126 lines
3.9 KiB
C++
126 lines
3.9 KiB
C++
// Boost.Geometry
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// Copyright (c) 2016 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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#ifndef BOOST_GEOMETRY_FORMULAS_GNOMONIC_SPHEROID_HPP
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#define BOOST_GEOMETRY_FORMULAS_GNOMONIC_SPHEROID_HPP
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#include <boost/geometry/core/radius.hpp>
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#include <boost/geometry/util/condition.hpp>
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#include <boost/geometry/util/math.hpp>
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#include <boost/geometry/formulas/andoyer_inverse.hpp>
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#include <boost/geometry/formulas/flattening.hpp>
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#include <boost/geometry/formulas/thomas_inverse.hpp>
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#include <boost/geometry/formulas/vincenty_direct.hpp>
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#include <boost/geometry/formulas/vincenty_inverse.hpp>
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namespace boost { namespace geometry { namespace formula
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{
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/*!
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\brief Gnomonic projection on spheroid (ellipsoid of revolution).
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\author See
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- Charles F.F Karney, Algorithms for geodesics, 2011
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https://arxiv.org/pdf/1109.4448.pdf
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*/
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template <
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typename CT,
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template <typename, bool, bool, bool, bool ,bool> class Inverse,
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template <typename, bool, bool, bool, bool> class Direct
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>
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class gnomonic_spheroid
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{
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typedef Inverse<CT, false, true, true, true, true> inverse_type;
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typedef typename inverse_type::result_type inverse_result;
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typedef Direct<CT, false, false, true, true> direct_quantities_type;
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typedef Direct<CT, true, false, false, false> direct_coordinates_type;
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typedef typename direct_coordinates_type::result_type direct_result;
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public:
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template <typename Spheroid>
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static inline bool forward(CT const& lon0, CT const& lat0,
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CT const& lon, CT const& lat,
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CT & x, CT & y,
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Spheroid const& spheroid)
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{
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inverse_result i_res = inverse_type::apply(lon0, lat0, lon, lat, spheroid);
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CT const& m = i_res.reduced_length;
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CT const& M = i_res.geodesic_scale;
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if (math::smaller_or_equals(M, CT(0)))
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{
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return false;
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}
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CT rho = m / M;
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x = sin(i_res.azimuth) * rho;
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y = cos(i_res.azimuth) * rho;
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return true;
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}
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template <typename Spheroid>
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static inline bool inverse(CT const& lon0, CT const& lat0,
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CT const& x, CT const& y,
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CT & lon, CT & lat,
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Spheroid const& spheroid)
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{
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CT const a = get_radius<0>(spheroid);
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CT const ds_threshold = a * std::numeric_limits<CT>::epsilon(); // TODO: 0 for non-fundamental type
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CT const azimuth = atan2(x, y);
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CT const rho = math::sqrt(math::sqr(x) + math::sqr(y)); // use hypot?
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CT distance = a * atan(rho / a);
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bool found = false;
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for (int i = 0 ; i < 10 ; ++i)
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{
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direct_result d_res = direct_quantities_type::apply(lon0, lat0, distance, azimuth, spheroid);
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CT const& m = d_res.reduced_length;
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CT const& M = d_res.geodesic_scale;
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if (math::smaller_or_equals(M, CT(0)))
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{
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// found = false;
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return found;
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}
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CT const drho = m / M - rho; // rho = m / M
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CT const ds = drho * math::sqr(M); // drho/ds = 1/M^2
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distance -= ds;
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// ds_threshold may be 0
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if (math::abs(ds) <= ds_threshold)
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{
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found = true;
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break;
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}
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}
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if (found)
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{
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direct_result d_res = direct_coordinates_type::apply(lon0, lat0, distance, azimuth, spheroid);
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lon = d_res.lon2;
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lat = d_res.lat2;
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}
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return found;
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}
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};
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}}} // namespace boost::geometry::formula
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#endif // BOOST_GEOMETRY_FORMULAS_GNOMONIC_SPHEROID_HPP
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