boost/geometry/srs/projections/proj/etmerc.hpp
// Boost.Geometry - gis-projections (based on PROJ4) // Copyright (c) 2008-2015 Barend Gehrels, Amsterdam, the Netherlands. // This file was modified by Oracle on 2017, 2018. // Modifications copyright (c) 2017-2018, 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: 5.0.0 // 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. /* 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 */ #ifndef BOOST_GEOMETRY_PROJECTIONS_ETMERC_HPP #define BOOST_GEOMETRY_PROJECTIONS_ETMERC_HPP #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> #include <boost/geometry/srs/projections/impl/function_overloads.hpp> namespace boost { namespace geometry { 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. */ }; 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)); } /* Complex Clenshaw summation */ 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); } /* Real Clenshaw summation */ 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 T, typename Parameters> struct base_etmerc_ellipsoid : public base_t_fi<base_etmerc_ellipsoid<T, Parameters>, T, Parameters> { par_etmerc<T> m_proj_parm; inline base_etmerc_ellipsoid(const Parameters& par) : base_t_fi<base_etmerc_ellipsoid<T, Parameters>, T, Parameters>(*this, par) {} // FORWARD(e_forward) ellipsoid // Project coordinates from geographic (lon, lat) to cartesian (x, y) inline void fwd(T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const { T sin_Cn, cos_Cn, cos_Ce, sin_Ce, dCn, dCe; T 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(fourth_pi + 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(T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const { T sin_Cn, cos_Cn, cos_Ce, sin_Ce, dCn, dCe; T 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)) - fourth_pi); */ /* 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"; } }; template <typename Parameters, typename T> inline void setup(Parameters& par, par_etmerc<T>& proj_parm) { T f, n, np, Z; if (par.es <= 0) { BOOST_THROW_EXCEPTION( projection_exception(error_ellipsoid_use_required) ); } 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)); } // Extended Transverse Mercator template <typename Parameters, typename T> inline void setup_etmerc(Parameters& par, par_etmerc<T>& proj_parm) { setup(par, proj_parm); } // Universal Transverse Mercator (UTM) template <typename Params, typename Parameters, typename T> inline void setup_utm(Params const& params, Parameters& par, par_etmerc<T>& proj_parm) { static const T pi = detail::pi<T>(); int zone; if (par.es == 0.0) { BOOST_THROW_EXCEPTION( projection_exception(error_ellipsoid_use_required) ); } par.y0 = pj_get_param_b<srs::spar::south>(params, "south", srs::dpar::south) ? 10000000. : 0.; par.x0 = 500000.; if (pj_param_i<srs::spar::zone>(params, "zone", srs::dpar::zone, zone)) /* zone input ? */ { if (zone > 0 && zone <= 60) --zone; else { BOOST_THROW_EXCEPTION( projection_exception(error_invalid_utm_zone) ); } } else /* nearest central meridian input */ { zone = int_floor((adjlon(par.lam0) + pi) * 30. / pi); if (zone < 0) zone = 0; else if (zone >= 60) zone = 59; } par.lam0 = (zone + .5) * pi / 30. - pi; par.k0 = 0.9996; par.phi0 = 0.; setup(par, proj_parm); } }} // 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 T, typename Parameters> struct etmerc_ellipsoid : public detail::etmerc::base_etmerc_ellipsoid<T, Parameters> { template <typename Params> inline etmerc_ellipsoid(Params const& , Parameters const& par) : detail::etmerc::base_etmerc_ellipsoid<T, Parameters>(par) { detail::etmerc::setup_etmerc(this->m_par, this->m_proj_parm); } }; /*! \brief Universal Transverse Mercator (UTM) 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 - zone: UTM Zone (integer) - south: Denotes southern hemisphere UTM zone (boolean) \par Example \image html ex_utm.gif */ template <typename T, typename Parameters> struct utm_ellipsoid : public detail::etmerc::base_etmerc_ellipsoid<T, Parameters> { template <typename Params> inline utm_ellipsoid(Params const& params, Parameters const& par) : detail::etmerc::base_etmerc_ellipsoid<T, Parameters>(par) { detail::etmerc::setup_utm(params, this->m_par, this->m_proj_parm); } }; #ifndef DOXYGEN_NO_DETAIL namespace detail { // Static projection BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION(srs::spar::proj_etmerc, etmerc_ellipsoid, etmerc_ellipsoid) BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION(srs::spar::proj_utm, utm_ellipsoid, utm_ellipsoid) // Factory entry(s) BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(etmerc_entry, etmerc_ellipsoid) BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(utm_entry, utm_ellipsoid) BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(etmerc_init) { BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(etmerc, etmerc_entry); BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(utm, utm_entry); } } // namespace detail #endif // doxygen } // namespace projections }} // namespace boost::geometry #endif // BOOST_GEOMETRY_PROJECTIONS_ETMERC_HPP