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- #ifndef BOOST_GEOMETRY_PROJECTIONS_IMPL_PJ_GAUSS_HPP
- #define BOOST_GEOMETRY_PROJECTIONS_IMPL_PJ_GAUSS_HPP
- #include <boost/geometry/srs/projections/constants.hpp>
- #include <boost/geometry/srs/projections/exception.hpp>
- namespace boost { namespace geometry { namespace projections {
- namespace detail {
- template <typename T>
- struct gauss
- {
- T C;
- T K;
- T e;
- T ratexp;
- };
- template <typename T>
- inline T srat(T const& esinp, T const& exp)
- {
- return (math::pow((T(1) - esinp) / (T(1) + esinp), exp));
- }
- template <typename T>
- inline gauss<T> gauss_ini(T const& e, T const& phi0, T& chi, T& rc)
- {
- static const T fourth_pi = detail::fourth_pi<T>();
- using std::asin;
- using std::cos;
- using std::sin;
- using std::sqrt;
- using std::tan;
- T sphi = 0;
- T cphi = 0;
- T es = 0;
- gauss<T> en;
- es = e * e;
- en.e = e;
- sphi = sin(phi0);
- cphi = cos(phi0);
- cphi *= cphi;
- rc = sqrt(1.0 - es) / (1.0 - es * sphi * sphi);
- en.C = sqrt(1.0 + es * cphi * cphi / (1.0 - es));
- chi = asin(sphi / en.C);
- en.ratexp = 0.5 * en.C * e;
- en.K = tan(0.5 * chi + fourth_pi)
- / (math::pow(tan(T(0.5) * phi0 + fourth_pi), en.C) * srat(en.e * sphi, en.ratexp));
- return en;
- }
- template <typename T>
- inline void gauss_fwd(gauss<T> const& en, T& lam, T& phi)
- {
- static const T fourth_pi = detail::fourth_pi<T>();
- static const T half_pi = detail::half_pi<T>();
- phi = T(2) * atan(en.K * math::pow(tan(T(0.5) * phi + fourth_pi), en.C)
- * srat(en.e * sin(phi), en.ratexp) ) - half_pi;
- lam *= en.C;
- }
- template <typename T>
- inline void gauss_inv(gauss<T> const& en, T& lam, T& phi)
- {
- static const int max_iter = 20;
- static const T fourth_pi = detail::fourth_pi<T>();
- static const T half_pi = detail::half_pi<T>();
- static const T del_tol = 1e-14;
- lam /= en.C;
- const T num = math::pow(tan(T(0.5) * phi + fourth_pi) / en.K, T(1) / en.C);
- int i = 0;
- for (i = max_iter; i; --i)
- {
- const T elp_phi = 2.0 * atan(num * srat(en.e * sin(phi), - 0.5 * en.e)) - half_pi;
- if (geometry::math::abs(elp_phi - phi) < del_tol)
- {
- break;
- }
- phi = elp_phi;
- }
-
- if (!i)
- {
- BOOST_THROW_EXCEPTION( projection_exception(error_non_conv_inv_meri_dist) );
- }
- }
- }
- }}}
- #endif
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