce += dCe;
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if (fabs (Ce) <= 2.623395162778) {
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xy_y = this->m_proj_parm.Qn * Cn + this->m_proj_parm.Zb; /* Northing */
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xy_x = this->m_proj_parm.Qn * Ce; /* Easting */
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} else {
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BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
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xy_x = xy_y = HUGE_VAL;
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}
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}
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/* Ellipsoidal, inverse */
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inline void inv(Parameters const& par,
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T const& xy_x,
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T const& xy_y,
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T& lp_lon,
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T& lp_lat) const
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{
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//PJ_LP lp = {0.0,0.0};
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//const auto *Q = &(static_cast<struct tmerc_data*>(par.opaque)->exact);
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/* normalize N, E */
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T Cn = (xy_y - this->m_proj_parm.Zb)/this->m_proj_parm.Qn;
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T Ce = xy_x/this->m_proj_parm.Qn;
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if (fabs(Ce) <= 2.623395162778) { /* 150 degrees */
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/* norm. N, E -> compl. sph. LAT, LNG */
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const T sin_arg_r = sin(2*Cn);
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const T cos_arg_r = cos(2*Cn);
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//const T sinh_arg_i = sinh(2*Ce);
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//const T cosh_arg_i = cosh(2*Ce);
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const T exp_2_Ce = exp(2*Ce);
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const T half_inv_exp_2_Ce = 0.5 / exp_2_Ce;
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const T sinh_arg_i = 0.5 * exp_2_Ce - half_inv_exp_2_Ce;
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const T cosh_arg_i = 0.5 * exp_2_Ce + half_inv_exp_2_Ce;
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T dCn_ignored, dCe;
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Cn += clenS(this->m_proj_parm.utg, proj_etmerc_order,
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sin_arg_r, cos_arg_r, sinh_arg_i, cosh_arg_i,
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&dCn_ignored, &dCe);
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Ce += dCe;
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/* compl. sph. LAT -> Gaussian LAT, LNG */
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const T sin_Cn = sin (Cn);
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const T cos_Cn = cos (Cn);
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#if 0
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// Non-optimized version:
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T sin_Ce, cos_Ce;
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Ce = atan (sinh (Ce)); // Replaces: Ce = 2*(atan(exp(Ce)) - FORTPI);
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sin_Ce = sin (Ce);
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cos_Ce = cos (Ce);
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Ce = atan2 (sin_Ce, cos_Ce*cos_Cn);
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Cn = atan2 (sin_Cn*cos_Ce, hypot (sin_Ce, cos_Ce*cos_Cn));
|
|
#else
|
|
/*
|
|
* One can divide both member of Ce = atan2(...) by cos_Ce, which gives:
|
|
* Ce = atan2 (tan_Ce, cos_Cn) = atan2(sinh(Ce), cos_Cn)
|
|
*
|
|
* and the same for Cn = atan2(...)
|
|
* Cn = atan2 (sin_Cn, hypot (sin_Ce, cos_Ce*cos_Cn)/cos_Ce)
|
|
* = atan2 (sin_Cn, hypot (sin_Ce/cos_Ce, cos_Cn))
|
|
* = atan2 (sin_Cn, hypot (tan_Ce, cos_Cn))
|
|
* = atan2 (sin_Cn, hypot (sinhCe, cos_Cn))
|
|
*/
|
|
const T sinhCe = sinh (Ce);
|
|
Ce = atan2 (sinhCe, cos_Cn);
|
|
const T modulus_Ce = hypot (sinhCe, cos_Cn);
|
|
Cn = atan2 (sin_Cn, modulus_Ce);
|
|
#endif
|
|
|
|
/* Gaussian LAT, LNG -> ell. LAT, LNG */
|
|
|
|
// Optimization of the computation of cos(2*Cn) and sin(2*Cn)
|
|
const T tmp = 2 * modulus_Ce / (sinhCe * sinhCe + 1);
|
|
const T sin_2_Cn = sin_Cn * tmp;
|
|
const T cos_2_Cn = tmp * modulus_Ce - 1.;
|
|
//const T cos_2_Cn = cos(2 * Cn);
|
|
//const T sin_2_Cn = sin(2 * Cn);
|
|
|
|
lp_lat = gatg (this->m_proj_parm.cgb, proj_etmerc_order, Cn, cos_2_Cn, sin_2_Cn);
|
|
lp_lon = Ce;
|
|
}
|
|
else {
|
|
BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
|
|
lp_lat = lp_lon = HUGE_VAL;
|
|
}
|
|
}
|
|
|
|
};
|
|
|
|
template <typename T, typename Parameters>
|
|
struct base_tmerc_spheroid
|
|
{
|
|
par_tmerc<T> m_proj_parm;
|
|
|
|
// FORWARD(s_forward) sphere
|
|
// Project coordinates from geographic (lon, lat) to cartesian (x, y)
|
|
inline void fwd(Parameters const& par, T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const
|
|
{
|
|
static const T half_pi = detail::half_pi<T>();
|
|
|
|
T b, cosphi;
|
|
|
|
/*
|
|
* Fail if our longitude is more than 90 degrees from the
|
|
* central meridian since the results are essentially garbage.
|
|
* Is error -20 really an appropriate return value?
|
|
*
|
|
* http://trac.osgeo.org/proj/ticket/5
|
|
*/
|
|
if( lp_lon < -half_pi || lp_lon > half_pi )
|
|
{
|
|
xy_x = HUGE_VAL;
|
|
xy_y = HUGE_VAL;
|
|
BOOST_THROW_EXCEPTION( projection_exception(error_lat_or_lon_exceed_limit) );
|
|
return;
|
|
}
|
|
|
|
cosphi = cos(lp_lat);
|
|
b = cosphi * sin(lp_lon);
|
|
if (fabs(fabs(b) - 1.) <= epsilon10)
|
|
BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
|
|
|
|
xy_x = this->m_proj_parm.ml0 * log((1. + b) / (1. - b));
|
|
xy_y = cosphi * cos(lp_lon) / sqrt(1. - b * b);
|
|
|
|
b = fabs( xy_y );
|
|
if (b >= 1.) {
|
|
if ((b - 1.) > epsilon10)
|
|
BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
|
|
else xy_y = 0.;
|
|
} else
|
|
xy_y = acos(xy_y);
|
|
|
|
if (lp_lat < 0.)
|
|
xy_y = -xy_y;
|
|
xy_y = this->m_proj_parm.esp * (xy_y - par.phi0);
|
|
}
|
|
|
|
// INVERSE(s_inverse) sphere
|
|
// Project coordinates from cartesian (x, y) to geographic (lon, lat)
|
|
inline void inv(Parameters const& par, T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const
|
|
{
|
|
T h, g;
|
|
|
|
h = exp(xy_x / this->m_proj_parm.esp);
|
|
g = .5 * (h - 1. / h);
|
|
h = cos(par.phi0 + xy_y / this->m_proj_parm.esp);
|
|
lp_lat = asin(sqrt((1. - h * h) / (1. + g * g)));
|
|
|
|
/* Make sure that phi is on the correct hemisphere when false northing is used */
|
|
if (xy_y < 0. && -lp_lat+par.phi0 < 0.0) lp_lat = -lp_lat;
|
|
|
|
lp_lon = (g != 0.0 || h != 0.0) ? atan2(g, h) : 0.;
|
|
}
|
|
|
|
static inline std::string get_name()
|
|
{
|
|
return "tmerc_spheroid";
|
|
}
|
|
|
|
};
|
|
|
|
template <typename Parameters, typename T>
|
|
inline void setup(Parameters const& par, par_tmerc<T>& proj_parm)
|
|
{
|
|
if (par.es != 0.0) {
|
|
proj_parm.en = pj_enfn<T>(par.es);
|
|
proj_parm.ml0 = pj_mlfn(par.phi0, sin(par.phi0), cos(par.phi0), proj_parm.en);
|
|
proj_parm.esp = par.es / (1. - par.es);
|
|
} else {
|
|
proj_parm.esp = par.k0;
|
|
proj_parm.ml0 = .5 * proj_parm.esp;
|
|
}
|
|
}
|
|
|
|
template <typename Parameters, typename T>
|
|
inline void setup_exact(Parameters const& par, par_tmerc_exact<T>& proj_parm)
|
|
{
|
|
assert( par.es > 0 );
|
|
|
|
/* third flattening n */
|
|
//since we do not keep n in parameters we compute it here;
|
|
const T n = pow(tan(asin(par.e)/2),2);
|
|
T np = n;
|
|
|
|
/* COEF. OF TRIG SERIES GEO <-> GAUSS */
|
|
/* cgb := Gaussian -> Geodetic, KW p190 - 191 (61) - (62) */
|
|
/* cbg := Geodetic -> Gaussian, KW p186 - 187 (51) - (52) */
|
|
/* PROJ_ETMERC_ORDER = 6th degree : Engsager and Poder: ICC2007 */
|
|
|
|
proj_parm.cgb[0] = n*( 2 + n*(-2/3.0 + n*(-2 + n*(116/45.0 + n*(26/45.0 +
|
|
n*(-2854/675.0 ))))));
|
|
proj_parm.cbg[0] = n*(-2 + n*( 2/3.0 + n*( 4/3.0 + n*(-82/45.0 + n*(32/45.0 +
|
|
n*( 4642/4725.0))))));
|
|
np *= n;
|
|
proj_parm.cgb[1] = np*(7/3.0 + n*( -8/5.0 + n*(-227/45.0 + n*(2704/315.0 +
|
|
n*( 2323/945.0)))));
|
|
proj_parm.cbg[1] = np*(5/3.0 + n*(-16/15.0 + n*( -13/9.0 + n*( 904/315.0 +
|
|
n*(-1522/945.0)))));
|
|
np *= n;
|
|
/* n^5 coeff corrected from 1262/105 -> -1262/105 */
|
|
proj_parm.cgb[2] = np*( 56/15.0 + n*(-136/35.0 + n*(-1262/105.0 +
|
|
n*( 73814/2835.0))));
|
|
proj_parm.cbg[2] = np*(-26/15.0 + n*( 34/21.0 + n*( 8/5.0 +
|
|
n*(-12686/2835.0))));
|
|
np *= n;
|
|
/* n^5 coeff corrected from 322/35 -> 332/35 */
|
|
proj_parm.cgb[3] = np*(4279/630.0 + n*(-332/35.0 + n*(-399572/14175.0)));
|
|
proj_parm.cbg[3] = np*(1237/630.0 + n*( -12/5.0 + n*( -24832/14175.0)));
|
|
np *= n;
|
|
proj_parm.cgb[4] = np*(4174/315.0 + n*(-144838/6237.0 ));
|
|
proj_parm.cbg[4] = np*(-734/315.0 + n*( 109598/31185.0));
|
|
np *= n;
|
|
proj_parm.cgb[5] = np*(601676/22275.0 );
|
|
proj_parm.cbg[5] = np*(444337/155925.0);
|
|
|
|
/* Constants of the projections */
|
|
/* Transverse Mercator (UTM, ITM, etc) */
|
|
np = n*n;
|
|
/* Norm. mer. quad, K&W p.50 (96), p.19 (38b), p.5 (2) */
|
|
proj_parm.Qn = par.k0/(1 + n) * (1 + np*(1/4.0 + np*(1/64.0 + np/256.0)));
|
|
/* coef of trig series */
|
|
/* utg := ell. N, E -> sph. N, E, KW p194 (65) */
|
|
/* gtu := sph. N, E -> ell. N, E, KW p196 (69) */
|
|
proj_parm.utg[0] = n*(-0.5 + n*( 2/3.0 + n*(-37/96.0 + n*( 1/360.0 +
|
|
n*( 81/512.0 + n*(-96199/604800.0))))));
|
|
proj_parm.gtu[0] = n*( 0.5 + n*(-2/3.0 + n*( 5/16.0 + n*(41/180.0 +
|
|
n*(-127/288.0 + n*( 7891/37800.0 ))))));
|
|
proj_parm.utg[1] = np*(-1/48.0 + n*(-1/15.0 + n*(437/1440.0 + n*(-46/105.0 +
|
|
n*( 1118711/3870720.0)))));
|
|
proj_parm.gtu[1] = np*(13/48.0 + n*(-3/5.0 + n*(557/1440.0 + n*(281/630.0 +
|
|
n*(-1983433/1935360.0)))));
|
|
np *= n;
|
|
proj_parm.utg[2] = np*(-17/480.0 + n*( 37/840.0 + n*( 209/4480.0 +
|
|
n*( -5569/90720.0 ))));
|
|
proj_parm.gtu[2] = np*( 61/240.0 + n*(-103/140.0 + n*(15061/26880.0 +
|
|
n*(167603/181440.0))));
|
|
np *= n;
|
|
proj_parm.utg[3] = np*(-4397/161280.0 + n*( 11/504.0 + n*( 830251/7257600.0)));
|
|
proj_parm.gtu[3] = np*(49561/161280.0 + n*(-179/168.0 + n*(6601661/7257600.0)));
|
|
np *= n;
|
|
proj_parm.utg[4] = np*(-4583/161280.0 + n*( 108847/3991680.0));
|
|
proj_parm.gtu[4] = np*(34729/80640.0 + n*(-3418889/1995840.0));
|
|
np *= n;
|
|
proj_parm.utg[5] = np*(-20648693/638668800.0);
|
|
proj_parm.gtu[5] = np*(212378941/319334400.0);
|
|
|
|
/* Gaussian latitude value of the origin latitude */
|
|
const T Z = base_tmerc_ellipsoid_exact<T, Parameters>::gatg (proj_parm.cbg, proj_etmerc_order, par.phi0, cos(2*par.phi0), sin(2*par.phi0));
|
|
|
|
/* Origin northing minus true northing at the origin latitude */
|
|
/* i.e. true northing = N - par.Zb */
|
|
proj_parm.Zb = - proj_parm.Qn*(Z + base_tmerc_ellipsoid_exact<T, Parameters>::clens(proj_parm.gtu, proj_etmerc_order, 2*Z));
|
|
}
|
|
|
|
}} // namespace detail::tmerc
|
|
#endif // doxygen
|
|
|
|
/*!
|
|
\brief Transverse Mercator projection
|
|
\ingroup projections
|
|
\tparam Geographic latlong point type
|
|
\tparam Cartesian xy point type
|
|
\tparam Parameters parameter type
|
|
\par Projection characteristics
|
|
- Cylindrical
|
|
- Spheroid
|
|
- Ellipsoid
|
|
\par Example
|
|
\image html ex_tmerc.gif
|
|
*/
|
|
//approximate tmerc algorithm
|
|
/*
|
|
template <typename T, typename Parameters>
|
|
struct tmerc_ellipsoid : public detail::tmerc::base_tmerc_ellipsoid<T, Parameters>
|
|
{
|
|
template <typename Params>
|
|
inline tmerc_ellipsoid(Params const&, Parameters const& par)
|
|
{
|
|
detail::tmerc::setup(par, this->m_proj_parm);
|
|
}
|
|
};
|
|
*/
|
|
template <typename T, typename Parameters>
|
|
struct tmerc_ellipsoid : public detail::tmerc::base_tmerc_ellipsoid_exact<T, Parameters>
|
|
{
|
|
template <typename Params>
|
|
inline tmerc_ellipsoid(Params const&, Parameters const& par)
|
|
{
|
|
detail::tmerc::setup_exact(par, this->m_proj_parm);
|
|
}
|
|
};
|
|
|
|
/*!
|
|
\brief Transverse Mercator projection
|
|
\ingroup projections
|
|
\tparam Geographic latlong point type
|
|
\tparam Cartesian xy point type
|
|
\tparam Parameters parameter type
|
|
\par Projection characteristics
|
|
- Cylindrical
|
|
- Spheroid
|
|
- Ellipsoid
|
|
\par Example
|
|
\image html ex_tmerc.gif
|
|
*/
|
|
template <typename T, typename Parameters>
|
|
struct tmerc_spheroid : public detail::tmerc::base_tmerc_spheroid<T, Parameters>
|
|
{
|
|
template <typename Params>
|
|
inline tmerc_spheroid(Params const&, Parameters const& par)
|
|
{
|
|
detail::tmerc::setup(par, this->m_proj_parm);
|
|
}
|
|
};
|
|
|
|
#ifndef DOXYGEN_NO_DETAIL
|
|
namespace detail
|
|
{
|
|
|
|
// Static projection
|
|
BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI2(srs::spar::proj_tmerc, tmerc_spheroid, tmerc_ellipsoid)
|
|
|
|
// Factory entry(s) - dynamic projection
|
|
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI2(tmerc_entry, tmerc_spheroid, tmerc_ellipsoid)
|
|
|
|
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(tmerc_init)
|
|
{
|
|
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(tmerc, tmerc_entry)
|
|
}
|
|
|
|
} // namespace detail
|
|
#endif // doxygen
|
|
|
|
} // namespace projections
|
|
|
|
}} // namespace boost::geometry
|
|
|
|
#endif // BOOST_GEOMETRY_PROJECTIONS_TMERC_HPP
|
|
|