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Diffstat (limited to 'boost/geometry/formulas/vincenty_inverse.hpp')
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1 files changed, 220 insertions, 0 deletions
diff --git a/boost/geometry/formulas/vincenty_inverse.hpp b/boost/geometry/formulas/vincenty_inverse.hpp new file mode 100644 index 0000000000..bbda00036b --- /dev/null +++ b/boost/geometry/formulas/vincenty_inverse.hpp @@ -0,0 +1,220 @@ +// Boost.Geometry + +// Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands. + +// This file was modified by Oracle on 2014, 2016. +// Modifications copyright (c) 2014-2016 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_INVERSE_HPP +#define BOOST_GEOMETRY_FORMULAS_VINCENTY_INVERSE_HPP + + +#include <boost/math/constants/constants.hpp> + +#include <boost/geometry/core/radius.hpp> +#include <boost/geometry/core/srs.hpp> + +#include <boost/geometry/util/condition.hpp> +#include <boost/geometry/util/math.hpp> + +#include <boost/geometry/algorithms/detail/flattening.hpp> + +#include <boost/geometry/formulas/differential_quantities.hpp> +#include <boost/geometry/formulas/result_inverse.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 inverse 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 EnableDistance, + bool EnableAzimuth, + bool EnableReverseAzimuth = false, + bool EnableReducedLength = false, + bool EnableGeodesicScale = false +> +struct vincenty_inverse +{ + static const bool CalcQuantities = EnableReducedLength || EnableGeodesicScale; + static const bool CalcAzimuths = EnableAzimuth || EnableReverseAzimuth || CalcQuantities; + static const bool CalcFwdAzimuth = EnableAzimuth || CalcQuantities; + static const bool CalcRevAzimuth = EnableReverseAzimuth || CalcQuantities; + +public: + typedef result_inverse<CT> result_type; + + template <typename T1, typename T2, typename Spheroid> + static inline result_type apply(T1 const& lon1, + T1 const& lat1, + T2 const& lon2, + T2 const& lat2, + Spheroid const& spheroid) + { + result_type result; + + if (math::equals(lat1, lat2) && math::equals(lon1, lon2)) + { + return result; + } + + CT const c1 = 1; + CT const c2 = 2; + CT const c3 = 3; + CT const c4 = 4; + CT const c16 = 16; + CT const c_e_12 = CT(1e-12); + + CT const pi = geometry::math::pi<CT>(); + CT const two_pi = c2 * pi; + + // lambda: difference in longitude on an auxiliary sphere + CT L = lon2 - lon1; + CT lambda = L; + + if (L < -pi) L += two_pi; + if (L > pi) L -= two_pi; + + CT const radius_a = CT(get_radius<0>(spheroid)); + CT const radius_b = CT(get_radius<2>(spheroid)); + CT const flattening = geometry::detail::flattening<CT>(spheroid); + + // U: reduced latitude, defined by tan U = (1-f) tan phi + CT const one_min_f = c1 - flattening; + CT const tan_U1 = one_min_f * tan(lat1); // above (1) + CT const tan_U2 = one_min_f * tan(lat2); // above (1) + + // calculate sin U and cos U using trigonometric identities + CT const temp_den_U1 = math::sqrt(c1 + math::sqr(tan_U1)); + CT const temp_den_U2 = math::sqrt(c1 + math::sqr(tan_U2)); + // cos = 1 / sqrt(1 + tan^2) + CT const cos_U1 = c1 / temp_den_U1; + CT const cos_U2 = c1 / temp_den_U2; + // sin = tan / sqrt(1 + tan^2) + CT const sin_U1 = tan_U1 / temp_den_U1; + CT const sin_U2 = tan_U2 / temp_den_U2; + + // calculate sin U and cos U directly + //CT const U1 = atan(tan_U1); + //CT const U2 = atan(tan_U2); + //cos_U1 = cos(U1); + //cos_U2 = cos(U2); + //sin_U1 = tan_U1 * cos_U1; // sin(U1); + //sin_U2 = tan_U2 * cos_U2; // sin(U2); + + CT previous_lambda; + CT sin_lambda; + CT cos_lambda; + CT sin_sigma; + CT sin_alpha; + CT cos2_alpha; + CT cos2_sigma_m; + CT sigma; + + int counter = 0; // robustness + + do + { + previous_lambda = lambda; // (13) + sin_lambda = sin(lambda); + cos_lambda = cos(lambda); + sin_sigma = math::sqrt(math::sqr(cos_U2 * sin_lambda) + math::sqr(cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda)); // (14) + CT cos_sigma = sin_U1 * sin_U2 + cos_U1 * cos_U2 * cos_lambda; // (15) + sin_alpha = cos_U1 * cos_U2 * sin_lambda / sin_sigma; // (17) + cos2_alpha = c1 - math::sqr(sin_alpha); + cos2_sigma_m = math::equals(cos2_alpha, 0) ? 0 : cos_sigma - c2 * sin_U1 * sin_U2 / cos2_alpha; // (18) + + CT C = flattening/c16 * cos2_alpha * (c4 + flattening * (c4 - c3 * cos2_alpha)); // (10) + sigma = atan2(sin_sigma, cos_sigma); // (16) + lambda = L + (c1 - C) * flattening * sin_alpha * + (sigma + C * sin_sigma * ( cos2_sigma_m + C * cos_sigma * (-c1 + c2 * math::sqr(cos2_sigma_m)))); // (11) + + ++counter; // robustness + + } while ( geometry::math::abs(previous_lambda - lambda) > c_e_12 + && geometry::math::abs(lambda) < pi + && counter < BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS ); // robustness + + if ( BOOST_GEOMETRY_CONDITION(EnableDistance) ) + { + // Oops getting hard here + // (again, problem is that ttmath cannot divide by doubles, which is OK) + CT const c1 = 1; + CT const c2 = 2; + CT const c3 = 3; + CT const c4 = 4; + CT const c6 = 6; + CT const c47 = 47; + CT const c74 = 74; + CT const c128 = 128; + CT const c256 = 256; + CT const c175 = 175; + CT const c320 = 320; + CT const c768 = 768; + CT const c1024 = 1024; + CT const c4096 = 4096; + CT const c16384 = 16384; + + //CT sqr_u = cos2_alpha * (math::sqr(radius_a) - math::sqr(radius_b)) / math::sqr(radius_b); // above (1) + CT sqr_u = cos2_alpha * ( math::sqr(radius_a / radius_b) - c1 ); // above (1) + + CT A = c1 + sqr_u/c16384 * (c4096 + sqr_u * (-c768 + sqr_u * (c320 - c175 * sqr_u))); // (3) + CT B = sqr_u/c1024 * (c256 + sqr_u * ( -c128 + sqr_u * (c74 - c47 * sqr_u))); // (4) + CT delta_sigma = B * sin_sigma * ( cos2_sigma_m + (B/c4) * (cos(sigma)* (-c1 + c2 * cos2_sigma_m) + - (B/c6) * cos2_sigma_m * (-c3 + c4 * math::sqr(sin_sigma)) * (-c3 + c4 * cos2_sigma_m))); // (6) + + result.distance = radius_b * A * (sigma - delta_sigma); // (19) + } + + if ( BOOST_GEOMETRY_CONDITION(CalcAzimuths) ) + { + if (BOOST_GEOMETRY_CONDITION(CalcFwdAzimuth)) + { + result.azimuth = atan2(cos_U2 * sin_lambda, cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda); // (20) + } + + if (BOOST_GEOMETRY_CONDITION(CalcRevAzimuth)) + { + result.reverse_azimuth = atan2(cos_U1 * sin_lambda, -sin_U1 * cos_U2 + cos_U1 * sin_U2 * cos_lambda); // (21) + } + } + + if (BOOST_GEOMETRY_CONDITION(CalcQuantities)) + { + typedef differential_quantities<CT, EnableReducedLength, EnableGeodesicScale, 2> quantities; + quantities::apply(lon1, lat1, lon2, lat2, + result.azimuth, result.reverse_azimuth, + radius_b, flattening, + result.reduced_length, result.geodesic_scale); + } + + return result; + } +}; + +}}} // namespace boost::geometry::formula + + +#endif // BOOST_GEOMETRY_FORMULAS_VINCENTY_INVERSE_HPP |