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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
// 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_MOD_STER_HPP
#define BOOST_GEOMETRY_PROJECTIONS_MOD_STER_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/aasincos.hpp>
#include <boost/geometry/srs/projections/impl/pj_zpoly1.hpp>
namespace boost { namespace geometry
{
namespace projections
{
#ifndef DOXYGEN_NO_DETAIL
namespace detail { namespace mod_ster
{
static const double epsilon = 1e-12;
template <typename T>
struct par_mod_ster
{
T cchio, schio;
pj_complex<T>* zcoeff;
int n;
};
/* based upon Snyder and Linck, USGS-NMD */
template <typename T, typename Parameters>
struct base_mod_ster_ellipsoid
{
par_mod_ster<T> m_proj_parm;
// FORWARD(e_forward) ellipsoid
// 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 sinlon, coslon, esphi, chi, schi, cchi, s;
pj_complex<T> p;
sinlon = sin(lp_lon);
coslon = cos(lp_lon);
esphi = par.e * sin(lp_lat);
chi = 2. * atan(tan((half_pi + lp_lat) * .5) *
math::pow((T(1) - esphi) / (T(1) + esphi), par.e * T(0.5))) - half_pi;
schi = sin(chi);
cchi = cos(chi);
s = 2. / (1. + this->m_proj_parm.schio * schi + this->m_proj_parm.cchio * cchi * coslon);
p.r = s * cchi * sinlon;
p.i = s * (this->m_proj_parm.cchio * schi - this->m_proj_parm.schio * cchi * coslon);
p = pj_zpoly1(p, this->m_proj_parm.zcoeff, this->m_proj_parm.n);
xy_x = p.r;
xy_y = p.i;
}
// 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>();
int nn;
pj_complex<T> p, fxy, fpxy, dp;
T den, rh = 0, z, sinz = 0, cosz = 0, chi, phi = 0, dphi, esphi;
p.r = xy_x;
p.i = xy_y;
for (nn = 20; nn ;--nn) {
fxy = pj_zpolyd1(p, this->m_proj_parm.zcoeff, this->m_proj_parm.n, &fpxy);
fxy.r -= xy_x;
fxy.i -= xy_y;
den = fpxy.r * fpxy.r + fpxy.i * fpxy.i;
dp.r = -(fxy.r * fpxy.r + fxy.i * fpxy.i) / den;
dp.i = -(fxy.i * fpxy.r - fxy.r * fpxy.i) / den;
p.r += dp.r;
p.i += dp.i;
if ((fabs(dp.r) + fabs(dp.i)) <= epsilon)
break;
}
if (nn) {
rh = boost::math::hypot(p.r, p.i);
z = 2. * atan(.5 * rh);
sinz = sin(z);
cosz = cos(z);
lp_lon = par.lam0;
if (fabs(rh) <= epsilon) {
/* if we end up here input coordinates were (0,0).
* pj_inv() adds P->lam0 to lp.lam, this way we are
* sure to get the correct offset */
lp_lon = 0.0;
lp_lat = par.phi0;
return;
}
chi = aasin(cosz * this->m_proj_parm.schio + p.i * sinz * this->m_proj_parm.cchio / rh);
phi = chi;
for (nn = 20; nn ;--nn) {
esphi = par.e * sin(phi);
dphi = 2. * atan(tan((half_pi + chi) * .5) *
math::pow((T(1) + esphi) / (T(1) - esphi), par.e * T(0.5))) - half_pi - phi;
phi += dphi;
if (fabs(dphi) <= epsilon)
break;
}
}
if (nn) {
lp_lat = phi;
lp_lon = atan2(p.r * sinz, rh * this->m_proj_parm.cchio * cosz - p.i *
this->m_proj_parm.schio * sinz);
} else
lp_lon = lp_lat = HUGE_VAL;
}
static inline std::string get_name()
{
return "mod_ster_ellipsoid";
}
};
template <typename Parameters, typename T>
inline void setup(Parameters& par, par_mod_ster<T>& proj_parm) /* general initialization */
{
static T const half_pi = detail::half_pi<T>();
T esphi, chio;
if (par.es != 0.0) {
esphi = par.e * sin(par.phi0);
chio = 2. * atan(tan((half_pi + par.phi0) * .5) *
math::pow((T(1) - esphi) / (T(1) + esphi), par.e * T(0.5))) - half_pi;
} else
chio = par.phi0;
proj_parm.schio = sin(chio);
proj_parm.cchio = cos(chio);
}
/* Miller Oblated Stereographic */
template <typename Parameters, typename T>
inline void setup_mil_os(Parameters& par, par_mod_ster<T>& proj_parm)
{
static const T d2r = geometry::math::d2r<T>();
static pj_complex<T> AB[] = {
{0.924500, 0.},
{0., 0.},
{0.019430, 0.}
};
proj_parm.n = 2;
par.lam0 = d2r * 20.;
par.phi0 = d2r * 18.;
proj_parm.zcoeff = AB;
par.es = 0.;
setup(par, proj_parm);
}
/* Lee Oblated Stereographic */
template <typename Parameters, typename T>
inline void setup_lee_os(Parameters& par, par_mod_ster<T>& proj_parm)
{
static const T d2r = geometry::math::d2r<T>();
static pj_complex<T> AB[] = {
{ 0.721316, 0.},
{ 0., 0.},
{-0.0088162, -0.00617325}
};
proj_parm.n = 2;
par.lam0 = d2r * -165.;
par.phi0 = d2r * -10.;
proj_parm.zcoeff = AB;
par.es = 0.;
setup(par, proj_parm);
}
// Mod. Stererographics of 48 U.S.
template <typename Parameters, typename T>
inline void setup_gs48(Parameters& par, par_mod_ster<T>& proj_parm)
{
static const T d2r = geometry::math::d2r<T>();
static pj_complex<T> AB[] = { /* 48 United States */
{ 0.98879, 0.},
{ 0., 0.},
{-0.050909, 0.},
{ 0., 0.},
{ 0.075528, 0.}
};
proj_parm.n = 4;
par.lam0 = d2r * -96.;
par.phi0 = d2r * -39.;
proj_parm.zcoeff = AB;
par.es = 0.;
par.a = 6370997.;
setup(par, proj_parm);
}
// Mod. Stererographics of Alaska
template <typename Parameters, typename T>
inline void setup_alsk(Parameters& par, par_mod_ster<T>& proj_parm)
{
static const T d2r = geometry::math::d2r<T>();
static pj_complex<T> ABe[] = { /* Alaska ellipsoid */
{ .9945303, 0.},
{ .0052083, -.0027404},
{ .0072721, .0048181},
{-.0151089, -.1932526},
{ .0642675, -.1381226},
{ .3582802, -.2884586}
};
static pj_complex<T> ABs[] = { /* Alaska sphere */
{ .9972523, 0.},
{ .0052513, -.0041175},
{ .0074606, .0048125},
{-.0153783, -.1968253},
{ .0636871, -.1408027},
{ .3660976, -.2937382}
};
proj_parm.n = 5;
par.lam0 = d2r * -152.;
par.phi0 = d2r * 64.;
if (par.es != 0.0) { /* fixed ellipsoid/sphere */
proj_parm.zcoeff = ABe;
par.a = 6378206.4;
par.e = sqrt(par.es = 0.00676866);
} else {
proj_parm.zcoeff = ABs;
par.a = 6370997.;
}
setup(par, proj_parm);
}
// Mod. Stererographics of 50 U.S.
template <typename Parameters, typename T>
inline void setup_gs50(Parameters& par, par_mod_ster<T>& proj_parm)
{
static const T d2r = geometry::math::d2r<T>();
static pj_complex<T> ABe[] = { /* GS50 ellipsoid */
{ .9827497, 0.},
{ .0210669, .0053804},
{-.1031415, -.0571664},
{-.0323337, -.0322847},
{ .0502303, .1211983},
{ .0251805, .0895678},
{-.0012315, -.1416121},
{ .0072202, -.1317091},
{-.0194029, .0759677},
{-.0210072, .0834037}
};
static pj_complex<T> ABs[] = { /* GS50 sphere */
{ .9842990, 0.},
{ .0211642, .0037608},
{-.1036018, -.0575102},
{-.0329095, -.0320119},
{ .0499471, .1223335},
{ .0260460, .0899805},
{ .0007388, -.1435792},
{ .0075848, -.1334108},
{-.0216473, .0776645},
{-.0225161, .0853673}
};
proj_parm.n = 9;
par.lam0 = d2r * -120.;
par.phi0 = d2r * 45.;
if (par.es != 0.0) { /* fixed ellipsoid/sphere */
proj_parm.zcoeff = ABe;
par.a = 6378206.4;
par.e = sqrt(par.es = 0.00676866);
} else {
proj_parm.zcoeff = ABs;
par.a = 6370997.;
}
setup(par, proj_parm);
}
}} // namespace detail::mod_ster
#endif // doxygen
/*!
\brief Miller Oblated Stereographic projection
\ingroup projections
\tparam Geographic latlong point type
\tparam Cartesian xy point type
\tparam Parameters parameter type
\par Projection characteristics
- Azimuthal (mod)
\par Example
\image html ex_mil_os.gif
*/
template <typename T, typename Parameters>
struct mil_os_ellipsoid : public detail::mod_ster::base_mod_ster_ellipsoid<T, Parameters>
{
template <typename Params>
inline mil_os_ellipsoid(Params const& , Parameters & par)
{
detail::mod_ster::setup_mil_os(par, this->m_proj_parm);
}
};
/*!
\brief Lee Oblated Stereographic projection
\ingroup projections
\tparam Geographic latlong point type
\tparam Cartesian xy point type
\tparam Parameters parameter type
\par Projection characteristics
- Azimuthal (mod)
\par Example
\image html ex_lee_os.gif
*/
template <typename T, typename Parameters>
struct lee_os_ellipsoid : public detail::mod_ster::base_mod_ster_ellipsoid<T, Parameters>
{
template <typename Params>
inline lee_os_ellipsoid(Params const& , Parameters & par)
{
detail::mod_ster::setup_lee_os(par, this->m_proj_parm);
}
};
/*!
\brief Mod. Stererographics of 48 U.S. projection
\ingroup projections
\tparam Geographic latlong point type
\tparam Cartesian xy point type
\tparam Parameters parameter type
\par Projection characteristics
- Azimuthal (mod)
\par Example
\image html ex_gs48.gif
*/
template <typename T, typename Parameters>
struct gs48_ellipsoid : public detail::mod_ster::base_mod_ster_ellipsoid<T, Parameters>
{
template <typename Params>
inline gs48_ellipsoid(Params const& , Parameters & par)
{
detail::mod_ster::setup_gs48(par, this->m_proj_parm);
}
};
/*!
\brief Mod. Stererographics of Alaska projection
\ingroup projections
\tparam Geographic latlong point type
\tparam Cartesian xy point type
\tparam Parameters parameter type
\par Projection characteristics
- Azimuthal (mod)
\par Example
\image html ex_alsk.gif
*/
template <typename T, typename Parameters>
struct alsk_ellipsoid : public detail::mod_ster::base_mod_ster_ellipsoid<T, Parameters>
{
template <typename Params>
inline alsk_ellipsoid(Params const& , Parameters & par)
{
detail::mod_ster::setup_alsk(par, this->m_proj_parm);
}
};
/*!
\brief Mod. Stererographics of 50 U.S. projection
\ingroup projections
\tparam Geographic latlong point type
\tparam Cartesian xy point type
\tparam Parameters parameter type
\par Projection characteristics
- Azimuthal (mod)
\par Example
\image html ex_gs50.gif
*/
template <typename T, typename Parameters>
struct gs50_ellipsoid : public detail::mod_ster::base_mod_ster_ellipsoid<T, Parameters>
{
template <typename Params>
inline gs50_ellipsoid(Params const& , Parameters & par)
{
detail::mod_ster::setup_gs50(par, this->m_proj_parm);
}
};
#ifndef DOXYGEN_NO_DETAIL
namespace detail
{
// Static projection
BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_mil_os, mil_os_ellipsoid)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_lee_os, lee_os_ellipsoid)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_gs48, gs48_ellipsoid)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_alsk, alsk_ellipsoid)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_gs50, gs50_ellipsoid)
// Factory entry(s)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(mil_os_entry, mil_os_ellipsoid)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(lee_os_entry, lee_os_ellipsoid)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(gs48_entry, gs48_ellipsoid)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(alsk_entry, alsk_ellipsoid)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(gs50_entry, gs50_ellipsoid)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(mod_ster_init)
{
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(mil_os, mil_os_entry)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(lee_os, lee_os_entry)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(gs48, gs48_entry)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(alsk, alsk_entry)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(gs50, gs50_entry)
}
} // namespace detail
#endif // doxygen
} // namespace projections
}} // namespace boost::geometry
#endif // BOOST_GEOMETRY_PROJECTIONS_MOD_STER_HPP
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