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// Boost.Geometry
// Copyright (c) 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_QUARTER_MERIDIAN_HPP
#define BOOST_GEOMETRY_FORMULAS_QUARTER_MERIDIAN_HPP
#include <boost/geometry/core/radius.hpp>
#include <boost/geometry/core/tag.hpp>
#include <boost/geometry/core/tags.hpp>
#include <boost/geometry/algorithms/not_implemented.hpp>
namespace boost { namespace geometry
{
#ifndef DOXYGEN_NO_DISPATCH
namespace formula_dispatch
{
template <typename ResultType, typename Geometry, typename Tag = typename tag<Geometry>::type>
struct quarter_meridian
: not_implemented<Tag>
{};
template <typename ResultType, typename Geometry>
struct quarter_meridian<ResultType, Geometry, srs_spheroid_tag>
{
//https://en.wikipedia.org/wiki/Meridian_arc#Generalized_series
//http://www.wolframalpha.com/input/?i=(sum(((2*j-3)!!%2F(2*j)!!)%5E2*n%5E(2*j),j,0,8))
static inline ResultType apply(Geometry const& geometry)
{
//order 8 expansion
ResultType const C[] =
{
1073741824,
268435456,
16777216,
4194304,
1638400,
802816,
451584,
278784,
184041
};
ResultType const c2 = 2;
ResultType const c4 = 4;
ResultType const f = formula::flattening<ResultType>(geometry);
ResultType const n = f / (c2 - f);
ResultType const ab4 = (get_radius<0>(geometry)
+ get_radius<2>(geometry)) / c4;
return geometry::math::pi<ResultType>() * ab4 *
horner_evaluate(n*n, C, C+8) / C[0];
}
private :
//TODO: move the following to a more general space to be used by other
// classes as well
/*
Evaluate the polynomial in x using Horner's method.
*/
template <typename NT, typename IteratorType>
static inline NT horner_evaluate(NT x,
IteratorType begin,
IteratorType end)
{
NT result(0);
if (begin == end)
{
return result;
}
IteratorType it = end;
do
{
result = result * x + *--it;
}
while (it != begin);
return result;
}
};
} // namespace formula_dispatch
#endif // DOXYGEN_NO_DISPATCH
#ifndef DOXYGEN_NO_DETAIL
namespace formula
{
template <typename ResultType, typename Geometry>
ResultType quarter_meridian(Geometry const& geometry)
{
return formula_dispatch::quarter_meridian<ResultType, Geometry>::apply(geometry);
}
} // namespace formula
#endif // DOXYGEN_NO_DETAIL
}} // namespace boost::geometry
#endif // BOOST_GEOMETRY_FORMULAS_QUARTER_MERIDIAN_HPP
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