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-// Boost.Geometry
-
-// Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands.
-
-// This file was modified by Oracle on 2014.
-// Modifications copyright (c) 2014 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_ALGORITHMS_DETAIL_VINCENTY_INVERSE_HPP
-#define BOOST_GEOMETRY_ALGORITHMS_DETAIL_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/algorithms/detail/result_inverse.hpp>
-
-
-#ifndef BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS
-#define BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS 1000
-#endif
-
-
-namespace boost { namespace geometry { namespace detail
-{
-
-/*!
-\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>
-struct vincenty_inverse
-{
- typedef result_inverse<CT> result_type;
-
-public:
- 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))
- {
- result.set(CT(0), CT(0));
- 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)
- }
- else
- {
- result.distance = CT(0);
- }
-
- if ( BOOST_GEOMETRY_CONDITION(EnableAzimuth) )
- {
- result.azimuth = atan2(cos_U2 * sin_lambda, cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda); // (20)
- }
- else
- {
- result.azimuth = CT(0);
- }
-
- return result;
- }
-
-// inline CT azimuth21() const
-// {
-// // NOTE: signs of X and Y are different than in the original paper
-// atan2(-cos_U1 * sin_lambda, sin_U1 * cos_U2 - cos_U1 * sin_U2 * cos_lambda); // (21)
-// }
-};
-
-}}} // namespace boost::geometry::detail
-
-
-#endif // BOOST_GEOMETRY_ALGORITHMS_DETAIL_VINCENTY_INVERSE_HPP
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