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// Boost.Geometry
// Copyright (c) 2016, 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_SPHERICAL_HPP
#define BOOST_GEOMETRY_FORMULAS_SPHERICAL_HPP
#include <boost/geometry/core/coordinate_system.hpp>
#include <boost/geometry/core/coordinate_type.hpp>
#include <boost/geometry/core/access.hpp>
#include <boost/geometry/core/radian_access.hpp>
//#include <boost/geometry/arithmetic/arithmetic.hpp>
#include <boost/geometry/arithmetic/cross_product.hpp>
#include <boost/geometry/arithmetic/dot_product.hpp>
#include <boost/geometry/util/math.hpp>
#include <boost/geometry/util/normalize_spheroidal_coordinates.hpp>
#include <boost/geometry/util/select_coordinate_type.hpp>
namespace boost { namespace geometry {
namespace formula {
template <typename T>
struct result_spherical
{
result_spherical()
: azimuth(0)
, reverse_azimuth(0)
{}
T azimuth;
T reverse_azimuth;
};
template <typename T>
static inline void sph_to_cart3d(T const& lon, T const& lat, T & x, T & y, T & z)
{
T const cos_lat = cos(lat);
x = cos_lat * cos(lon);
y = cos_lat * sin(lon);
z = sin(lat);
}
template <typename Point3d, typename PointSph>
static inline Point3d sph_to_cart3d(PointSph const& point_sph)
{
typedef typename coordinate_type<Point3d>::type calc_t;
calc_t const lon = get_as_radian<0>(point_sph);
calc_t const lat = get_as_radian<1>(point_sph);
calc_t x, y, z;
sph_to_cart3d(lon, lat, x, y, z);
Point3d res;
set<0>(res, x);
set<1>(res, y);
set<2>(res, z);
return res;
}
template <typename T>
static inline void cart3d_to_sph(T const& x, T const& y, T const& z, T & lon, T & lat)
{
lon = atan2(y, x);
lat = asin(z);
}
template <typename PointSph, typename Point3d>
static inline PointSph cart3d_to_sph(Point3d const& point_3d)
{
typedef typename coordinate_type<PointSph>::type coord_t;
typedef typename coordinate_type<Point3d>::type calc_t;
calc_t const x = get<0>(point_3d);
calc_t const y = get<1>(point_3d);
calc_t const z = get<2>(point_3d);
calc_t lonr, latr;
cart3d_to_sph(x, y, z, lonr, latr);
PointSph res;
set_from_radian<0>(res, lonr);
set_from_radian<1>(res, latr);
coord_t lon = get<0>(res);
coord_t lat = get<1>(res);
math::normalize_spheroidal_coordinates
<
typename coordinate_system<PointSph>::type::units,
coord_t
>(lon, lat);
set<0>(res, lon);
set<1>(res, lat);
return res;
}
// -1 right
// 1 left
// 0 on
template <typename Point3d1, typename Point3d2>
static inline int sph_side_value(Point3d1 const& norm, Point3d2 const& pt)
{
typedef typename select_coordinate_type<Point3d1, Point3d2>::type calc_t;
calc_t c0 = 0;
calc_t d = dot_product(norm, pt);
return math::equals(d, c0) ? 0
: d > c0 ? 1
: -1; // d < 0
}
template <typename CT, bool ReverseAzimuth, typename T1, typename T2>
static inline result_spherical<CT> spherical_azimuth(T1 const& lon1,
T1 const& lat1,
T2 const& lon2,
T2 const& lat2)
{
typedef result_spherical<CT> result_type;
result_type result;
// http://williams.best.vwh.net/avform.htm#Crs
// https://en.wikipedia.org/wiki/Great-circle_navigation
CT dlon = lon2 - lon1;
// An optimization which should kick in often for Boxes
//if ( math::equals(dlon, ReturnType(0)) )
//if ( get<0>(p1) == get<0>(p2) )
//{
// return - sin(get_as_radian<1>(p1)) * cos_p2lat);
//}
CT const cos_dlon = cos(dlon);
CT const sin_dlon = sin(dlon);
CT const cos_lat1 = cos(lat1);
CT const cos_lat2 = cos(lat2);
CT const sin_lat1 = sin(lat1);
CT const sin_lat2 = sin(lat2);
{
// "An alternative formula, not requiring the pre-computation of d"
// In the formula below dlon is used as "d"
CT const y = sin_dlon * cos_lat2;
CT const x = cos_lat1 * sin_lat2 - sin_lat1 * cos_lat2 * cos_dlon;
result.azimuth = atan2(y, x);
}
if (ReverseAzimuth)
{
CT const y = sin_dlon * cos_lat1;
CT const x = sin_lat2 * cos_lat1 * cos_dlon - cos_lat2 * sin_lat1;
result.reverse_azimuth = atan2(y, x);
}
return result;
}
template <typename ReturnType, typename T1, typename T2>
inline ReturnType spherical_azimuth(T1 const& lon1, T1 const& lat1,
T2 const& lon2, T2 const& lat2)
{
return spherical_azimuth<ReturnType, false>(lon1, lat1, lon2, lat2).azimuth;
}
template <typename T>
inline T spherical_azimuth(T const& lon1, T const& lat1, T const& lon2, T const& lat2)
{
return spherical_azimuth<T, false>(lon1, lat1, lon2, lat2).azimuth;
}
template <typename T>
inline int azimuth_side_value(T const& azi_a1_p, T const& azi_a1_a2)
{
T const pi = math::pi<T>();
T const two_pi = math::two_pi<T>();
// instead of the formula from XTD
//calc_t a_diff = asin(sin(azi_a1_p - azi_a1_a2));
T a_diff = azi_a1_p - azi_a1_a2;
// normalize, angle in [-pi, pi]
while (a_diff > pi)
a_diff -= two_pi;
while (a_diff < -pi)
a_diff += two_pi;
// NOTE: in general it shouldn't be required to support the pi/-pi case
// because in non-cartesian systems it makes sense to check the side
// only "between" the endpoints.
// However currently the winding strategy calls the side strategy
// for vertical segments to check if the point is "between the endpoints.
// This could be avoided since the side strategy is not required for that
// because meridian is the shortest path. So a difference of
// longitudes would be sufficient (of course normalized to [-pi, pi]).
// NOTE: with the above said, the pi/-pi check is temporary
// however in case if this was required
// the geodesics on ellipsoid aren't "symmetrical"
// therefore instead of comparing a_diff to pi and -pi
// one should probably use inverse azimuths and compare
// the difference to 0 as well
// positive azimuth is on the right side
return math::equals(a_diff, 0)
|| math::equals(a_diff, pi)
|| math::equals(a_diff, -pi) ? 0
: a_diff > 0 ? -1 // right
: 1; // left
}
} // namespace formula
}} // namespace boost::geometry
#endif // BOOST_GEOMETRY_FORMULAS_SPHERICAL_HPP
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