ceph/src/boost/boost/geometry/formulas/vincenty_inverse.hpp

   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>
  69     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             // Some types cannot divide by doubles
 166             CT const c6 = 6;
 167             CT const c47 = 47;
 168             CT const c74 = 74;
 169             CT const c128 = 128;
 170             CT const c256 = 256;
 171             CT const c175 = 175;
 172             CT const c320 = 320;
 173             CT const c768 = 768;
 174             CT const c1024 = 1024;
 175             CT const c4096 = 4096;
 176             CT const c16384 = 16384;
 177
 178             //CT sqr_u = cos2_alpha * (math::sqr(radius_a) - math::sqr(radius_b)) / math::sqr(radius_b); // above (1)
 179             CT sqr_u = cos2_alpha * ( math::sqr(radius_a / radius_b) - c1 ); // above (1)
 180
 181             CT A = c1 + sqr_u/c16384 * (c4096 + sqr_u * (-c768 + sqr_u * (c320 - c175 * sqr_u))); // (3)
 182             CT B = sqr_u/c1024 * (c256 + sqr_u * ( -c128 + sqr_u * (c74 - c47 * sqr_u))); // (4)
 183             CT const cos_sigma = cos(sigma);
 184             CT const sin2_sigma = math::sqr(sin_sigma);
 185             CT delta_sigma = B * sin_sigma * (cos_2sigma_m + (B/c4) * (cos_sigma* (-c1 + c2 * cos2_2sigma_m)
 186                 - (B/c6) * cos_2sigma_m * (-c3 + c4 * sin2_sigma) * (-c3 + c4 * cos2_2sigma_m))); // (6)
 187
 188             result.distance = radius_b * A * (sigma - delta_sigma); // (19)
 189         }
 190
 191         if ( BOOST_GEOMETRY_CONDITION(CalcAzimuths) )
 192         {
 193             if (BOOST_GEOMETRY_CONDITION(CalcFwdAzimuth))
 194             {
 195                 result.azimuth = atan2(cos_U2 * sin_lambda, cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda); // (20)
 196             }
 197
 198             if (BOOST_GEOMETRY_CONDITION(CalcRevAzimuth))
 199             {
 200                 result.reverse_azimuth = atan2(cos_U1 * sin_lambda, -sin_U1 * cos_U2 + cos_U1 * sin_U2 * cos_lambda); // (21)
 201             }
 202         }
 203
 204         if (BOOST_GEOMETRY_CONDITION(CalcQuantities))
 205         {
 206             typedef differential_quantities<CT, EnableReducedLength, EnableGeodesicScale, 2> quantities;
 207             quantities::apply(lon1, lat1, lon2, lat2,
 208                               result.azimuth, result.reverse_azimuth,
 209                               radius_b, f,
 210                               result.reduced_length, result.geodesic_scale);
 211         }
 212
 213         return result;
 214     }
 215 };
 216
 217 }}} // namespace boost::geometry::formula
 218
 219
 220 #endif // BOOST_GEOMETRY_FORMULAS_VINCENTY_INVERSE_HPP