1 // Boost.Geometry 2 3 // Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands. 4 5 // This file was modified by Oracle on 2014, 2016, 2017. 6 // Modifications copyright (c) 2014-2017 Oracle and/or its affiliates. 7 8 // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle 9 10 // Use, modification and distribution is subject to the Boost Software License, 11 // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at 12 // http://www.boost.org/LICENSE_1_0.txt) 13 14 #ifndef BOOST_GEOMETRY_FORMULAS_VINCENTY_INVERSE_HPP 15 #define BOOST_GEOMETRY_FORMULAS_VINCENTY_INVERSE_HPP 16 17 18 #include <boost/math/constants/constants.hpp> 19 20 #include <boost/geometry/core/radius.hpp> 21 #include <boost/geometry/core/srs.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 c1 = 1; 83 CT const c2 = 2; 84 CT const c3 = 3; 85 CT const c4 = 4; 86 CT const c16 = 16; 87 CT const c_e_12 = CT(1e-12); 88 89 CT const pi = geometry::math::pi<CT>(); 90 CT const two_pi = c2 * pi; 91 92 // lambda: difference in longitude on an auxiliary sphere 93 CT L = lon2 - lon1; 94 CT lambda = L; 95 96 if (L < -pi) L += two_pi; 97 if (L > pi) L -= two_pi; 98 99 CT const radius_a = CT(get_radius<0>(spheroid)); 100 CT const radius_b = CT(get_radius<2>(spheroid)); 101 CT const f = formula::flattening<CT>(spheroid); 102 103 // U: reduced latitude, defined by tan U = (1-f) tan phi 104 CT const one_min_f = c1 - f; 105 CT const tan_U1 = one_min_f * tan(lat1); // above (1) 106 CT const tan_U2 = one_min_f * tan(lat2); // above (1) 107 108 // calculate sin U and cos U using trigonometric identities 109 CT const temp_den_U1 = math::sqrt(c1 + math::sqr(tan_U1)); 110 CT const temp_den_U2 = math::sqrt(c1 + math::sqr(tan_U2)); 111 // cos = 1 / sqrt(1 + tan^2) 112 CT const cos_U1 = c1 / temp_den_U1; 113 CT const cos_U2 = c1 / temp_den_U2; 114 // sin = tan / sqrt(1 + tan^2) 115 // sin = tan * cos 116 CT const sin_U1 = tan_U1 * cos_U1; 117 CT const sin_U2 = tan_U2 * cos_U2; 118 119 // calculate sin U and cos U directly 120 //CT const U1 = atan(tan_U1); 121 //CT const U2 = atan(tan_U2); 122 //cos_U1 = cos(U1); 123 //cos_U2 = cos(U2); 124 //sin_U1 = tan_U1 * cos_U1; // sin(U1); 125 //sin_U2 = tan_U2 * cos_U2; // sin(U2); 126 127 CT previous_lambda; 128 CT sin_lambda; 129 CT cos_lambda; 130 CT sin_sigma; 131 CT sin_alpha; 132 CT cos2_alpha; 133 CT cos_2sigma_m; 134 CT cos2_2sigma_m; 135 CT sigma; 136 137 int counter = 0; // robustness 138 139 do 140 { 141 previous_lambda = lambda; // (13) 142 sin_lambda = sin(lambda); 143 cos_lambda = cos(lambda); 144 sin_sigma = math::sqrt(math::sqr(cos_U2 * sin_lambda) + math::sqr(cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda)); // (14) 145 CT cos_sigma = sin_U1 * sin_U2 + cos_U1 * cos_U2 * cos_lambda; // (15) 146 sin_alpha = cos_U1 * cos_U2 * sin_lambda / sin_sigma; // (17) 147 cos2_alpha = c1 - math::sqr(sin_alpha); 148 cos_2sigma_m = math::equals(cos2_alpha, 0) ? 0 : cos_sigma - c2 * sin_U1 * sin_U2 / cos2_alpha; // (18) 149 cos2_2sigma_m = math::sqr(cos_2sigma_m); 150 151 CT C = f/c16 * cos2_alpha * (c4 + f * (c4 - c3 * cos2_alpha)); // (10) 152 sigma = atan2(sin_sigma, cos_sigma); // (16) 153 lambda = L + (c1 - C) * f * sin_alpha * 154 (sigma + C * sin_sigma * (cos_2sigma_m + C * cos_sigma * (-c1 + c2 * cos2_2sigma_m))); // (11) 155 156 ++counter; // robustness 157 158 } while ( geometry::math::abs(previous_lambda - lambda) > c_e_12 159 && geometry::math::abs(lambda) < pi 160 && counter < BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS ); // robustness 161 162 if ( BOOST_GEOMETRY_CONDITION(EnableDistance) ) 163 { 164 // Oops getting hard here 165 // (again, problem is that ttmath cannot divide by doubles, which is OK) 166 CT const c1 = 1; 167 CT const c2 = 2; 168 CT const c3 = 3; 169 CT const c4 = 4; 170 CT const c6 = 6; 171 CT const c47 = 47; 172 CT const c74 = 74; 173 CT const c128 = 128; 174 CT const c256 = 256; 175 CT const c175 = 175; 176 CT const c320 = 320; 177 CT const c768 = 768; 178 CT const c1024 = 1024; 179 CT const c4096 = 4096; 180 CT const c16384 = 16384; 181 182 //CT sqr_u = cos2_alpha * (math::sqr(radius_a) - math::sqr(radius_b)) / math::sqr(radius_b); // above (1) 183 CT sqr_u = cos2_alpha * ( math::sqr(radius_a / radius_b) - c1 ); // above (1) 184 185 CT A = c1 + sqr_u/c16384 * (c4096 + sqr_u * (-c768 + sqr_u * (c320 - c175 * sqr_u))); // (3) 186 CT B = sqr_u/c1024 * (c256 + sqr_u * ( -c128 + sqr_u * (c74 - c47 * sqr_u))); // (4) 187 CT const cos_sigma = cos(sigma); 188 CT const sin2_sigma = math::sqr(sin_sigma); 189 CT delta_sigma = B * sin_sigma * (cos_2sigma_m + (B/c4) * (cos_sigma* (-c1 + c2 * cos2_2sigma_m) 190 - (B/c6) * cos_2sigma_m * (-c3 + c4 * sin2_sigma) * (-c3 + c4 * cos2_2sigma_m))); // (6) 191 192 result.distance = radius_b * A * (sigma - delta_sigma); // (19) 193 } 194 195 if ( BOOST_GEOMETRY_CONDITION(CalcAzimuths) ) 196 { 197 if (BOOST_GEOMETRY_CONDITION(CalcFwdAzimuth)) 198 { 199 result.azimuth = atan2(cos_U2 * sin_lambda, cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda); // (20) 200 } 201 202 if (BOOST_GEOMETRY_CONDITION(CalcRevAzimuth)) 203 { 204 result.reverse_azimuth = atan2(cos_U1 * sin_lambda, -sin_U1 * cos_U2 + cos_U1 * sin_U2 * cos_lambda); // (21) 205 } 206 } 207 208 if (BOOST_GEOMETRY_CONDITION(CalcQuantities)) 209 { 210 typedef differential_quantities<CT, EnableReducedLength, EnableGeodesicScale, 2> quantities; 211 quantities::apply(lon1, lat1, lon2, lat2, 212 result.azimuth, result.reverse_azimuth, 213 radius_b, f, 214 result.reduced_length, result.geodesic_scale); 215 } 216 217 return result; 218 } 219 }; 220 221 }}} // namespace boost::geometry::formula 222 223 224 #endif // BOOST_GEOMETRY_FORMULAS_VINCENTY_INVERSE_HPP 225