boost/geometry/srs/projections/proj/tmerc.hpp
// Boost.Geometry - gis-projections (based on PROJ4) // Copyright (c) 2008-2015 Barend Gehrels, Amsterdam, the Netherlands. // Copyright (c) 2023 Adam Wulkiewicz, Lodz, Poland. // This file was modified by Oracle on 2017, 2018, 2019, 2022. // Modifications copyright (c) 2017-2022, Oracle and/or its affiliates. // Contributed and/or modified by Vissarion Fysikopoulos, on behalf of Oracle. // 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: 8.2.1 // Original copyright notice: // 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. #ifndef BOOST_GEOMETRY_PROJECTIONS_TMERC_HPP #define BOOST_GEOMETRY_PROJECTIONS_TMERC_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> #include <boost/geometry/srs/projections/impl/function_overloads.hpp> #include <boost/geometry/srs/projections/impl/pj_mlfn.hpp> #include <boost/geometry/util/condition.hpp> #include <boost/geometry/util/math.hpp> namespace boost { namespace geometry { namespace projections { #ifndef DOXYGEN_NO_DETAIL namespace detail { namespace tmerc { static const double epsilon10 = 1.e-10; /* Constant for "exact" transverse mercator */ static const int proj_etmerc_order = 6; template <typename T> inline T FC1() { return 1.; } template <typename T> inline T FC2() { return .5; } template <typename T> inline T FC3() { return .16666666666666666666666666666666666666; } template <typename T> inline T FC4() { return .08333333333333333333333333333333333333; } template <typename T> inline T FC5() { return .05; } template <typename T> inline T FC6() { return .03333333333333333333333333333333333333; } template <typename T> inline T FC7() { return .02380952380952380952380952380952380952; } template <typename T> inline T FC8() { return .01785714285714285714285714285714285714; } template <typename T> struct par_tmerc { T esp; T ml0; detail::en<T> en; }; // More exact: Poder/Engsager template <typename T> struct par_tmerc_exact { 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. */ }; template <typename T, typename Parameters> struct base_tmerc_ellipsoid { par_tmerc<T> m_proj_parm; // FORWARD(e_forward) ellipse // 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>(); static const T FC1 = tmerc::FC1<T>(); static const T FC2 = tmerc::FC2<T>(); static const T FC3 = tmerc::FC3<T>(); static const T FC4 = tmerc::FC4<T>(); static const T FC5 = tmerc::FC5<T>(); static const T FC6 = tmerc::FC6<T>(); static const T FC7 = tmerc::FC7<T>(); static const T FC8 = tmerc::FC8<T>(); T al, als, n, cosphi, sinphi, t; /* * 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; } sinphi = sin(lp_lat); cosphi = cos(lp_lat); t = fabs(cosphi) > 1e-10 ? sinphi/cosphi : 0.; t *= t; al = cosphi * lp_lon; als = al * al; al /= sqrt(1. - par.es * sinphi * sinphi); n = this->m_proj_parm.esp * cosphi * cosphi; xy_x = par.k0 * al * (FC1 + FC3 * als * (1. - t + n + FC5 * als * (5. + t * (t - 18.) + n * (14. - 58. * t) + FC7 * als * (61. + t * ( t * (179. - t) - 479. ) ) ))); xy_y = par.k0 * (pj_mlfn(lp_lat, sinphi, cosphi, this->m_proj_parm.en) - this->m_proj_parm.ml0 + sinphi * al * lp_lon * FC2 * ( 1. + FC4 * als * (5. - t + n * (9. + 4. * n) + FC6 * als * (61. + t * (t - 58.) + n * (270. - 330 * t) + FC8 * als * (1385. + t * ( t * (543. - t) - 3111.) ) )))); } // INVERSE(e_inverse) ellipsoid // 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 { static const T half_pi = detail::half_pi<T>(); static const T FC1 = tmerc::FC1<T>(); static const T FC2 = tmerc::FC2<T>(); static const T FC3 = tmerc::FC3<T>(); static const T FC4 = tmerc::FC4<T>(); static const T FC5 = tmerc::FC5<T>(); static const T FC6 = tmerc::FC6<T>(); static const T FC7 = tmerc::FC7<T>(); static const T FC8 = tmerc::FC8<T>(); T n, con, cosphi, d, ds, sinphi, t; lp_lat = pj_inv_mlfn(this->m_proj_parm.ml0 + xy_y / par.k0, par.es, this->m_proj_parm.en); if (fabs(lp_lat) >= half_pi) { lp_lat = xy_y < 0. ? -half_pi : half_pi; lp_lon = 0.; } else { sinphi = sin(lp_lat); cosphi = cos(lp_lat); t = fabs(cosphi) > 1e-10 ? sinphi/cosphi : 0.; n = this->m_proj_parm.esp * cosphi * cosphi; d = xy_x * sqrt(con = 1. - par.es * sinphi * sinphi) / par.k0; con *= t; t *= t; ds = d * d; lp_lat -= (con * ds / (1.-par.es)) * FC2 * (1. - ds * FC4 * (5. + t * (3. - 9. * n) + n * (1. - 4 * n) - ds * FC6 * (61. + t * (90. - 252. * n + 45. * t) + 46. * n - ds * FC8 * (1385. + t * (3633. + t * (4095. + 1574. * t)) ) ))); lp_lon = d*(FC1 - ds*FC3*( 1. + 2.*t + n - ds*FC5*(5. + t*(28. + 24.*t + 8.*n) + 6.*n - ds * FC7 * (61. + t * (662. + t * (1320. + 720. * t)) ) ))) / cosphi; } } static inline std::string get_name() { return "tmerc_ellipsoid"; } }; template <typename T, typename Parameters> struct base_tmerc_ellipsoid_exact { par_tmerc_exact<T> m_proj_parm; static inline std::string get_name() { return "tmerc_ellipsoid"; } /* Helper functions for "exact" transverse mercator */ inline static T gatg(const T *p1, int len_p1, T B, T cos_2B, T sin_2B) { T h = 0, h1, h2 = 0; const T two_cos_2B = 2*cos_2B; const T* p = p1 + len_p1; h1 = *--p; while (p - p1) { h = -h2 + two_cos_2B*h1 + *--p; h2 = h1; h1 = h; } return (B + h*sin_2B); } /* Complex Clenshaw summation */ inline static T clenS(const T *a, int size, T sin_arg_r, T cos_arg_r, T sinh_arg_i, T cosh_arg_i, T *R, T *I) { T r, i, hr, hr1, hr2, hi, hi1, hi2; /* arguments */ const T* p = a + size; r = 2*cos_arg_r*cosh_arg_i; i = -2*sin_arg_r*sinh_arg_i; /* summation loop */ hi1 = hr1 = hi = 0; hr = *--p; for (; 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; } /* Real Clenshaw summation */ static T clens(const T *a, int size, T 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 */ hr1 = 0; hr = *--p; for (; a - p;) { hr2 = hr1; hr1 = hr; hr = -hr2 + r*hr1 + *--p; } return sin(arg_r)*hr; } /* Ellipsoidal, forward */ //static PJ_XY exact_e_fwd (PJ_LP lp, PJ *P) inline void fwd(Parameters const& /*par*/, T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const { //PJ_XY xy = {0.0,0.0}; //const auto *Q = &(static_cast<struct tmerc_data*>(par.opaque)->exact); /* ell. LAT, LNG -> Gaussian LAT, LNG */ T Cn = gatg (this->m_proj_parm.cbg, proj_etmerc_order, lp_lat, cos(2*lp_lat), sin(2*lp_lat)); /* Gaussian LAT, LNG -> compl. sph. LAT */ const T sin_Cn = sin (Cn); const T cos_Cn = cos (Cn); const T sin_Ce = sin (lp_lon); const T cos_Ce = cos (lp_lon); const T cos_Cn_cos_Ce = cos_Cn*cos_Ce; Cn = atan2 (sin_Cn, cos_Cn_cos_Ce); const T inv_denom_tan_Ce = 1. / hypot (sin_Cn, cos_Cn_cos_Ce); const T tan_Ce = sin_Ce*cos_Cn * inv_denom_tan_Ce; #if 0 // Variant of the above: found not to be measurably faster const T sin_Ce_cos_Cn = sin_Ce*cos_Cn; const T denom = sqrt(1 - sin_Ce_cos_Cn * sin_Ce_cos_Cn); const T tan_Ce = sin_Ce_cos_Cn / denom; #endif /* compl. sph. N, E -> ell. norm. N, E */ T Ce = asinh ( tan_Ce ); /* Replaces: Ce = log(tan(FORTPI + Ce*0.5)); */ /* * Non-optimized version: * const T sin_arg_r = sin(2*Cn); * const T cos_arg_r = cos(2*Cn); * * Given: * sin(2 * Cn) = 2 sin(Cn) cos(Cn) * sin(atan(y)) = y / sqrt(1 + y^2) * cos(atan(y)) = 1 / sqrt(1 + y^2) * ==> sin(2 * Cn) = 2 tan_Cn / (1 + tan_Cn^2) * * cos(2 * Cn) = 2cos^2(Cn) - 1 * = 2 / (1 + tan_Cn^2) - 1 */ const T two_inv_denom_tan_Ce = 2 * inv_denom_tan_Ce; const T two_inv_denom_tan_Ce_square = two_inv_denom_tan_Ce * inv_denom_tan_Ce; const T tmp_r = cos_Cn_cos_Ce * two_inv_denom_tan_Ce_square; const T sin_arg_r = sin_Cn * tmp_r; const T cos_arg_r = cos_Cn_cos_Ce * tmp_r - 1; /* * Non-optimized version: * const T sinh_arg_i = sinh(2*Ce); * const T cosh_arg_i = cosh(2*Ce); * * Given * sinh(2 * Ce) = 2 sinh(Ce) cosh(Ce) * sinh(asinh(y)) = y * cosh(asinh(y)) = sqrt(1 + y^2) * ==> sinh(2 * Ce) = 2 tan_Ce sqrt(1 + tan_Ce^2) * * cosh(2 * Ce) = 2cosh^2(Ce) - 1 * = 2 * (1 + tan_Ce^2) - 1 * * and 1+tan_Ce^2 = 1 + sin_Ce^2 * cos_Cn^2 / (sin_Cn^2 + cos_Cn^2 * cos_Ce^2) * = (sin_Cn^2 + cos_Cn^2 * cos_Ce^2 + sin_Ce^2 * cos_Cn^2) / (sin_Cn^2 + cos_Cn^2 * cos_Ce^2) * = 1. / (sin_Cn^2 + cos_Cn^2 * cos_Ce^2) * = inv_denom_tan_Ce^2 * */ const T sinh_arg_i = tan_Ce * two_inv_denom_tan_Ce; const T cosh_arg_i = two_inv_denom_tan_Ce_square - 1; T dCn, dCe; Cn += clenS (this->m_proj_parm.gtu, proj_etmerc_order, sin_arg_r, cos_arg_r, sinh_arg_i, cosh_arg_i, &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 { BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) ); xy_x = xy_y = HUGE_VAL; } } /* Ellipsoidal, inverse */ inline void inv(Parameters const& /*par*/, T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const { //PJ_LP lp = {0.0,0.0}; //const auto *Q = &(static_cast<struct tmerc_data*>(par.opaque)->exact); /* normalize N, E */ T Cn = (xy_y - this->m_proj_parm.Zb)/this->m_proj_parm.Qn; T Ce = xy_x/this->m_proj_parm.Qn; if (fabs(Ce) <= 2.623395162778) { /* 150 degrees */ /* norm. N, E -> compl. sph. LAT, LNG */ const T sin_arg_r = sin(2*Cn); const T cos_arg_r = cos(2*Cn); //const T sinh_arg_i = sinh(2*Ce); //const T cosh_arg_i = cosh(2*Ce); const T exp_2_Ce = exp(2*Ce); const T half_inv_exp_2_Ce = 0.5 / exp_2_Ce; const T sinh_arg_i = 0.5 * exp_2_Ce - half_inv_exp_2_Ce; const T cosh_arg_i = 0.5 * exp_2_Ce + half_inv_exp_2_Ce; T dCn_ignored, dCe; Cn += clenS(this->m_proj_parm.utg, proj_etmerc_order, sin_arg_r, cos_arg_r, sinh_arg_i, cosh_arg_i, &dCn_ignored, &dCe); Ce += dCe; /* compl. sph. LAT -> Gaussian LAT, LNG */ const T sin_Cn = sin (Cn); const T cos_Cn = cos (Cn); #if 0 // Non-optimized version: T sin_Ce, cos_Ce; Ce = atan (sinh (Ce)); // Replaces: Ce = 2*(atan(exp(Ce)) - FORTPI); sin_Ce = sin (Ce); cos_Ce = cos (Ce); Ce = atan2 (sin_Ce, cos_Ce*cos_Cn); 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