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// Boost.Geometry
// Copyright (c) 2021, Oracle and/or its affiliates.
// Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
// Licensed under the Boost Software License version 1.0.
// http://www.boost.org/users/license.html
#ifndef BOOST_GEOMETRY_STRATEGY_SPHERICAL_AREA_BOX_HPP
#define BOOST_GEOMETRY_STRATEGY_SPHERICAL_AREA_BOX_HPP
#include <boost/geometry/core/coordinate_type.hpp>
#include <boost/geometry/core/coordinate_dimension.hpp>
#include <boost/geometry/core/radian_access.hpp>
#include <boost/geometry/srs/sphere.hpp>
#include <boost/geometry/strategies/spherical/get_radius.hpp>
#include <boost/geometry/strategy/area.hpp>
#include <boost/geometry/util/normalize_spheroidal_box_coordinates.hpp>
namespace boost { namespace geometry
{
namespace strategy { namespace area
{
// https://math.stackexchange.com/questions/131735/surface-element-in-spherical-coordinates
// http://www.cs.cmu.edu/afs/cs/academic/class/16823-s16/www/pdfs/appearance-modeling-3.pdf
// https://www.astronomyclub.xyz/celestial-sphere-2/solid-angle-on-the-celestial-sphere.html
// https://mathworld.wolfram.com/SolidAngle.html
// https://en.wikipedia.org/wiki/Spherical_coordinate_system
// Note that the equations used in the above articles are spherical polar coordinates.
// We use spherical equatorial, so the equation is different:
// assume(y_max > y_min);
// assume(x_max > x_min);
// /* because of polar to equatorial conversion */
// sin(%pi / 2 - y);
// O: r ^ 2 * cos(y);
// S: integrate(integrate(O, y, y_min, y_max), x, x_min, x_max);
template
<
typename RadiusTypeOrSphere = double,
typename CalculationType = void
>
class spherical_box
{
typedef typename strategy_detail::get_radius
<
RadiusTypeOrSphere
>::type radius_type;
public:
template <typename Box>
struct result_type
: strategy::area::detail::result_type
<
Box,
CalculationType
>
{};
// For consistency with other strategies the radius is set to 1
inline spherical_box()
: m_radius(1.0)
{}
template <typename RadiusOrSphere>
explicit inline spherical_box(RadiusOrSphere const& radius_or_sphere)
: m_radius(strategy_detail::get_radius
<
RadiusOrSphere
>::apply(radius_or_sphere))
{}
template <typename Box>
inline auto apply(Box const& box) const
{
typedef typename result_type<Box>::type return_type;
return_type x_min = get_as_radian<min_corner, 0>(box); // lon
return_type y_min = get_as_radian<min_corner, 1>(box); // lat
return_type x_max = get_as_radian<max_corner, 0>(box);
return_type y_max = get_as_radian<max_corner, 1>(box);
if (x_min == x_max || y_max == y_min)
{
return return_type(0);
}
math::normalize_spheroidal_box_coordinates<radian>(x_min, y_min, x_max, y_max);
return (x_max - x_min)
* (sin(y_max) - sin(y_min))
* return_type(m_radius * m_radius);
}
srs::sphere<radius_type> model() const
{
return srs::sphere<radius_type>(m_radius);
}
private:
radius_type m_radius;
};
}} // namespace strategy::area
}} // namespace boost::geometry
#endif // BOOST_GEOMETRY_STRATEGY_SPHERICAL_AREA_BOX_HPP
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