// 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, 2019.
// Modifications copyright (c) 2017-2019, 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:
// 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/util/math.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>
namespace boost { namespace geometry
{
namespace projections
{
#ifndef DOXYGEN_NO_DETAIL
namespace detail { namespace tmerc
{
static const double epsilon10 = 1.e-10;
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;
};
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_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;
}
}
}} // 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
*/
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);
}
};
/*!
\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