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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 2017-2020.
// Modifications copyright (c) 2017-2020, 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:
// Purpose: Implementation of the aeqd (Azimuthal Equidistant) 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_AEQD_HPP
#define BOOST_GEOMETRY_PROJECTIONS_AEQD_HPP
#include <type_traits>
#include <boost/config.hpp>
#include <boost/geometry/formulas/vincenty_direct.hpp>
#include <boost/geometry/formulas/vincenty_inverse.hpp>
#include <boost/geometry/srs/projections/impl/aasincos.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/factory_entry.hpp>
#include <boost/geometry/srs/projections/impl/pj_mlfn.hpp>
#include <boost/geometry/srs/projections/impl/pj_param.hpp>
#include <boost/geometry/srs/projections/impl/projects.hpp>
#include <boost/geometry/util/math.hpp>
#include <boost/math/special_functions/hypot.hpp>
namespace boost { namespace geometry
{
namespace projections
{
#ifndef DOXYGEN_NO_DETAIL
namespace detail { namespace aeqd
{
static const double epsilon10 = 1.e-10;
static const double tolerance = 1.e-14;
enum mode_type {
n_pole = 0,
s_pole = 1,
equit = 2,
obliq = 3
};
template <typename T>
struct par_aeqd
{
T sinph0;
T cosph0;
detail::en<T> en;
T M1;
//T N1;
T Mp;
//T He;
//T G;
T b;
mode_type mode;
};
template <typename T, typename Par, typename ProjParm>
inline void e_forward(T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y, Par const& par, ProjParm const& proj_parm)
{
T coslam, cosphi, sinphi, rho;
//T azi1, s12;
//T lam1, phi1, lam2, phi2;
coslam = cos(lp_lon);
cosphi = cos(lp_lat);
sinphi = sin(lp_lat);
switch (proj_parm.mode) {
case n_pole:
coslam = - coslam;
BOOST_FALLTHROUGH;
case s_pole:
xy_x = (rho = fabs(proj_parm.Mp - pj_mlfn(lp_lat, sinphi, cosphi, proj_parm.en))) *
sin(lp_lon);
xy_y = rho * coslam;
break;
case equit:
case obliq:
if (fabs(lp_lon) < epsilon10 && fabs(lp_lat - par.phi0) < epsilon10) {
xy_x = xy_y = 0.;
break;
}
//phi1 = par.phi0; lam1 = par.lam0;
//phi2 = lp_lat; lam2 = lp_lon + par.lam0;
formula::result_inverse<T> const inv =
formula::vincenty_inverse
<
T, true, true
>::apply(par.lam0, par.phi0, lp_lon + par.lam0, lp_lat, srs::spheroid<T>(par.a, proj_parm.b));
//azi1 = inv.azimuth; s12 = inv.distance;
xy_x = inv.distance * sin(inv.azimuth) / par.a;
xy_y = inv.distance * cos(inv.azimuth) / par.a;
break;
}
}
template <typename T, typename Par, typename ProjParm>
inline void e_inverse(T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat, Par const& par, ProjParm const& proj_parm)
{
T c;
if ((c = boost::math::hypot(xy_x, xy_y)) < epsilon10) {
lp_lat = par.phi0;
lp_lon = 0.;
return;
}
if (proj_parm.mode == obliq || proj_parm.mode == equit) {
T const x2 = xy_x * par.a;
T const y2 = xy_y * par.a;
//T const lat1 = par.phi0;
//T const lon1 = par.lam0;
T const azi1 = atan2(x2, y2);
T const s12 = sqrt(x2 * x2 + y2 * y2);
formula::result_direct<T> const dir =
formula::vincenty_direct
<
T, true
>::apply(par.lam0, par.phi0, s12, azi1, srs::spheroid<T>(par.a, proj_parm.b));
lp_lat = dir.lat2;
lp_lon = dir.lon2;
lp_lon -= par.lam0;
} else { /* Polar */
lp_lat = pj_inv_mlfn(proj_parm.mode == n_pole ? proj_parm.Mp - c : proj_parm.Mp + c,
par.es, proj_parm.en);
lp_lon = atan2(xy_x, proj_parm.mode == n_pole ? -xy_y : xy_y);
}
}
template <typename T, typename Par, typename ProjParm>
inline void e_guam_fwd(T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y, Par const& par, ProjParm const& proj_parm)
{
T cosphi, sinphi, t;
cosphi = cos(lp_lat);
sinphi = sin(lp_lat);
t = 1. / sqrt(1. - par.es * sinphi * sinphi);
xy_x = lp_lon * cosphi * t;
xy_y = pj_mlfn(lp_lat, sinphi, cosphi, proj_parm.en) - proj_parm.M1 +
.5 * lp_lon * lp_lon * cosphi * sinphi * t;
}
template <typename T, typename Par, typename ProjParm>
inline void e_guam_inv(T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat, Par const& par, ProjParm const& proj_parm)
{
T x2, t = 0.0;
int i;
x2 = 0.5 * xy_x * xy_x;
lp_lat = par.phi0;
for (i = 0; i < 3; ++i) {
t = par.e * sin(lp_lat);
lp_lat = pj_inv_mlfn(proj_parm.M1 + xy_y -
x2 * tan(lp_lat) * (t = sqrt(1. - t * t)), par.es, proj_parm.en);
}
lp_lon = xy_x * t / cos(lp_lat);
}
template <typename T, typename Par, typename ProjParm>
inline void s_forward(T const& lp_lon, T lp_lat, T& xy_x, T& xy_y, Par const& /*par*/, ProjParm const& proj_parm)
{
static const T half_pi = detail::half_pi<T>();
T coslam, cosphi, sinphi;
sinphi = sin(lp_lat);
cosphi = cos(lp_lat);
coslam = cos(lp_lon);
switch (proj_parm.mode) {
case equit:
xy_y = cosphi * coslam;
goto oblcon;
case obliq:
xy_y = proj_parm.sinph0 * sinphi + proj_parm.cosph0 * cosphi * coslam;
oblcon:
if (fabs(fabs(xy_y) - 1.) < tolerance)
if (xy_y < 0.)
BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
else
xy_x = xy_y = 0.;
else {
xy_y = acos(xy_y);
xy_y /= sin(xy_y);
xy_x = xy_y * cosphi * sin(lp_lon);
xy_y *= (proj_parm.mode == equit) ? sinphi :
proj_parm.cosph0 * sinphi - proj_parm.sinph0 * cosphi * coslam;
}
break;
case n_pole:
lp_lat = -lp_lat;
coslam = -coslam;
BOOST_FALLTHROUGH;
case s_pole:
if (fabs(lp_lat - half_pi) < epsilon10)
BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
xy_x = (xy_y = (half_pi + lp_lat)) * sin(lp_lon);
xy_y *= coslam;
break;
}
}
template <typename T, typename Par, typename ProjParm>
inline void s_inverse(T xy_x, T xy_y, T& lp_lon, T& lp_lat, Par const& par, ProjParm const& proj_parm)
{
static const T pi = detail::pi<T>();
static const T half_pi = detail::half_pi<T>();
T cosc, c_rh, sinc;
if ((c_rh = boost::math::hypot(xy_x, xy_y)) > pi) {
if (c_rh - epsilon10 > pi)
BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
c_rh = pi;
} else if (c_rh < epsilon10) {
lp_lat = par.phi0;
lp_lon = 0.;
return;
}
if (proj_parm.mode == obliq || proj_parm.mode == equit) {
sinc = sin(c_rh);
cosc = cos(c_rh);
if (proj_parm.mode == equit) {
lp_lat = aasin(xy_y * sinc / c_rh);
xy_x *= sinc;
xy_y = cosc * c_rh;
} else {
lp_lat = aasin(cosc * proj_parm.sinph0 + xy_y * sinc * proj_parm.cosph0 /
c_rh);
xy_y = (cosc - proj_parm.sinph0 * sin(lp_lat)) * c_rh;
xy_x *= sinc * proj_parm.cosph0;
}
lp_lon = xy_y == 0. ? 0. : atan2(xy_x, xy_y);
} else if (proj_parm.mode == n_pole) {
lp_lat = half_pi - c_rh;
lp_lon = atan2(xy_x, -xy_y);
} else {
lp_lat = c_rh - half_pi;
lp_lon = atan2(xy_x, xy_y);
}
}
// Azimuthal Equidistant
template <typename Params, typename Parameters, typename T>
inline void setup_aeqd(Params const& params, Parameters& par, par_aeqd<T>& proj_parm, bool is_sphere, bool is_guam)
{
static const T half_pi = detail::half_pi<T>();
par.phi0 = pj_get_param_r<T, srs::spar::lat_0>(params, "lat_0", srs::dpar::lat_0);
if (fabs(fabs(par.phi0) - half_pi) < epsilon10) {
proj_parm.mode = par.phi0 < 0. ? s_pole : n_pole;
proj_parm.sinph0 = par.phi0 < 0. ? -1. : 1.;
proj_parm.cosph0 = 0.;
} else if (fabs(par.phi0) < epsilon10) {
proj_parm.mode = equit;
proj_parm.sinph0 = 0.;
proj_parm.cosph0 = 1.;
} else {
proj_parm.mode = obliq;
proj_parm.sinph0 = sin(par.phi0);
proj_parm.cosph0 = cos(par.phi0);
}
if (is_sphere) {
/* empty */
} else {
proj_parm.en = pj_enfn<T>(par.es);
if (is_guam) {
proj_parm.M1 = pj_mlfn(par.phi0, proj_parm.sinph0, proj_parm.cosph0, proj_parm.en);
} else {
switch (proj_parm.mode) {
case n_pole:
proj_parm.Mp = pj_mlfn<T>(half_pi, 1., 0., proj_parm.en);
break;
case s_pole:
proj_parm.Mp = pj_mlfn<T>(-half_pi, -1., 0., proj_parm.en);
break;
case equit:
case obliq:
//proj_parm.N1 = 1. / sqrt(1. - par.es * proj_parm.sinph0 * proj_parm.sinph0);
//proj_parm.G = proj_parm.sinph0 * (proj_parm.He = par.e / sqrt(par.one_es));
//proj_parm.He *= proj_parm.cosph0;
break;
}
// Boost.Geometry specific, in proj4 geodesic is initialized at the beginning
proj_parm.b = math::sqrt(math::sqr(par.a) * (1. - par.es));
}
}
}
template <typename T, typename Parameters>
struct base_aeqd_e
{
par_aeqd<T> m_proj_parm;
// FORWARD(e_forward) elliptical
// 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
{
e_forward(lp_lon, lp_lat, xy_x, xy_y, par, this->m_proj_parm);
}
// INVERSE(e_inverse) elliptical
// 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
{
e_inverse(xy_x, xy_y, lp_lon, lp_lat, par, this->m_proj_parm);
}
static inline std::string get_name()
{
return "aeqd_e";
}
};
template <typename T, typename Parameters>
struct base_aeqd_e_guam
{
par_aeqd<T> m_proj_parm;
// FORWARD(e_guam_fwd) Guam elliptical
// 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
{
e_guam_fwd(lp_lon, lp_lat, xy_x, xy_y, par, this->m_proj_parm);
}
// INVERSE(e_guam_inv) Guam elliptical
// 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
{
e_guam_inv(xy_x, xy_y, lp_lon, lp_lat, par, this->m_proj_parm);
}
static inline std::string get_name()
{
return "aeqd_e_guam";
}
};
template <typename T, typename Parameters>
struct base_aeqd_s
{
par_aeqd<T> m_proj_parm;
// FORWARD(s_forward) spherical
// 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
{
s_forward(lp_lon, lp_lat, xy_x, xy_y, par, this->m_proj_parm);
}
// INVERSE(s_inverse) spherical
// 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
{
s_inverse(xy_x, xy_y, lp_lon, lp_lat, par, this->m_proj_parm);
}
static inline std::string get_name()
{
return "aeqd_s";
}
};
}} // namespace detail::aeqd
#endif // doxygen
/*!
\brief Azimuthal Equidistant projection
\ingroup projections
\tparam Geographic latlong point type
\tparam Cartesian xy point type
\tparam Parameters parameter type
\par Projection characteristics
- Azimuthal
- Spheroid
- Ellipsoid
\par Projection parameters
- lat_0: Latitude of origin (degrees)
- guam (boolean)
\par Example
\image html ex_aeqd.gif
*/
template <typename T, typename Parameters>
struct aeqd_e : public detail::aeqd::base_aeqd_e<T, Parameters>
{
template <typename Params>
inline aeqd_e(Params const& params, Parameters & par)
{
detail::aeqd::setup_aeqd(params, par, this->m_proj_parm, false, false);
}
};
/*!
\brief Azimuthal Equidistant projection
\ingroup projections
\tparam Geographic latlong point type
\tparam Cartesian xy point type
\tparam Parameters parameter type
\par Projection characteristics
- Azimuthal
- Spheroid
- Ellipsoid
\par Projection parameters
- lat_0: Latitude of origin (degrees)
- guam (boolean)
\par Example
\image html ex_aeqd.gif
*/
template <typename T, typename Parameters>
struct aeqd_e_guam : public detail::aeqd::base_aeqd_e_guam<T, Parameters>
{
template <typename Params>
inline aeqd_e_guam(Params const& params, Parameters & par)
{
detail::aeqd::setup_aeqd(params, par, this->m_proj_parm, false, true);
}
};
/*!
\brief Azimuthal Equidistant projection
\ingroup projections
\tparam Geographic latlong point type
\tparam Cartesian xy point type
\tparam Parameters parameter type
\par Projection characteristics
- Azimuthal
- Spheroid
- Ellipsoid
\par Projection parameters
- lat_0: Latitude of origin (degrees)
- guam (boolean)
\par Example
\image html ex_aeqd.gif
*/
template <typename T, typename Parameters>
struct aeqd_s : public detail::aeqd::base_aeqd_s<T, Parameters>
{
template <typename Params>
inline aeqd_s(Params const& params, Parameters & par)
{
detail::aeqd::setup_aeqd(params, par, this->m_proj_parm, true, false);
}
};
#ifndef DOXYGEN_NO_DETAIL
namespace detail
{
// Static projection
template <typename BGP, typename CT, typename P>
struct static_projection_type<srs::spar::proj_aeqd, srs_sphere_tag, BGP, CT, P>
{
typedef static_wrapper_fi<aeqd_s<CT, P>, P> type;
};
template <typename BGP, typename CT, typename P>
struct static_projection_type<srs::spar::proj_aeqd, srs_spheroid_tag, BGP, CT, P>
{
typedef static_wrapper_fi
<
std::conditional_t
<
std::is_void
<
typename geometry::tuples::find_if
<
BGP,
//srs::par4::detail::is_guam
srs::spar::detail::is_param<srs::spar::guam>::pred
>::type
>::value,
aeqd_e<CT, P>,
aeqd_e_guam<CT, P>
>
, P
> type;
};
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_BEGIN(aeqd_entry)
{
bool const guam = pj_get_param_b<srs::spar::guam>(params, "guam", srs::dpar::guam);
if (parameters.es && ! guam)
return new dynamic_wrapper_fi<aeqd_e<T, Parameters>, T, Parameters>(params, parameters);
else if (parameters.es && guam)
return new dynamic_wrapper_fi<aeqd_e_guam<T, Parameters>, T, Parameters>(params, parameters);
else
return new dynamic_wrapper_fi<aeqd_s<T, Parameters>, T, Parameters>(params, parameters);
}
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_END
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(aeqd_init)
{
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(aeqd, aeqd_entry)
}
} // namespace detail
#endif // doxygen
} // namespace projections
}} // namespace boost::geometry
#endif // BOOST_GEOMETRY_PROJECTIONS_AEQD_HPP
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