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// Boost.Geometry
// Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands.
// This file was modified by Oracle on 2014.
// Modifications copyright (c) 2014 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_ALGORITHMS_DETAIL_VINCENTY_INVERSE_HPP
#define BOOST_GEOMETRY_ALGORITHMS_DETAIL_VINCENTY_INVERSE_HPP
#include <boost/math/constants/constants.hpp>
#include <boost/geometry/core/radius.hpp>
#include <boost/geometry/core/srs.hpp>
#include <boost/geometry/util/math.hpp>
#include <boost/geometry/algorithms/detail/flattening.hpp>
#ifndef BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS
#define BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS 1000
#endif
namespace boost { namespace geometry { namespace detail
{
/*!
\brief The solution of the inverse problem of geodesics on latlong coordinates, after Vincenty, 1975
\author See
- http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf
- http://www.icsm.gov.au/gda/gdav2.3.pdf
\author Adapted from various implementations to get it close to the original document
- http://www.movable-type.co.uk/scripts/LatLongVincenty.html
- http://exogen.case.edu/projects/geopy/source/geopy.distance.html
- http://futureboy.homeip.net/fsp/colorize.fsp?fileName=navigation.frink
*/
template <typename CT>
class vincenty_inverse
{
public:
template <typename T1, typename T2, typename Spheroid>
vincenty_inverse(T1 const& lon1,
T1 const& lat1,
T2 const& lon2,
T2 const& lat2,
Spheroid const& spheroid)
: is_result_zero(false)
{
if (math::equals(lat1, lat2) && math::equals(lon1, lon2))
{
is_result_zero = true;
return;
}
CT const c1 = 1;
CT const c2 = 2;
CT const c3 = 3;
CT const c4 = 4;
CT const c16 = 16;
CT const c_e_12 = CT(1e-12);
CT const pi = geometry::math::pi<CT>();
CT const two_pi = c2 * pi;
// lambda: difference in longitude on an auxiliary sphere
CT L = lon2 - lon1;
CT lambda = L;
if (L < -pi) L += two_pi;
if (L > pi) L -= two_pi;
radius_a = CT(get_radius<0>(spheroid));
radius_b = CT(get_radius<2>(spheroid));
CT const flattening = geometry::detail::flattening<CT>(spheroid);
// U: reduced latitude, defined by tan U = (1-f) tan phi
CT const one_min_f = c1 - flattening;
CT const tan_U1 = one_min_f * tan(lat1); // above (1)
CT const tan_U2 = one_min_f * tan(lat2); // above (1)
// calculate sin U and cos U using trigonometric identities
CT const temp_den_U1 = math::sqrt(c1 + math::sqr(tan_U1));
CT const temp_den_U2 = math::sqrt(c1 + math::sqr(tan_U2));
// cos = 1 / sqrt(1 + tan^2)
cos_U1 = c1 / temp_den_U1;
cos_U2 = c1 / temp_den_U2;
// sin = tan / sqrt(1 + tan^2)
sin_U1 = tan_U1 / temp_den_U1;
sin_U2 = tan_U2 / temp_den_U2;
// calculate sin U and cos U directly
//CT const U1 = atan(tan_U1);
//CT const U2 = atan(tan_U2);
//cos_U1 = cos(U1);
//cos_U2 = cos(U2);
//sin_U1 = tan_U1 * cos_U1; // sin(U1);
//sin_U2 = tan_U2 * cos_U2; // sin(U2);
CT previous_lambda;
int counter = 0; // robustness
do
{
previous_lambda = lambda; // (13)
sin_lambda = sin(lambda);
cos_lambda = cos(lambda);
sin_sigma = math::sqrt(math::sqr(cos_U2 * sin_lambda) + math::sqr(cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda)); // (14)
CT cos_sigma = sin_U1 * sin_U2 + cos_U1 * cos_U2 * cos_lambda; // (15)
sin_alpha = cos_U1 * cos_U2 * sin_lambda / sin_sigma; // (17)
cos2_alpha = c1 - math::sqr(sin_alpha);
cos2_sigma_m = math::equals(cos2_alpha, 0) ? 0 : cos_sigma - c2 * sin_U1 * sin_U2 / cos2_alpha; // (18)
CT C = flattening/c16 * cos2_alpha * (c4 + flattening * (c4 - c3 * cos2_alpha)); // (10)
sigma = atan2(sin_sigma, cos_sigma); // (16)
lambda = L + (c1 - C) * flattening * sin_alpha *
(sigma + C * sin_sigma * ( cos2_sigma_m + C * cos_sigma * (-c1 + c2 * math::sqr(cos2_sigma_m)))); // (11)
++counter; // robustness
} while ( geometry::math::abs(previous_lambda - lambda) > c_e_12
&& geometry::math::abs(lambda) < pi
&& counter < BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS ); // robustness
}
inline CT distance() const
{
if ( is_result_zero )
{
return CT(0);
}
// Oops getting hard here
// (again, problem is that ttmath cannot divide by doubles, which is OK)
CT const c1 = 1;
CT const c2 = 2;
CT const c3 = 3;
CT const c4 = 4;
CT const c6 = 6;
CT const c47 = 47;
CT const c74 = 74;
CT const c128 = 128;
CT const c256 = 256;
CT const c175 = 175;
CT const c320 = 320;
CT const c768 = 768;
CT const c1024 = 1024;
CT const c4096 = 4096;
CT const c16384 = 16384;
//CT sqr_u = cos2_alpha * (math::sqr(radius_a) - math::sqr(radius_b)) / math::sqr(radius_b); // above (1)
CT sqr_u = cos2_alpha * ( math::sqr(radius_a / radius_b) - c1 ); // above (1)
CT A = c1 + sqr_u/c16384 * (c4096 + sqr_u * (-c768 + sqr_u * (c320 - c175 * sqr_u))); // (3)
CT B = sqr_u/c1024 * (c256 + sqr_u * ( -c128 + sqr_u * (c74 - c47 * sqr_u))); // (4)
CT delta_sigma = B * sin_sigma * ( cos2_sigma_m + (B/c4) * (cos(sigma)* (-c1 + c2 * cos2_sigma_m)
- (B/c6) * cos2_sigma_m * (-c3 + c4 * math::sqr(sin_sigma)) * (-c3 + c4 * cos2_sigma_m))); // (6)
return radius_b * A * (sigma - delta_sigma); // (19)
}
inline CT azimuth12() const
{
return is_result_zero ?
CT(0) :
atan2(cos_U2 * sin_lambda, cos_U1 * sin_U2 - sin_U1 * cos_U2 * cos_lambda); // (20)
}
inline CT azimuth21() const
{
// NOTE: signs of X and Y are different than in the original paper
return is_result_zero ?
CT(0) :
atan2(-cos_U1 * sin_lambda, sin_U1 * cos_U2 - cos_U1 * sin_U2 * cos_lambda); // (21)
}
private:
// alpha: azimuth of the geodesic at the equator
CT cos2_alpha;
CT sin_alpha;
// sigma: angular distance p1,p2 on the sphere
// sigma1: angular distance on the sphere from the equator to p1
// sigma_m: angular distance on the sphere from the equator to the midpoint of the line
CT sigma;
CT sin_sigma;
CT cos2_sigma_m;
CT sin_lambda;
CT cos_lambda;
// set only once
CT cos_U1;
CT cos_U2;
CT sin_U1;
CT sin_U2;
// set only once
CT radius_a;
CT radius_b;
bool is_result_zero;
};
}}} // namespace boost::geometry::detail
#endif // BOOST_GEOMETRY_ALGORITHMS_DETAIL_VINCENTY_INVERSE_HPP
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