geometry/formulas/vincenty_inverse.hpp

0001 // Boost.Geometry
0002
0003 // Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands.
0004 // Copyright (c) 2018-2023 Adam Wulkiewicz, Lodz, Poland.
0005
0006 // This file was modified by Oracle on 2014, 2016, 2017.
0007 // Modifications copyright (c) 2014-2017 Oracle and/or its affiliates.
0008 // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
0009
0010 // Use, modification and distribution is subject to the Boost Software License,
0011 // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
0012 // http://www.boost.org/LICENSE_1_0.txt)
0013
0014 #ifndef BOOST_GEOMETRY_FORMULAS_VINCENTY_INVERSE_HPP
0015 #define BOOST_GEOMETRY_FORMULAS_VINCENTY_INVERSE_HPP
0016
0017
0018 #include <boost/math/constants/constants.hpp>
0019
0020 #include <boost/geometry/core/radius.hpp>
0021
0022 #include <boost/geometry/util/constexpr.hpp>
0023 #include <boost/geometry/util/math.hpp>
0024
0025 #include <boost/geometry/formulas/differential_quantities.hpp>
0026 #include <boost/geometry/formulas/flattening.hpp>
0027 #include <boost/geometry/formulas/result_inverse.hpp>
0028
0029
0030 #ifndef BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS
0031 #define BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS 1000
0032 #endif
0033
0034
0035 namespace boost { namespace geometry { namespace formula
0036 {
0037
0038 /*!
0039 \brief The solution of the inverse problem of geodesics on latlong coordinates, after Vincenty, 1975
0040 \author See
0041     - http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf
0042     - http://www.icsm.gov.au/gda/gda-v_2.4.pdf
0043 \author Adapted from various implementations to get it close to the original document
0044     - http://www.movable-type.co.uk/scripts/LatLongVincenty.html
0045     - http://exogen.case.edu/projects/geopy/source/geopy.distance.html
0046     - http://futureboy.homeip.net/fsp/colorize.fsp?fileName=navigation.frink
0047
0048 */
0049 template <
0050     typename CT,
0051     bool EnableDistance,
0052     bool EnableAzimuth,
0053     bool EnableReverseAzimuth = false,
0054     bool EnableReducedLength = false,
0055     bool EnableGeodesicScale = false
0056 >
0057 struct vincenty_inverse
0058 {
0059     static const bool CalcQuantities = EnableReducedLength || EnableGeodesicScale;
0060     static const bool CalcAzimuths = EnableAzimuth || EnableReverseAzimuth || CalcQuantities;
0061     static const bool CalcFwdAzimuth = EnableAzimuth || CalcQuantities;
0062     static const bool CalcRevAzimuth = EnableReverseAzimuth || CalcQuantities;
0063
0064 public:
0065     typedef result_inverse<CT> result_type;
0066
0067     template <typename T1, typename T2, typename Spheroid>
0068     static inline result_type apply(T1 const& lon1,
0069                                     T1 const& lat1,
0070                                     T2 const& lon2,
0071                                     T2 const& lat2,
0072                                     Spheroid const& spheroid)
0073     {
0074         result_type result;
0075
0076         if (math::equals(lat1, lat2) && math::equals(lon1, lon2))
0077         {
0078             return result;
0079         }
0080
0081         CT const c0 = 0;
0082         CT const c1 = 1;
0083         CT const c2 = 2;
0084         CT const c3 = 3;
0085         CT const c4 = 4;
0086         CT const c16 = 16;
0087         CT const c_e_12 = CT(1e-12);
0088
0089         CT const pi = geometry::math::pi<CT>();
0090         CT const two_pi = c2 * pi;
0091
0092         // lambda: difference in longitude on an auxiliary sphere
0093         CT L = lon2 - lon1;
0094         CT lambda = L;
0095
0096         if (L < -pi) L += two_pi;
0097         if (L > pi) L -= two_pi;
0098
0099         CT const radius_a = CT(get_radius<0>(spheroid));
0100         CT const radius_b = CT(get_radius<2>(spheroid));
0101         CT const f = formula::flattening<CT>(spheroid);
0102
0103         // U: reduced latitude, defined by tan U = (1-f) tan phi
0104         CT const one_min_f = c1 - f;
0105         CT const tan_U1 = one_min_f * tan(lat1); // above (1)
0106         CT const tan_U2 = one_min_f * tan(lat2); // above (1)
0107
0108         // calculate sin U and cos U using trigonometric identities
0109         CT const temp_den_U1 = math::sqrt(c1 + math::sqr(tan_U1));
0110         CT const temp_den_U2 = math::sqrt(c1 + math::sqr(tan_U2));
0111         // cos = 1 / sqrt(1 + tan^2)
0112         CT const cos_U1 = c1 / temp_den_U1;
0113         CT const cos_U2 = c1 / temp_den_U2;
0114         // sin = tan / sqrt(1 + tan^2)
0115         // sin = tan * cos
0116         CT const sin_U1 = tan_U1 * cos_U1;
0117         CT const sin_U2 = tan_U2 * cos_U2;
0118
0119         // calculate sin U and cos U directly
0120         //CT const U1 = atan(tan_U1);
0121         //CT const U2 = atan(tan_U2);
0122         //cos_U1 = cos(U1);
0123         //cos_U2 = cos(U2);
0124         //sin_U1 = tan_U1 * cos_U1; // sin(U1);
0125         //sin_U2 = tan_U2 * cos_U2; // sin(U2);
0126
0127         CT previous_lambda;
0128         CT sin_lambda;
0129         CT cos_lambda;
0130         CT sin_sigma;
0131         CT sin_alpha;
0132         CT cos2_alpha;
0133         CT cos_2sigma_m;
0134         CT cos2_2sigma_m;
0135         CT sigma;
0136
0137         int counter = 0; // robustness
0138
0139         do
0140         {
0141             previous_lambda = lambda; // (13)
0142             sin_lambda = sin(lambda);
0143             cos_lambda = cos(lambda);
0144             sin_sigma = math::sqrt(math::sqr(cos_U2 * sin_lambda) + math::sqr(cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda)); // (14)
0145             CT cos_sigma = sin_U1 * sin_U2 + cos_U1 * cos_U2 * cos_lambda; // (15)
0146             sin_alpha = cos_U1 * cos_U2 * sin_lambda / sin_sigma; // (17)
0147             cos2_alpha = c1 - math::sqr(sin_alpha);
0148             cos_2sigma_m = math::equals(cos2_alpha, c0) ? c0 : cos_sigma - c2 * sin_U1 * sin_U2 / cos2_alpha; // (18)
0149             cos2_2sigma_m = math::sqr(cos_2sigma_m);
0150
0151             CT C = f/c16 * cos2_alpha * (c4 + f * (c4 - c3 * cos2_alpha)); // (10)
0152             sigma = atan2(sin_sigma, cos_sigma); // (16)
0153             lambda = L + (c1 - C) * f * sin_alpha *
0154                 (sigma + C * sin_sigma * (cos_2sigma_m + C * cos_sigma * (-c1 + c2 * cos2_2sigma_m))); // (11)
0155
0156             ++counter; // robustness
0157
0158         } while ( geometry::math::abs(previous_lambda - lambda) > c_e_12
0159                && geometry::math::abs(lambda) < pi
0160                && counter < BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS ); // robustness
0161
0162         if BOOST_GEOMETRY_CONSTEXPR (EnableDistance)
0163         {
0164             // Some types cannot divide by doubles
0165             CT const c6 = 6;
0166             CT const c47 = 47;
0167             CT const c74 = 74;
0168             CT const c128 = 128;
0169             CT const c256 = 256;
0170             CT const c175 = 175;
0171             CT const c320 = 320;
0172             CT const c768 = 768;
0173             CT const c1024 = 1024;
0174             CT const c4096 = 4096;
0175             CT const c16384 = 16384;
0176
0177             //CT sqr_u = cos2_alpha * (math::sqr(radius_a) - math::sqr(radius_b)) / math::sqr(radius_b); // above (1)
0178             CT sqr_u = cos2_alpha * ( math::sqr(radius_a / radius_b) - c1 ); // above (1)
0179
0180             CT A = c1 + sqr_u/c16384 * (c4096 + sqr_u * (-c768 + sqr_u * (c320 - c175 * sqr_u))); // (3)
0181             CT B = sqr_u/c1024 * (c256 + sqr_u * ( -c128 + sqr_u * (c74 - c47 * sqr_u))); // (4)
0182             CT const cos_sigma = cos(sigma);
0183             CT const sin2_sigma = math::sqr(sin_sigma);
0184             CT delta_sigma = B * sin_sigma * (cos_2sigma_m + (B/c4) * (cos_sigma* (-c1 + c2 * cos2_2sigma_m)
0185                 - (B/c6) * cos_2sigma_m * (-c3 + c4 * sin2_sigma) * (-c3 + c4 * cos2_2sigma_m))); // (6)
0186
0187             result.distance = radius_b * A * (sigma - delta_sigma); // (19)
0188         }
0189
0190         if BOOST_GEOMETRY_CONSTEXPR (CalcAzimuths)
0191         {
0192             if BOOST_GEOMETRY_CONSTEXPR (CalcFwdAzimuth)
0193             {
0194                 result.azimuth = atan2(cos_U2 * sin_lambda, cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda); // (20)
0195             }
0196
0197             if BOOST_GEOMETRY_CONSTEXPR (CalcRevAzimuth)
0198             {
0199                 result.reverse_azimuth = atan2(cos_U1 * sin_lambda, -sin_U1 * cos_U2 + cos_U1 * sin_U2 * cos_lambda); // (21)
0200             }
0201         }
0202
0203         if BOOST_GEOMETRY_CONSTEXPR (CalcQuantities)
0204         {
0205             typedef differential_quantities<CT, EnableReducedLength, EnableGeodesicScale, 2> quantities;
0206             quantities::apply(lon1, lat1, lon2, lat2,
0207                               result.azimuth, result.reverse_azimuth,
0208                               radius_b, f,
0209                               result.reduced_length, result.geodesic_scale);
0210         }
0211
0212         return result;
0213     }
0214 };
0215
0216 }}} // namespace boost::geometry::formula
0217
0218
0219 #endif // BOOST_GEOMETRY_FORMULAS_VINCENTY_INVERSE_HPP