geometry/formulas/authalic_radius_sqr.hpp

0001 // Boost.Geometry
0002
0003 // Copyright (c) 2017 Oracle and/or its affiliates.
0004
0005 // Contributed and/or modified by Adam Wulkiewicz, on behalf of Oracle
0006
0007 // Use, modification and distribution is subject to the Boost Software License,
0008 // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
0009 // http://www.boost.org/LICENSE_1_0.txt)
0010
0011 #ifndef BOOST_GEOMETRY_FORMULAS_AUTHALIC_RADIUS_SQR_HPP
0012 #define BOOST_GEOMETRY_FORMULAS_AUTHALIC_RADIUS_SQR_HPP
0013
0014 #include <boost/geometry/core/radius.hpp>
0015 #include <boost/geometry/core/tag.hpp>
0016 #include <boost/geometry/core/tags.hpp>
0017
0018 #include <boost/geometry/formulas/eccentricity_sqr.hpp>
0019
0020 #include <boost/geometry/util/math.hpp>
0021
0022 #include <boost/geometry/algorithms/not_implemented.hpp>
0023
0024 #include <boost/math/special_functions/atanh.hpp>
0025
0026 namespace boost { namespace geometry
0027 {
0028
0029 #ifndef DOXYGEN_NO_DISPATCH
0030 namespace formula_dispatch
0031 {
0032
0033 template <typename ResultType, typename Geometry, typename Tag = typename tag<Geometry>::type>
0034 struct authalic_radius_sqr
0035     : not_implemented<Tag>
0036 {};
0037
0038 template <typename ResultType, typename Geometry>
0039 struct authalic_radius_sqr<ResultType, Geometry, srs_sphere_tag>
0040 {
0041     static inline ResultType apply(Geometry const& geometry)
0042     {
0043         return math::sqr<ResultType>(get_radius<0>(geometry));
0044     }
0045 };
0046
0047 template <typename ResultType, typename Geometry>
0048 struct authalic_radius_sqr<ResultType, Geometry, srs_spheroid_tag>
0049 {
0050     static inline ResultType apply(Geometry const& geometry)
0051     {
0052         ResultType const a2 = math::sqr<ResultType>(get_radius<0>(geometry));
0053         ResultType const e2 = formula::eccentricity_sqr<ResultType>(geometry);
0054
0055         return apply(a2, e2);
0056     }
0057
0058     static inline ResultType apply(ResultType const& a2, ResultType const& e2)
0059     {
0060         ResultType const c0 = 0;
0061
0062         if (math::equals(e2, c0))
0063         {
0064             return a2;
0065         }
0066
0067         ResultType const e = math::sqrt(e2);
0068         ResultType const c2 = 2;
0069
0070         //ResultType const b2 = math::sqr(get_radius<2>(geometry));
0071         //return a2 / c2 + b2 * boost::math::atanh(e) / (c2 * e);
0072
0073         ResultType const c1 = 1;
0074         return (a2 / c2) * ( c1 + (c1 - e2) * boost::math::atanh(e) / e );
0075     }
0076 };
0077
0078 } // namespace formula_dispatch
0079 #endif // DOXYGEN_NO_DISPATCH
0080
0081 #ifndef DOXYGEN_NO_DETAIL
0082 namespace formula
0083 {
0084
0085 template <typename ResultType, typename Geometry>
0086 inline ResultType authalic_radius_sqr(Geometry const& geometry)
0087 {
0088     return formula_dispatch::authalic_radius_sqr<ResultType, Geometry>::apply(geometry);
0089 }
0090
0091 } // namespace formula
0092 #endif // DOXYGEN_NO_DETAIL
0093
0094 }} // namespace boost::geometry
0095
0096 #endif // BOOST_GEOMETRY_FORMULAS_AUTHALIC_RADIUS_SQR_HPP