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// Boost.Geometry
// Copyright (c) 2007-2012 Barend Gehrels, Amsterdam, the Netherlands.
// This file was modified by Oracle on 2014-2020.
// Modifications copyright (c) 2014-2020 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_VINCENTY_DIRECT_HPP
#define BOOST_GEOMETRY_FORMULAS_VINCENTY_DIRECT_HPP
#include <boost/math/constants/constants.hpp>
#include <boost/geometry/core/radius.hpp>
#include <boost/geometry/util/condition.hpp>
#include <boost/geometry/util/math.hpp>
#include <boost/geometry/util/normalize_spheroidal_coordinates.hpp>
#include <boost/geometry/formulas/differential_quantities.hpp>
#include <boost/geometry/formulas/flattening.hpp>
#include <boost/geometry/formulas/result_direct.hpp>
#ifndef BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS
#define BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS 1000
#endif
namespace boost { namespace geometry { namespace formula
{
/*!
\brief The solution of the direct 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,
bool EnableCoordinates = true,
bool EnableReverseAzimuth = false,
bool EnableReducedLength = false,
bool EnableGeodesicScale = false
>
class vincenty_direct
{
static const bool CalcQuantities = EnableReducedLength || EnableGeodesicScale;
static const bool CalcCoordinates = EnableCoordinates || CalcQuantities;
static const bool CalcRevAzimuth = EnableReverseAzimuth || 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;
CT const radius_a = CT(get_radius<0>(spheroid));
CT const radius_b = CT(get_radius<2>(spheroid));
CT const flattening = formula::flattening<CT>(spheroid);
CT const sin_azimuth12 = sin(azimuth12);
CT const cos_azimuth12 = cos(azimuth12);
// U: reduced latitude, defined by tan U = (1-f) tan phi
CT const one_min_f = CT(1) - flattening;
CT const tan_U1 = one_min_f * tan(lat1);
CT const sigma1 = atan2(tan_U1, cos_azimuth12); // (1)
// may be calculated from tan using 1 sqrt()
CT const U1 = atan(tan_U1);
CT const sin_U1 = sin(U1);
CT const cos_U1 = cos(U1);
CT const sin_alpha = cos_U1 * sin_azimuth12; // (2)
CT const sin_alpha_sqr = math::sqr(sin_alpha);
CT const cos_alpha_sqr = CT(1) - sin_alpha_sqr;
CT const b_sqr = radius_b * radius_b;
CT const u_sqr = cos_alpha_sqr * (radius_a * radius_a - b_sqr) / b_sqr;
CT const A = CT(1) + (u_sqr/CT(16384)) * (CT(4096) + u_sqr*(CT(-768) + u_sqr*(CT(320) - u_sqr*CT(175)))); // (3)
CT const B = (u_sqr/CT(1024))*(CT(256) + u_sqr*(CT(-128) + u_sqr*(CT(74) - u_sqr*CT(47)))); // (4)
CT s_div_bA = distance / (radius_b * A);
CT sigma = s_div_bA; // (7)
CT previous_sigma;
CT sin_sigma;
CT cos_sigma;
CT cos_2sigma_m;
CT cos_2sigma_m_sqr;
int counter = 0; // robustness
do
{
previous_sigma = sigma;
CT const two_sigma_m = CT(2) * sigma1 + sigma; // (5)
sin_sigma = sin(sigma);
cos_sigma = cos(sigma);
CT const sin_sigma_sqr = math::sqr(sin_sigma);
cos_2sigma_m = cos(two_sigma_m);
cos_2sigma_m_sqr = math::sqr(cos_2sigma_m);
CT const delta_sigma = B * sin_sigma * (cos_2sigma_m
+ (B/CT(4)) * ( cos_sigma * (CT(-1) + CT(2)*cos_2sigma_m_sqr)
- (B/CT(6) * cos_2sigma_m * (CT(-3)+CT(4)*sin_sigma_sqr) * (CT(-3)+CT(4)*cos_2sigma_m_sqr)) )); // (6)
sigma = s_div_bA + delta_sigma; // (7)
++counter; // robustness
} while ( geometry::math::abs(previous_sigma - sigma) > CT(1e-12)
//&& geometry::math::abs(sigma) < pi
&& counter < BOOST_GEOMETRY_DETAIL_VINCENTY_MAX_STEPS ); // robustness
if (BOOST_GEOMETRY_CONDITION(CalcCoordinates))
{
result.lat2
= atan2( sin_U1 * cos_sigma + cos_U1 * sin_sigma * cos_azimuth12,
one_min_f * math::sqrt(sin_alpha_sqr + math::sqr(sin_U1 * sin_sigma - cos_U1 * cos_sigma * cos_azimuth12))); // (8)
CT const lambda = atan2( sin_sigma * sin_azimuth12,
cos_U1 * cos_sigma - sin_U1 * sin_sigma * cos_azimuth12); // (9)
CT const C = (flattening/CT(16)) * cos_alpha_sqr * ( CT(4) + flattening * ( CT(4) - CT(3) * cos_alpha_sqr ) ); // (10)
CT const L = lambda - (CT(1) - C) * flattening * sin_alpha
* ( sigma + C * sin_sigma * ( cos_2sigma_m + C * cos_sigma * ( CT(-1) + CT(2) * cos_2sigma_m_sqr ) ) ); // (11)
result.lon2 = lon1 + L;
}
if (BOOST_GEOMETRY_CONDITION(CalcRevAzimuth))
{
result.reverse_azimuth
= atan2(sin_alpha, -sin_U1 * sin_sigma + cos_U1 * cos_sigma * cos_azimuth12); // (12)
}
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,
radius_b, flattening,
result.reduced_length, result.geodesic_scale);
}
if (BOOST_GEOMETRY_CONDITION(CalcCoordinates))
{
// For longitudes close to the antimeridian the result can be out
// of range. Therefore normalize.
// It has to be done at the end because otherwise differential
// quantities are calculated incorrectly.
math::detail::normalize_angle_cond<radian>(result.lon2);
}
return result;
}
};
}}} // namespace boost::geometry::formula
#endif // BOOST_GEOMETRY_FORMULAS_VINCENTY_DIRECT_HPP
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