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// Boost.Geometry
// Copyright (c) 2023 Adam Wulkiewicz, Lodz, Poland.
// Copyright (c) 2017-2018 Oracle and/or its affiliates.
// Contributed and/or modified by Vissarion Fysikopoulos, 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_INVERSE_HPP
#define BOOST_GEOMETRY_FORMULAS_MERIDIAN_INVERSE_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/flattening.hpp>
#include <boost/geometry/formulas/meridian_segment.hpp>
namespace boost { namespace geometry { namespace formula
{
/*!
\brief Compute the arc length of an ellipse.
*/
template <typename CT, unsigned int Order = 1>
class meridian_inverse
{
public :
struct result
{
result()
: distance(0)
, meridian(false)
{}
CT distance;
bool meridian;
};
template <typename T>
static bool meridian_not_crossing_pole(T lat1, T lat2, CT diff)
{
CT half_pi = math::pi<CT>()/CT(2);
return math::equals(diff, CT(0)) ||
(math::equals(lat2, half_pi) && math::equals(lat1, -half_pi));
}
static bool meridian_crossing_pole(CT diff)
{
return math::equals(math::abs(diff), math::pi<CT>());
}
template <typename T, typename Spheroid>
static CT meridian_not_crossing_pole_dist(T lat1, T lat2, Spheroid const& spheroid)
{
return math::abs(apply(lat2, spheroid) - apply(lat1, spheroid));
}
template <typename T, typename Spheroid>
static CT meridian_crossing_pole_dist(T lat1, T lat2, Spheroid const& spheroid)
{
CT c0 = 0;
CT half_pi = math::pi<CT>()/CT(2);
CT lat_sign = 1;
if (lat1+lat2 < c0)
{
lat_sign = CT(-1);
}
return math::abs(lat_sign * CT(2) * apply(half_pi, spheroid)
- apply(lat1, spheroid) - apply(lat2, spheroid));
}
template <typename T, typename Spheroid>
static result apply(T lon1, T lat1, T lon2, T lat2, Spheroid const& spheroid)
{
result res;
CT diff = geometry::math::longitude_distance_signed<geometry::radian>(lon1, lon2);
if (lat1 > lat2)
{
std::swap(lat1, lat2);
}
if ( meridian_not_crossing_pole(lat1, lat2, diff) )
{
res.distance = meridian_not_crossing_pole_dist(lat1, lat2, spheroid);
res.meridian = true;
}
else if ( meridian_crossing_pole(diff) )
{
res.distance = meridian_crossing_pole_dist(lat1, lat2, spheroid);
res.meridian = true;
}
return res;
}
// Distance computation on meridians using series approximations
// to elliptic integrals. Formula to compute distance from lattitude 0 to lat
// https://en.wikipedia.org/wiki/Meridian_arc
// latitudes are assumed to be in radians and in [-pi/2,pi/2]
template <typename T, typename Spheroid>
static CT apply(T lat, Spheroid const& spheroid)
{
CT const a = get_radius<0>(spheroid);
CT const f = formula::flattening<CT>(spheroid);
CT n = f / (CT(2) - f);
CT M = a/(1+n);
CT C0 = 1;
if (BOOST_GEOMETRY_CONDITION(Order == 0))
{
return M * C0 * lat;
}
CT C2 = -1.5 * n;
if (BOOST_GEOMETRY_CONDITION(Order == 1))
{
return M * (C0 * lat + C2 * sin(2*lat));
}
CT n2 = n * n;
C0 += .25 * n2;
CT C4 = 0.9375 * n2;
if (BOOST_GEOMETRY_CONDITION(Order == 2))
{
return M * (C0 * lat + C2 * sin(2*lat) + C4 * sin(4*lat));
}
CT n3 = n2 * n;
C2 += 0.1875 * n3;
CT C6 = -0.729166667 * n3;
if (BOOST_GEOMETRY_CONDITION(Order == 3))
{
return M * (C0 * lat + C2 * sin(2*lat) + C4 * sin(4*lat)
+ C6 * sin(6*lat));
}
CT n4 = n2 * n2;
C4 -= 0.234375 * n4;
CT C8 = 0.615234375 * n4;
if (BOOST_GEOMETRY_CONDITION(Order == 4))
{
return M * (C0 * lat + C2 * sin(2*lat) + C4 * sin(4*lat)
+ C6 * sin(6*lat) + C8 * sin(8*lat));
}
CT n5 = n4 * n;
C6 += 0.227864583 * n5;
CT C10 = -0.54140625 * n5;
// Order 5 or higher
return M * (C0 * lat + C2 * sin(2*lat) + C4 * sin(4*lat)
+ C6 * sin(6*lat) + C8 * sin(8*lat) + C10 * sin(10*lat));
}
};
}}} // namespace boost::geometry::formula
#endif // BOOST_GEOMETRY_FORMULAS_MERIDIAN_INVERSE_HPP
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