307 lines
13 KiB
C++
307 lines
13 KiB
C++
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// Boost.Geometry - gis-projections (based on PROJ4)
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// Copyright (c) 2008-2015 Barend Gehrels, Amsterdam, the Netherlands.
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// This file was modified by Oracle on 2017, 2018, 2019.
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// Modifications copyright (c) 2017-2019, Oracle and/or its affiliates.
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// Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle.
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// Use, modification and distribution is subject to the Boost Software License,
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// Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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// This file is converted from PROJ4, http://trac.osgeo.org/proj
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// PROJ4 is originally written by Gerald Evenden (then of the USGS)
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// PROJ4 is maintained by Frank Warmerdam
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// PROJ4 is converted to Boost.Geometry by Barend Gehrels
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// Last updated version of proj: 5.0.0
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// Original copyright notice:
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// Purpose: Implementation of the aitoff (Aitoff) and wintri (Winkel Tripel)
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// projections.
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// Author: Gerald Evenden (1995)
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// Drazen Tutic, Lovro Gradiser (2015) - add inverse
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// Thomas Knudsen (2016) - revise/add regression tests
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// Copyright (c) 1995, Gerald Evenden
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// Permission is hereby granted, free of charge, to any person obtaining a
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// copy of this software and associated documentation files (the "Software"),
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// to deal in the Software without restriction, including without limitation
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// the rights to use, copy, modify, merge, publish, distribute, sublicense,
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// and/or sell copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following conditions:
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// The above copyright notice and this permission notice shall be included
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// in all copies or substantial portions of the Software.
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
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// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
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// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
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// DEALINGS IN THE SOFTWARE.
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#ifndef BOOST_GEOMETRY_PROJECTIONS_AITOFF_HPP
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#define BOOST_GEOMETRY_PROJECTIONS_AITOFF_HPP
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#include <boost/core/ignore_unused.hpp>
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#include <boost/geometry/srs/projections/impl/base_static.hpp>
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#include <boost/geometry/srs/projections/impl/base_dynamic.hpp>
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#include <boost/geometry/srs/projections/impl/factory_entry.hpp>
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#include <boost/geometry/srs/projections/impl/pj_param.hpp>
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#include <boost/geometry/srs/projections/impl/projects.hpp>
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#include <boost/geometry/util/math.hpp>
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namespace boost { namespace geometry
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{
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namespace projections
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{
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#ifndef DOXYGEN_NO_DETAIL
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namespace detail { namespace aitoff
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{
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enum mode_type {
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mode_aitoff = 0,
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mode_winkel_tripel = 1
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};
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template <typename T>
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struct par_aitoff
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{
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T cosphi1;
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mode_type mode;
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};
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template <typename T, typename Parameters>
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struct base_aitoff_spheroid
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{
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par_aitoff<T> m_proj_parm;
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// FORWARD(s_forward) spheroid
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// Project coordinates from geographic (lon, lat) to cartesian (x, y)
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inline void fwd(Parameters const& , T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const
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{
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T c, d;
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if((d = acos(cos(lp_lat) * cos(c = 0.5 * lp_lon)))) {/* basic Aitoff */
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xy_x = 2. * d * cos(lp_lat) * sin(c) * (xy_y = 1. / sin(d));
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xy_y *= d * sin(lp_lat);
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} else
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xy_x = xy_y = 0.;
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if (this->m_proj_parm.mode == mode_winkel_tripel) { /* Winkel Tripel */
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xy_x = (xy_x + lp_lon * this->m_proj_parm.cosphi1) * 0.5;
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xy_y = (xy_y + lp_lat) * 0.5;
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}
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}
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/***********************************************************************************
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*
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* Inverse functions added by Drazen Tutic and Lovro Gradiser based on paper:
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*
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* I.Özbug Biklirici and Cengizhan Ipbüker. A General Algorithm for the Inverse
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* Transformation of Map Projections Using Jacobian Matrices. In Proceedings of the
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* Third International Symposium Mathematical & Computational Applications,
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* pages 175{182, Turkey, September 2002.
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*
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* Expected accuracy is defined by epsilon = 1e-12. Should be appropriate for
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* most applications of Aitoff and Winkel Tripel projections.
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*
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* Longitudes of 180W and 180E can be mixed in solution obtained.
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*
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* Inverse for Aitoff projection in poles is undefined, longitude value of 0 is assumed.
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*
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* Contact : dtutic@geof.hr
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* Date: 2015-02-16
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*
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************************************************************************************/
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// INVERSE(s_inverse) sphere
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// Project coordinates from cartesian (x, y) to geographic (lon, lat)
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inline void inv(Parameters const& , T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const
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{
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static const T pi = detail::pi<T>();
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static const T two_pi = detail::two_pi<T>();
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static const T epsilon = 1e-12;
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int iter, max_iter = 10, round = 0, max_round = 20;
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T D, C, f1, f2, f1p, f1l, f2p, f2l, dp, dl, sl, sp, cp, cl, x, y;
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if ((fabs(xy_x) < epsilon) && (fabs(xy_y) < epsilon )) {
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lp_lat = 0.; lp_lon = 0.;
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return;
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}
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/* intial values for Newton-Raphson method */
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lp_lat = xy_y; lp_lon = xy_x;
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do {
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iter = 0;
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do {
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sl = sin(lp_lon * 0.5); cl = cos(lp_lon * 0.5);
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sp = sin(lp_lat); cp = cos(lp_lat);
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D = cp * cl;
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C = 1. - D * D;
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D = acos(D) / math::pow(C, T(1.5));
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f1 = 2. * D * C * cp * sl;
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f2 = D * C * sp;
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f1p = 2.* (sl * cl * sp * cp / C - D * sp * sl);
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f1l = cp * cp * sl * sl / C + D * cp * cl * sp * sp;
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f2p = sp * sp * cl / C + D * sl * sl * cp;
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f2l = 0.5 * (sp * cp * sl / C - D * sp * cp * cp * sl * cl);
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if (this->m_proj_parm.mode == mode_winkel_tripel) { /* Winkel Tripel */
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f1 = 0.5 * (f1 + lp_lon * this->m_proj_parm.cosphi1);
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f2 = 0.5 * (f2 + lp_lat);
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f1p *= 0.5;
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f1l = 0.5 * (f1l + this->m_proj_parm.cosphi1);
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f2p = 0.5 * (f2p + 1.);
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f2l *= 0.5;
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}
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f1 -= xy_x; f2 -= xy_y;
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dl = (f2 * f1p - f1 * f2p) / (dp = f1p * f2l - f2p * f1l);
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dp = (f1 * f2l - f2 * f1l) / dp;
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dl = fmod(dl, pi); /* set to interval [-M_PI, M_PI] */
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lp_lat -= dp; lp_lon -= dl;
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} while ((fabs(dp) > epsilon || fabs(dl) > epsilon) && (iter++ < max_iter));
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if (lp_lat > two_pi) lp_lat -= 2.*(lp_lat-two_pi); /* correct if symmetrical solution for Aitoff */
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if (lp_lat < -two_pi) lp_lat -= 2.*(lp_lat+two_pi); /* correct if symmetrical solution for Aitoff */
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if ((fabs(fabs(lp_lat) - two_pi) < epsilon) && (!this->m_proj_parm.mode)) lp_lon = 0.; /* if pole in Aitoff, return longitude of 0 */
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/* calculate x,y coordinates with solution obtained */
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if((D = acos(cos(lp_lat) * cos(C = 0.5 * lp_lon))) != 0.0) {/* Aitoff */
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x = 2. * D * cos(lp_lat) * sin(C) * (y = 1. / sin(D));
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y *= D * sin(lp_lat);
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} else
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x = y = 0.;
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if (this->m_proj_parm.mode == mode_winkel_tripel) { /* Winkel Tripel */
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x = (x + lp_lon * this->m_proj_parm.cosphi1) * 0.5;
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y = (y + lp_lat) * 0.5;
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}
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/* if too far from given values of x,y, repeat with better approximation of phi,lam */
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} while (((fabs(xy_x-x) > epsilon) || (fabs(xy_y-y) > epsilon)) && (round++ < max_round));
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if (iter == max_iter && round == max_round)
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{
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BOOST_THROW_EXCEPTION( projection_exception(error_non_convergent) );
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//fprintf(stderr, "Warning: Accuracy of 1e-12 not reached. Last increments: dlat=%e and dlon=%e\n", dp, dl);
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}
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}
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static inline std::string get_name()
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{
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return "aitoff_spheroid";
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}
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};
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template <typename Parameters>
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inline void setup(Parameters& par)
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{
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par.es = 0.;
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}
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// Aitoff
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template <typename Parameters, typename T>
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inline void setup_aitoff(Parameters& par, par_aitoff<T>& proj_parm)
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{
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proj_parm.mode = mode_aitoff;
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setup(par);
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}
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// Winkel Tripel
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template <typename Params, typename Parameters, typename T>
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inline void setup_wintri(Params& params, Parameters& par, par_aitoff<T>& proj_parm)
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{
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static const T two_div_pi = detail::two_div_pi<T>();
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T phi1;
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proj_parm.mode = mode_winkel_tripel;
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if (pj_param_r<srs::spar::lat_1>(params, "lat_1", srs::dpar::lat_1, phi1)) {
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if ((proj_parm.cosphi1 = cos(phi1)) == 0.)
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BOOST_THROW_EXCEPTION( projection_exception(error_lat_larger_than_90) );
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} else /* 50d28' or phi1=acos(2/pi) */
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proj_parm.cosphi1 = two_div_pi;
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setup(par);
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}
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}} // namespace detail::aitoff
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#endif // doxygen
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/*!
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\brief Aitoff projection
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\ingroup projections
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\tparam Geographic latlong point type
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\tparam Cartesian xy point type
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\tparam Parameters parameter type
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\par Projection characteristics
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- Miscellaneous
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- Spheroid
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\par Example
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\image html ex_aitoff.gif
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*/
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template <typename T, typename Parameters>
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struct aitoff_spheroid : public detail::aitoff::base_aitoff_spheroid<T, Parameters>
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{
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template <typename Params>
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inline aitoff_spheroid(Params const& , Parameters & par)
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{
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detail::aitoff::setup_aitoff(par, this->m_proj_parm);
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}
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};
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/*!
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\brief Winkel Tripel projection
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\ingroup projections
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\tparam Geographic latlong point type
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\tparam Cartesian xy point type
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\tparam Parameters parameter type
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\par Projection characteristics
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- Miscellaneous
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- Spheroid
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\par Projection parameters
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- lat_1: Latitude of first standard parallel (degrees)
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\par Example
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\image html ex_wintri.gif
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*/
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template <typename T, typename Parameters>
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struct wintri_spheroid : public detail::aitoff::base_aitoff_spheroid<T, Parameters>
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{
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template <typename Params>
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inline wintri_spheroid(Params const& params, Parameters & par)
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{
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detail::aitoff::setup_wintri(params, par, this->m_proj_parm);
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}
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};
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#ifndef DOXYGEN_NO_DETAIL
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namespace detail
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{
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// Static projection
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_aitoff, aitoff_spheroid)
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_STATIC_PROJECTION_FI(srs::spar::proj_wintri, wintri_spheroid)
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// Factory entry(s)
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(aitoff_entry, aitoff_spheroid)
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_ENTRY_FI(wintri_entry, wintri_spheroid)
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_BEGIN(aitoff_init)
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{
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(aitoff, aitoff_entry)
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BOOST_GEOMETRY_PROJECTIONS_DETAIL_FACTORY_INIT_ENTRY(wintri, wintri_entry)
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}
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} // namespace detail
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#endif // doxygen
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} // namespace projections
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}} // namespace boost::geometry
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#endif // BOOST_GEOMETRY_PROJECTIONS_AITOFF_HPP
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