geometry/formulas/thomas_direct.hpp

0001 // Boost.Geometry
0002
0003 // Copyright (c) 2016-2020 Oracle and/or its affiliates.
0004
0005 // Contributed and/or modified by Vissarion Fysikopoulos, on behalf of Oracle
0006 // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
0007
0008 // Use, modification and distribution is subject to the Boost Software License,
0009 // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
0010 // http://www.boost.org/LICENSE_1_0.txt)
0011
0012 #ifndef BOOST_GEOMETRY_FORMULAS_THOMAS_DIRECT_HPP
0013 #define BOOST_GEOMETRY_FORMULAS_THOMAS_DIRECT_HPP
0014
0015
0016 #include <boost/math/constants/constants.hpp>
0017
0018 #include <boost/geometry/core/assert.hpp>
0019 #include <boost/geometry/core/radius.hpp>
0020
0021 #include <boost/geometry/util/condition.hpp>
0022 #include <boost/geometry/util/math.hpp>
0023 #include <boost/geometry/util/normalize_spheroidal_coordinates.hpp>
0024
0025 #include <boost/geometry/formulas/differential_quantities.hpp>
0026 #include <boost/geometry/formulas/flattening.hpp>
0027 #include <boost/geometry/formulas/result_direct.hpp>
0028
0029
0030 namespace boost { namespace geometry { namespace formula
0031 {
0032
0033
0034 /*!
0035 \brief The solution of the direct problem of geodesics on latlong coordinates,
0036        Forsyth-Andoyer-Lambert type approximation with first/second order terms.
0037 \author See
0038     - Technical Report: PAUL D. THOMAS, MATHEMATICAL MODELS FOR NAVIGATION SYSTEMS, 1965
0039       http://www.dtic.mil/docs/citations/AD0627893
0040     - Technical Report: PAUL D. THOMAS, SPHEROIDAL GEODESICS, REFERENCE SYSTEMS, AND LOCAL GEOMETRY, 1970
0041       http://www.dtic.mil/docs/citations/AD0703541
0042 */
0043 template <
0044     typename CT,
0045     bool SecondOrder = true,
0046     bool EnableCoordinates = true,
0047     bool EnableReverseAzimuth = false,
0048     bool EnableReducedLength = false,
0049     bool EnableGeodesicScale = false
0050 >
0051 class thomas_direct
0052 {
0053     static const bool CalcQuantities = EnableReducedLength || EnableGeodesicScale;
0054     static const bool CalcCoordinates = EnableCoordinates || CalcQuantities;
0055     static const bool CalcRevAzimuth = EnableReverseAzimuth || CalcCoordinates || CalcQuantities;
0056
0057 public:
0058     typedef result_direct<CT> result_type;
0059
0060     template <typename T, typename Dist, typename Azi, typename Spheroid>
0061     static inline result_type apply(T const& lo1,
0062                                     T const& la1,
0063                                     Dist const& distance,
0064                                     Azi const& azimuth12,
0065                                     Spheroid const& spheroid)
0066     {
0067         result_type result;
0068
0069         CT const lon1 = lo1;
0070         CT const lat1 = la1;
0071
0072         CT const c0 = 0;
0073         CT const c1 = 1;
0074         CT const c2 = 2;
0075         CT const c4 = 4;
0076
0077         CT const a = CT(get_radius<0>(spheroid));
0078         CT const b = CT(get_radius<2>(spheroid));
0079         CT const f = formula::flattening<CT>(spheroid);
0080         CT const one_minus_f = c1 - f;
0081
0082         CT const pi = math::pi<CT>();
0083         CT const pi_half = pi / c2;
0084
0085         BOOST_GEOMETRY_ASSERT(-pi <= azimuth12 && azimuth12 <= pi);
0086
0087         // keep azimuth small - experiments show low accuracy
0088         // if the azimuth is closer to (+-)180 deg.
0089         CT azi12_alt = azimuth12;
0090         CT lat1_alt = lat1;
0091         bool alter_result = vflip_if_south(lat1, azimuth12, lat1_alt, azi12_alt);
0092
0093         CT const theta1 = math::equals(lat1_alt, pi_half) ? lat1_alt :
0094                           math::equals(lat1_alt, -pi_half) ? lat1_alt :
0095                           atan(one_minus_f * tan(lat1_alt));
0096         CT const sin_theta1 = sin(theta1);
0097         CT const cos_theta1 = cos(theta1);
0098
0099         CT const sin_a12 = sin(azi12_alt);
0100         CT const cos_a12 = cos(azi12_alt);
0101
0102         CT const M = cos_theta1 * sin_a12; // cos_theta0
0103         CT const theta0 = acos(M);
0104         CT const sin_theta0 = sin(theta0);
0105
0106         CT const N = cos_theta1 * cos_a12;
0107         CT const C1 = f * M; // lower-case c1 in the technical report
0108         CT const C2 = f * (c1 - math::sqr(M)) / c4; // lower-case c2 in the technical report
0109         CT D = 0;
0110         CT P = 0;
0111         if ( BOOST_GEOMETRY_CONDITION(SecondOrder) )
0112         {
0113             D = (c1 - C2) * (c1 - C2 - C1 * M);
0114             P = C2 * (c1 + C1 * M / c2) / D;
0115         }
0116         else
0117         {
0118             D = c1 - c2 * C2 - C1 * M;
0119             P = C2 / D;
0120         }
0121         // special case for equator:
0122         // sin_theta0 = 0 <=> lat1 = 0 ^ |azimuth12| = pi/2
0123         // NOTE: in this case it doesn't matter what's the value of cos_sigma1 because
0124         //       theta1=0, theta0=0, M=1|-1, C2=0 so X=0 and Y=0 so d_sigma=d
0125         //       cos_a12=0 so N=0, therefore
0126         //       lat2=0, azi21=pi/2|-pi/2
0127         //       d_eta = atan2(sin_d_sigma, cos_d_sigma)
0128         //       H = C1 * d_sigma
0129         CT const cos_sigma1 = math::equals(sin_theta0, c0)
0130                                 ? c1
0131                                 : normalized1_1(sin_theta1 / sin_theta0);
0132         CT const sigma1 = acos(cos_sigma1);
0133         CT const d = distance / (a * D);
0134         CT const u = 2 * (sigma1 - d);
0135         CT const cos_d = cos(d);
0136         CT const sin_d = sin(d);
0137         CT const cos_u = cos(u);
0138         CT const sin_u = sin(u);
0139
0140         CT const W = c1 - c2 * P * cos_u;
0141         CT const V = cos_u * cos_d - sin_u * sin_d;
0142         CT const Y = c2 * P * V * W * sin_d;
0143         CT X = 0;
0144         CT d_sigma = d - Y;
0145         if ( BOOST_GEOMETRY_CONDITION(SecondOrder) )
0146         {
0147             X = math::sqr(C2) * sin_d * cos_d * (2 * math::sqr(V) - c1);
0148             d_sigma += X;
0149         }
0150         CT const sin_d_sigma = sin(d_sigma);
0151         CT const cos_d_sigma = cos(d_sigma);
0152
0153         if (BOOST_GEOMETRY_CONDITION(CalcRevAzimuth))
0154         {
0155             result.reverse_azimuth = atan2(M, N * cos_d_sigma - sin_theta1 * sin_d_sigma);
0156
0157             if (alter_result)
0158             {
0159                 vflip_rev_azi(result.reverse_azimuth, azimuth12);
0160             }
0161         }
0162
0163         if (BOOST_GEOMETRY_CONDITION(CalcCoordinates))
0164         {
0165             CT const S_sigma = c2 * sigma1 - d_sigma;
0166             CT cos_S_sigma = 0;
0167             CT H = C1 * d_sigma;
0168             if ( BOOST_GEOMETRY_CONDITION(SecondOrder) )
0169             {
0170                 cos_S_sigma = cos(S_sigma);
0171                 H = H * (c1 - C2) - C1 * C2 * sin_d_sigma * cos_S_sigma;
0172             }
0173             CT const d_eta = atan2(sin_d_sigma * sin_a12, cos_theta1 * cos_d_sigma - sin_theta1 * sin_d_sigma * cos_a12);
0174             CT const d_lambda = d_eta - H;
0175
0176             result.lon2 = lon1 + d_lambda;
0177
0178             if (! math::equals(M, c0))
0179             {
0180                 CT const sin_a21 = sin(result.reverse_azimuth);
0181                 CT const tan_theta2 = (sin_theta1 * cos_d_sigma + N * sin_d_sigma) * sin_a21 / M;
0182                 result.lat2 = atan(tan_theta2 / one_minus_f);
0183             }
0184             else
0185             {
0186                 CT const sigma2 = S_sigma - sigma1;
0187                 //theta2 = asin(cos(sigma2)) <=> sin_theta0 = 1
0188                 // NOTE: cos(sigma2) defines the sign of tan_theta2
0189                 CT const tan_theta2 = cos(sigma2) / math::abs(sin(sigma2));
0190                 result.lat2 = atan(tan_theta2 / one_minus_f);
0191             }
0192
0193             if (alter_result)
0194             {
0195                 result.lat2 = -result.lat2;
0196             }
0197         }
0198
0199         if (BOOST_GEOMETRY_CONDITION(CalcQuantities))
0200         {
0201             typedef differential_quantities<CT, EnableReducedLength, EnableGeodesicScale, 2> quantities;
0202             quantities::apply(lon1, lat1, result.lon2, result.lat2,
0203                               azimuth12, result.reverse_azimuth,
0204                               b, f,
0205                               result.reduced_length, result.geodesic_scale);
0206         }
0207
0208         if (BOOST_GEOMETRY_CONDITION(CalcCoordinates))
0209         {
0210             // For longitudes close to the antimeridian the result can be out
0211             // of range. Therefore normalize.
0212             // It has to be done at the end because otherwise differential
0213             // quantities are calculated incorrectly.
0214             math::detail::normalize_angle_cond<radian>(result.lon2);
0215         }
0216
0217         return result;
0218     }
0219
0220 private:
0221     static inline bool vflip_if_south(CT const& lat1, CT const& azi12, CT & lat1_alt, CT & azi12_alt)
0222     {
0223         CT const c2 = 2;
0224         CT const pi = math::pi<CT>();
0225         CT const pi_half = pi / c2;
0226
0227         if (azi12 > pi_half)
0228         {
0229             azi12_alt = pi - azi12;
0230             lat1_alt = -lat1;
0231             return true;
0232         }
0233         else if (azi12 < -pi_half)
0234         {
0235             azi12_alt = -pi - azi12;
0236             lat1_alt = -lat1;
0237             return true;
0238         }
0239
0240         return false;
0241     }
0242
0243     static inline void vflip_rev_azi(CT & rev_azi, CT const& azimuth12)
0244     {
0245         CT const c0 = 0;
0246         CT const pi = math::pi<CT>();
0247
0248         if (rev_azi == c0)
0249         {
0250             rev_azi = azimuth12 >= 0 ? pi : -pi;
0251         }
0252         else if (rev_azi > c0)
0253         {
0254             rev_azi = pi - rev_azi;
0255         }
0256         else
0257         {
0258             rev_azi = -pi - rev_azi;
0259         }
0260     }
0261
0262     static inline CT normalized1_1(CT const& value)
0263     {
0264         CT const c1 = 1;
0265         return value > c1 ? c1 :
0266                value < -c1 ? -c1 :
0267                value;
0268     }
0269 };
0270
0271 }}} // namespace boost::geometry::formula
0272
0273
0274 #endif // BOOST_GEOMETRY_FORMULAS_THOMAS_DIRECT_HPP