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+#ifndef BOOST_GEOMETRY_PROJECTIONS_ETMERC_HPP
+#define BOOST_GEOMETRY_PROJECTIONS_ETMERC_HPP
+
+// Boost.Geometry - extensions-gis-projections (based on PROJ4)
+// This file is automatically generated. DO NOT EDIT.
+
+// Copyright (c) 2008-2015 Barend Gehrels, Amsterdam, the Netherlands.
+
+// This file was modified by Oracle on 2017.
+// Modifications copyright (c) 2017, Oracle and/or its affiliates.
+// Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle.
+
+// Use, modification and distribution is subject to the Boost Software License,
+// Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt)
+
+// This file is converted from PROJ4, http://trac.osgeo.org/proj
+// PROJ4 is originally written by Gerald Evenden (then of the USGS)
+// PROJ4 is maintained by Frank Warmerdam
+// PROJ4 is converted to Boost.Geometry by Barend Gehrels
+
+// Last updated version of proj: 4.9.1
+
+// Original copyright notice:
+
+// Copyright (c) 2008 Gerald I. Evenden
+
+// Permission is hereby granted, free of charge, to any person obtaining a
+// copy of this software and associated documentation files (the "Software"),
+// to deal in the Software without restriction, including without limitation
+// the rights to use, copy, modify, merge, publish, distribute, sublicense,
+// and/or sell copies of the Software, and to permit persons to whom the
+// Software is furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included
+// in all copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+// DEALINGS IN THE SOFTWARE.
+
+#include <boost/math/special_functions/hypot.hpp>
+
+#include <boost/geometry/srs/projections/impl/base_static.hpp>
+#include <boost/geometry/srs/projections/impl/base_dynamic.hpp>
+#include <boost/geometry/srs/projections/impl/projects.hpp>
+#include <boost/geometry/srs/projections/impl/factory_entry.hpp>
+
+namespace boost { namespace geometry
+{
+
+namespace srs { namespace par4
+{
+ struct etmerc {};
+
+}} //namespace srs::par4
+
+namespace projections
+{
+ #ifndef DOXYGEN_NO_DETAIL
+ namespace detail { namespace etmerc
+ {
+
+ static const int PROJ_ETMERC_ORDER = 6;
+
+ template <typename T>
+ struct par_etmerc
+ {
+ T Qn; /* Merid. quad., scaled to the projection */
+ T Zb; /* Radius vector in polar coord. systems */
+ T cgb[6]; /* Constants for Gauss -> Geo lat */
+ T cbg[6]; /* Constants for Geo lat -> Gauss */
+ T utg[6]; /* Constants for transv. merc. -> geo */
+ T gtu[6]; /* Constants for geo -> transv. merc. */
+ };
+
+ /* The code in this file is largly based upon procedures:
+ *
+ * Written by: Knud Poder and Karsten Engsager
+ *
+ * Based on math from: R.Koenig and K.H. Weise, "Mathematische
+ * Grundlagen der hoeheren Geodaesie und Kartographie,
+ * Springer-Verlag, Berlin/Goettingen" Heidelberg, 1951.
+ *
+ * Modified and used here by permission of Reference Networks
+ * Division, Kort og Matrikelstyrelsen (KMS), Copenhagen, Denmark
+ */
+
+
+
+
+
+ template <typename T>
+ inline T
+ log1py(T const& x) { /* Compute log(1+x) accurately */
+ volatile T
+ y = 1 + x,
+ z = y - 1;
+ /* Here's the explanation for this magic: y = 1 + z, exactly, and z
+ * approx x, thus log(y)/z (which is nearly constant near z = 0) returns
+ * a good approximation to the true log(1 + x)/x. The multiplication x *
+ * (log(y)/z) introduces little additional error. */
+ return z == 0 ? x : x * log(y) / z;
+ }
+
+ template <typename T>
+ inline T
+ asinhy(T const& x) { /* Compute asinh(x) accurately */
+ T y = fabs(x); /* Enforce odd parity */
+ y = log1py(y * (1 + y/(boost::math::hypot(1.0, y) + 1)));
+ return x < 0 ? -y : y;
+ }
+
+ template <typename T>
+ inline T
+ gatg(const T *p1, int len_p1, T const& B) {
+ const T *p;
+ T h = 0, h1, h2 = 0, cos_2B;
+
+ cos_2B = 2*cos(2*B);
+ for (p = p1 + len_p1, h1 = *--p; p - p1; h2 = h1, h1 = h)
+ h = -h2 + cos_2B*h1 + *--p;
+ return (B + h*sin(2*B));
+ }
+
+ template <typename T>
+ inline T
+ clenS(const T *a, int size, T const& arg_r, T const& arg_i, T *R, T *I) {
+ T r, i, hr, hr1, hr2, hi, hi1, hi2;
+ T sin_arg_r, cos_arg_r, sinh_arg_i, cosh_arg_i;
+
+ /* arguments */
+ const T* p = a + size;
+ sin_arg_r = sin(arg_r);
+ cos_arg_r = cos(arg_r);
+ sinh_arg_i = sinh(arg_i);
+ cosh_arg_i = cosh(arg_i);
+ r = 2*cos_arg_r*cosh_arg_i;
+ i = -2*sin_arg_r*sinh_arg_i;
+ /* summation loop */
+ for (hi1 = hr1 = hi = 0, hr = *--p; a - p;) {
+ hr2 = hr1;
+ hi2 = hi1;
+ hr1 = hr;
+ hi1 = hi;
+ hr = -hr2 + r*hr1 - i*hi1 + *--p;
+ hi = -hi2 + i*hr1 + r*hi1;
+ }
+ r = sin_arg_r*cosh_arg_i;
+ i = cos_arg_r*sinh_arg_i;
+ *R = r*hr - i*hi;
+ *I = r*hi + i*hr;
+ return(*R);
+ }
+
+ template <typename T>
+ inline T
+ clens(const T *a, int size, T const& arg_r) {
+ T r, hr, hr1, hr2, cos_arg_r;
+
+ const T* p = a + size;
+ cos_arg_r = cos(arg_r);
+ r = 2*cos_arg_r;
+ /* summation loop */
+ for (hr1 = 0, hr = *--p; a - p;) {
+ hr2 = hr1;
+ hr1 = hr;
+ hr = -hr2 + r*hr1 + *--p;
+ }
+ return(sin(arg_r)*hr);
+ }
+
+ // template class, using CRTP to implement forward/inverse
+ template <typename CalculationType, typename Parameters>
+ struct base_etmerc_ellipsoid : public base_t_fi<base_etmerc_ellipsoid<CalculationType, Parameters>,
+ CalculationType, Parameters>
+ {
+
+ typedef CalculationType geographic_type;
+ typedef CalculationType cartesian_type;
+
+ par_etmerc<CalculationType> m_proj_parm;
+
+ inline base_etmerc_ellipsoid(const Parameters& par)
+ : base_t_fi<base_etmerc_ellipsoid<CalculationType, Parameters>,
+ CalculationType, Parameters>(*this, par) {}
+
+ // FORWARD(e_forward) ellipsoid
+ // Project coordinates from geographic (lon, lat) to cartesian (x, y)
+ inline void fwd(geographic_type& lp_lon, geographic_type& lp_lat, cartesian_type& xy_x, cartesian_type& xy_y) const
+ {
+ CalculationType sin_Cn, cos_Cn, cos_Ce, sin_Ce, dCn, dCe;
+ CalculationType Cn = lp_lat, Ce = lp_lon;
+
+ /* ell. LAT, LNG -> Gaussian LAT, LNG */
+ Cn = gatg(this->m_proj_parm.cbg, PROJ_ETMERC_ORDER, Cn);
+ /* Gaussian LAT, LNG -> compl. sph. LAT */
+ sin_Cn = sin(Cn);
+ cos_Cn = cos(Cn);
+ sin_Ce = sin(Ce);
+ cos_Ce = cos(Ce);
+
+ Cn = atan2(sin_Cn, cos_Ce*cos_Cn);
+ Ce = atan2(sin_Ce*cos_Cn, boost::math::hypot(sin_Cn, cos_Cn*cos_Ce));
+ /* compl. sph. N, E -> ell. norm. N, E */
+ Ce = asinhy(tan(Ce)); /* Replaces: Ce = log(tan(FORTPI + Ce*0.5)); */
+ Cn += clenS(this->m_proj_parm.gtu, PROJ_ETMERC_ORDER, 2*Cn, 2*Ce, &dCn, &dCe);
+ Ce += dCe;
+ if (fabs(Ce) <= 2.623395162778) {
+ xy_y = this->m_proj_parm.Qn * Cn + this->m_proj_parm.Zb; /* Northing */
+ xy_x = this->m_proj_parm.Qn * Ce; /* Easting */
+ } else
+ xy_x = xy_y = HUGE_VAL;
+ }
+
+ // INVERSE(e_inverse) ellipsoid
+ // Project coordinates from cartesian (x, y) to geographic (lon, lat)
+ inline void inv(cartesian_type& xy_x, cartesian_type& xy_y, geographic_type& lp_lon, geographic_type& lp_lat) const
+ {
+ CalculationType sin_Cn, cos_Cn, cos_Ce, sin_Ce, dCn, dCe;
+ CalculationType Cn = xy_y, Ce = xy_x;
+
+ /* normalize N, E */
+ Cn = (Cn - this->m_proj_parm.Zb)/this->m_proj_parm.Qn;
+ Ce = Ce/this->m_proj_parm.Qn;
+ if (fabs(Ce) <= 2.623395162778) { /* 150 degrees */
+ /* norm. N, E -> compl. sph. LAT, LNG */
+ Cn += clenS(this->m_proj_parm.utg, PROJ_ETMERC_ORDER, 2*Cn, 2*Ce, &dCn, &dCe);
+ Ce += dCe;
+ Ce = atan(sinh(Ce)); /* Replaces: Ce = 2*(atan(exp(Ce)) - FORTPI); */
+ /* compl. sph. LAT -> Gaussian LAT, LNG */
+ sin_Cn = sin(Cn);
+ cos_Cn = cos(Cn);
+ sin_Ce = sin(Ce);
+ cos_Ce = cos(Ce);
+ Ce = atan2(sin_Ce, cos_Ce*cos_Cn);
+ Cn = atan2(sin_Cn*cos_Ce, boost::math::hypot(sin_Ce, cos_Ce*cos_Cn));
+ /* Gaussian LAT, LNG -> ell. LAT, LNG */
+ lp_lat = gatg(this->m_proj_parm.cgb, PROJ_ETMERC_ORDER, Cn);
+ lp_lon = Ce;
+ }
+ else
+ lp_lat = lp_lon = HUGE_VAL;
+ }
+
+ static inline std::string get_name()
+ {
+ return "etmerc_ellipsoid";
+ }
+
+ };
+
+ // Extended Transverse Mercator
+ template <typename Parameters, typename T>
+ inline void setup_etmerc(Parameters& par, par_etmerc<T>& proj_parm)
+ {
+ T f, n, np, Z;
+
+ if (par.es <= 0)
+ BOOST_THROW_EXCEPTION( projection_exception(-34) );
+ f = par.es / (1 + sqrt(1 - par.es)); /* Replaces: f = 1 - sqrt(1-par.es); */
+ /* third flattening */
+ np = n = f/(2 - f);
+
+ /* 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 */
+ Z = gatg(proj_parm.cbg, PROJ_ETMERC_ORDER, par.phi0);
+ /* Origin northing minus true northing at the origin latitude */
+ /* i.e. true northing = N - proj_parm.Zb */
+ proj_parm.Zb = - proj_parm.Qn*(Z + clens(proj_parm.gtu, PROJ_ETMERC_ORDER, 2*Z));
+ }
+
+ }} // namespace detail::etmerc
+ #endif // doxygen
+
+ /*!
+ \brief Extended Transverse Mercator projection
+ \ingroup projections
+ \tparam Geographic latlong point type
+ \tparam Cartesian xy point type
+ \tparam Parameters parameter type
+ \par Projection characteristics
+ - Cylindrical
+ - Spheroid
+ \par Projection parameters
+ - lat_ts: Latitude of true scale
+ - lat_0: Latitude of origin
+ \par Example
+ \image html ex_etmerc.gif
+ */
+ template <typename CalculationType, typename Parameters>
+ struct etmerc_ellipsoid : public detail::etmerc::base_etmerc_ellipsoid<CalculationType, Parameters>
+ {
+ inline etmerc_ellipsoid(const Parameters& par) : detail::etmerc::base_etmerc_ellipsoid<CalculationType, Parameters>(par)
+ {
+ detail::etmerc::setup_etmerc(this->m_par, this->m_proj_parm);
+ }
+ };
+
+ #ifndef DOXYGEN_NO_DETAIL
+ namespace detail
+ {
+
+ // Static projection
+ BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION(srs::par4::etmerc, etmerc_ellipsoid, etmerc_ellipsoid)
+
+ // Factory entry(s)
+ template <typename CalculationType, typename Parameters>
+ class etmerc_entry : public detail::factory_entry<CalculationType, Parameters>
+ {
+ public :
+ virtual base_v<CalculationType, Parameters>* create_new(const Parameters& par) const
+ {
+ return new base_v_fi<etmerc_ellipsoid<CalculationType, Parameters>, CalculationType, Parameters>(par);
+ }
+ };
+
+ template <typename CalculationType, typename Parameters>
+ inline void etmerc_init(detail::base_factory<CalculationType, Parameters>& factory)
+ {
+ factory.add_to_factory("etmerc", new etmerc_entry<CalculationType, Parameters>);
+ }
+
+ } // namespace detail
+ #endif // doxygen
+
+} // namespace projections
+
+}} // namespace boost::geometry
+
+#endif // BOOST_GEOMETRY_PROJECTIONS_ETMERC_HPP
+