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// Boost.Geometry
// Copyright (c) 2023 Adam Wulkiewicz, Lodz, Poland.
// Copyright (c) 2018 Oracle and/or its affiliates.
// Contributed and/or modified by Vissarion Fysikopoulos, on behalf of Oracle
// 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_MERIDIAN_DIRECT_HPP
#define BOOST_GEOMETRY_FORMULAS_MERIDIAN_DIRECT_HPP
#include <boost/math/constants/constants.hpp>
#include <boost/geometry/core/radius.hpp>
#include <boost/geometry/formulas/differential_quantities.hpp>
#include <boost/geometry/formulas/flattening.hpp>
#include <boost/geometry/formulas/meridian_inverse.hpp>
#include <boost/geometry/formulas/quarter_meridian.hpp>
#include <boost/geometry/formulas/result_direct.hpp>
#include <boost/geometry/util/condition.hpp>
#include <boost/geometry/util/math.hpp>
namespace boost { namespace geometry { namespace formula
{
/*!
\brief Compute the direct geodesic problem on a meridian
*/
template <
typename CT,
bool EnableCoordinates = true,
bool EnableReverseAzimuth = false,
bool EnableReducedLength = false,
bool EnableGeodesicScale = false,
unsigned int Order = 4
>
class meridian_direct
{
static const bool CalcQuantities = EnableReducedLength || EnableGeodesicScale;
static const bool CalcRevAzimuth = EnableReverseAzimuth || CalcQuantities;
static const bool CalcCoordinates = EnableCoordinates || CalcRevAzimuth;
public:
typedef result_direct<CT> result_type;
template <typename T, typename Dist, typename Spheroid>
static inline result_type apply(T const& lo1,
T const& la1,
Dist const& distance,
bool north,
Spheroid const& spheroid)
{
result_type result;
CT const half_pi = math::half_pi<CT>();
CT const pi = math::pi<CT>();
CT const one_and_a_half_pi = pi + half_pi;
CT const c0 = 0;
CT azimuth = north ? c0 : pi;
if (BOOST_GEOMETRY_CONDITION(CalcCoordinates))
{
CT s0 = meridian_inverse<CT, Order>::apply(la1, spheroid);
int signed_distance = north ? distance : -distance;
result.lon2 = lo1;
result.lat2 = apply(s0 + signed_distance, spheroid);
}
if (BOOST_GEOMETRY_CONDITION(CalcRevAzimuth))
{
result.reverse_azimuth = azimuth;
if (result.lat2 > half_pi &&
result.lat2 < one_and_a_half_pi)
{
result.reverse_azimuth = pi;
}
else if (result.lat2 < -half_pi &&
result.lat2 > -one_and_a_half_pi)
{
result.reverse_azimuth = c0;
}
}
if (BOOST_GEOMETRY_CONDITION(CalcQuantities))
{
CT const b = CT(get_radius<2>(spheroid));
CT const f = formula::flattening<CT>(spheroid);
boost::geometry::math::normalize_spheroidal_coordinates
<
boost::geometry::radian,
double
>(result.lon2, result.lat2);
typedef differential_quantities
<
CT,
EnableReducedLength,
EnableGeodesicScale,
Order
> quantities;
quantities::apply(lo1, la1, result.lon2, result.lat2,
azimuth, result.reverse_azimuth,
b, f,
result.reduced_length, result.geodesic_scale);
}
return result;
}
// https://en.wikipedia.org/wiki/Meridian_arc#The_inverse_meridian_problem_for_the_ellipsoid
// latitudes are assumed to be in radians and in [-pi/2,pi/2]
template <typename T, typename Spheroid>
static CT apply(T m, Spheroid const& spheroid)
{
CT const f = formula::flattening<CT>(spheroid);
CT n = f / (CT(2) - f);
CT mp = formula::quarter_meridian<CT>(spheroid);
CT mu = geometry::math::pi<CT>()/CT(2) * m / mp;
if (BOOST_GEOMETRY_CONDITION(Order == 0))
{
return mu;
}
CT H2 = 1.5 * n;
if (BOOST_GEOMETRY_CONDITION(Order == 1))
{
return mu + H2 * sin(2*mu);
}
CT n2 = n * n;
CT H4 = 1.3125 * n2;
if (BOOST_GEOMETRY_CONDITION(Order == 2))
{
return mu + H2 * sin(2*mu) + H4 * sin(4*mu);
}
CT n3 = n2 * n;
H2 -= 0.84375 * n3;
CT H6 = 1.572916667 * n3;
if (BOOST_GEOMETRY_CONDITION(Order == 3))
{
return mu + H2 * sin(2*mu) + H4 * sin(4*mu) + H6 * sin(6*mu);
}
CT n4 = n2 * n2;
H4 -= 1.71875 * n4;
CT H8 = 2.142578125 * n4;
// Order 4 or higher
return mu + H2 * sin(2*mu) + H4 * sin(4*mu) + H6 * sin(6*mu) + H8 * sin(8*mu);
}
};
}}} // namespace boost::geometry::formula
#endif // BOOST_GEOMETRY_FORMULAS_MERIDIAN_DIRECT_HPP
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