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// Boost.Geometry
// Copyright (c) 2017 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_AUTHALIC_RADIUS_SQR_HPP
#define BOOST_GEOMETRY_FORMULAS_AUTHALIC_RADIUS_SQR_HPP
#include <boost/geometry/core/radius.hpp>
#include <boost/geometry/core/tag.hpp>
#include <boost/geometry/core/tags.hpp>
#include <boost/geometry/formulas/eccentricity_sqr.hpp>
#include <boost/geometry/util/math.hpp>
#include <boost/geometry/algorithms/not_implemented.hpp>
#include <boost/math/special_functions/atanh.hpp>
namespace boost { namespace geometry
{
#ifndef DOXYGEN_NO_DISPATCH
namespace formula_dispatch
{
template <typename ResultType, typename Geometry, typename Tag = typename tag<Geometry>::type>
struct authalic_radius_sqr
: not_implemented<Tag>
{};
template <typename ResultType, typename Geometry>
struct authalic_radius_sqr<ResultType, Geometry, srs_sphere_tag>
{
static inline ResultType apply(Geometry const& geometry)
{
return math::sqr<ResultType>(get_radius<0>(geometry));
}
};
template <typename ResultType, typename Geometry>
struct authalic_radius_sqr<ResultType, Geometry, srs_spheroid_tag>
{
static inline ResultType apply(Geometry const& geometry)
{
ResultType const a2 = math::sqr<ResultType>(get_radius<0>(geometry));
ResultType const e2 = formula::eccentricity_sqr<ResultType>(geometry);
return apply(a2, e2);
}
static inline ResultType apply(ResultType const& a2, ResultType const& e2)
{
ResultType const c0 = 0;
if (math::equals(e2, c0))
{
return a2;
}
ResultType const e = math::sqrt(e2);
ResultType const c2 = 2;
//ResultType const b2 = math::sqr(get_radius<2>(geometry));
//return a2 / c2 + b2 * boost::math::atanh(e) / (c2 * e);
ResultType const c1 = 1;
return (a2 / c2) * ( c1 + (c1 - e2) * boost::math::atanh(e) / e );
}
};
} // namespace formula_dispatch
#endif // DOXYGEN_NO_DISPATCH
#ifndef DOXYGEN_NO_DETAIL
namespace formula
{
template <typename ResultType, typename Geometry>
inline ResultType authalic_radius_sqr(Geometry const& geometry)
{
return formula_dispatch::authalic_radius_sqr<ResultType, Geometry>::apply(geometry);
}
} // namespace formula
#endif // DOXYGEN_NO_DETAIL
}} // namespace boost::geometry
#endif // BOOST_GEOMETRY_FORMULAS_AUTHALIC_RADIUS_SQR_HPP
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