113 lines
3.1 KiB
C++
113 lines
3.1 KiB
C++
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// Boost.Geometry
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// Copyright (c) 2018 Oracle and/or its affiliates.
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// Contributed and/or modified by Vissarion Fysikopoulos, on behalf of Oracle
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// Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
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// Use, modification and distribution is subject to the Boost Software License,
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// Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_GEOMETRY_FORMULAS_QUARTER_MERIDIAN_HPP
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#define BOOST_GEOMETRY_FORMULAS_QUARTER_MERIDIAN_HPP
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#include <boost/geometry/algorithms/not_implemented.hpp>
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#include <boost/geometry/core/radius.hpp>
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#include <boost/geometry/core/tag.hpp>
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#include <boost/geometry/core/tags.hpp>
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#include <boost/geometry/formulas/flattening.hpp>
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#include <boost/geometry/util/math.hpp>
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namespace boost { namespace geometry
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{
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#ifndef DOXYGEN_NO_DISPATCH
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namespace formula_dispatch
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{
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template <typename ResultType, typename Geometry, typename Tag = typename tag<Geometry>::type>
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struct quarter_meridian
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: not_implemented<Tag>
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{};
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template <typename ResultType, typename Geometry>
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struct quarter_meridian<ResultType, Geometry, srs_spheroid_tag>
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{
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//https://en.wikipedia.org/wiki/Meridian_arc#Generalized_series
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//http://www.wolframalpha.com/input/?i=(sum(((2*j-3)!!%2F(2*j)!!)%5E2*n%5E(2*j),j,0,8))
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static inline ResultType apply(Geometry const& geometry)
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{
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//order 8 expansion
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ResultType const C[] =
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{
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1073741824,
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268435456,
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16777216,
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4194304,
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1638400,
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802816,
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451584,
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278784,
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184041
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};
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ResultType const c2 = 2;
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ResultType const c4 = 4;
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ResultType const f = formula::flattening<ResultType>(geometry);
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ResultType const n = f / (c2 - f);
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ResultType const ab4 = (get_radius<0>(geometry)
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+ get_radius<2>(geometry)) / c4;
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return geometry::math::pi<ResultType>() * ab4 *
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horner_evaluate(n*n, C, C+8) / C[0];
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}
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private :
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//TODO: move the following to a more general space to be used by other
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// classes as well
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/*
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Evaluate the polynomial in x using Horner's method.
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*/
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template <typename NT, typename IteratorType>
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static inline NT horner_evaluate(NT x,
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IteratorType begin,
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IteratorType end)
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{
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NT result(0);
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if (begin == end)
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{
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return result;
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}
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IteratorType it = end;
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do
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{
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result = result * x + *--it;
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}
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while (it != begin);
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return result;
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}
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};
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} // namespace formula_dispatch
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#endif // DOXYGEN_NO_DISPATCH
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#ifndef DOXYGEN_NO_DETAIL
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namespace formula
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{
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template <typename ResultType, typename Geometry>
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ResultType quarter_meridian(Geometry const& geometry)
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{
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return formula_dispatch::quarter_meridian<ResultType, Geometry>::apply(geometry);
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}
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} // namespace formula
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#endif // DOXYGEN_NO_DETAIL
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}} // namespace boost::geometry
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#endif // BOOST_GEOMETRY_FORMULAS_QUARTER_MERIDIAN_HPP
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