// 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:
// Copyright (c) 2003, 2006 Gerald I. 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_OMERC_HPP
#define BOOST_GEOMETRY_PROJECTIONS_OMERC_HPP
#include <boost/geometry/util/math.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_phi2.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 omerc
{
template <typename T>
struct par_omerc
{
T A, B, E, AB, ArB, BrA, rB, singam, cosgam, sinrot, cosrot;
T v_pole_n, v_pole_s, u_0;
bool no_rot;
};
static const double tolerance = 1.e-7;
static const double epsilon = 1.e-10;
template <typename T, typename Parameters>
struct base_omerc_ellipsoid
{
par_omerc<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 s, t, U, V, W, temp, u, v;
if (fabs(fabs(lp_lat) - half_pi) > epsilon) {
W = this->m_proj_parm.E / math::pow(pj_tsfn(lp_lat, sin(lp_lat), par.e), this->m_proj_parm.B);
temp = 1. / W;
s = .5 * (W - temp);
t = .5 * (W + temp);
V = sin(this->m_proj_parm.B * lp_lon);
U = (s * this->m_proj_parm.singam - V * this->m_proj_parm.cosgam) / t;
if (fabs(fabs(U) - 1.0) < epsilon) {
BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
}
v = 0.5 * this->m_proj_parm.ArB * log((1. - U)/(1. + U));
temp = cos(this->m_proj_parm.B * lp_lon);
if(fabs(temp) < tolerance) {
u = this->m_proj_parm.A * lp_lon;
} else {
u = this->m_proj_parm.ArB * atan2((s * this->m_proj_parm.cosgam + V * this->m_proj_parm.singam), temp);
}
} else {
v = lp_lat > 0 ? this->m_proj_parm.v_pole_n : this->m_proj_parm.v_pole_s;
u = this->m_proj_parm.ArB * lp_lat;
}
if (this->m_proj_parm.no_rot) {
xy_x = u;
xy_y = v;
} else {
u -= this->m_proj_parm.u_0;
xy_x = v * this->m_proj_parm.cosrot + u * this->m_proj_parm.sinrot;
xy_y = u * this->m_proj_parm.cosrot - v * this->m_proj_parm.sinrot;
}
}
// 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>();
T u, v, Qp, Sp, Tp, Vp, Up;
if (this->m_proj_parm.no_rot) {
v = xy_y;
u = xy_x;
} else {
v = xy_x * this->m_proj_parm.cosrot - xy_y * this->m_proj_parm.sinrot;
u = xy_y * this->m_proj_parm.cosrot + xy_x * this->m_proj_parm.sinrot + this->m_proj_parm.u_0;
}
Qp = exp(- this->m_proj_parm.BrA * v);
Sp = .5 * (Qp - 1. / Qp);
Tp = .5 * (Qp + 1. / Qp);
Vp = sin(this->m_proj_parm.BrA * u);
Up = (Vp * this->m_proj_parm.cosgam + Sp * this->m_proj_parm.singam) / Tp;
if (fabs(fabs(Up) - 1.) < epsilon) {
lp_lon = 0.;
lp_lat = Up < 0. ? -half_pi : half_pi;
} else {
lp_lat = this->m_proj_parm.E / sqrt((1. + Up) / (1. - Up));
if ((lp_lat = pj_phi2(math::pow(lp_lat, T(1) / this->m_proj_parm.B), par.e)) == HUGE_VAL) {
BOOST_THROW_EXCEPTION( projection_exception(error_tolerance_condition) );
}
lp_lon = - this->m_proj_parm.rB * atan2((Sp * this->m_proj_parm.cosgam -
Vp * this->m_proj_parm.singam), cos(this->m_proj_parm.BrA * u));
}
}
static inline std::string get_name()
{
return "omerc_ellipsoid";
}
};
// Oblique Mercator
template <typename Params, typename Parameters, typename T>
inline void setup_omerc(Params const& params, Parameters & par, par_omerc<T>& proj_parm)
{
static const T fourth_pi = detail::fourth_pi<T>();
static const T half_pi = detail::half_pi<T>();
static const T pi = detail::pi<T>();
static const T two_pi = detail::two_pi<T>();
T con, com, cosph0, D, F, H, L, sinph0, p, J, gamma=0,
gamma0, lamc=0, lam1=0, lam2=0, phi1=0, phi2=0, alpha_c=0;
int alp, gam, no_off = 0;
proj_parm.no_rot = pj_get_param_b<srs::spar::no_rot>(params, "no_rot", srs::dpar::no_rot);
alp = pj_param_r<srs::spar::alpha>(params, "alpha", srs::dpar::alpha, alpha_c);
gam = pj_param_r<srs::spar::gamma>(params, "gamma", srs::dpar::gamma, gamma);
if (alp || gam) {
lamc = pj_get_param_r<T, srs::spar::lonc>(params, "lonc", srs::dpar::lonc);
// NOTE: This is not needed in Boost.Geometry
//no_off =
// /* For libproj4 compatability */
// pj_param_exists(par.params, "no_off")
// /* for backward compatibility */
// || pj_param_exists(par.params, "no_uoff");
//if( no_off )
//{
// /* Mark the parameter as used, so that the pj_get_def() return them */
// pj_get_param_s(par.params, "no_uoff");
// pj_get_param_s(par.params, "no_off");
//}
} else {
lam1 = pj_get_param_r<T, srs::spar::lon_1>(params, "lon_1", srs::dpar::lon_1);
phi1 = pj_get_param_r<T, srs::spar::lat_1>(params, "lat_1", srs::dpar::lat_1);
lam2 = pj_get_param_r<T, srs::spar::lon_2>(params, "lon_2", srs::dpar::lon_2);
phi2 = pj_get_param_r<T, srs::spar::lat_2>(params, "lat_2", srs::dpar::lat_2);
if (fabs(phi1 - phi2) <= tolerance ||
(con = fabs(phi1)) <= tolerance ||
fabs(con - half_pi) <= tolerance ||
fabs(fabs(par.phi0) - half_pi) <= tolerance ||
fabs(fabs(phi2) - half_pi) <= tolerance)
BOOST_THROW_EXCEPTION( projection_exception(error_lat_0_or_alpha_eq_90) );
}
com = sqrt(par.one_es);
if (fabs(par.phi0) > epsilon) {
sinph0 = sin(par.phi0);
cosph0 = cos(par.phi0);
con = 1. - par.es * sinph0 * sinph0;
proj_parm.B = cosph0 * cosph0;
proj_parm.B = sqrt(1. + par.es * proj_parm.B * proj_parm.B / par.one_es);
proj_parm.A = proj_parm.B * par.k0 * com / con;
D = proj_parm.B * com / (cosph0 * sqrt(con));
if ((F = D * D - 1.) <= 0.)
F = 0.;
else {
F = sqrt(F);
if (par.phi0 < 0.)
F = -F;
}
proj_parm.E = F += D;
proj_parm.E *= math::pow(pj_tsfn(par.phi0, sinph0, par.e), proj_parm.B);
} else {
proj_parm.B = 1. / com;
proj_parm.A = par.k0;
proj_parm.E = D = F = 1.;
}
if (alp || gam) {
if (alp) {
gamma0 = aasin(sin(alpha_c) / D);
if (!gam)
gamma = alpha_c;
} else
alpha_c = aasin(D*sin(gamma0 = gamma));
par.lam0 = lamc - aasin(.5 * (F - 1. / F) *
tan(gamma0)) / proj_parm.B;
} else {
H = math::pow(pj_tsfn(phi1, sin(phi1), par.e), proj_parm.B);
L = math::pow(pj_tsfn(phi2, sin(phi2), par.e), proj_parm.B);
F = proj_parm.E / H;
p = (L - H) / (L + H);
J = proj_parm.E * proj_parm.E;
J = (J - L * H) / (J + L * H);
if ((con = lam1 - lam2) < -pi)
lam2 -= two_pi;
else if (con > pi)
lam2 += two_pi;
par.lam0 = adjlon(.5 * (lam1 + lam2) - atan(
J * tan(.5 * proj_parm.B * (lam1 - lam2)) / p) / proj_parm.B);
gamma0 = atan(2. * sin(proj_parm.B * adjlon(lam1 - par.lam0)) /
(F - 1. / F));
gamma = alpha_c = aasin(D * sin(gamma0));
}
proj_parm.singam = sin(gamma0);
proj_parm.cosgam = cos(gamma0);
proj_parm.sinrot = sin(gamma);
proj_parm.cosrot = cos(gamma);
proj_parm.BrA = 1. / (proj_parm.ArB = proj_parm.A * (proj_parm.rB = 1. / proj_parm.B));
proj_parm.AB = proj_parm.A * proj_parm.B;
if (no_off)
proj_parm.u_0 = 0;
else {
proj_parm.u_0 = fabs(proj_parm.ArB * atan(sqrt(D * D - 1.) / cos(alpha_c)));
if (par.phi0 < 0.)
proj_parm.u_0 = - proj_parm.u_0;
}
F = 0.5 * gamma0;
proj_parm.v_pole_n = proj_parm.ArB * log(tan(fourth_pi - F));
proj_parm.v_pole_s = proj_parm.ArB * log(tan(fourth_pi + F));
}
}} // namespace detail::omerc
#endif // doxygen
/*!
\brief Oblique Mercator projection
\ingroup projections
\tparam Geographic latlong point type
\tparam Cartesian xy point type
\tparam Parameters parameter type
\par Projection characteristics
- Cylindrical
- Spheroid
- Ellipsoid
\par Projection parameters
- no_rot: No rotation
- alpha: Alpha (degrees)
- gamma: Gamma (degrees)
- no_off: Only for compatibility with libproj, proj4 (string)
- lonc: Longitude (only used if alpha (or gamma) is specified) (degrees)
- lon_1 (degrees)
- lat_1: Latitude of first standard parallel (degrees)
- lon_2 (degrees)
- lat_2: Latitude of second standard parallel (degrees)
- no_uoff (string)
\par Example
\image html ex_omerc.gif
*/
template <typename T, typename Parameters>
struct omerc_ellipsoid : public detail::omerc::base_omerc_ellipsoid<T, Parameters>
{
template <typename Params>
inline omerc_ellipsoid(Params const& params, Parameters & par)
{
detail::omerc::setup_omerc(params, par, this->m_proj_parm);
}
};
#ifndef DOXYGEN_NO_DETAIL
namespace detail
{
// Static projection
BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_omerc, omerc_ellipsoid)
// Factory entry(s)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(omerc_entry, omerc_ellipsoid)
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(omerc_init)
{
BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(omerc, omerc_entry)
}
} // namespace detail
#endif // doxygen
} // namespace projections
}} // namespace boost::geometry
#endif // BOOST_GEOMETRY_PROJECTIONS_OMERC_HPP