FM / formulas

/usr/include/boost/geometry/formulas

Name	Size	Mode	Actions
andoyer_inverse.hpp	9909	0644	edit dl rm
area_formulas.hpp	21897	0644	edit dl rm
authalic_radius_sqr.hpp	2654	0644	edit dl rm
differential_quantities.hpp	10976	0644	edit dl rm
eccentricity_sqr.hpp	1959	0644	edit dl rm
flattening.hpp	1847	0644	edit dl rm
geographic.hpp	14251	0644	edit dl rm
gnomonic_intersection.hpp	4905	0644	edit dl rm
gnomonic_spheroid.hpp	3989	0644	edit dl rm
interpolate_point_spherical.hpp	3586	0644	edit dl rm
karney_direct.hpp	10063	0644	edit dl rm
karney_inverse.hpp	35130	0644	edit dl rm
mean_radius.hpp	1894	0644	edit dl rm
meridian_direct.hpp	5139	0644	edit dl rm
meridian_inverse.hpp	4782	0644	edit dl rm
meridian_segment.hpp	2009	0644	edit dl rm
quarter_meridian.hpp	3174	0644	edit dl rm
result_direct.hpp	879	0644	edit dl rm
result_inverse.hpp	903	0644	edit dl rm
sjoberg_intersection.hpp	43099	0644	edit dl rm
spherical.hpp	8788	0644	edit dl rm
thomas_direct.hpp	9256	0644	edit dl rm
thomas_inverse.hpp	7768	0644	edit dl rm
unit_spheroid.hpp	1199	0644	edit dl rm
vertex_latitude.hpp	4489	0644	edit dl rm
vertex_longitude.hpp	10613	0644	edit dl rm
vincenty_direct.hpp	7105	0644	edit dl rm
vincenty_inverse.hpp	8254	0644	edit dl rm

Edit: /usr/include/boost/geometry/formulas/quarter_meridian.hpp (3174B)

// Boost.Geometry

// 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_QUARTER_MERIDIAN_HPP
#define BOOST_GEOMETRY_FORMULAS_QUARTER_MERIDIAN_HPP

#include <boost/geometry/algorithms/not_implemented.hpp>

#include <boost/geometry/core/radius.hpp>
#include <boost/geometry/core/tag.hpp>
#include <boost/geometry/core/tags.hpp>

#include <boost/geometry/formulas/flattening.hpp>

#include <boost/geometry/util/math.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

// Boost.Geometry // Copyright (c) 2018 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_QUARTER_MERIDIAN_HPP #define BOOST_GEOMETRY_FORMULAS_QUARTER_MERIDIAN_HPP #include #include #include #include #include #include namespace boost { namespace geometry { #ifndef DOXYGEN_NO_DISPATCH namespace formula_dispatch { template ::type> struct quarter_meridian : not_implemented {}; template struct quarter_meridian { //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(geometry); ResultType const n = f / (c2 - f); ResultType const ab4 = (get_radius<0>(geometry) + get_radius<2>(geometry)) / c4; return geometry::math::pi() * 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 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 ResultType quarter_meridian(Geometry const& geometry) { return formula_dispatch::quarter_meridian::apply(geometry); } } // namespace formula #endif // DOXYGEN_NO_DETAIL }} // namespace boost::geometry #endif // BOOST_GEOMETRY_FORMULAS_QUARTER_MERIDIAN_HPP