221 lines
8.0 KiB
C++
221 lines
8.0 KiB
C++
// Boost.Geometry
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// Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands.
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// Copyright (c) 2018 Adam Wulkiewicz, Lodz, Poland.
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// This file was modified by Oracle on 2014, 2016, 2017.
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// Modifications copyright (c) 2014-2017 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_VINCENTY_INVERSE_HPP
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#define BOOST_GEOMETRY_FORMULAS_VINCENTY_INVERSE_HPP
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#include <boost/math/constants/constants.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/differential_quantities.hpp>
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#include <boost/geometry/formulas/flattening.hpp>
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#include <boost/geometry/formulas/result_inverse.hpp>
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#ifndef BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS
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#define BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS 1000
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#endif
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namespace boost { namespace geometry { namespace formula
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{
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/*!
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\brief The solution of the inverse problem of geodesics on latlong coordinates, after Vincenty, 1975
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\author See
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- http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf
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- http://www.icsm.gov.au/gda/gda-v_2.4.pdf
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\author Adapted from various implementations to get it close to the original document
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- http://www.movable-type.co.uk/scripts/LatLongVincenty.html
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- http://exogen.case.edu/projects/geopy/source/geopy.distance.html
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- http://futureboy.homeip.net/fsp/colorize.fsp?fileName=navigation.frink
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*/
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template <
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typename CT,
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bool EnableDistance,
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bool EnableAzimuth,
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bool EnableReverseAzimuth = false,
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bool EnableReducedLength = false,
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bool EnableGeodesicScale = false
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>
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struct vincenty_inverse
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{
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static const bool CalcQuantities = EnableReducedLength || EnableGeodesicScale;
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static const bool CalcAzimuths = EnableAzimuth || EnableReverseAzimuth || CalcQuantities;
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static const bool CalcFwdAzimuth = EnableAzimuth || CalcQuantities;
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static const bool CalcRevAzimuth = EnableReverseAzimuth || CalcQuantities;
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public:
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typedef result_inverse<CT> result_type;
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template <typename T1, typename T2, typename Spheroid>
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static inline result_type apply(T1 const& lon1,
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T1 const& lat1,
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T2 const& lon2,
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T2 const& lat2,
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Spheroid const& spheroid)
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{
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result_type result;
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if (math::equals(lat1, lat2) && math::equals(lon1, lon2))
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{
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return result;
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}
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CT const c0 = 0;
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CT const c1 = 1;
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CT const c2 = 2;
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CT const c3 = 3;
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CT const c4 = 4;
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CT const c16 = 16;
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CT const c_e_12 = CT(1e-12);
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CT const pi = geometry::math::pi<CT>();
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CT const two_pi = c2 * pi;
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// lambda: difference in longitude on an auxiliary sphere
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CT L = lon2 - lon1;
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CT lambda = L;
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if (L < -pi) L += two_pi;
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if (L > pi) L -= two_pi;
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CT const radius_a = CT(get_radius<0>(spheroid));
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CT const radius_b = CT(get_radius<2>(spheroid));
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CT const f = formula::flattening<CT>(spheroid);
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// U: reduced latitude, defined by tan U = (1-f) tan phi
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CT const one_min_f = c1 - f;
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CT const tan_U1 = one_min_f * tan(lat1); // above (1)
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CT const tan_U2 = one_min_f * tan(lat2); // above (1)
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// calculate sin U and cos U using trigonometric identities
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CT const temp_den_U1 = math::sqrt(c1 + math::sqr(tan_U1));
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CT const temp_den_U2 = math::sqrt(c1 + math::sqr(tan_U2));
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// cos = 1 / sqrt(1 + tan^2)
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CT const cos_U1 = c1 / temp_den_U1;
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CT const cos_U2 = c1 / temp_den_U2;
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// sin = tan / sqrt(1 + tan^2)
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// sin = tan * cos
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CT const sin_U1 = tan_U1 * cos_U1;
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CT const sin_U2 = tan_U2 * cos_U2;
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// calculate sin U and cos U directly
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//CT const U1 = atan(tan_U1);
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//CT const U2 = atan(tan_U2);
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//cos_U1 = cos(U1);
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//cos_U2 = cos(U2);
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//sin_U1 = tan_U1 * cos_U1; // sin(U1);
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//sin_U2 = tan_U2 * cos_U2; // sin(U2);
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CT previous_lambda;
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CT sin_lambda;
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CT cos_lambda;
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CT sin_sigma;
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CT sin_alpha;
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CT cos2_alpha;
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CT cos_2sigma_m;
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CT cos2_2sigma_m;
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CT sigma;
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int counter = 0; // robustness
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do
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{
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previous_lambda = lambda; // (13)
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sin_lambda = sin(lambda);
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cos_lambda = cos(lambda);
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sin_sigma = math::sqrt(math::sqr(cos_U2 * sin_lambda) + math::sqr(cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda)); // (14)
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CT cos_sigma = sin_U1 * sin_U2 + cos_U1 * cos_U2 * cos_lambda; // (15)
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sin_alpha = cos_U1 * cos_U2 * sin_lambda / sin_sigma; // (17)
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cos2_alpha = c1 - math::sqr(sin_alpha);
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cos_2sigma_m = math::equals(cos2_alpha, c0) ? c0 : cos_sigma - c2 * sin_U1 * sin_U2 / cos2_alpha; // (18)
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cos2_2sigma_m = math::sqr(cos_2sigma_m);
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CT C = f/c16 * cos2_alpha * (c4 + f * (c4 - c3 * cos2_alpha)); // (10)
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sigma = atan2(sin_sigma, cos_sigma); // (16)
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lambda = L + (c1 - C) * f * sin_alpha *
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(sigma + C * sin_sigma * (cos_2sigma_m + C * cos_sigma * (-c1 + c2 * cos2_2sigma_m))); // (11)
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++counter; // robustness
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} while ( geometry::math::abs(previous_lambda - lambda) > c_e_12
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&& geometry::math::abs(lambda) < pi
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&& counter < BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS ); // robustness
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if ( BOOST_GEOMETRY_CONDITION(EnableDistance) )
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{
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// Some types cannot divide by doubles
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CT const c6 = 6;
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CT const c47 = 47;
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CT const c74 = 74;
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CT const c128 = 128;
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CT const c256 = 256;
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CT const c175 = 175;
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CT const c320 = 320;
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CT const c768 = 768;
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CT const c1024 = 1024;
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CT const c4096 = 4096;
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CT const c16384 = 16384;
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//CT sqr_u = cos2_alpha * (math::sqr(radius_a) - math::sqr(radius_b)) / math::sqr(radius_b); // above (1)
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CT sqr_u = cos2_alpha * ( math::sqr(radius_a / radius_b) - c1 ); // above (1)
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CT A = c1 + sqr_u/c16384 * (c4096 + sqr_u * (-c768 + sqr_u * (c320 - c175 * sqr_u))); // (3)
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CT B = sqr_u/c1024 * (c256 + sqr_u * ( -c128 + sqr_u * (c74 - c47 * sqr_u))); // (4)
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CT const cos_sigma = cos(sigma);
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CT const sin2_sigma = math::sqr(sin_sigma);
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CT delta_sigma = B * sin_sigma * (cos_2sigma_m + (B/c4) * (cos_sigma* (-c1 + c2 * cos2_2sigma_m)
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- (B/c6) * cos_2sigma_m * (-c3 + c4 * sin2_sigma) * (-c3 + c4 * cos2_2sigma_m))); // (6)
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result.distance = radius_b * A * (sigma - delta_sigma); // (19)
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}
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if ( BOOST_GEOMETRY_CONDITION(CalcAzimuths) )
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{
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if (BOOST_GEOMETRY_CONDITION(CalcFwdAzimuth))
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{
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result.azimuth = atan2(cos_U2 * sin_lambda, cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda); // (20)
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}
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if (BOOST_GEOMETRY_CONDITION(CalcRevAzimuth))
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{
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result.reverse_azimuth = atan2(cos_U1 * sin_lambda, -sin_U1 * cos_U2 + cos_U1 * sin_U2 * cos_lambda); // (21)
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}
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}
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if (BOOST_GEOMETRY_CONDITION(CalcQuantities))
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{
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typedef differential_quantities<CT, EnableReducedLength, EnableGeodesicScale, 2> quantities;
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quantities::apply(lon1, lat1, lon2, lat2,
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result.azimuth, result.reverse_azimuth,
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radius_b, f,
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result.reduced_length, result.geodesic_scale);
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}
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return result;
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}
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};
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}}} // namespace boost::geometry::formula
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#endif // BOOST_GEOMETRY_FORMULAS_VINCENTY_INVERSE_HPP
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