// 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.
// The Natural Earth projection was designed by Tom Patterson, US National Park
// Service, in 2007, using Flex Projector. The shape of the original projection
// was defined at every 5 degrees and piece-wise cubic spline interpolation was
// used to compute the complete graticule.
// The code here uses polynomial functions instead of cubic splines and
// is therefore much simpler to program. The polynomial approximation was
// developed by Bojan Savric, in collaboration with Tom Patterson and Bernhard
// Jenny, Institute of Cartography, ETH Zurich. It slightly deviates from
// Patterson's original projection by adding additional curvature to meridians
// where they meet the horizontal pole line. This improvement is by intention
// and designed in collaboration with Tom Patterson.
// Port to PROJ.4 by Bernhard Jenny, 6 June 2011
#ifndef BOOST_GEOMETRY_PROJECTIONS_NATEARTH_HPP
#define BOOST_GEOMETRY_PROJECTIONS_NATEARTH_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>
namespace boost { namespace geometry
{
namespace projections
{
#ifndef DOXYGEN_NO_DETAIL
namespace detail { namespace natearth
{
static const double A0 = 0.8707;
static const double A1 = -0.131979;
static const double A2 = -0.013791;
static const double A3 = 0.003971;
static const double A4 = -0.001529;
static const double B0 = 1.007226;
static const double B1 = 0.015085;
static const double B2 = -0.044475;
static const double B3 = 0.028874;
static const double B4 = -0.005916;
static const double C0 = B0;
static const double C1 = (3 * B1);
static const double C2 = (7 * B2);
static const double C3 = (9 * B3);
static const double C4 = (11 * B4);
static const double epsilon = 1e-11;
template <typename T>
inline T max_y() { return (0.8707 * 0.52 * detail::pi<T>()); }
/* Not sure at all of the appropriate number for max_iter... */
static const int max_iter = 100;
template <typename T, typename Parameters>
struct base_natearth_spheroid
{
// 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 phi2, phi4;
phi2 = lp_lat * lp_lat;
phi4 = phi2 * phi2;
xy_x = lp_lon * (A0 + phi2 * (A1 + phi2 * (A2 + phi4 * phi2 * (A3 + phi2 * A4))));
xy_y = lp_lat * (B0 + phi2 * (B1 + phi4 * (B2 + B3 * phi2 + B4 * phi4)));
}
// INVERSE(s_inverse) spheroid
// Project coordinates from cartesian (x, y) to geographic (lon, lat)
inline void inv(Parameters const& , T const& xy_x, T xy_y, T& lp_lon, T& lp_lat) const
{
static const T max_y = natearth::max_y<T>();
T yc, tol, y2, y4, f, fder;
int i;
/* make sure y is inside valid range */
if (xy_y > max_y) {
xy_y = max_y;
} else if (xy_y < -max_y) {
xy_y = -max_y;
}
/* latitude */
yc = xy_y;
for (i = max_iter; i ; --i) { /* Newton-Raphson */
y2 = yc * yc;
y4 = y2 * y2;
f = (yc * (B0 + y2 * (B1 + y4 * (B2 + B3 * y2 + B4 * y4)))) - xy_y;
fder = C0 + y2 * (C1 + y4 * (C2 + C3 * y2 + C4 * y4));
yc -= tol = f / fder;
if (fabs(tol) < epsilon) {
break;
}
}
if( i == 0 )
BOOST_THROW_EXCEPTION( projection_exception(error_non_convergent) );
lp_lat = yc;
/* longitude */
y2 = yc * yc;
lp_lon = xy_x / (A0 + y2 * (A1 + y2 * (A2 + y2 * y2 * y2 * (A3 + y2 * A4))));
}
static inline std::string get_name()
{
return "natearth_spheroid";
}
};
// Natural Earth
template <typename Parameters>
inline void setup_natearth(Parameters& par)
{
par.es = 0;
}
}} // namespace detail::natearth
#endif // doxygen
/*!
\brief Natural Earth projection
\ingroup projections
\tparam Geographic latlong point type
\tparam Cartesian xy point type
\tparam Parameters parameter type
\par Projection characteristics
- Pseudocylindrical
- Spheroid
\par Example
\image html ex_natearth.gif
*/
template <typename T, typename Parameters>
struct natearth_spheroid : public detail::natearth::base_natearth_spheroid<T, Parameters>
{
template <typename Params>
inline natearth_spheroid(Params const& , Parameters & par)
{
detail::natearth::setup_natearth(par);
}
};
#ifndef DOXYGEN_NO_DETAIL
namespace detail
{
// Static projection
BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_natearth, natearth_spheroid)
// Factory entry(s)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(natearth_entry, natearth_spheroid)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(natearth_init)
{
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(natearth, natearth_entry)
}
} // namespace detail
#endif // doxygen
} // namespace projections
}} // namespace boost::geometry
#endif // BOOST_GEOMETRY_PROJECTIONS_NATEARTH_HPP