Imported Upstream version 1.63.0upstream/1.63.0

Change-Id: Iac85556a04b7e58d63ba636dedb0986e3555714a
Signed-off-by: DongHun Kwak <dh0128.kwak@samsung.com>

1 files changed, 249 insertions, 0 deletions

diff --git a/boost/geometry/formulas/thomas_direct.hpp b/boost/geometry/formulas/thomas_direct.hpp
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+// Boost.Geometry
+
+// Copyright (c) 2016 Oracle and/or its affiliates.
+
+// Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
+
+// Use, modification and distribution is subject to the Boost Software License,
+// Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_GEOMETRY_FORMULAS_THOMAS_DIRECT_HPP
+#define BOOST_GEOMETRY_FORMULAS_THOMAS_DIRECT_HPP
+
+
+#include <boost/math/constants/constants.hpp>
+
+#include <boost/geometry/core/radius.hpp>
+#include <boost/geometry/core/srs.hpp>
+
+#include <boost/geometry/util/condition.hpp>
+#include <boost/geometry/util/math.hpp>
+
+#include <boost/geometry/algorithms/detail/flattening.hpp>
+
+#include <boost/geometry/formulas/differential_quantities.hpp>
+#include <boost/geometry/formulas/result_direct.hpp>
+
+
+namespace boost { namespace geometry { namespace formula
+{
+
+
+/*!
+\brief The solution of the direct problem of geodesics on latlong coordinates,
+       Forsyth-Andoyer-Lambert type approximation with second order terms.
+\author See
+    - Technical Report: PAUL D. THOMAS, MATHEMATICAL MODELS FOR NAVIGATION SYSTEMS, 1965
+      http://www.dtic.mil/docs/citations/AD0627893
+    - Technical Report: PAUL D. THOMAS, SPHEROIDAL GEODESICS, REFERENCE SYSTEMS, AND LOCAL GEOMETRY, 1970
+      http://www.dtic.mil/docs/citations/AD0703541
+
+*/
+template <
+    typename CT,
+    bool EnableCoordinates = true,
+    bool EnableReverseAzimuth = false,
+    bool EnableReducedLength = false,
+    bool EnableGeodesicScale = false
+>
+class thomas_direct
+{
+    static const bool CalcQuantities = EnableReducedLength || EnableGeodesicScale;
+    static const bool CalcCoordinates = EnableCoordinates || CalcQuantities;
+    static const bool CalcRevAzimuth = EnableReverseAzimuth || CalcCoordinates || CalcQuantities;
+
+public:
+    typedef result_direct<CT> result_type;
+
+    template <typename T, typename Dist, typename Azi, typename Spheroid>
+    static inline result_type apply(T const& lo1,
+                                    T const& la1,
+                                    Dist const& distance,
+                                    Azi const& azimuth12,
+                                    Spheroid const& spheroid)
+    {
+        result_type result;
+
+        CT const lon1 = lo1;
+        CT const lat1 = la1;
+
+        if ( math::equals(distance, Dist(0)) || distance < Dist(0) )
+        {
+            result.lon2 = lon1;
+            result.lat2 = lat1;
+            return result;
+        }
+
+        CT const c0 = 0;
+        CT const c1 = 1;
+        CT const c2 = 2;
+        CT const c4 = 4;
+
+        CT const a = CT(get_radius<0>(spheroid));
+        CT const b = CT(get_radius<2>(spheroid));
+        CT const f = detail::flattening<CT>(spheroid);
+        CT const one_minus_f = c1 - f;
+
+        CT const pi = math::pi<CT>();
+        CT const pi_half = pi / c2;
+
+        // keep azimuth small - experiments show low accuracy
+        // if the azimuth is closer to (+-)180 deg.
+        CT azi12_alt = azimuth12;
+        CT lat1_alt = lat1;
+        bool alter_result = vflip_if_south(lat1, azimuth12, lat1_alt, azi12_alt);
+        
+        CT const theta1 = math::equals(lat1_alt, pi_half) ? lat1_alt :
+                          math::equals(lat1_alt, -pi_half) ? lat1_alt :
+                          atan(one_minus_f * tan(lat1_alt));
+        CT const sin_theta1 = sin(theta1);
+        CT const cos_theta1 = cos(theta1);
+
+        CT const sin_a12 = sin(azi12_alt);
+        CT const cos_a12 = cos(azi12_alt);
+
+        CT const M = cos_theta1 * sin_a12; // cos_theta0
+        CT const theta0 = acos(M);
+        CT const sin_theta0 = sin(theta0);
+
+        CT const N = cos_theta1 * cos_a12;
+        CT const C1 = f * M; // lower-case c1 in the technical report
+        CT const C2 = f * (c1 - math::sqr(M)) / c4; // lower-case c2 in the technical report
+        CT const D = (c1 - C2) * (c1 - C2 - C1 * M);
+        CT const P = C2 * (c1 + C1 * M / c2) / D;
+
+        // special case for equator:
+        // sin_theta0 = 0 <=> lat1 = 0 ^ |azimuth12| = pi/2
+        // NOTE: in this case it doesn't matter what's the value of cos_sigma1 because
+        //       theta1=0, theta0=0, M=1|-1, C2=0 so X=0 and Y=0 so d_sigma=d
+        //       cos_a12=0 so N=0, therefore
+        //       lat2=0, azi21=pi/2|-pi/2
+        //       d_eta = atan2(sin_d_sigma, cos_d_sigma)
+        //       H = C1 * d_sigma
+        CT const cos_sigma1 = math::equals(sin_theta0, c0)
+                                ? c1
+                                : normalized1_1(sin_theta1 / sin_theta0);
+        CT const sigma1 = acos(cos_sigma1);
+        CT const d = distance / (a * D);
+        CT const u = 2 * (sigma1 - d);
+        CT const cos_d = cos(d);
+        CT const sin_d = sin(d);
+        CT const cos_u = cos(u);
+        CT const sin_u = sin(u);
+
+        CT const W = c1 - c2 * P * cos_u;
+        CT const V = cos_u * cos_d - sin_u * sin_d;
+        CT const X = math::sqr(C2) * sin_d * cos_d * (2 * math::sqr(V) - c1);
+        CT const Y = c2 * P * V * W * sin_d;
+        CT const d_sigma = d + X - Y;
+        CT const sin_d_sigma = sin(d_sigma);
+        CT const cos_d_sigma = cos(d_sigma);
+
+        if (BOOST_GEOMETRY_CONDITION(CalcRevAzimuth))
+        {
+            result.reverse_azimuth = atan2(M, N * cos_d_sigma - sin_theta1 * sin_d_sigma);
+
+            if (alter_result)
+            {
+                vflip_rev_azi(result.reverse_azimuth, azimuth12);
+            }
+        }
+
+        if (BOOST_GEOMETRY_CONDITION(CalcCoordinates))
+        {
+            CT const S_sigma = c2 * sigma1 - d_sigma;
+            CT const cos_S_sigma = cos(S_sigma);
+            CT const d_eta = atan2(sin_d_sigma * sin_a12, cos_theta1 * cos_d_sigma - sin_theta1 * sin_d_sigma * cos_a12);
+            CT const H = C1 * (c1 - C2) * d_sigma - C1 * C2 * sin_d_sigma * cos_S_sigma;
+            CT const d_lambda = d_eta - H;
+            
+            result.lon2 = lon1 + d_lambda;
+
+            if (! math::equals(M, c0))
+            {
+                CT const sin_a21 = sin(result.reverse_azimuth);
+                CT const tan_theta2 = (sin_theta1 * cos_d_sigma + N * sin_d_sigma) * sin_a21 / M;
+                result.lat2 = atan(tan_theta2 / one_minus_f);
+            }
+            else
+            {
+                CT const sigma2 = S_sigma - sigma1;
+                //theta2 = asin(cos(sigma2)) <=> sin_theta0 = 1
+                CT const tan_theta2 = cos(sigma2) / sin(sigma2);
+                result.lat2 = atan(tan_theta2 / one_minus_f);
+            }
+
+            if (alter_result)
+            {
+                result.lat2 = -result.lat2;
+            }
+        }        
+
+        if (BOOST_GEOMETRY_CONDITION(CalcQuantities))
+        {
+            typedef differential_quantities<CT, EnableReducedLength, EnableGeodesicScale, 2> quantities;
+            quantities::apply(lon1, lat1, result.lon2, result.lat2,
+                              azimuth12, result.reverse_azimuth,
+                              b, f,
+                              result.reduced_length, result.geodesic_scale);
+        }
+
+        return result;
+    }
+
+private:
+    static inline bool vflip_if_south(CT const& lat1, CT const& azi12, CT & lat1_alt, CT & azi12_alt)
+    {
+        CT const c2 = 2;
+        CT const pi = math::pi<CT>();
+        CT const pi_half = pi / c2;
+
+        if (azi12 > pi_half)
+        {
+            azi12_alt = pi - azi12;
+            lat1_alt = -lat1;
+            return true;
+        }
+        else if (azi12 < -pi_half)
+        {
+            azi12_alt = -pi - azi12;
+            lat1_alt = -lat1;
+            return true;
+        }
+
+        return false;
+    }
+
+    static inline void vflip_rev_azi(CT & rev_azi, CT const& azimuth12)
+    {
+        CT const c0 = 0;
+        CT const pi = math::pi<CT>();
+
+        if (rev_azi == c0)
+        {
+            rev_azi = azimuth12 >= 0 ? pi : -pi;
+        }
+        else if (rev_azi > c0)
+        {
+            rev_azi = pi - rev_azi;
+        }
+        else
+        {
+            rev_azi = -pi - rev_azi;
+        }
+    }
+
+    static inline CT normalized1_1(CT const& value)
+    {
+        CT const c1 = 1;
+        return value > c1 ? c1 :
+               value < -c1 ? -c1 :
+               value;
+    }
+};
+
+}}} // namespace boost::geometry::formula
+
+
+#endif // BOOST_GEOMETRY_FORMULAS_THOMAS_DIRECT_HPP