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