327 lines
15 KiB
C++
327 lines
15 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, 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: 5.0.0
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// Original copyright notice:
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// Copyright (c) 2003, 2006 Gerald I. Evenden
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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_OMERC_HPP
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#define BOOST_GEOMETRY_PROJECTIONS_OMERC_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/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/pj_phi2.hpp>
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#include <boost/geometry/srs/projections/impl/pj_tsfn.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 omerc
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{
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template <typename T>
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struct par_omerc
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{
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T A, B, E, AB, ArB, BrA, rB, singam, cosgam, sinrot, cosrot;
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T v_pole_n, v_pole_s, u_0;
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bool no_rot;
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};
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static const double tolerance = 1.e-7;
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static const double epsilon = 1.e-10;
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template <typename T, typename Parameters>
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struct base_omerc_ellipsoid
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{
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par_omerc<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,
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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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T s, t, U, V, W, temp, u, v;
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if (fabs(fabs(lp_lat) - half_pi) > epsilon) {
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W = this->m_proj_parm.E / math::pow(pj_tsfn(lp_lat, sin(lp_lat), par.e),
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this->m_proj_parm.B);
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temp = 1. / W;
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s = .5 * (W - temp);
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t = .5 * (W + temp);
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V = sin(this->m_proj_parm.B * lp_lon);
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U = (s * this->m_proj_parm.singam - V * this->m_proj_parm.cosgam) / t;
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if (fabs(fabs(U) - 1.0) < epsilon) {
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BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
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}
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v = 0.5 * this->m_proj_parm.ArB * log((1. - U)/(1. + U));
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temp = cos(this->m_proj_parm.B * lp_lon);
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if(fabs(temp) < tolerance) {
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u = this->m_proj_parm.A * lp_lon;
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} else {
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u = this->m_proj_parm.ArB * atan2((s * this->m_proj_parm.cosgam
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+ V * this->m_proj_parm.singam), temp);
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}
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} else {
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v = lp_lat > 0 ? this->m_proj_parm.v_pole_n : this->m_proj_parm.v_pole_s;
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u = this->m_proj_parm.ArB * lp_lat;
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}
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if (this->m_proj_parm.no_rot) {
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xy_x = u;
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xy_y = v;
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} else {
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u -= this->m_proj_parm.u_0;
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xy_x = v * this->m_proj_parm.cosrot + u * this->m_proj_parm.sinrot;
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xy_y = u * this->m_proj_parm.cosrot - v * this->m_proj_parm.sinrot;
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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,
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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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T u, v, Qp, Sp, Tp, Vp, Up;
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if (this->m_proj_parm.no_rot) {
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v = xy_y;
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u = xy_x;
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} else {
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v = xy_x * this->m_proj_parm.cosrot - xy_y * this->m_proj_parm.sinrot;
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u = xy_y * this->m_proj_parm.cosrot + xy_x * this->m_proj_parm.sinrot
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+ this->m_proj_parm.u_0;
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}
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Qp = exp(- this->m_proj_parm.BrA * v);
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Sp = .5 * (Qp - 1. / Qp);
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Tp = .5 * (Qp + 1. / Qp);
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Vp = sin(this->m_proj_parm.BrA * u);
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Up = (Vp * this->m_proj_parm.cosgam + Sp * this->m_proj_parm.singam) / Tp;
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if (fabs(fabs(Up) - 1.) < epsilon) {
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lp_lon = 0.;
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lp_lat = Up < 0. ? -half_pi : half_pi;
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} else {
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lp_lat = this->m_proj_parm.E / sqrt((1. + Up) / (1. - Up));
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if ((lp_lat = pj_phi2(math::pow(lp_lat, T(1) / this->m_proj_parm.B), par.e))
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== HUGE_VAL) {
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BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
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}
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lp_lon = - this->m_proj_parm.rB * atan2((Sp * this->m_proj_parm.cosgam -
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Vp * this->m_proj_parm.singam), cos(this->m_proj_parm.BrA * u));
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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 "omerc_ellipsoid";
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}
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};
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// Oblique Mercator
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template <typename Params, typename Parameters, typename T>
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inline void setup_omerc(Params const& params, Parameters & par, par_omerc<T>& proj_parm)
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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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static const T pi = detail::pi<T>();
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static const T two_pi = detail::two_pi<T>();
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T con, com, cosph0, D, F, H, L, sinph0, p, J, gamma=0,
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gamma0, lamc=0, lam1=0, lam2=0, phi1=0, phi2=0, alpha_c=0;
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int alp, gam, no_off = 0;
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proj_parm.no_rot = pj_get_param_b<srs::spar::no_rot>(params, "no_rot",
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srs::dpar::no_rot);
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alp = pj_param_r<srs::spar::alpha>(params, "alpha", srs::dpar::alpha, alpha_c);
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gam = pj_param_r<srs::spar::gamma>(params, "gamma", srs::dpar::gamma, gamma);
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if (alp || gam) {
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lamc = pj_get_param_r<T, srs::spar::lonc>(params, "lonc", srs::dpar::lonc);
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// NOTE: This is needed for Hotline Oblique Mercator variant A projection
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no_off = pj_get_param_b<srs::spar::no_off>(params, "no_off", srs::dpar::no_off);
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} else {
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lam1 = pj_get_param_r<T, srs::spar::lon_1>(params, "lon_1", srs::dpar::lon_1);
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phi1 = pj_get_param_r<T, srs::spar::lat_1>(params, "lat_1", srs::dpar::lat_1);
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lam2 = pj_get_param_r<T, srs::spar::lon_2>(params, "lon_2", srs::dpar::lon_2);
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phi2 = pj_get_param_r<T, srs::spar::lat_2>(params, "lat_2", srs::dpar::lat_2);
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if (fabs(phi1 - phi2) <= tolerance ||
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(con = fabs(phi1)) <= tolerance ||
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fabs(con - half_pi) <= tolerance ||
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fabs(fabs(par.phi0) - half_pi) <= tolerance ||
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fabs(fabs(phi2) - half_pi) <= tolerance)
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BOOST_THROW_EXCEPTION( projection_exception(error_lat_0_or_alpha_eq_90) );
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}
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com = sqrt(par.one_es);
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if (fabs(par.phi0) > epsilon) {
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sinph0 = sin(par.phi0);
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cosph0 = cos(par.phi0);
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con = 1. - par.es * sinph0 * sinph0;
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proj_parm.B = cosph0 * cosph0;
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proj_parm.B = sqrt(1. + par.es * proj_parm.B * proj_parm.B / par.one_es);
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proj_parm.A = proj_parm.B * par.k0 * com / con;
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D = proj_parm.B * com / (cosph0 * sqrt(con));
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if ((F = D * D - 1.) <= 0.)
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F = 0.;
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else {
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F = sqrt(F);
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if (par.phi0 < 0.)
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F = -F;
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}
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proj_parm.E = F += D;
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proj_parm.E *= math::pow(pj_tsfn(par.phi0, sinph0, par.e), proj_parm.B);
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} else {
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proj_parm.B = 1. / com;
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proj_parm.A = par.k0;
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proj_parm.E = D = F = 1.;
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}
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if (alp || gam) {
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if (alp) {
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gamma0 = aasin(sin(alpha_c) / D);
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if (!gam)
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gamma = alpha_c;
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} else
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alpha_c = aasin(D*sin(gamma0 = gamma));
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par.lam0 = lamc - aasin(.5 * (F - 1. / F) *
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tan(gamma0)) / proj_parm.B;
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} else {
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H = math::pow(pj_tsfn(phi1, sin(phi1), par.e), proj_parm.B);
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L = math::pow(pj_tsfn(phi2, sin(phi2), par.e), proj_parm.B);
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F = proj_parm.E / H;
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p = (L - H) / (L + H);
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J = proj_parm.E * proj_parm.E;
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J = (J - L * H) / (J + L * H);
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if ((con = lam1 - lam2) < -pi)
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lam2 -= two_pi;
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else if (con > pi)
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lam2 += two_pi;
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par.lam0 = adjlon(.5 * (lam1 + lam2) - atan(
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J * tan(.5 * proj_parm.B * (lam1 - lam2)) / p) / proj_parm.B);
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gamma0 = atan(2. * sin(proj_parm.B * adjlon(lam1 - par.lam0)) /
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(F - 1. / F));
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gamma = alpha_c = aasin(D * sin(gamma0));
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}
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proj_parm.singam = sin(gamma0);
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proj_parm.cosgam = cos(gamma0);
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proj_parm.sinrot = sin(gamma);
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proj_parm.cosrot = cos(gamma);
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proj_parm.BrA = 1. / (proj_parm.ArB = proj_parm.A * (proj_parm.rB = 1. / proj_parm.B));
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proj_parm.AB = proj_parm.A * proj_parm.B;
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if (no_off)
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proj_parm.u_0 = 0;
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else {
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proj_parm.u_0 = fabs(proj_parm.ArB * atan(sqrt(D * D - 1.) / cos(alpha_c)));
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if (par.phi0 < 0.)
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proj_parm.u_0 = - proj_parm.u_0;
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}
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F = 0.5 * gamma0;
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proj_parm.v_pole_n = proj_parm.ArB * log(tan(fourth_pi - F));
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proj_parm.v_pole_s = proj_parm.ArB * log(tan(fourth_pi + F));
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}
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}} // namespace detail::omerc
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#endif // doxygen
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/*!
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\brief Oblique Mercator 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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- Cylindrical
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- Spheroid
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- Ellipsoid
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\par Projection parameters
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- no_rot: No rotation
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- alpha: Alpha (degrees)
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- gamma: Gamma (degrees)
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- no_off: Do not offset origin to center of projection
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(useful for Hotline Oblique Mercator variant A).
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- lonc: Longitude (only used if alpha (or gamma) is specified) (degrees)
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- lon_1 (degrees)
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- lat_1: Latitude of first standard parallel (degrees)
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- lon_2 (degrees)
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- lat_2: Latitude of second standard parallel (degrees)
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- no_uoff: deprecated (string)
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\par Example
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\image html ex_omerc.gif
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*/
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template <typename T, typename Parameters>
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struct omerc_ellipsoid : public detail::omerc::base_omerc_ellipsoid<T, Parameters>
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{
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template <typename Params>
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inline omerc_ellipsoid(Params const& params, Parameters & par)
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{
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detail::omerc::setup_omerc(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_omerc, omerc_ellipsoid)
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// Factory entry(s)
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(omerc_entry, omerc_ellipsoid)
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(omerc_init)
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{
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(omerc, omerc_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_OMERC_HPP
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