Chris@102: // Boost.Geometry
Chris@102: 
Chris@102: // Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands.
Chris@102: 
Chris@102: // This file was modified by Oracle on 2014.
Chris@102: // Modifications copyright (c) 2014 Oracle and/or its affiliates.
Chris@102: 
Chris@102: // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
Chris@102: 
Chris@102: // Use, modification and distribution is subject to the Boost Software License,
Chris@102: // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
Chris@102: // http://www.boost.org/LICENSE_1_0.txt)
Chris@102: 
Chris@102: #ifndef BOOST_GEOMETRY_ALGORITHMS_DETAIL_VINCENTY_INVERSE_HPP
Chris@102: #define BOOST_GEOMETRY_ALGORITHMS_DETAIL_VINCENTY_INVERSE_HPP
Chris@102: 
Chris@102: 
Chris@102: #include <boost/math/constants/constants.hpp>
Chris@102: 
Chris@102: #include <boost/geometry/core/radius.hpp>
Chris@102: #include <boost/geometry/core/srs.hpp>
Chris@102: 
Chris@102: #include <boost/geometry/util/math.hpp>
Chris@102: 
Chris@102: #include <boost/geometry/algorithms/detail/flattening.hpp>
Chris@102: 
Chris@102: 
Chris@102: #ifndef BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS
Chris@102: #define BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS 1000
Chris@102: #endif
Chris@102: 
Chris@102: 
Chris@102: namespace boost { namespace geometry { namespace detail
Chris@102: {
Chris@102: 
Chris@102: /*!
Chris@102: \brief The solution of the inverse problem of geodesics on latlong coordinates, after Vincenty, 1975
Chris@102: \author See
Chris@102:     - http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf
Chris@102:     - http://www.icsm.gov.au/gda/gdav2.3.pdf
Chris@102: \author Adapted from various implementations to get it close to the original document
Chris@102:     - http://www.movable-type.co.uk/scripts/LatLongVincenty.html
Chris@102:     - http://exogen.case.edu/projects/geopy/source/geopy.distance.html
Chris@102:     - http://futureboy.homeip.net/fsp/colorize.fsp?fileName=navigation.frink
Chris@102: 
Chris@102: */
Chris@102: template <typename CT>
Chris@102: class vincenty_inverse
Chris@102: {
Chris@102: public:
Chris@102:     template <typename T1, typename T2, typename Spheroid>
Chris@102:     vincenty_inverse(T1 const& lon1,
Chris@102:                      T1 const& lat1,
Chris@102:                      T2 const& lon2,
Chris@102:                      T2 const& lat2,
Chris@102:                      Spheroid const& spheroid)
Chris@102:         : is_result_zero(false)
Chris@102:     {
Chris@102:         if (math::equals(lat1, lat2) && math::equals(lon1, lon2))
Chris@102:         {
Chris@102:             is_result_zero = true;
Chris@102:             return;
Chris@102:         }
Chris@102: 
Chris@102:         CT const c1 = 1;
Chris@102:         CT const c2 = 2;
Chris@102:         CT const c3 = 3;
Chris@102:         CT const c4 = 4;
Chris@102:         CT const c16 = 16;
Chris@102:         CT const c_e_12 = CT(1e-12);
Chris@102: 
Chris@102:         CT const pi = geometry::math::pi<CT>();
Chris@102:         CT const two_pi = c2 * pi;
Chris@102: 
Chris@102:         // lambda: difference in longitude on an auxiliary sphere
Chris@102:         CT L = lon2 - lon1;
Chris@102:         CT lambda = L;
Chris@102: 
Chris@102:         if (L < -pi) L += two_pi;
Chris@102:         if (L > pi) L -= two_pi;
Chris@102: 
Chris@102:         radius_a = CT(get_radius<0>(spheroid));
Chris@102:         radius_b = CT(get_radius<2>(spheroid));
Chris@102:         CT const flattening = geometry::detail::flattening<CT>(spheroid);
Chris@102: 
Chris@102:         // U: reduced latitude, defined by tan U = (1-f) tan phi
Chris@102:         CT const one_min_f = c1 - flattening;
Chris@102:         CT const tan_U1 = one_min_f * tan(lat1); // above (1)
Chris@102:         CT const tan_U2 = one_min_f * tan(lat2); // above (1)
Chris@102: 
Chris@102:         // calculate sin U and cos U using trigonometric identities
Chris@102:         CT const temp_den_U1 = math::sqrt(c1 + math::sqr(tan_U1));
Chris@102:         CT const temp_den_U2 = math::sqrt(c1 + math::sqr(tan_U2));
Chris@102:         // cos = 1 / sqrt(1 + tan^2)
Chris@102:         cos_U1 = c1 / temp_den_U1;
Chris@102:         cos_U2 = c1 / temp_den_U2;
Chris@102:         // sin = tan / sqrt(1 + tan^2)
Chris@102:         sin_U1 = tan_U1 / temp_den_U1;
Chris@102:         sin_U2 = tan_U2 / temp_den_U2;
Chris@102: 
Chris@102:         // calculate sin U and cos U directly
Chris@102:         //CT const U1 = atan(tan_U1);
Chris@102:         //CT const U2 = atan(tan_U2);
Chris@102:         //cos_U1 = cos(U1);
Chris@102:         //cos_U2 = cos(U2);
Chris@102:         //sin_U1 = tan_U1 * cos_U1; // sin(U1);
Chris@102:         //sin_U2 = tan_U2 * cos_U2; // sin(U2);
Chris@102: 
Chris@102:         CT previous_lambda;
Chris@102: 
Chris@102:         int counter = 0; // robustness
Chris@102: 
Chris@102:         do
Chris@102:         {
Chris@102:             previous_lambda = lambda; // (13)
Chris@102:             sin_lambda = sin(lambda);
Chris@102:             cos_lambda = cos(lambda);
Chris@102:             sin_sigma = math::sqrt(math::sqr(cos_U2 * sin_lambda) + math::sqr(cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda)); // (14)
Chris@102:             CT cos_sigma = sin_U1 * sin_U2 + cos_U1 * cos_U2 * cos_lambda; // (15)
Chris@102:             sin_alpha = cos_U1 * cos_U2 * sin_lambda / sin_sigma; // (17)
Chris@102:             cos2_alpha = c1 - math::sqr(sin_alpha);
Chris@102:             cos2_sigma_m = math::equals(cos2_alpha, 0) ? 0 : cos_sigma - c2 * sin_U1 * sin_U2 / cos2_alpha; // (18)
Chris@102: 
Chris@102:             CT C = flattening/c16 * cos2_alpha * (c4 + flattening * (c4 - c3 * cos2_alpha)); // (10)
Chris@102:             sigma = atan2(sin_sigma, cos_sigma); // (16)
Chris@102:             lambda = L + (c1 - C) * flattening * sin_alpha *
Chris@102:                 (sigma + C * sin_sigma * ( cos2_sigma_m + C * cos_sigma * (-c1 + c2 * math::sqr(cos2_sigma_m)))); // (11)
Chris@102: 
Chris@102:             ++counter; // robustness
Chris@102: 
Chris@102:         } while ( geometry::math::abs(previous_lambda - lambda) > c_e_12
Chris@102:                && geometry::math::abs(lambda) < pi
Chris@102:                && counter < BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS ); // robustness
Chris@102:     }
Chris@102: 
Chris@102:     inline CT distance() const
Chris@102:     {
Chris@102:         if ( is_result_zero )
Chris@102:         {
Chris@102:             return CT(0);
Chris@102:         }
Chris@102: 
Chris@102:         // Oops getting hard here
Chris@102:         // (again, problem is that ttmath cannot divide by doubles, which is OK)
Chris@102:         CT const c1 = 1;
Chris@102:         CT const c2 = 2;
Chris@102:         CT const c3 = 3;
Chris@102:         CT const c4 = 4;
Chris@102:         CT const c6 = 6;
Chris@102:         CT const c47 = 47;
Chris@102:         CT const c74 = 74;
Chris@102:         CT const c128 = 128;
Chris@102:         CT const c256 = 256;
Chris@102:         CT const c175 = 175;
Chris@102:         CT const c320 = 320;
Chris@102:         CT const c768 = 768;
Chris@102:         CT const c1024 = 1024;
Chris@102:         CT const c4096 = 4096;
Chris@102:         CT const c16384 = 16384;
Chris@102: 
Chris@102:         //CT sqr_u = cos2_alpha * (math::sqr(radius_a) - math::sqr(radius_b)) / math::sqr(radius_b); // above (1)
Chris@102:         CT sqr_u = cos2_alpha * ( math::sqr(radius_a / radius_b) - c1 ); // above (1)
Chris@102: 
Chris@102:         CT A = c1 + sqr_u/c16384 * (c4096 + sqr_u * (-c768 + sqr_u * (c320 - c175 * sqr_u))); // (3)
Chris@102:         CT B = sqr_u/c1024 * (c256 + sqr_u * ( -c128 + sqr_u * (c74 - c47 * sqr_u))); // (4)
Chris@102:         CT delta_sigma = B * sin_sigma * ( cos2_sigma_m + (B/c4) * (cos(sigma)* (-c1 + c2 * cos2_sigma_m)
Chris@102:             - (B/c6) * cos2_sigma_m * (-c3 + c4 * math::sqr(sin_sigma)) * (-c3 + c4 * cos2_sigma_m))); // (6)
Chris@102: 
Chris@102:         return radius_b * A * (sigma - delta_sigma); // (19)
Chris@102:     }
Chris@102: 
Chris@102:     inline CT azimuth12() const
Chris@102:     {
Chris@102:         return is_result_zero ?
Chris@102:                CT(0) :
Chris@102:                atan2(cos_U2 * sin_lambda, cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda); // (20)
Chris@102:     }
Chris@102: 
Chris@102:     inline CT azimuth21() const
Chris@102:     {
Chris@102:         // NOTE: signs of X and Y are different than in the original paper
Chris@102:         return is_result_zero ?
Chris@102:                CT(0) :
Chris@102:                atan2(-cos_U1 * sin_lambda, sin_U1 * cos_U2 - cos_U1 * sin_U2 * cos_lambda); // (21)
Chris@102:     }
Chris@102: 
Chris@102: private:
Chris@102:     // alpha: azimuth of the geodesic at the equator
Chris@102:     CT cos2_alpha;
Chris@102:     CT sin_alpha;
Chris@102: 
Chris@102:     // sigma: angular distance p1,p2 on the sphere
Chris@102:     // sigma1: angular distance on the sphere from the equator to p1
Chris@102:     // sigma_m: angular distance on the sphere from the equator to the midpoint of the line
Chris@102:     CT sigma;
Chris@102:     CT sin_sigma;
Chris@102:     CT cos2_sigma_m;
Chris@102: 
Chris@102:     CT sin_lambda;
Chris@102:     CT cos_lambda;
Chris@102: 
Chris@102:     // set only once
Chris@102:     CT cos_U1;
Chris@102:     CT cos_U2;
Chris@102:     CT sin_U1;
Chris@102:     CT sin_U2;
Chris@102: 
Chris@102:     // set only once
Chris@102:     CT radius_a;
Chris@102:     CT radius_b;
Chris@102: 
Chris@102:     bool is_result_zero;
Chris@102: };
Chris@102: 
Chris@102: }}} // namespace boost::geometry::detail
Chris@102: 
Chris@102: 
Chris@102: #endif // BOOST_GEOMETRY_ALGORITHMS_DETAIL_VINCENTY_INVERSE_HPP