boost/geometry/formulas/vincenty_direct.hpp
// Boost.Geometry // Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands. // Copyright (c) 2023 Adam Wulkiewicz, Lodz, Poland. // This file was modified by Oracle on 2014-2020. // Modifications copyright (c) 2014-2020 Oracle and/or its affiliates. // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle // Use, modification and distribution is subject to the Boost Software License, // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at // http://www.boost.org/LICENSE_1_0.txt) #ifndef BOOST_GEOMETRY_FORMULAS_VINCENTY_DIRECT_HPP #define BOOST_GEOMETRY_FORMULAS_VINCENTY_DIRECT_HPP #include <boost/math/constants/constants.hpp> #include <boost/geometry/core/radius.hpp> #include <boost/geometry/util/constexpr.hpp> #include <boost/geometry/util/math.hpp> #include <boost/geometry/util/normalize_spheroidal_coordinates.hpp> #include <boost/geometry/formulas/differential_quantities.hpp> #include <boost/geometry/formulas/flattening.hpp> #include <boost/geometry/formulas/result_direct.hpp> #ifndef BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS #define BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS 1000 #endif namespace boost { namespace geometry { namespace formula { /*! \brief The solution of the direct problem of geodesics on latlong coordinates, after Vincenty, 1975 \author See - http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf - http://www.icsm.gov.au/gda/gdav2.3.pdf \author Adapted from various implementations to get it close to the original document - http://www.movable-type.co.uk/scripts/LatLongVincenty.html - http://exogen.case.edu/projects/geopy/source/geopy.distance.html - http://futureboy.homeip.net/fsp/colorize.fsp?fileName=navigation.frink */ template < typename CT, bool EnableCoordinates = true, bool EnableReverseAzimuth = false, bool EnableReducedLength = false, bool EnableGeodesicScale = false > class vincenty_direct { static const bool CalcQuantities = EnableReducedLength || EnableGeodesicScale; static const bool CalcCoordinates = EnableCoordinates || CalcQuantities; static const bool CalcRevAzimuth = EnableReverseAzimuth || CalcQuantities; public: typedef result_direct<CT> result_type; template <typename T, typename Dist, typename Azi, typename Spheroid> static inline result_type apply(T const& lo1, T const& la1, Dist const& distance, Azi const& azimuth12, Spheroid const& spheroid) { result_type result; CT const lon1 = lo1; CT const lat1 = la1; CT const radius_a = CT(get_radius<0>(spheroid)); CT const radius_b = CT(get_radius<2>(spheroid)); CT const flattening = formula::flattening<CT>(spheroid); CT const sin_azimuth12 = sin(azimuth12); CT const cos_azimuth12 = cos(azimuth12); // U: reduced latitude, defined by tan U = (1-f) tan phi CT const one_min_f = CT(1) - flattening; CT const tan_U1 = one_min_f * tan(lat1); CT const sigma1 = atan2(tan_U1, cos_azimuth12); // (1) // may be calculated from tan using 1 sqrt() CT const U1 = atan(tan_U1); CT const sin_U1 = sin(U1); CT const cos_U1 = cos(U1); CT const sin_alpha = cos_U1 * sin_azimuth12; // (2) CT const sin_alpha_sqr = math::sqr(sin_alpha); CT const cos_alpha_sqr = CT(1) - sin_alpha_sqr; CT const b_sqr = radius_b * radius_b; CT const u_sqr = cos_alpha_sqr * (radius_a * radius_a - b_sqr) / b_sqr; CT const A = CT(1) + (u_sqr/CT(16384)) * (CT(4096) + u_sqr*(CT(-768) + u_sqr*(CT(320) - u_sqr*CT(175)))); // (3) CT const B = (u_sqr/CT(1024))*(CT(256) + u_sqr*(CT(-128) + u_sqr*(CT(74) - u_sqr*CT(47)))); // (4) CT s_div_bA = distance / (radius_b * A); CT sigma = s_div_bA; // (7) CT previous_sigma; CT sin_sigma; CT cos_sigma; CT cos_2sigma_m; CT cos_2sigma_m_sqr; int counter = 0; // robustness do { previous_sigma = sigma; CT const two_sigma_m = CT(2) * sigma1 + sigma; // (5) sin_sigma = sin(sigma); cos_sigma = cos(sigma); CT const sin_sigma_sqr = math::sqr(sin_sigma); cos_2sigma_m = cos(two_sigma_m); cos_2sigma_m_sqr = math::sqr(cos_2sigma_m); CT const delta_sigma = B * sin_sigma * (cos_2sigma_m + (B/CT(4)) * ( cos_sigma * (CT(-1) + CT(2)*cos_2sigma_m_sqr) - (B/CT(6) * cos_2sigma_m * (CT(-3)+CT(4)*sin_sigma_sqr) * (CT(-3)+CT(4)*cos_2sigma_m_sqr)) )); // (6) sigma = s_div_bA + delta_sigma; // (7) ++counter; // robustness } while ( geometry::math::abs(previous_sigma - sigma) > CT(1e-12) //&& geometry::math::abs(sigma) < pi && counter < BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS ); // robustness if BOOST_GEOMETRY_CONSTEXPR (CalcCoordinates) { result.lat2 = atan2( sin_U1 * cos_sigma + cos_U1 * sin_sigma * cos_azimuth12, one_min_f * math::sqrt(sin_alpha_sqr + math::sqr(sin_U1 * sin_sigma - cos_U1 * cos_sigma * cos_azimuth12))); // (8) CT const lambda = atan2( sin_sigma * sin_azimuth12, cos_U1 * cos_sigma - sin_U1 * sin_sigma * cos_azimuth12); // (9) CT const C = (flattening/CT(16)) * cos_alpha_sqr * ( CT(4) + flattening * ( CT(4) - CT(3) * cos_alpha_sqr ) ); // (10) CT const L = lambda - (CT(1) - C) * flattening * sin_alpha * ( sigma + C * sin_sigma * ( cos_2sigma_m + C * cos_sigma * ( CT(-1) + CT(2) * cos_2sigma_m_sqr ) ) ); // (11) result.lon2 = lon1 + L; } if BOOST_GEOMETRY_CONSTEXPR (CalcRevAzimuth) { result.reverse_azimuth = atan2(sin_alpha, -sin_U1 * sin_sigma + cos_U1 * cos_sigma * cos_azimuth12); // (12) } if BOOST_GEOMETRY_CONSTEXPR (CalcQuantities) { typedef differential_quantities<CT, EnableReducedLength, EnableGeodesicScale, 2> quantities; quantities::apply(lon1, lat1, result.lon2, result.lat2, azimuth12, result.reverse_azimuth, radius_b, flattening, result.reduced_length, result.geodesic_scale); } if BOOST_GEOMETRY_CONSTEXPR (CalcCoordinates) { // For longitudes close to the antimeridian the result can be out // of range. Therefore normalize. // It has to be done at the end because otherwise differential // quantities are calculated incorrectly. math::detail::normalize_angle_cond<radian>(result.lon2); } return result; } }; }}} // namespace boost::geometry::formula #endif // BOOST_GEOMETRY_FORMULAS_VINCENTY_DIRECT_HPP