148 lines
4.4 KiB
C++
148 lines
4.4 KiB
C++
// Boost.Geometry
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// Copyright (c) 2016-2020 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_MAXIMUM_LATITUDE_HPP
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#define BOOST_GEOMETRY_FORMULAS_MAXIMUM_LATITUDE_HPP
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#include <boost/geometry/core/static_assert.hpp>
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#include <boost/geometry/formulas/flattening.hpp>
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#include <boost/geometry/formulas/spherical.hpp>
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namespace boost { namespace geometry { namespace formula
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{
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/*!
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\brief Algorithm to compute the vertex latitude of a geodesic segment. Vertex is
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a point on the geodesic that maximizes (or minimizes) the latitude.
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\author See
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[Wood96] Wood - Vertex Latitudes on Ellipsoid Geodesics, SIAM Rev., 38(4),
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637–644, 1996
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*/
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template <typename CT>
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class vertex_latitude_on_sphere
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{
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public:
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template<typename T1, typename T2>
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static inline CT apply(T1 const& lat1,
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T2 const& alp1)
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{
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return std::acos( math::abs(cos(lat1) * sin(alp1)) );
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}
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};
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template <typename CT>
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class vertex_latitude_on_spheroid
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{
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public:
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/*
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* formula based on paper
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* [Wood96] Wood - Vertex Latitudes on Ellipsoid Geodesics, SIAM Rev., 38(4),
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* 637–644, 1996
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template <typename T1, typename T2, typename Spheroid>
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static inline CT apply(T1 const& lat1,
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T2 const& alp1,
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Spheroid const& spheroid)
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{
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CT const f = formula::flattening<CT>(spheroid);
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CT const e2 = f * (CT(2) - f);
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CT const sin_alp1 = sin(alp1);
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CT const sin2_lat1 = math::sqr(sin(lat1));
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CT const cos2_lat1 = CT(1) - sin2_lat1;
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CT const e2_sin2 = CT(1) - e2 * sin2_lat1;
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CT const cos2_sin2 = cos2_lat1 * math::sqr(sin_alp1);
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CT const vertex_lat = std::asin( math::sqrt((e2_sin2 - cos2_sin2)
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/ (e2_sin2 - e2 * cos2_sin2)));
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return vertex_lat;
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}
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*/
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// simpler formula based on Clairaut relation for spheroids
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template <typename T1, typename T2, typename Spheroid>
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static inline CT apply(T1 const& lat1,
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T2 const& alp1,
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Spheroid const& spheroid)
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{
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CT const f = formula::flattening<CT>(spheroid);
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CT const one_minus_f = (CT(1) - f);
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//get the reduced latitude
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CT const bet1 = atan( one_minus_f * tan(lat1) );
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//apply Clairaut relation
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CT const betv = vertex_latitude_on_sphere<CT>::apply(bet1, alp1);
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//return the spheroid latitude
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return atan( tan(betv) / one_minus_f );
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}
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/*
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template <typename T>
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inline static void sign_adjustment(CT lat1, CT lat2, CT vertex_lat, T& vrt_result)
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{
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// signbit returns a non-zero value (true) if the sign is negative;
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// and zero (false) otherwise.
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bool sign = std::signbit(std::abs(lat1) > std::abs(lat2) ? lat1 : lat2);
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vrt_result.north = sign ? std::max(lat1, lat2) : vertex_lat;
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vrt_result.south = sign ? vertex_lat * CT(-1) : std::min(lat1, lat2);
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}
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template <typename T>
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inline static bool vertex_on_segment(CT alp1, CT alp2, CT lat1, CT lat2, T& vrt_result)
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{
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CT const half_pi = math::pi<CT>() / CT(2);
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// if the segment does not contain the vertex of the geodesic
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// then return the endpoint of max (min) latitude
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if ((alp1 < half_pi && alp2 < half_pi)
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|| (alp1 > half_pi && alp2 > half_pi))
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{
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vrt_result.north = std::max(lat1, lat2);
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vrt_result.south = std::min(lat1, lat2);
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return false;
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}
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return true;
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}
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*/
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};
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template <typename CT, typename CS_Tag>
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struct vertex_latitude
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{
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BOOST_GEOMETRY_STATIC_ASSERT_FALSE(
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"Not implemented for this coordinate system.",
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CT, CS_Tag);
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};
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template <typename CT>
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struct vertex_latitude<CT, spherical_equatorial_tag>
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: vertex_latitude_on_sphere<CT>
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{};
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template <typename CT>
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struct vertex_latitude<CT, geographic_tag>
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: vertex_latitude_on_spheroid<CT>
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{};
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}}} // namespace boost::geometry::formula
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#endif // BOOST_GEOMETRY_FORMULAS_MAXIMUM_LATITUDE_HPP
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