// 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:
// Purpose: Implementation of the aitoff (Aitoff) and wintri (Winkel Tripel)
// projections.
// Author: Gerald Evenden (1995)
// Drazen Tutic, Lovro Gradiser (2015) - add inverse
// Thomas Knudsen (2016) - revise/add regression tests
// 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_AITOFF_HPP
#define BOOST_GEOMETRY_PROJECTIONS_AITOFF_HPP
#include <boost/core/ignore_unused.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/projects.hpp>
#include <boost/geometry/util/math.hpp>
namespace boost { namespace geometry
{
namespace projections
{
#ifndef DOXYGEN_NO_DETAIL
namespace detail { namespace aitoff
{
enum mode_type {
mode_aitoff = 0,
mode_winkel_tripel = 1
};
template <typename T>
struct par_aitoff
{
T cosphi1;
mode_type mode;
};
template <typename T, typename Parameters>
struct base_aitoff_spheroid
{
par_aitoff<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 const& lp_lat, T& xy_x, T& xy_y) const
{
T c, d;
if((d = acos(cos(lp_lat) * cos(c = 0.5 * lp_lon)))) {/* basic Aitoff */
xy_x = 2. * d * cos(lp_lat) * sin(c) * (xy_y = 1. / sin(d));
xy_y *= d * sin(lp_lat);
} else
xy_x = xy_y = 0.;
if (this->m_proj_parm.mode == mode_winkel_tripel) { /* Winkel Tripel */
xy_x = (xy_x + lp_lon * this->m_proj_parm.cosphi1) * 0.5;
xy_y = (xy_y + lp_lat) * 0.5;
}
}
/***********************************************************************************
*
* Inverse functions added by Drazen Tutic and Lovro Gradiser based on paper:
*
* I.Özbug Biklirici and Cengizhan Ipbüker. A General Algorithm for the Inverse
* Transformation of Map Projections Using Jacobian Matrices. In Proceedings of the
* Third International Symposium Mathematical & Computational Applications,
* pages 175{182, Turkey, September 2002.
*
* Expected accuracy is defined by epsilon = 1e-12. Should be appropriate for
* most applications of Aitoff and Winkel Tripel projections.
*
* Longitudes of 180W and 180E can be mixed in solution obtained.
*
* Inverse for Aitoff projection in poles is undefined, longitude value of 0 is assumed.
*
* Contact : dtutic@geof.hr
* Date: 2015-02-16
*
************************************************************************************/
// INVERSE(s_inverse) sphere
// Project coordinates from cartesian (x, y) to geographic (lon, lat)
inline void inv(Parameters const& , T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const
{
static const T pi = detail::pi<T>();
static const T two_pi = detail::two_pi<T>();
static const T epsilon = 1e-12;
int iter, max_iter = 10, round = 0, max_round = 20;
T D, C, f1, f2, f1p, f1l, f2p, f2l, dp, dl, sl, sp, cp, cl, x, y;
if ((fabs(xy_x) < epsilon) && (fabs(xy_y) < epsilon )) {
lp_lat = 0.; lp_lon = 0.;
return;
}
/* intial values for Newton-Raphson method */
lp_lat = xy_y; lp_lon = xy_x;
do {
iter = 0;
do {
sl = sin(lp_lon * 0.5); cl = cos(lp_lon * 0.5);
sp = sin(lp_lat); cp = cos(lp_lat);
D = cp * cl;
C = 1. - D * D;
D = acos(D) / math::pow(C, T(1.5));
f1 = 2. * D * C * cp * sl;
f2 = D * C * sp;
f1p = 2.* (sl * cl * sp * cp / C - D * sp * sl);
f1l = cp * cp * sl * sl / C + D * cp * cl * sp * sp;
f2p = sp * sp * cl / C + D * sl * sl * cp;
f2l = 0.5 * (sp * cp * sl / C - D * sp * cp * cp * sl * cl);
if (this->m_proj_parm.mode == mode_winkel_tripel) { /* Winkel Tripel */
f1 = 0.5 * (f1 + lp_lon * this->m_proj_parm.cosphi1);
f2 = 0.5 * (f2 + lp_lat);
f1p *= 0.5;
f1l = 0.5 * (f1l + this->m_proj_parm.cosphi1);
f2p = 0.5 * (f2p + 1.);
f2l *= 0.5;
}
f1 -= xy_x; f2 -= xy_y;
dl = (f2 * f1p - f1 * f2p) / (dp = f1p * f2l - f2p * f1l);
dp = (f1 * f2l - f2 * f1l) / dp;
dl = fmod(dl, pi); /* set to interval [-M_PI, M_PI] */
lp_lat -= dp; lp_lon -= dl;
} while ((fabs(dp) > epsilon || fabs(dl) > epsilon) && (iter++ < max_iter));
if (lp_lat > two_pi) lp_lat -= 2.*(lp_lat-two_pi); /* correct if symmetrical solution for Aitoff */
if (lp_lat < -two_pi) lp_lat -= 2.*(lp_lat+two_pi); /* correct if symmetrical solution for Aitoff */
if ((fabs(fabs(lp_lat) - two_pi) < epsilon) && (!this->m_proj_parm.mode)) lp_lon = 0.; /* if pole in Aitoff, return longitude of 0 */
/* calculate x,y coordinates with solution obtained */
if((D = acos(cos(lp_lat) * cos(C = 0.5 * lp_lon))) != 0.0) {/* Aitoff */
x = 2. * D * cos(lp_lat) * sin(C) * (y = 1. / sin(D));
y *= D * sin(lp_lat);
} else
x = y = 0.;
if (this->m_proj_parm.mode == mode_winkel_tripel) { /* Winkel Tripel */
x = (x + lp_lon * this->m_proj_parm.cosphi1) * 0.5;
y = (y + lp_lat) * 0.5;
}
/* if too far from given values of x,y, repeat with better approximation of phi,lam */
} while (((fabs(xy_x-x) > epsilon) || (fabs(xy_y-y) > epsilon)) && (round++ < max_round));
if (iter == max_iter && round == max_round)
{
BOOST_THROW_EXCEPTION( projection_exception(error_non_convergent) );
//fprintf(stderr, "Warning: Accuracy of 1e-12 not reached. Last increments: dlat=%e and dlon=%e\n", dp, dl);
}
}
static inline std::string get_name()
{
return "aitoff_spheroid";
}
};
template <typename Parameters>
inline void setup(Parameters& par)
{
par.es = 0.;
}
// Aitoff
template <typename Parameters, typename T>
inline void setup_aitoff(Parameters& par, par_aitoff<T>& proj_parm)
{
proj_parm.mode = mode_aitoff;
setup(par);
}
// Winkel Tripel
template <typename Params, typename Parameters, typename T>
inline void setup_wintri(Params& params, Parameters& par, par_aitoff<T>& proj_parm)
{
static const T two_div_pi = detail::two_div_pi<T>();
T phi1;
proj_parm.mode = mode_winkel_tripel;
if (pj_param_r<srs::spar::lat_1>(params, "lat_1", srs::dpar::lat_1, phi1)) {
if ((proj_parm.cosphi1 = cos(phi1)) == 0.)
BOOST_THROW_EXCEPTION( projection_exception(error_lat_larger_than_90) );
} else /* 50d28' or phi1=acos(2/pi) */
proj_parm.cosphi1 = two_div_pi;
setup(par);
}
}} // namespace detail::aitoff
#endif // doxygen
/*!
\brief Aitoff projection
\ingroup projections
\tparam Geographic latlong point type
\tparam Cartesian xy point type
\tparam Parameters parameter type
\par Projection characteristics
- Miscellaneous
- Spheroid
\par Example
\image html ex_aitoff.gif
*/
template <typename T, typename Parameters>
struct aitoff_spheroid : public detail::aitoff::base_aitoff_spheroid<T, Parameters>
{
template <typename Params>
inline aitoff_spheroid(Params const& , Parameters & par)
{
detail::aitoff::setup_aitoff(par, this->m_proj_parm);
}
};
/*!
\brief Winkel Tripel projection
\ingroup projections
\tparam Geographic latlong point type
\tparam Cartesian xy point type
\tparam Parameters parameter type
\par Projection characteristics
- Miscellaneous
- Spheroid
\par Projection parameters
- lat_1: Latitude of first standard parallel (degrees)
\par Example
\image html ex_wintri.gif
*/
template <typename T, typename Parameters>
struct wintri_spheroid : public detail::aitoff::base_aitoff_spheroid<T, Parameters>
{
template <typename Params>
inline wintri_spheroid(Params const& params, Parameters & par)
{
detail::aitoff::setup_wintri(params, par, this->m_proj_parm);
}
};
#ifndef DOXYGEN_NO_DETAIL
namespace detail
{
// Static projection
BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_aitoff, aitoff_spheroid)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_wintri, wintri_spheroid)
// Factory entry(s)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(aitoff_entry, aitoff_spheroid)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(wintri_entry, wintri_spheroid)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(aitoff_init)
{
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(aitoff, aitoff_entry)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(wintri, wintri_entry)
}
} // namespace detail
#endif // doxygen
} // namespace projections
}} // namespace boost::geometry
#endif // BOOST_GEOMETRY_PROJECTIONS_AITOFF_HPP