446 lines
19 KiB
C++
446 lines
19 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.
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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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// Copyright (c) 2008 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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/* The code in this file is largly based upon procedures:
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*
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* Written by: Knud Poder and Karsten Engsager
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*
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* Based on math from: R.Koenig and K.H. Weise, "Mathematische
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* Grundlagen der hoeheren Geodaesie und Kartographie,
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* Springer-Verlag, Berlin/Goettingen" Heidelberg, 1951.
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*
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* Modified and used here by permission of Reference Networks
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* Division, Kort og Matrikelstyrelsen (KMS), Copenhagen, Denmark
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*/
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#ifndef BOOST_GEOMETRY_PROJECTIONS_ETMERC_HPP
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#define BOOST_GEOMETRY_PROJECTIONS_ETMERC_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/function_overloads.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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#include <boost/math/special_functions/hypot.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 etmerc
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{
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static const int PROJ_ETMERC_ORDER = 6;
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template <typename T>
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struct par_etmerc
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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>
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inline T log1py(T const& x) { /* Compute log(1+x) accurately */
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volatile T
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y = 1 + x,
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z = y - 1;
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/* Here's the explanation for this magic: y = 1 + z, exactly, and z
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* approx x, thus log(y)/z (which is nearly constant near z = 0) returns
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* a good approximation to the true log(1 + x)/x. The multiplication x *
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* (log(y)/z) introduces little additional error. */
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return z == 0 ? x : x * log(y) / z;
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}
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template <typename T>
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inline T asinhy(T const& x) { /* Compute asinh(x) accurately */
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T y = fabs(x); /* Enforce odd parity */
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y = log1py(y * (1 + y/(boost::math::hypot(1.0, y) + 1)));
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return x < 0 ? -y : y;
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}
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template <typename T>
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inline T gatg(const T *p1, int len_p1, T const& B) {
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const T *p;
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T h = 0, h1, h2 = 0, cos_2B;
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cos_2B = 2*cos(2*B);
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for (p = p1 + len_p1, h1 = *--p; p - p1; h2 = h1, h1 = h)
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h = -h2 + cos_2B*h1 + *--p;
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return (B + h*sin(2*B));
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}
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/* Complex Clenshaw summation */
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template <typename T>
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inline T clenS(const T *a, int size, T const& arg_r, T const& arg_i, T *R, T *I) {
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T r, i, hr, hr1, hr2, hi, hi1, hi2;
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T sin_arg_r, cos_arg_r, sinh_arg_i, cosh_arg_i;
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/* arguments */
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const T* p = a + size;
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sin_arg_r = sin(arg_r);
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cos_arg_r = cos(arg_r);
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sinh_arg_i = sinh(arg_i);
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cosh_arg_i = cosh(arg_i);
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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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for (hi1 = hr1 = hi = 0, hr = *--p; 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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template <typename T>
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inline T clens(const T *a, int size, T const& arg_r) {
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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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for (hr1 = 0, hr = *--p; 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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template <typename T, typename Parameters>
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struct base_etmerc_ellipsoid
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{
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par_etmerc<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& , T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const
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{
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T sin_Cn, cos_Cn, cos_Ce, sin_Ce, dCn, dCe;
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T Cn = lp_lat, Ce = lp_lon;
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/* ell. LAT, LNG -> Gaussian LAT, LNG */
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Cn = gatg(this->m_proj_parm.cbg, PROJ_ETMERC_ORDER, Cn);
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/* Gaussian LAT, LNG -> compl. sph. LAT */
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sin_Cn = sin(Cn);
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cos_Cn = cos(Cn);
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sin_Ce = sin(Ce);
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cos_Ce = cos(Ce);
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Cn = atan2(sin_Cn, cos_Ce*cos_Cn);
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Ce = atan2(sin_Ce*cos_Cn, boost::math::hypot(sin_Cn, cos_Cn*cos_Ce));
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/* compl. sph. N, E -> ell. norm. N, E */
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Ce = asinhy(tan(Ce)); /* Replaces: Ce = log(tan(fourth_pi + Ce*0.5)); */
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Cn += clenS(this->m_proj_parm.gtu, PROJ_ETMERC_ORDER, 2*Cn, 2*Ce, &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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xy_x = xy_y = HUGE_VAL;
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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& , T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const
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{
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T sin_Cn, cos_Cn, cos_Ce, sin_Ce, dCn, dCe;
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T Cn = xy_y, Ce = xy_x;
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/* normalize N, E */
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Cn = (Cn - this->m_proj_parm.Zb)/this->m_proj_parm.Qn;
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Ce = Ce/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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Cn += clenS(this->m_proj_parm.utg, PROJ_ETMERC_ORDER, 2*Cn, 2*Ce, &dCn, &dCe);
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Ce += dCe;
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Ce = atan(sinh(Ce)); /* Replaces: Ce = 2*(atan(exp(Ce)) - fourth_pi); */
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/* compl. sph. LAT -> Gaussian LAT, LNG */
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sin_Cn = sin(Cn);
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cos_Cn = cos(Cn);
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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, boost::math::hypot(sin_Ce, cos_Ce*cos_Cn));
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/* Gaussian LAT, LNG -> ell. LAT, LNG */
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lp_lat = gatg(this->m_proj_parm.cgb, PROJ_ETMERC_ORDER, Cn);
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lp_lon = Ce;
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}
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else
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lp_lat = lp_lon = HUGE_VAL;
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}
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static inline std::string get_name()
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{
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return "etmerc_ellipsoid";
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}
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};
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template <typename Parameters, typename T>
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inline void setup(Parameters& par, par_etmerc<T>& proj_parm)
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{
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T f, n, np, Z;
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if (par.es <= 0) {
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BOOST_THROW_EXCEPTION( projection_exception(error_ellipsoid_use_required) );
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}
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f = par.es / (1 + sqrt(1 - par.es)); /* Replaces: f = 1 - sqrt(1-par.es); */
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/* third flattening */
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np = n = f/(2 - f);
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/* COEF. OF TRIG SERIES GEO <-> GAUSS */
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/* cgb := Gaussian -> Geodetic, KW p190 - 191 (61) - (62) */
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/* cbg := Geodetic -> Gaussian, KW p186 - 187 (51) - (52) */
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/* PROJ_ETMERC_ORDER = 6th degree : Engsager and Poder: ICC2007 */
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proj_parm.cgb[0] = n*( 2 + n*(-2/3.0 + n*(-2 + n*(116/45.0 + n*(26/45.0 +
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n*(-2854/675.0 ))))));
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proj_parm.cbg[0] = n*(-2 + n*( 2/3.0 + n*( 4/3.0 + n*(-82/45.0 + n*(32/45.0 +
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n*( 4642/4725.0))))));
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np *= n;
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proj_parm.cgb[1] = np*(7/3.0 + n*( -8/5.0 + n*(-227/45.0 + n*(2704/315.0 +
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n*( 2323/945.0)))));
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proj_parm.cbg[1] = np*(5/3.0 + n*(-16/15.0 + n*( -13/9.0 + n*( 904/315.0 +
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n*(-1522/945.0)))));
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np *= n;
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/* n^5 coeff corrected from 1262/105 -> -1262/105 */
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proj_parm.cgb[2] = np*( 56/15.0 + n*(-136/35.0 + n*(-1262/105.0 +
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n*( 73814/2835.0))));
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proj_parm.cbg[2] = np*(-26/15.0 + n*( 34/21.0 + n*( 8/5.0 +
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n*(-12686/2835.0))));
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np *= n;
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/* n^5 coeff corrected from 322/35 -> 332/35 */
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proj_parm.cgb[3] = np*(4279/630.0 + n*(-332/35.0 + n*(-399572/14175.0)));
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proj_parm.cbg[3] = np*(1237/630.0 + n*( -12/5.0 + n*( -24832/14175.0)));
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np *= n;
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proj_parm.cgb[4] = np*(4174/315.0 + n*(-144838/6237.0 ));
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proj_parm.cbg[4] = np*(-734/315.0 + n*( 109598/31185.0));
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np *= n;
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proj_parm.cgb[5] = np*(601676/22275.0 );
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proj_parm.cbg[5] = np*(444337/155925.0);
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/* Constants of the projections */
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/* Transverse Mercator (UTM, ITM, etc) */
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np = n*n;
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/* Norm. mer. quad, K&W p.50 (96), p.19 (38b), p.5 (2) */
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proj_parm.Qn = par.k0/(1 + n) * (1 + np*(1/4.0 + np*(1/64.0 + np/256.0)));
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/* coef of trig series */
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/* utg := ell. N, E -> sph. N, E, KW p194 (65) */
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/* gtu := sph. N, E -> ell. N, E, KW p196 (69) */
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proj_parm.utg[0] = n*(-0.5 + n*( 2/3.0 + n*(-37/96.0 + n*( 1/360.0 +
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n*( 81/512.0 + n*(-96199/604800.0))))));
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proj_parm.gtu[0] = n*( 0.5 + n*(-2/3.0 + n*( 5/16.0 + n*(41/180.0 +
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n*(-127/288.0 + n*( 7891/37800.0 ))))));
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proj_parm.utg[1] = np*(-1/48.0 + n*(-1/15.0 + n*(437/1440.0 + n*(-46/105.0 +
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n*( 1118711/3870720.0)))));
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proj_parm.gtu[1] = np*(13/48.0 + n*(-3/5.0 + n*(557/1440.0 + n*(281/630.0 +
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n*(-1983433/1935360.0)))));
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np *= n;
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proj_parm.utg[2] = np*(-17/480.0 + n*( 37/840.0 + n*( 209/4480.0 +
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n*( -5569/90720.0 ))));
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proj_parm.gtu[2] = np*( 61/240.0 + n*(-103/140.0 + n*(15061/26880.0 +
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n*(167603/181440.0))));
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np *= n;
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proj_parm.utg[3] = np*(-4397/161280.0 + n*( 11/504.0 + n*( 830251/7257600.0)));
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proj_parm.gtu[3] = np*(49561/161280.0 + n*(-179/168.0 + n*(6601661/7257600.0)));
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np *= n;
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proj_parm.utg[4] = np*(-4583/161280.0 + n*( 108847/3991680.0));
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proj_parm.gtu[4] = np*(34729/80640.0 + n*(-3418889/1995840.0));
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np *= n;
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proj_parm.utg[5] = np*(-20648693/638668800.0);
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proj_parm.gtu[5] = np*(212378941/319334400.0);
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/* Gaussian latitude value of the origin latitude */
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Z = gatg(proj_parm.cbg, PROJ_ETMERC_ORDER, par.phi0);
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/* Origin northing minus true northing at the origin latitude */
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/* i.e. true northing = N - proj_parm.Zb */
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proj_parm.Zb = - proj_parm.Qn*(Z + clens(proj_parm.gtu, PROJ_ETMERC_ORDER, 2*Z));
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}
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// Extended Transverse Mercator
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template <typename Parameters, typename T>
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inline void setup_etmerc(Parameters& par, par_etmerc<T>& proj_parm)
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{
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setup(par, proj_parm);
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}
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// Universal Transverse Mercator (UTM)
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template <typename Params, typename Parameters, typename T>
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inline void setup_utm(Params const& params, Parameters& par, par_etmerc<T>& proj_parm)
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{
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static const T pi = detail::pi<T>();
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int zone;
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if (par.es == 0.0) {
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BOOST_THROW_EXCEPTION( projection_exception(error_ellipsoid_use_required) );
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}
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par.y0 = pj_get_param_b<srs::spar::south>(params, "south", srs::dpar::south) ? 10000000. : 0.;
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par.x0 = 500000.;
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if (pj_param_i<srs::spar::zone>(params, "zone", srs::dpar::zone, zone)) /* zone input ? */
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{
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if (zone > 0 && zone <= 60)
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--zone;
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else {
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BOOST_THROW_EXCEPTION( projection_exception(error_invalid_utm_zone) );
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}
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}
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else /* nearest central meridian input */
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{
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zone = int_floor((adjlon(par.lam0) + pi) * 30. / pi);
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if (zone < 0)
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zone = 0;
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else if (zone >= 60)
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zone = 59;
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}
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par.lam0 = (zone + .5) * pi / 30. - pi;
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par.k0 = 0.9996;
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par.phi0 = 0.;
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setup(par, proj_parm);
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}
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}} // namespace detail::etmerc
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#endif // doxygen
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/*!
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\brief Extended Transverse 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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\par Projection parameters
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- lat_ts: Latitude of true scale
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- lat_0: Latitude of origin
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\par Example
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\image html ex_etmerc.gif
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*/
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template <typename T, typename Parameters>
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struct etmerc_ellipsoid : public detail::etmerc::base_etmerc_ellipsoid<T, Parameters>
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{
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template <typename Params>
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inline etmerc_ellipsoid(Params const& , Parameters & par)
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{
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detail::etmerc::setup_etmerc(par, this->m_proj_parm);
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}
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};
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/*!
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\brief Universal Transverse Mercator (UTM) 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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\par Projection parameters
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- zone: UTM Zone (integer)
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- south: Denotes southern hemisphere UTM zone (boolean)
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\par Example
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\image html ex_utm.gif
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*/
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template <typename T, typename Parameters>
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struct utm_ellipsoid : public detail::etmerc::base_etmerc_ellipsoid<T, Parameters>
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{
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template <typename Params>
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inline utm_ellipsoid(Params const& params, Parameters & par)
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{
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detail::etmerc::setup_utm(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_etmerc, etmerc_ellipsoid)
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_utm, utm_ellipsoid)
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// Factory entry(s)
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(etmerc_entry, etmerc_ellipsoid)
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(utm_entry, utm_ellipsoid)
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(etmerc_init)
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{
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(etmerc, etmerc_entry);
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(utm, utm_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_ETMERC_HPP
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