426 lines
17 KiB
C++
426 lines
17 KiB
C++
|
// 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_LAEA_HPP
|
||
|
|
#define BOOST_GEOMETRY_PROJECTIONS_LAEA_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/projects.hpp>
|
||
|
|
#include <boost/geometry/srs/projections/impl/factory_entry.hpp>
|
||
|
|
#include <boost/geometry/srs/projections/impl/pj_auth.hpp>
|
||
|
|
#include <boost/geometry/srs/projections/impl/pj_qsfn.hpp>
|
||
|
|
|
||
|
|
namespace boost { namespace geometry
|
||
|
|
{
|
||
|
|
|
||
|
|
namespace projections
|
||
|
|
{
|
||
|
|
#ifndef DOXYGEN_NO_DETAIL
|
||
|
|
namespace detail { namespace laea
|
||
|
|
{
|
||
|
|
static const double epsilon10 = 1.e-10;
|
||
|
|
|
||
|
|
enum mode_type {
|
||
|
|
n_pole = 0,
|
||
|
|
s_pole = 1,
|
||
|
|
equit = 2,
|
||
|
|
obliq = 3
|
||
|
|
};
|
||
|
|
|
||
|
|
template <typename T>
|
||
|
|
struct par_laea
|
||
|
|
{
|
||
|
|
T sinb1;
|
||
|
|
T cosb1;
|
||
|
|
T xmf;
|
||
|
|
T ymf;
|
||
|
|
T mmf;
|
||
|
|
T qp;
|
||
|
|
T dd;
|
||
|
|
T rq;
|
||
|
|
detail::apa<T> apa;
|
||
|
|
mode_type mode;
|
||
|
|
};
|
||
|
|
|
||
|
|
template <typename T, typename Parameters>
|
||
|
|
struct base_laea_ellipsoid
|
||
|
|
{
|
||
|
|
par_laea<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 coslam, sinlam, sinphi, q, sinb=0.0, cosb=0.0, b=0.0;
|
||
|
|
|
||
|
|
coslam = cos(lp_lon);
|
||
|
|
sinlam = sin(lp_lon);
|
||
|
|
sinphi = sin(lp_lat);
|
||
|
|
q = pj_qsfn(sinphi, par.e, par.one_es);
|
||
|
|
|
||
|
|
if (this->m_proj_parm.mode == obliq || this->m_proj_parm.mode == equit) {
|
||
|
|
sinb = q / this->m_proj_parm.qp;
|
||
|
|
cosb = sqrt(1. - sinb * sinb);
|
||
|
|
}
|
||
|
|
|
||
|
|
switch (this->m_proj_parm.mode) {
|
||
|
|
case obliq:
|
||
|
|
b = 1. + this->m_proj_parm.sinb1 * sinb + this->m_proj_parm.cosb1 * cosb * coslam;
|
||
|
|
break;
|
||
|
|
case equit:
|
||
|
|
b = 1. + cosb * coslam;
|
||
|
|
break;
|
||
|
|
case n_pole:
|
||
|
|
b = half_pi + lp_lat;
|
||
|
|
q = this->m_proj_parm.qp - q;
|
||
|
|
break;
|
||
|
|
case s_pole:
|
||
|
|
b = lp_lat - half_pi;
|
||
|
|
q = this->m_proj_parm.qp + q;
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
if (fabs(b) < epsilon10) {
|
||
|
|
BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
|
||
|
|
}
|
||
|
|
|
||
|
|
switch (this->m_proj_parm.mode) {
|
||
|
|
case obliq:
|
||
|
|
b = sqrt(2. / b);
|
||
|
|
xy_y = this->m_proj_parm.ymf * b * (this->m_proj_parm.cosb1 * sinb - this->m_proj_parm.sinb1 * cosb * coslam);
|
||
|
|
goto eqcon;
|
||
|
|
break;
|
||
|
|
case equit:
|
||
|
|
b = sqrt(2. / (1. + cosb * coslam));
|
||
|
|
xy_y = b * sinb * this->m_proj_parm.ymf;
|
||
|
|
eqcon:
|
||
|
|
xy_x = this->m_proj_parm.xmf * b * cosb * sinlam;
|
||
|
|
break;
|
||
|
|
case n_pole:
|
||
|
|
case s_pole:
|
||
|
|
if (q >= 0.) {
|
||
|
|
b = sqrt(q);
|
||
|
|
xy_x = b * sinlam;
|
||
|
|
xy_y = coslam * (this->m_proj_parm.mode == s_pole ? b : -b);
|
||
|
|
} else
|
||
|
|
xy_x = xy_y = 0.;
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// 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
|
||
|
|
{
|
||
|
|
T cCe, sCe, q, rho, ab=0.0;
|
||
|
|
|
||
|
|
switch (this->m_proj_parm.mode) {
|
||
|
|
case equit:
|
||
|
|
case obliq:
|
||
|
|
xy_x /= this->m_proj_parm.dd;
|
||
|
|
xy_y *= this->m_proj_parm.dd;
|
||
|
|
rho = boost::math::hypot(xy_x, xy_y);
|
||
|
|
if (rho < epsilon10) {
|
||
|
|
lp_lon = 0.;
|
||
|
|
lp_lat = par.phi0;
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
sCe = 2. * asin(.5 * rho / this->m_proj_parm.rq);
|
||
|
|
cCe = cos(sCe);
|
||
|
|
sCe = sin(sCe);
|
||
|
|
xy_x *= sCe;
|
||
|
|
if (this->m_proj_parm.mode == obliq) {
|
||
|
|
ab = cCe * this->m_proj_parm.sinb1 + xy_y * sCe * this->m_proj_parm.cosb1 / rho;
|
||
|
|
xy_y = rho * this->m_proj_parm.cosb1 * cCe - xy_y * this->m_proj_parm.sinb1 * sCe;
|
||
|
|
} else {
|
||
|
|
ab = xy_y * sCe / rho;
|
||
|
|
xy_y = rho * cCe;
|
||
|
|
}
|
||
|
|
break;
|
||
|
|
case n_pole:
|
||
|
|
xy_y = -xy_y;
|
||
|
|
BOOST_FALLTHROUGH;
|
||
|
|
case s_pole:
|
||
|
|
q = (xy_x * xy_x + xy_y * xy_y);
|
||
|
|
if (q == 0.0) {
|
||
|
|
lp_lon = 0.;
|
||
|
|
lp_lat = par.phi0;
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
ab = 1. - q / this->m_proj_parm.qp;
|
||
|
|
if (this->m_proj_parm.mode == s_pole)
|
||
|
|
ab = - ab;
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
lp_lon = atan2(xy_x, xy_y);
|
||
|
|
lp_lat = pj_authlat(asin(ab), this->m_proj_parm.apa);
|
||
|
|
}
|
||
|
|
|
||
|
|
static inline std::string get_name()
|
||
|
|
{
|
||
|
|
return "laea_ellipsoid";
|
||
|
|
}
|
||
|
|
|
||
|
|
};
|
||
|
|
|
||
|
|
template <typename T, typename Parameters>
|
||
|
|
struct base_laea_spheroid
|
||
|
|
{
|
||
|
|
par_laea<T> m_proj_parm;
|
||
|
|
|
||
|
|
// FORWARD(s_forward) spheroid
|
||
|
|
// 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 fourth_pi = detail::fourth_pi<T>();
|
||
|
|
|
||
|
|
T coslam, cosphi, sinphi;
|
||
|
|
|
||
|
|
sinphi = sin(lp_lat);
|
||
|
|
cosphi = cos(lp_lat);
|
||
|
|
coslam = cos(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.sinb1 * sinphi + this->m_proj_parm.cosb1 * cosphi * coslam;
|
||
|
|
oblcon:
|
||
|
|
if (xy_y <= epsilon10) {
|
||
|
|
BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
|
||
|
|
}
|
||
|
|
xy_y = sqrt(2. / xy_y);
|
||
|
|
xy_x = xy_y * cosphi * sin(lp_lon);
|
||
|
|
xy_y *= this->m_proj_parm.mode == equit ? sinphi :
|
||
|
|
this->m_proj_parm.cosb1 * sinphi - this->m_proj_parm.sinb1 * cosphi * coslam;
|
||
|
|
break;
|
||
|
|
case n_pole:
|
||
|
|
coslam = -coslam;
|
||
|
|
BOOST_FALLTHROUGH;
|
||
|
|
case s_pole:
|
||
|
|
if (fabs(lp_lat + par.phi0) < epsilon10) {
|
||
|
|
BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
|
||
|
|
}
|
||
|
|
xy_y = fourth_pi - lp_lat * .5;
|
||
|
|
xy_y = 2. * (this->m_proj_parm.mode == s_pole ? cos(xy_y) : sin(xy_y));
|
||
|
|
xy_x = xy_y * sin(lp_lon);
|
||
|
|
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 xy_x, T xy_y, T& lp_lon, T& lp_lat) const
|
||
|
|
{
|
||
|
|
static const T half_pi = detail::half_pi<T>();
|
||
|
|
|
||
|
|
T cosz=0.0, rh, sinz=0.0;
|
||
|
|
|
||
|
|
rh = boost::math::hypot(xy_x, xy_y);
|
||
|
|
if ((lp_lat = rh * .5 ) > 1.) {
|
||
|
|
BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
|
||
|
|
}
|
||
|
|
lp_lat = 2. * asin(lp_lat);
|
||
|
|
if (this->m_proj_parm.mode == obliq || this->m_proj_parm.mode == equit) {
|
||
|
|
sinz = sin(lp_lat);
|
||
|
|
cosz = cos(lp_lat);
|
||
|
|
}
|
||
|
|
switch (this->m_proj_parm.mode) {
|
||
|
|
case equit:
|
||
|
|
lp_lat = fabs(rh) <= epsilon10 ? 0. : asin(xy_y * sinz / rh);
|
||
|
|
xy_x *= sinz;
|
||
|
|
xy_y = cosz * rh;
|
||
|
|
break;
|
||
|
|
case obliq:
|
||
|
|
lp_lat = fabs(rh) <= epsilon10 ? par.phi0 :
|
||
|
|
asin(cosz * this->m_proj_parm.sinb1 + xy_y * sinz * this->m_proj_parm.cosb1 / rh);
|
||
|
|
xy_x *= sinz * this->m_proj_parm.cosb1;
|
||
|
|
xy_y = (cosz - sin(lp_lat) * this->m_proj_parm.sinb1) * rh;
|
||
|
|
break;
|
||
|
|
case n_pole:
|
||
|
|
xy_y = -xy_y;
|
||
|
|
lp_lat = half_pi - lp_lat;
|
||
|
|
break;
|
||
|
|
case s_pole:
|
||
|
|
lp_lat -= half_pi;
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
lp_lon = (xy_y == 0. && (this->m_proj_parm.mode == equit || this->m_proj_parm.mode == obliq)) ?
|
||
|
|
0. : atan2(xy_x, xy_y);
|
||
|
|
}
|
||
|
|
|
||
|
|
static inline std::string get_name()
|
||
|
|
{
|
||
|
|
return "laea_spheroid";
|
||
|
|
}
|
||
|
|
|
||
|
|
};
|
||
|
|
|
||
|
|
// Lambert Azimuthal Equal Area
|
||
|
|
template <typename Parameters, typename T>
|
||
|
|
inline void setup_laea(Parameters& par, par_laea<T>& proj_parm)
|
||
|
|
{
|
||
|
|
static const T half_pi = detail::half_pi<T>();
|
||
|
|
|
||
|
|
T t;
|
||
|
|
|
||
|
|
t = fabs(par.phi0);
|
||
|
|
if (fabs(t - half_pi) < epsilon10)
|
||
|
|
proj_parm.mode = par.phi0 < 0. ? s_pole : n_pole;
|
||
|
|
else if (fabs(t) < epsilon10)
|
||
|
|
proj_parm.mode = equit;
|
||
|
|
else
|
||
|
|
proj_parm.mode = obliq;
|
||
|
|
if (par.es != 0.0) {
|
||
|
|
double sinphi;
|
||
|
|
|
||
|
|
par.e = sqrt(par.es); // TODO : Isn't it already set?
|
||
|
|
proj_parm.qp = pj_qsfn(1., par.e, par.one_es);
|
||
|
|
proj_parm.mmf = .5 / (1. - par.es);
|
||
|
|
proj_parm.apa = pj_authset<T>(par.es);
|
||
|
|
switch (proj_parm.mode) {
|
||
|
|
case n_pole:
|
||
|
|
case s_pole:
|
||
|
|
proj_parm.dd = 1.;
|
||
|
|
break;
|
||
|
|
case equit:
|
||
|
|
proj_parm.dd = 1. / (proj_parm.rq = sqrt(.5 * proj_parm.qp));
|
||
|
|
proj_parm.xmf = 1.;
|
||
|
|
proj_parm.ymf = .5 * proj_parm.qp;
|
||
|
|
break;
|
||
|
|
case obliq:
|
||
|
|
proj_parm.rq = sqrt(.5 * proj_parm.qp);
|
||
|
|
sinphi = sin(par.phi0);
|
||
|
|
proj_parm.sinb1 = pj_qsfn(sinphi, par.e, par.one_es) / proj_parm.qp;
|
||
|
|
proj_parm.cosb1 = sqrt(1. - proj_parm.sinb1 * proj_parm.sinb1);
|
||
|
|
proj_parm.dd = cos(par.phi0) / (sqrt(1. - par.es * sinphi * sinphi) *
|
||
|
|
proj_parm.rq * proj_parm.cosb1);
|
||
|
|
proj_parm.ymf = (proj_parm.xmf = proj_parm.rq) / proj_parm.dd;
|
||
|
|
proj_parm.xmf *= proj_parm.dd;
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
if (proj_parm.mode == obliq) {
|
||
|
|
proj_parm.sinb1 = sin(par.phi0);
|
||
|
|
proj_parm.cosb1 = cos(par.phi0);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
}} // namespace laea
|
||
|
|
#endif // doxygen
|
||
|
|
|
||
|
|
/*!
|
||
|
|
\brief Lambert Azimuthal Equal Area projection
|
||
|
|
\ingroup projections
|
||
|
|
\tparam Geographic latlong point type
|
||
|
|
\tparam Cartesian xy point type
|
||
|
|
\tparam Parameters parameter type
|
||
|
|
\par Projection characteristics
|
||
|
|
- Azimuthal
|
||
|
|
- Spheroid
|
||
|
|
- Ellipsoid
|
||
|
|
\par Example
|
||
|
|
\image html ex_laea.gif
|
||
|
|
*/
|
||
|
|
template <typename T, typename Parameters>
|
||
|
|
struct laea_ellipsoid : public detail::laea::base_laea_ellipsoid<T, Parameters>
|
||
|
|
{
|
||
|
|
template <typename Params>
|
||
|
|
inline laea_ellipsoid(Params const& , Parameters & par)
|
||
|
|
{
|
||
|
|
detail::laea::setup_laea(par, this->m_proj_parm);
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
/*!
|
||
|
|
\brief Lambert Azimuthal Equal Area projection
|
||
|
|
\ingroup projections
|
||
|
|
\tparam Geographic latlong point type
|
||
|
|
\tparam Cartesian xy point type
|
||
|
|
\tparam Parameters parameter type
|
||
|
|
\par Projection characteristics
|
||
|
|
- Azimuthal
|
||
|
|
- Spheroid
|
||
|
|
- Ellipsoid
|
||
|
|
\par Example
|
||
|
|
\image html ex_laea.gif
|
||
|
|
*/
|
||
|
|
template <typename T, typename Parameters>
|
||
|
|
struct laea_spheroid : public detail::laea::base_laea_spheroid<T, Parameters>
|
||
|
|
{
|
||
|
|
template <typename Params>
|
||
|
|
inline laea_spheroid(Params const& , Parameters & par)
|
||
|
|
{
|
||
|
|
detail::laea::setup_laea(par, this->m_proj_parm);
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
#ifndef DOXYGEN_NO_DETAIL
|
||
|
|
namespace detail
|
||
|
|
{
|
||
|
|
|
||
|
|
// Static projection
|
||
|
|
BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI2(srs::spar::proj_laea, laea_spheroid, laea_ellipsoid)
|
||
|
|
|
||
|
|
// Factory entry(s)
|
||
|
|
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI2(laea_entry, laea_spheroid, laea_ellipsoid)
|
||
|
|
|
||
|
|
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(laea_init)
|
||
|
|
{
|
||
|
|
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(laea, laea_entry)
|
||
|
|
}
|
||
|
|
|
||
|
|
} // namespace detail
|
||
|
|
#endif // doxygen
|
||
|
|
|
||
|
|
} // namespace projections
|
||
|
|
|
||
|
|
}} // namespace boost::geometry
|
||
|
|
|
||
|
|
#endif // BOOST_GEOMETRY_PROJECTIONS_LAEA_HPP
|
||
|
|
|