187 lines
6.9 KiB
C++
187 lines
6.9 KiB
C++
// Boost.Geometry
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// Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands.
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// This file was modified by Oracle on 2014-2020.
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// Modifications copyright (c) 2014-2020 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_DIRECT_HPP
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#define BOOST_GEOMETRY_FORMULAS_VINCENTY_DIRECT_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/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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#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 direct 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/gdav2.3.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 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 vincenty_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 || 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 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 flattening = formula::flattening<CT>(spheroid);
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CT const sin_azimuth12 = sin(azimuth12);
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CT const cos_azimuth12 = cos(azimuth12);
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// U: reduced latitude, defined by tan U = (1-f) tan phi
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CT const one_min_f = CT(1) - flattening;
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CT const tan_U1 = one_min_f * tan(lat1);
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CT const sigma1 = atan2(tan_U1, cos_azimuth12); // (1)
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// may be calculated from tan using 1 sqrt()
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CT const U1 = atan(tan_U1);
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CT const sin_U1 = sin(U1);
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CT const cos_U1 = cos(U1);
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CT const sin_alpha = cos_U1 * sin_azimuth12; // (2)
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CT const sin_alpha_sqr = math::sqr(sin_alpha);
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CT const cos_alpha_sqr = CT(1) - sin_alpha_sqr;
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CT const b_sqr = radius_b * radius_b;
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CT const u_sqr = cos_alpha_sqr * (radius_a * radius_a - b_sqr) / b_sqr;
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CT const A = CT(1) + (u_sqr/CT(16384)) * (CT(4096) + u_sqr*(CT(-768) + u_sqr*(CT(320) - u_sqr*CT(175)))); // (3)
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CT const B = (u_sqr/CT(1024))*(CT(256) + u_sqr*(CT(-128) + u_sqr*(CT(74) - u_sqr*CT(47)))); // (4)
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CT s_div_bA = distance / (radius_b * A);
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CT sigma = s_div_bA; // (7)
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CT previous_sigma;
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CT sin_sigma;
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CT cos_sigma;
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CT cos_2sigma_m;
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CT cos_2sigma_m_sqr;
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int counter = 0; // robustness
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do
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{
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previous_sigma = sigma;
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CT const two_sigma_m = CT(2) * sigma1 + sigma; // (5)
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sin_sigma = sin(sigma);
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cos_sigma = cos(sigma);
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CT const sin_sigma_sqr = math::sqr(sin_sigma);
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cos_2sigma_m = cos(two_sigma_m);
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cos_2sigma_m_sqr = math::sqr(cos_2sigma_m);
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CT const delta_sigma = B * sin_sigma * (cos_2sigma_m
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+ (B/CT(4)) * ( cos_sigma * (CT(-1) + CT(2)*cos_2sigma_m_sqr)
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- (B/CT(6) * cos_2sigma_m * (CT(-3)+CT(4)*sin_sigma_sqr) * (CT(-3)+CT(4)*cos_2sigma_m_sqr)) )); // (6)
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sigma = s_div_bA + delta_sigma; // (7)
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++counter; // robustness
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} while ( geometry::math::abs(previous_sigma - sigma) > CT(1e-12)
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//&& geometry::math::abs(sigma) < pi
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&& counter < BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS ); // robustness
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if (BOOST_GEOMETRY_CONDITION(CalcCoordinates))
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{
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result.lat2
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= atan2( sin_U1 * cos_sigma + cos_U1 * sin_sigma * cos_azimuth12,
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one_min_f * math::sqrt(sin_alpha_sqr + math::sqr(sin_U1 * sin_sigma - cos_U1 * cos_sigma * cos_azimuth12))); // (8)
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CT const lambda = atan2( sin_sigma * sin_azimuth12,
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cos_U1 * cos_sigma - sin_U1 * sin_sigma * cos_azimuth12); // (9)
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CT const C = (flattening/CT(16)) * cos_alpha_sqr * ( CT(4) + flattening * ( CT(4) - CT(3) * cos_alpha_sqr ) ); // (10)
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CT const L = lambda - (CT(1) - C) * flattening * sin_alpha
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* ( sigma + C * sin_sigma * ( cos_2sigma_m + C * cos_sigma * ( CT(-1) + CT(2) * cos_2sigma_m_sqr ) ) ); // (11)
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result.lon2 = lon1 + L;
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}
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if (BOOST_GEOMETRY_CONDITION(CalcRevAzimuth))
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{
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result.reverse_azimuth
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= atan2(sin_alpha, -sin_U1 * sin_sigma + cos_U1 * cos_sigma * cos_azimuth12); // (12)
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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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radius_b, flattening,
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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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};
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}}} // namespace boost::geometry::formula
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#endif // BOOST_GEOMETRY_FORMULAS_VINCENTY_DIRECT_HPP
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