275 lines
9.0 KiB
C++
275 lines
9.0 KiB
C++
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// Boost.Geometry
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// Copyright (c) 2016-2020 Oracle and/or its affiliates.
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// Contributed and/or modified by Vissarion Fysikopoulos, on behalf of Oracle
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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_THOMAS_DIRECT_HPP
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#define BOOST_GEOMETRY_FORMULAS_THOMAS_DIRECT_HPP
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#include <boost/math/constants/constants.hpp>
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#include <boost/geometry/core/assert.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/util/normalize_spheroidal_coordinates.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_direct.hpp>
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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 direct problem of geodesics on latlong coordinates,
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Forsyth-Andoyer-Lambert type approximation with first/second order terms.
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\author See
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- Technical Report: PAUL D. THOMAS, MATHEMATICAL MODELS FOR NAVIGATION SYSTEMS, 1965
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http://www.dtic.mil/docs/citations/AD0627893
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- Technical Report: PAUL D. THOMAS, SPHEROIDAL GEODESICS, REFERENCE SYSTEMS, AND LOCAL GEOMETRY, 1970
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http://www.dtic.mil/docs/citations/AD0703541
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*/
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template <
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typename CT,
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bool SecondOrder = true,
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bool EnableCoordinates = true,
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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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class thomas_direct
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{
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static const bool CalcQuantities = EnableReducedLength || EnableGeodesicScale;
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static const bool CalcCoordinates = EnableCoordinates || CalcQuantities;
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static const bool CalcRevAzimuth = EnableReverseAzimuth || CalcCoordinates || CalcQuantities;
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public:
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typedef result_direct<CT> result_type;
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template <typename T, typename Dist, typename Azi, typename Spheroid>
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static inline result_type apply(T const& lo1,
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T const& la1,
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Dist const& distance,
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Azi const& azimuth12,
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Spheroid const& spheroid)
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{
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result_type result;
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CT const lon1 = lo1;
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CT const lat1 = la1;
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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 c4 = 4;
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CT const a = CT(get_radius<0>(spheroid));
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CT const b = CT(get_radius<2>(spheroid));
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CT const f = formula::flattening<CT>(spheroid);
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CT const one_minus_f = c1 - f;
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CT const pi = math::pi<CT>();
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CT const pi_half = pi / c2;
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BOOST_GEOMETRY_ASSERT(-pi <= azimuth12 && azimuth12 <= pi);
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// keep azimuth small - experiments show low accuracy
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// if the azimuth is closer to (+-)180 deg.
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CT azi12_alt = azimuth12;
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CT lat1_alt = lat1;
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bool alter_result = vflip_if_south(lat1, azimuth12, lat1_alt, azi12_alt);
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CT const theta1 = math::equals(lat1_alt, pi_half) ? lat1_alt :
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math::equals(lat1_alt, -pi_half) ? lat1_alt :
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atan(one_minus_f * tan(lat1_alt));
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CT const sin_theta1 = sin(theta1);
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CT const cos_theta1 = cos(theta1);
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CT const sin_a12 = sin(azi12_alt);
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CT const cos_a12 = cos(azi12_alt);
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CT const M = cos_theta1 * sin_a12; // cos_theta0
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CT const theta0 = acos(M);
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CT const sin_theta0 = sin(theta0);
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CT const N = cos_theta1 * cos_a12;
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CT const C1 = f * M; // lower-case c1 in the technical report
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CT const C2 = f * (c1 - math::sqr(M)) / c4; // lower-case c2 in the technical report
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CT D = 0;
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CT P = 0;
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if ( BOOST_GEOMETRY_CONDITION(SecondOrder) )
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{
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D = (c1 - C2) * (c1 - C2 - C1 * M);
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P = C2 * (c1 + C1 * M / c2) / D;
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}
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else
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{
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D = c1 - c2 * C2 - C1 * M;
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P = C2 / D;
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}
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// special case for equator:
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// sin_theta0 = 0 <=> lat1 = 0 ^ |azimuth12| = pi/2
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// NOTE: in this case it doesn't matter what's the value of cos_sigma1 because
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// theta1=0, theta0=0, M=1|-1, C2=0 so X=0 and Y=0 so d_sigma=d
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// cos_a12=0 so N=0, therefore
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// lat2=0, azi21=pi/2|-pi/2
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// d_eta = atan2(sin_d_sigma, cos_d_sigma)
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// H = C1 * d_sigma
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CT const cos_sigma1 = math::equals(sin_theta0, c0)
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? c1
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: normalized1_1(sin_theta1 / sin_theta0);
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CT const sigma1 = acos(cos_sigma1);
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CT const d = distance / (a * D);
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CT const u = 2 * (sigma1 - d);
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CT const cos_d = cos(d);
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CT const sin_d = sin(d);
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CT const cos_u = cos(u);
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CT const sin_u = sin(u);
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CT const W = c1 - c2 * P * cos_u;
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CT const V = cos_u * cos_d - sin_u * sin_d;
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CT const Y = c2 * P * V * W * sin_d;
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CT X = 0;
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CT d_sigma = d - Y;
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if ( BOOST_GEOMETRY_CONDITION(SecondOrder) )
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{
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X = math::sqr(C2) * sin_d * cos_d * (2 * math::sqr(V) - c1);
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d_sigma += X;
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}
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CT const sin_d_sigma = sin(d_sigma);
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CT const cos_d_sigma = cos(d_sigma);
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if (BOOST_GEOMETRY_CONDITION(CalcRevAzimuth))
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{
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result.reverse_azimuth = atan2(M, N * cos_d_sigma - sin_theta1 * sin_d_sigma);
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if (alter_result)
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{
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vflip_rev_azi(result.reverse_azimuth, azimuth12);
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}
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}
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if (BOOST_GEOMETRY_CONDITION(CalcCoordinates))
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{
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CT const S_sigma = c2 * sigma1 - d_sigma;
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CT cos_S_sigma = 0;
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CT H = C1 * d_sigma;
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if ( BOOST_GEOMETRY_CONDITION(SecondOrder) )
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{
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cos_S_sigma = cos(S_sigma);
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H = H * (c1 - C2) - C1 * C2 * sin_d_sigma * cos_S_sigma;
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}
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CT const d_eta = atan2(sin_d_sigma * sin_a12, cos_theta1 * cos_d_sigma - sin_theta1 * sin_d_sigma * cos_a12);
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CT const d_lambda = d_eta - H;
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result.lon2 = lon1 + d_lambda;
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if (! math::equals(M, c0))
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{
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CT const sin_a21 = sin(result.reverse_azimuth);
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CT const tan_theta2 = (sin_theta1 * cos_d_sigma + N * sin_d_sigma) * sin_a21 / M;
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result.lat2 = atan(tan_theta2 / one_minus_f);
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}
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else
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{
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CT const sigma2 = S_sigma - sigma1;
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//theta2 = asin(cos(sigma2)) <=> sin_theta0 = 1
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// NOTE: cos(sigma2) defines the sign of tan_theta2
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CT const tan_theta2 = cos(sigma2) / math::abs(sin(sigma2));
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result.lat2 = atan(tan_theta2 / one_minus_f);
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}
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if (alter_result)
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{
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result.lat2 = -result.lat2;
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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, result.lon2, result.lat2,
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azimuth12, result.reverse_azimuth,
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b, f,
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result.reduced_length, result.geodesic_scale);
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}
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if (BOOST_GEOMETRY_CONDITION(CalcCoordinates))
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{
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// For longitudes close to the antimeridian the result can be out
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// of range. Therefore normalize.
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// It has to be done at the end because otherwise differential
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// quantities are calculated incorrectly.
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math::detail::normalize_angle_cond<radian>(result.lon2);
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}
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return result;
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}
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private:
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static inline bool vflip_if_south(CT const& lat1, CT const& azi12, CT & lat1_alt, CT & azi12_alt)
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{
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CT const c2 = 2;
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CT const pi = math::pi<CT>();
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CT const pi_half = pi / c2;
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if (azi12 > pi_half)
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{
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azi12_alt = pi - azi12;
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lat1_alt = -lat1;
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return true;
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}
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else if (azi12 < -pi_half)
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{
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azi12_alt = -pi - azi12;
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lat1_alt = -lat1;
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return true;
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}
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return false;
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}
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static inline void vflip_rev_azi(CT & rev_azi, CT const& azimuth12)
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{
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CT const c0 = 0;
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CT const pi = math::pi<CT>();
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if (rev_azi == c0)
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{
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rev_azi = azimuth12 >= 0 ? pi : -pi;
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}
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else if (rev_azi > c0)
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{
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rev_azi = pi - rev_azi;
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}
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else
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{
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rev_azi = -pi - rev_azi;
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}
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}
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static inline CT normalized1_1(CT const& value)
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{
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CT const c1 = 1;
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return value > c1 ? c1 :
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value < -c1 ? -c1 :
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value;
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}
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};
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}}} // namespace boost::geometry::formula
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#endif // BOOST_GEOMETRY_FORMULAS_THOMAS_DIRECT_HPP
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