1 // Boost.Geometry 2 3 // Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands. 4 // Copyright (c) 2018 Adam Wulkiewicz, Lodz, Poland. 5 6 // This file was modified by Oracle on 2014, 2016, 2017. 7 // Modifications copyright (c) 2014-2017 Oracle and/or its affiliates. 8 9 // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle 10 11 // Use, modification and distribution is subject to the Boost Software License, 12 // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at 13 // http://www.boost.org/LICENSE_1_0.txt) 14 15 #ifndef BOOST_GEOMETRY_FORMULAS_VINCENTY_INVERSE_HPP 16 #define BOOST_GEOMETRY_FORMULAS_VINCENTY_INVERSE_HPP 17 18 19 #include <boost/math/constants/constants.hpp> 20 21 #include <boost/geometry/core/radius.hpp> 22 23 #include <boost/geometry/util/condition.hpp> 24 #include <boost/geometry/util/math.hpp> 25 26 #include <boost/geometry/formulas/differential_quantities.hpp> 27 #include <boost/geometry/formulas/flattening.hpp> 28 #include <boost/geometry/formulas/result_inverse.hpp> 29 30 31 #ifndef BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS 32 #define BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS 1000 33 #endif 34 35 36 namespace boost { namespace geometry { namespace formula 37 { 38 39 /*! 40 \brief The solution of the inverse problem of geodesics on latlong coordinates, after Vincenty, 1975 41 \author See 42 - http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf 43 - http://www.icsm.gov.au/gda/gda-v_2.4.pdf 44 \author Adapted from various implementations to get it close to the original document 45 - http://www.movable-type.co.uk/scripts/LatLongVincenty.html 46 - http://exogen.case.edu/projects/geopy/source/geopy.distance.html 47 - http://futureboy.homeip.net/fsp/colorize.fsp?fileName=navigation.frink 48 49 */ 50 template < 51 typename CT, 52 bool EnableDistance, 53 bool EnableAzimuth, 54 bool EnableReverseAzimuth = false, 55 bool EnableReducedLength = false, 56 bool EnableGeodesicScale = false 57 > 58 struct vincenty_inverse 59 { 60 static const bool CalcQuantities = EnableReducedLength || EnableGeodesicScale; 61 static const bool CalcAzimuths = EnableAzimuth || EnableReverseAzimuth || CalcQuantities; 62 static const bool CalcFwdAzimuth = EnableAzimuth || CalcQuantities; 63 static const bool CalcRevAzimuth = EnableReverseAzimuth || CalcQuantities; 64 65 public: 66 typedef result_inverse<CT> result_type; 67 68 template <typename T1, typename T2, typename Spheroid> applyboost::geometry::formula::vincenty_inverse69 static inline result_type apply(T1 const& lon1, 70 T1 const& lat1, 71 T2 const& lon2, 72 T2 const& lat2, 73 Spheroid const& spheroid) 74 { 75 result_type result; 76 77 if (math::equals(lat1, lat2) && math::equals(lon1, lon2)) 78 { 79 return result; 80 } 81 82 CT const c0 = 0; 83 CT const c1 = 1; 84 CT const c2 = 2; 85 CT const c3 = 3; 86 CT const c4 = 4; 87 CT const c16 = 16; 88 CT const c_e_12 = CT(1e-12); 89 90 CT const pi = geometry::math::pi<CT>(); 91 CT const two_pi = c2 * pi; 92 93 // lambda: difference in longitude on an auxiliary sphere 94 CT L = lon2 - lon1; 95 CT lambda = L; 96 97 if (L < -pi) L += two_pi; 98 if (L > pi) L -= two_pi; 99 100 CT const radius_a = CT(get_radius<0>(spheroid)); 101 CT const radius_b = CT(get_radius<2>(spheroid)); 102 CT const f = formula::flattening<CT>(spheroid); 103 104 // U: reduced latitude, defined by tan U = (1-f) tan phi 105 CT const one_min_f = c1 - f; 106 CT const tan_U1 = one_min_f * tan(lat1); // above (1) 107 CT const tan_U2 = one_min_f * tan(lat2); // above (1) 108 109 // calculate sin U and cos U using trigonometric identities 110 CT const temp_den_U1 = math::sqrt(c1 + math::sqr(tan_U1)); 111 CT const temp_den_U2 = math::sqrt(c1 + math::sqr(tan_U2)); 112 // cos = 1 / sqrt(1 + tan^2) 113 CT const cos_U1 = c1 / temp_den_U1; 114 CT const cos_U2 = c1 / temp_den_U2; 115 // sin = tan / sqrt(1 + tan^2) 116 // sin = tan * cos 117 CT const sin_U1 = tan_U1 * cos_U1; 118 CT const sin_U2 = tan_U2 * cos_U2; 119 120 // calculate sin U and cos U directly 121 //CT const U1 = atan(tan_U1); 122 //CT const U2 = atan(tan_U2); 123 //cos_U1 = cos(U1); 124 //cos_U2 = cos(U2); 125 //sin_U1 = tan_U1 * cos_U1; // sin(U1); 126 //sin_U2 = tan_U2 * cos_U2; // sin(U2); 127 128 CT previous_lambda; 129 CT sin_lambda; 130 CT cos_lambda; 131 CT sin_sigma; 132 CT sin_alpha; 133 CT cos2_alpha; 134 CT cos_2sigma_m; 135 CT cos2_2sigma_m; 136 CT sigma; 137 138 int counter = 0; // robustness 139 140 do 141 { 142 previous_lambda = lambda; // (13) 143 sin_lambda = sin(lambda); 144 cos_lambda = cos(lambda); 145 sin_sigma = math::sqrt(math::sqr(cos_U2 * sin_lambda) + math::sqr(cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda)); // (14) 146 CT cos_sigma = sin_U1 * sin_U2 + cos_U1 * cos_U2 * cos_lambda; // (15) 147 sin_alpha = cos_U1 * cos_U2 * sin_lambda / sin_sigma; // (17) 148 cos2_alpha = c1 - math::sqr(sin_alpha); 149 cos_2sigma_m = math::equals(cos2_alpha, c0) ? c0 : cos_sigma - c2 * sin_U1 * sin_U2 / cos2_alpha; // (18) 150 cos2_2sigma_m = math::sqr(cos_2sigma_m); 151 152 CT C = f/c16 * cos2_alpha * (c4 + f * (c4 - c3 * cos2_alpha)); // (10) 153 sigma = atan2(sin_sigma, cos_sigma); // (16) 154 lambda = L + (c1 - C) * f * sin_alpha * 155 (sigma + C * sin_sigma * (cos_2sigma_m + C * cos_sigma * (-c1 + c2 * cos2_2sigma_m))); // (11) 156 157 ++counter; // robustness 158 159 } while ( geometry::math::abs(previous_lambda - lambda) > c_e_12 160 && geometry::math::abs(lambda) < pi 161 && counter < BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS ); // robustness 162 163 if ( BOOST_GEOMETRY_CONDITION(EnableDistance) ) 164 { 165 // Oops getting hard here 166 // (again, problem is that ttmath cannot divide by doubles, which is OK) 167 CT const c6 = 6; 168 CT const c47 = 47; 169 CT const c74 = 74; 170 CT const c128 = 128; 171 CT const c256 = 256; 172 CT const c175 = 175; 173 CT const c320 = 320; 174 CT const c768 = 768; 175 CT const c1024 = 1024; 176 CT const c4096 = 4096; 177 CT const c16384 = 16384; 178 179 //CT sqr_u = cos2_alpha * (math::sqr(radius_a) - math::sqr(radius_b)) / math::sqr(radius_b); // above (1) 180 CT sqr_u = cos2_alpha * ( math::sqr(radius_a / radius_b) - c1 ); // above (1) 181 182 CT A = c1 + sqr_u/c16384 * (c4096 + sqr_u * (-c768 + sqr_u * (c320 - c175 * sqr_u))); // (3) 183 CT B = sqr_u/c1024 * (c256 + sqr_u * ( -c128 + sqr_u * (c74 - c47 * sqr_u))); // (4) 184 CT const cos_sigma = cos(sigma); 185 CT const sin2_sigma = math::sqr(sin_sigma); 186 CT delta_sigma = B * sin_sigma * (cos_2sigma_m + (B/c4) * (cos_sigma* (-c1 + c2 * cos2_2sigma_m) 187 - (B/c6) * cos_2sigma_m * (-c3 + c4 * sin2_sigma) * (-c3 + c4 * cos2_2sigma_m))); // (6) 188 189 result.distance = radius_b * A * (sigma - delta_sigma); // (19) 190 } 191 192 if ( BOOST_GEOMETRY_CONDITION(CalcAzimuths) ) 193 { 194 if (BOOST_GEOMETRY_CONDITION(CalcFwdAzimuth)) 195 { 196 result.azimuth = atan2(cos_U2 * sin_lambda, cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda); // (20) 197 } 198 199 if (BOOST_GEOMETRY_CONDITION(CalcRevAzimuth)) 200 { 201 result.reverse_azimuth = atan2(cos_U1 * sin_lambda, -sin_U1 * cos_U2 + cos_U1 * sin_U2 * cos_lambda); // (21) 202 } 203 } 204 205 if (BOOST_GEOMETRY_CONDITION(CalcQuantities)) 206 { 207 typedef differential_quantities<CT, EnableReducedLength, EnableGeodesicScale, 2> quantities; 208 quantities::apply(lon1, lat1, lon2, lat2, 209 result.azimuth, result.reverse_azimuth, 210 radius_b, f, 211 result.reduced_length, result.geodesic_scale); 212 } 213 214 return result; 215 } 216 }; 217 218 }}} // namespace boost::geometry::formula 219 220 221 #endif // BOOST_GEOMETRY_FORMULAS_VINCENTY_INVERSE_HPP 222