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// Boost.Geometry
// Copyright (c) 2022 Adam Wulkiewicz, Lodz, Poland.
// Copyright (c) 2022, Oracle and/or its affiliates.
// Contributed and/or modified by Vissarion Fysikopoulos, 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 PROJ, https://github.com/OSGeo/PROJ
// Last updated version of proj: 9.0.0
// Original copyright notice:
/******************************************************************************
*
* Project: PROJ
* Purpose: Generic method to compute inverse projection from forward method
* Author: Even Rouault <even dot rouault at spatialys dot com>
*
******************************************************************************
* Copyright (c) 2018, Even Rouault <even dot rouault at spatialys dot com>
*
* 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_IMPL_PJ_GENERIC_INVERSE_HPP
#define BOOST_GEOMETRY_PROJECTIONS_IMPL_PJ_GENERIC_INVERSE_HPP
#include <algorithm>
#include <cmath>
#include <boost/geometry/util/math.hpp>
/** Compute (lam, phi) corresponding to input (xy_x, xy_y) for projection P.
*
* Uses Newton-Raphson method, extended to 2D variables, that is using
* inversion of the Jacobian 2D matrix of partial derivatives. The derivatives
* are estimated numerically from the P->fwd method evaluated at close points.
*
* Note: thresholds used have been verified to work with adams_ws2 and wink2
*
* Starts with initial guess provided by user in lpInitial
*/
namespace boost { namespace geometry { namespace projections
{
namespace detail
{
template <typename T, typename Parameters, typename Projection>
void pj_generic_inverse_2d(T const& xy_x,
T const& xy_y,
Parameters const& par,
Projection const& proj,
T& lp_lat,
T& lp_lon)
{
T deriv_lam_X = 0;
T deriv_lam_Y = 0;
T deriv_phi_X = 0;
T deriv_phi_Y = 0;
for (int i = 0; i < 15; i++)
{
T xyApprox_x;
T xyApprox_y;
proj->fwd(par, lp_lon, lp_lat, xyApprox_x, xyApprox_y);
T const deltaX = xyApprox_x - xy_x;
T const deltaY = xyApprox_y - xy_y;
if (fabs(deltaX) < 1e-10 && fabs(deltaY) < 1e-10) return;
if (fabs(deltaX) > 1e-6 || fabs(deltaY) > 1e-6)
{
// Compute Jacobian matrix (only if we aren't close to the final
// result to speed things a bit)
T lp2_lat;
T lp2_lon;
T xy2_x;
T xy2_y;
T const dLam = lp_lat > 0 ? -1e-6 : 1e-6;
lp2_lat = lp_lat + dLam;
lp2_lon = lp_lon;
proj->fwd(par, lp2_lon, lp2_lat, xy2_x, xy2_y);
//xy2 = P->fwd(lp2, P);
T const deriv_X_lam = (xy2_x - xyApprox_x) / dLam;
T const deriv_Y_lam = (xy2_y - xyApprox_y) / dLam;
T const dPhi = lp_lon > 0 ? -1e-6 : 1e-6;
lp2_lat = lp_lat;
lp2_lon = lp_lon + dPhi;
proj->fwd(par, lp2_lon, lp2_lat, xy2_x, xy2_y);
//xy2 = P->fwd(lp2, P);
T const deriv_X_phi = (xy2_x - xyApprox_x) / dPhi;
T const deriv_Y_phi = (xy2_y - xyApprox_y) / dPhi;
// Inverse of Jacobian matrix
T const det = deriv_X_lam * deriv_Y_phi - deriv_X_phi * deriv_Y_lam;
if (det != 0)
{
deriv_lam_X = deriv_Y_phi / det;
deriv_lam_Y = -deriv_X_phi / det;
deriv_phi_X = -deriv_Y_lam / det;
deriv_phi_Y = deriv_X_lam / det;
}
}
if (xy_x != 0)
{
// Limit the amplitude of correction to avoid overshoots due to
// bad initial guess
T const delta_lam = (std::max)(
(std::min)(deltaX * deriv_lam_X + deltaY * deriv_lam_Y, 0.3),
-0.3);
lp_lat -= delta_lam;
if (lp_lat < -math::pi<T>())
lp_lat = -math::pi<T>();
else if (lp_lat > math::pi<T>())
lp_lat = math::pi<T>();
}
if (xy_y != 0)
{
T const delta_phi = (std::max)(
(std::min)(deltaX * deriv_phi_X + deltaY * deriv_phi_Y, 0.3),
-0.3);
lp_lon -= delta_phi;
static T const half_pi = math::half_pi<T>();
if (lp_lon < -half_pi)
lp_lon = -half_pi;
else if (lp_lon > half_pi)
lp_lon = half_pi;
}
}
//pj_ctx_set_errno(P->ctx, PJD_ERR_NON_CONVERGENT);
}
} // namespace detail
}}} // namespace boost::geometry::projections
#endif // BOOST_GEOMETRY_PROJECTIONS_IMPL_PJ_GENERIC_INVERSE_HPP
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