// 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_STERE_HPP
#define BOOST_GEOMETRY_PROJECTIONS_STERE_HPP
#include <boost/config.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/factory_entry.hpp>
#include <boost/geometry/srs/projections/impl/pj_param.hpp>
#include <boost/geometry/srs/projections/impl/pj_tsfn.hpp>
#include <boost/geometry/srs/projections/impl/projects.hpp>
namespace boost { namespace geometry
{
namespace projections
{
#ifndef DOXYGEN_NO_DETAIL
namespace detail { namespace stere
{
static const double epsilon10 = 1.e-10;
static const double tolerance = 1.e-8;
static const int n_iter = 8;
static const double conv_tolerance = 1.e-10;
enum mode_type {
s_pole = 0,
n_pole = 1,
obliq = 2,
equit = 3
};
template <typename T>
struct par_stere
{
T phits;
T sinX1;
T cosX1;
T akm1;
mode_type mode;
};
template <typename T>
inline T ssfn_(T const& phit, T sinphi, T const& eccen)
{
static const T half_pi = detail::half_pi<T>();
sinphi *= eccen;
return (tan (.5 * (half_pi + phit)) *
math::pow((T(1) - sinphi) / (T(1) + sinphi), T(0.5) * eccen));
}
template <typename T, typename Parameters>
struct base_stere_ellipsoid
{
par_stere<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 lp_lat, T& xy_x, T& xy_y) const
{
static const T half_pi = detail::half_pi<T>();
T coslam, sinlam, sinX=0.0, cosX=0.0, X, A = 0.0, sinphi;
coslam = cos(lp_lon);
sinlam = sin(lp_lon);
sinphi = sin(lp_lat);
if (this->m_proj_parm.mode == obliq || this->m_proj_parm.mode == equit) {
sinX = sin(X = 2. * atan(ssfn_(lp_lat, sinphi, par.e)) - half_pi);
cosX = cos(X);
}
switch (this->m_proj_parm.mode) {
case obliq:
A = this->m_proj_parm.akm1 / (this->m_proj_parm.cosX1 * (1. + this->m_proj_parm.sinX1 * sinX +
this->m_proj_parm.cosX1 * cosX * coslam));
xy_y = A * (this->m_proj_parm.cosX1 * sinX - this->m_proj_parm.sinX1 * cosX * coslam);
goto xmul; /* but why not just xy.x = A * cosX; break; ? */
case equit:
// TODO: calculate denominator once
/* avoid zero division */
if (1. + cosX * coslam == 0.0) {
xy_y = HUGE_VAL;
} else {
A = this->m_proj_parm.akm1 / (1. + cosX * coslam);
xy_y = A * sinX;
}
xmul:
xy_x = A * cosX;
break;
case s_pole:
lp_lat = -lp_lat;
coslam = - coslam;
sinphi = -sinphi;
BOOST_FALLTHROUGH;
case n_pole:
xy_x = this->m_proj_parm.akm1 * pj_tsfn(lp_lat, sinphi, par.e);
xy_y = - xy_x * coslam;
break;
}
xy_x = xy_x * sinlam;
}
// INVERSE(e_inverse) ellipsoid
// 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 cosphi, sinphi, tp=0.0, phi_l=0.0, rho, halfe=0.0, halfpi=0.0;
int i;
rho = boost::math::hypot(xy_x, xy_y);
switch (this->m_proj_parm.mode) {
case obliq:
case equit:
cosphi = cos( tp = 2. * atan2(rho * this->m_proj_parm.cosX1 , this->m_proj_parm.akm1) );
sinphi = sin(tp);
if( rho == 0.0 )
phi_l = asin(cosphi * this->m_proj_parm.sinX1);
else
phi_l = asin(cosphi * this->m_proj_parm.sinX1 + (xy_y * sinphi * this->m_proj_parm.cosX1 / rho));
tp = tan(.5 * (half_pi + phi_l));
xy_x *= sinphi;
xy_y = rho * this->m_proj_parm.cosX1 * cosphi - xy_y * this->m_proj_parm.sinX1* sinphi;
halfpi = half_pi;
halfe = .5 * par.e;
break;
case n_pole:
xy_y = -xy_y;
BOOST_FALLTHROUGH;
case s_pole:
phi_l = half_pi - 2. * atan(tp = - rho / this->m_proj_parm.akm1);
halfpi = -half_pi;
halfe = -.5 * par.e;
break;
}
for (i = n_iter; i--; phi_l = lp_lat) {
sinphi = par.e * sin(phi_l);
lp_lat = T(2) * atan(tp * math::pow((T(1)+sinphi)/(T(1)-sinphi), halfe)) - halfpi;
if (fabs(phi_l - lp_lat) < conv_tolerance) {
if (this->m_proj_parm.mode == s_pole)
lp_lat = -lp_lat;
lp_lon = (xy_x == 0. && xy_y == 0.) ? 0. : atan2(xy_x, xy_y);
return;
}
}
BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
}
static inline std::string get_name()
{
return "stere_ellipsoid";
}
};
template <typename T, typename Parameters>
struct base_stere_spheroid
{
par_stere<T> m_proj_parm;
// FORWARD(s_forward) spheroid
// Project coordinates from geographic (lon, lat) to cartesian (x, y)
inline void fwd(Parameters const& , T const& lp_lon, T lp_lat, T& xy_x, T& xy_y) const
{
static const T fourth_pi = detail::fourth_pi<T>();
static const T half_pi = detail::half_pi<T>();
T sinphi, cosphi, coslam, sinlam;
sinphi = sin(lp_lat);
cosphi = cos(lp_lat);
coslam = cos(lp_lon);
sinlam = sin(lp_lon);
switch (this->m_proj_parm.mode) {
case equit:
xy_y = 1. + cosphi * coslam;
goto oblcon;
case obliq:
xy_y = 1. + this->m_proj_parm.sinX1 * sinphi + this->m_proj_parm.cosX1 * cosphi * coslam;
oblcon:
if (xy_y <= epsilon10) {
BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
}
xy_x = (xy_y = this->m_proj_parm.akm1 / xy_y) * cosphi * sinlam;
xy_y *= (this->m_proj_parm.mode == equit) ? sinphi :
this->m_proj_parm.cosX1 * sinphi - this->m_proj_parm.sinX1 * cosphi * coslam;
break;
case n_pole:
coslam = - coslam;
lp_lat = - lp_lat;
BOOST_FALLTHROUGH;
case s_pole:
if (fabs(lp_lat - half_pi) < tolerance) {
BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
}
xy_x = sinlam * ( xy_y = this->m_proj_parm.akm1 * tan(fourth_pi + .5 * lp_lat) );
xy_y *= coslam;
break;
}
}
// INVERSE(s_inverse) spheroid
// Project coordinates from cartesian (x, y) to geographic (lon, lat)
inline void inv(Parameters const& par, T const& xy_x, T xy_y, T& lp_lon, T& lp_lat) const
{
T c, rh, sinc, cosc;
sinc = sin(c = 2. * atan((rh = boost::math::hypot(xy_x, xy_y)) / this->m_proj_parm.akm1));
cosc = cos(c);
lp_lon = 0.;
switch (this->m_proj_parm.mode) {
case equit:
if (fabs(rh) <= epsilon10)
lp_lat = 0.;
else
lp_lat = asin(xy_y * sinc / rh);
if (cosc != 0. || xy_x != 0.)
lp_lon = atan2(xy_x * sinc, cosc * rh);
break;
case obliq:
if (fabs(rh) <= epsilon10)
lp_lat = par.phi0;
else
lp_lat = asin(cosc * this->m_proj_parm.sinX1 + xy_y * sinc * this->m_proj_parm.cosX1 / rh);
if ((c = cosc - this->m_proj_parm.sinX1 * sin(lp_lat)) != 0. || xy_x != 0.)
lp_lon = atan2(xy_x * sinc * this->m_proj_parm.cosX1, c * rh);
break;
case n_pole:
xy_y = -xy_y;
BOOST_FALLTHROUGH;
case s_pole:
if (fabs(rh) <= epsilon10)
lp_lat = par.phi0;
else
lp_lat = asin(this->m_proj_parm.mode == s_pole ? - cosc : cosc);
lp_lon = (xy_x == 0. && xy_y == 0.) ? 0. : atan2(xy_x, xy_y);
break;
}
}
static inline std::string get_name()
{
return "stere_spheroid";
}
};
template <typename Parameters, typename T>
inline void setup(Parameters const& par, par_stere<T>& proj_parm) /* general initialization */
{
static const T fourth_pi = detail::fourth_pi<T>();
static const T half_pi = detail::half_pi<T>();
T t;
if (fabs((t = fabs(par.phi0)) - half_pi) < epsilon10)
proj_parm.mode = par.phi0 < 0. ? s_pole : n_pole;
else
proj_parm.mode = t > epsilon10 ? obliq : equit;
proj_parm.phits = fabs(proj_parm.phits);
if (par.es != 0.0) {
T X;
switch (proj_parm.mode) {
case n_pole:
case s_pole:
if (fabs(proj_parm.phits - half_pi) < epsilon10)
proj_parm.akm1 = 2. * par.k0 /
sqrt(math::pow(T(1)+par.e,T(1)+par.e)*math::pow(T(1)-par.e,T(1)-par.e));
else {
proj_parm.akm1 = cos(proj_parm.phits) /
pj_tsfn(proj_parm.phits, t = sin(proj_parm.phits), par.e);
t *= par.e;
proj_parm.akm1 /= sqrt(1. - t * t);
}
break;
case equit:
case obliq:
t = sin(par.phi0);
X = 2. * atan(ssfn_(par.phi0, t, par.e)) - half_pi;
t *= par.e;
proj_parm.akm1 = 2. * par.k0 * cos(par.phi0) / sqrt(1. - t * t);
proj_parm.sinX1 = sin(X);
proj_parm.cosX1 = cos(X);
break;
}
} else {
switch (proj_parm.mode) {
case obliq:
proj_parm.sinX1 = sin(par.phi0);
proj_parm.cosX1 = cos(par.phi0);
BOOST_FALLTHROUGH;
case equit:
proj_parm.akm1 = 2. * par.k0;
break;
case s_pole:
case n_pole:
proj_parm.akm1 = fabs(proj_parm.phits - half_pi) >= epsilon10 ?
cos(proj_parm.phits) / tan(fourth_pi - .5 * proj_parm.phits) :
2. * par.k0 ;
break;
}
}
}
// Stereographic
template <typename Params, typename Parameters, typename T>
inline void setup_stere(Params const& params, Parameters const& par, par_stere<T>& proj_parm)
{
static const T half_pi = detail::half_pi<T>();
if (! pj_param_r<srs::spar::lat_ts>(params, "lat_ts", srs::dpar::lat_ts, proj_parm.phits))
proj_parm.phits = half_pi;
setup(par, proj_parm);
}
// Universal Polar Stereographic
template <typename Params, typename Parameters, typename T>
inline void setup_ups(Params const& params, Parameters& par, par_stere<T>& proj_parm)
{
static const T half_pi = detail::half_pi<T>();
/* International Ellipsoid */
par.phi0 = pj_get_param_b<srs::spar::south>(params, "south", srs::dpar::south) ? -half_pi: half_pi;
if (par.es == 0.0) {
BOOST_THROW_EXCEPTION( projection_exception(error_ellipsoid_use_required) );
}
par.k0 = .994;
par.x0 = 2000000.;
par.y0 = 2000000.;
proj_parm.phits = half_pi;
par.lam0 = 0.;
setup(par, proj_parm);
}
}} // namespace detail::stere
#endif // doxygen
/*!
\brief Stereographic 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_ts: Latitude of true scale (degrees)
\par Example
\image html ex_stere.gif
*/
template <typename T, typename Parameters>
struct stere_ellipsoid : public detail::stere::base_stere_ellipsoid<T, Parameters>
{
template <typename Params>
inline stere_ellipsoid(Params const& params, Parameters const& par)
{
detail::stere::setup_stere(params, par, this->m_proj_parm);
}
};
/*!
\brief Stereographic 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_ts: Latitude of true scale (degrees)
\par Example
\image html ex_stere.gif
*/
template <typename T, typename Parameters>
struct stere_spheroid : public detail::stere::base_stere_spheroid<T, Parameters>
{
template <typename Params>
inline stere_spheroid(Params const& params, Parameters const& par)
{
detail::stere::setup_stere(params, par, this->m_proj_parm);
}
};
/*!
\brief Universal Polar Stereographic 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
- south: Denotes southern hemisphere UTM zone (boolean)
\par Example
\image html ex_ups.gif
*/
template <typename T, typename Parameters>
struct ups_ellipsoid : public detail::stere::base_stere_ellipsoid<T, Parameters>
{
template <typename Params>
inline ups_ellipsoid(Params const& params, Parameters & par)
{
detail::stere::setup_ups(params, par, this->m_proj_parm);
}
};
/*!
\brief Universal Polar Stereographic 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
- south: Denotes southern hemisphere UTM zone (boolean)
\par Example
\image html ex_ups.gif
*/
template <typename T, typename Parameters>
struct ups_spheroid : public detail::stere::base_stere_spheroid<T, Parameters>
{
template <typename Params>
inline ups_spheroid(Params const& params, Parameters & par)
{
detail::stere::setup_ups(params, par, this->m_proj_parm);
}
};
#ifndef DOXYGEN_NO_DETAIL
namespace detail
{
// Static projection
BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI2(srs::spar::proj_stere, stere_spheroid, stere_ellipsoid)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI2(srs::spar::proj_ups, ups_spheroid, ups_ellipsoid)
// Factory entry(s)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI2(stere_entry, stere_spheroid, stere_ellipsoid)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI2(ups_entry, ups_spheroid, ups_ellipsoid)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(stere_init)
{
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(stere, stere_entry)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(ups, ups_entry)
}
} // namespace detail
#endif // doxygen
} // namespace projections
}} // namespace boost::geometry
#endif // BOOST_GEOMETRY_PROJECTIONS_STERE_HPP