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// 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
// Author: Gerald Evenden (1995)
// Thomas Knudsen (2016) - revise/add regression tests
// Last updated version of proj: 5.0.0
// Original copyright notice:
// Purpose: Implementation of the aea (Albers Equal Area) projection.
// Author: Gerald Evenden
// Copyright (c) 1995, Gerald 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.
#ifndef BOOST_GEOMETRY_PROJECTIONS_AEA_HPP
#define BOOST_GEOMETRY_PROJECTIONS_AEA_HPP
#include <boost/core/ignore_unused.hpp>
#include <boost/geometry/util/math.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/pj_mlfn.hpp>
#include <boost/geometry/srs/projections/impl/pj_msfn.hpp>
#include <boost/geometry/srs/projections/impl/pj_param.hpp>
#include <boost/geometry/srs/projections/impl/pj_qsfn.hpp>
namespace boost { namespace geometry
{
namespace projections
{
#ifndef DOXYGEN_NO_DETAIL
namespace detail { namespace aea
{
static const double epsilon10 = 1.e-10;
static const double tolerance7 = 1.e-7;
static const double epsilon = 1.0e-7;
static const double tolerance = 1.0e-10;
static const int n_iter = 15;
template <typename T>
struct par_aea
{
T ec;
T n;
T c;
T dd;
T n2;
T rho0;
T phi1;
T phi2;
detail::en<T> en;
bool ellips;
};
/* determine latitude angle phi-1 */
template <typename T>
inline T phi1_(T const& qs, T const& Te, T const& Tone_es)
{
int i;
T Phi, sinpi, cospi, con, com, dphi;
Phi = asin (.5 * qs);
if (Te < epsilon)
return( Phi );
i = n_iter;
do {
sinpi = sin (Phi);
cospi = cos (Phi);
con = Te * sinpi;
com = 1. - con * con;
dphi = .5 * com * com / cospi * (qs / Tone_es -
sinpi / com + .5 / Te * log ((1. - con) /
(1. + con)));
Phi += dphi;
} while (fabs(dphi) > tolerance && --i);
return( i ? Phi : HUGE_VAL );
}
template <typename T, typename Parameters>
struct base_aea_ellipsoid
{
par_aea<T> m_proj_parm;
// FORWARD(e_forward) ellipsoid & spheroid
// Project coordinates from geographic (lon, lat) to cartesian (x, y)
inline void fwd(Parameters const& par, T lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const
{
T rho = this->m_proj_parm.c - (this->m_proj_parm.ellips
? this->m_proj_parm.n * pj_qsfn(sin(lp_lat), par.e, par.one_es)
: this->m_proj_parm.n2 * sin(lp_lat));
if (rho < 0.)
BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
rho = this->m_proj_parm.dd * sqrt(rho);
xy_x = rho * sin( lp_lon *= this->m_proj_parm.n );
xy_y = this->m_proj_parm.rho0 - rho * cos(lp_lon);
}
// INVERSE(e_inverse) ellipsoid & spheroid
// Project coordinates from cartesian (x, y) to geographic (lon, lat)
inline void inv(Parameters const& par, T xy_x, T xy_y, T& lp_lon, T& lp_lat) const
{
static const T half_pi = detail::half_pi<T>();
T rho = 0.0;
if( (rho = boost::math::hypot(xy_x, xy_y = this->m_proj_parm.rho0 - xy_y)) != 0.0 ) {
if (this->m_proj_parm.n < 0.) {
rho = -rho;
xy_x = -xy_x;
xy_y = -xy_y;
}
lp_lat = rho / this->m_proj_parm.dd;
if (this->m_proj_parm.ellips) {
lp_lat = (this->m_proj_parm.c - lp_lat * lp_lat) / this->m_proj_parm.n;
if (fabs(this->m_proj_parm.ec - fabs(lp_lat)) > tolerance7) {
if ((lp_lat = phi1_(lp_lat, par.e, par.one_es)) == HUGE_VAL)
BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
} else
lp_lat = lp_lat < 0. ? -half_pi : half_pi;
} else if (fabs(lp_lat = (this->m_proj_parm.c - lp_lat * lp_lat) / this->m_proj_parm.n2) <= 1.)
lp_lat = asin(lp_lat);
else
lp_lat = lp_lat < 0. ? -half_pi : half_pi;
lp_lon = atan2(xy_x, xy_y) / this->m_proj_parm.n;
} else {
lp_lon = 0.;
lp_lat = this->m_proj_parm.n > 0. ? half_pi : - half_pi;
}
}
static inline std::string get_name()
{
return "aea_ellipsoid";
}
};
template <typename Parameters, typename T>
inline void setup(Parameters const& par, par_aea<T>& proj_parm)
{
T cosphi, sinphi;
int secant;
if (fabs(proj_parm.phi1 + proj_parm.phi2) < epsilon10)
BOOST_THROW_EXCEPTION( projection_exception(error_conic_lat_equal) );
proj_parm.n = sinphi = sin(proj_parm.phi1);
cosphi = cos(proj_parm.phi1);
secant = fabs(proj_parm.phi1 - proj_parm.phi2) >= epsilon10;
if( (proj_parm.ellips = (par.es > 0.))) {
T ml1, m1;
proj_parm.en = pj_enfn<T>(par.es);
m1 = pj_msfn(sinphi, cosphi, par.es);
ml1 = pj_qsfn(sinphi, par.e, par.one_es);
if (secant) { /* secant cone */
T ml2, m2;
sinphi = sin(proj_parm.phi2);
cosphi = cos(proj_parm.phi2);
m2 = pj_msfn(sinphi, cosphi, par.es);
ml2 = pj_qsfn(sinphi, par.e, par.one_es);
if (ml2 == ml1)
BOOST_THROW_EXCEPTION( projection_exception(0) );
proj_parm.n = (m1 * m1 - m2 * m2) / (ml2 - ml1);
}
proj_parm.ec = 1. - .5 * par.one_es * log((1. - par.e) /
(1. + par.e)) / par.e;
proj_parm.c = m1 * m1 + proj_parm.n * ml1;
proj_parm.dd = 1. / proj_parm.n;
proj_parm.rho0 = proj_parm.dd * sqrt(proj_parm.c - proj_parm.n * pj_qsfn(sin(par.phi0),
par.e, par.one_es));
} else {
if (secant) proj_parm.n = .5 * (proj_parm.n + sin(proj_parm.phi2));
proj_parm.n2 = proj_parm.n + proj_parm.n;
proj_parm.c = cosphi * cosphi + proj_parm.n2 * sinphi;
proj_parm.dd = 1. / proj_parm.n;
proj_parm.rho0 = proj_parm.dd * sqrt(proj_parm.c - proj_parm.n2 * sin(par.phi0));
}
}
// Albers Equal Area
template <typename Params, typename Parameters, typename T>
inline void setup_aea(Params const& params, Parameters const& par, par_aea<T>& proj_parm)
{
proj_parm.phi1 = 0.0;
proj_parm.phi2 = 0.0;
bool is_phi1_set = pj_param_r<srs::spar::lat_1>(params, "lat_1", srs::dpar::lat_1, proj_parm.phi1);
bool is_phi2_set = pj_param_r<srs::spar::lat_2>(params, "lat_2", srs::dpar::lat_2, proj_parm.phi2);
// Boost.Geometry specific, set default parameters manually
if (! is_phi1_set || ! is_phi2_set) {
bool const use_defaults = ! pj_get_param_b<srs::spar::no_defs>(params, "no_defs", srs::dpar::no_defs);
if (use_defaults) {
if (!is_phi1_set)
proj_parm.phi1 = 29.5;
if (!is_phi2_set)
proj_parm.phi2 = 45.5;
}
}
setup(par, proj_parm);
}
// Lambert Equal Area Conic
template <typename Params, typename Parameters, typename T>
inline void setup_leac(Params const& params, Parameters const& par, par_aea<T>& proj_parm)
{
static const T half_pi = detail::half_pi<T>();
proj_parm.phi2 = pj_get_param_r<T, srs::spar::lat_1>(params, "lat_1", srs::dpar::lat_1);
proj_parm.phi1 = pj_get_param_b<srs::spar::south>(params, "south", srs::dpar::south) ? -half_pi : half_pi;
setup(par, proj_parm);
}
}} // namespace detail::aea
#endif // doxygen
/*!
\brief Albers Equal Area projection
\ingroup projections
\tparam Geographic latlong point type
\tparam Cartesian xy point type
\tparam Parameters parameter type
\par Projection characteristics
- Conic
- Spheroid
- Ellipsoid
\par Projection parameters
- lat_1: Latitude of first standard parallel (degrees)
- lat_2: Latitude of second standard parallel (degrees)
\par Example
\image html ex_aea.gif
*/
template <typename T, typename Parameters>
struct aea_ellipsoid : public detail::aea::base_aea_ellipsoid<T, Parameters>
{
template <typename Params>
inline aea_ellipsoid(Params const& params, Parameters const& par)
{
detail::aea::setup_aea(params, par, this->m_proj_parm);
}
};
/*!
\brief Lambert Equal Area Conic projection
\ingroup projections
\tparam Geographic latlong point type
\tparam Cartesian xy point type
\tparam Parameters parameter type
\par Projection characteristics
- Conic
- Spheroid
- Ellipsoid
\par Projection parameters
- lat_1: Latitude of first standard parallel (degrees)
- south: Denotes southern hemisphere UTM zone (boolean)
\par Example
\image html ex_leac.gif
*/
template <typename T, typename Parameters>
struct leac_ellipsoid : public detail::aea::base_aea_ellipsoid<T, Parameters>
{
template <typename Params>
inline leac_ellipsoid(Params const& params, Parameters const& par)
{
detail::aea::setup_leac(params, par, this->m_proj_parm);
}
};
#ifndef DOXYGEN_NO_DETAIL
namespace detail
{
// Static projection
BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_aea, aea_ellipsoid)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_leac, leac_ellipsoid)
// Factory entry(s)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(aea_entry, aea_ellipsoid)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(leac_entry, leac_ellipsoid)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(aea_init)
{
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(aea, aea_entry)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(leac, leac_entry)
}
} // namespace detail
#endif // doxygen
} // namespace projections
}} // namespace boost::geometry
#endif // BOOST_GEOMETRY_PROJECTIONS_AEA_HPP
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