111 lines
3.6 KiB
C++
111 lines
3.6 KiB
C++
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// Boost.Geometry
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// Copyright (c) 2019-2021 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_INTERPOLATE_POINT_SPHERICAL_HPP
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#define BOOST_GEOMETRY_FORMULAS_INTERPOLATE_POINT_SPHERICAL_HPP
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#include <boost/geometry/formulas/spherical.hpp>
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#include <boost/geometry/geometries/point.hpp>
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namespace boost { namespace geometry { namespace formula
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{
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template <typename CalculationType>
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class interpolate_point_spherical
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{
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typedef model::point<CalculationType, 3, cs::cartesian> point3d_t;
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public :
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template <typename Point>
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void compute_angle(Point const& p0,
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Point const& p1,
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CalculationType& angle01)
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{
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m_xyz0 = formula::sph_to_cart3d<point3d_t>(p0);
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m_xyz1 = formula::sph_to_cart3d<point3d_t>(p1);
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CalculationType const dot01 = geometry::dot_product(m_xyz0, m_xyz1);
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angle01 = acos(dot01);
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}
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template <typename Point>
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void compute_axis(Point const& p0,
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CalculationType const& angle01)
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{
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CalculationType const c0 = 0, c1 = 1;
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CalculationType const pi = math::pi<CalculationType>();
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if (! math::equals(angle01, pi))
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{
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m_axis = geometry::cross_product(m_xyz0, m_xyz1);
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geometry::detail::vec_normalize(m_axis);
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}
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else // antipodal
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{
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CalculationType const half_pi = math::half_pi<CalculationType>();
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CalculationType const lat = geometry::get_as_radian<1>(p0);
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if (math::equals(lat, half_pi))
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{
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// pointing east, segment lies on prime meridian, going south
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m_axis = point3d_t(c0, c1, c0);
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}
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else if (math::equals(lat, -half_pi))
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{
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// pointing west, segment lies on prime meridian, going north
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m_axis = point3d_t(c0, -c1, c0);
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}
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else
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{
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// lon rotated west by pi/2 at equator
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CalculationType const lon = geometry::get_as_radian<0>(p0);
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m_axis = point3d_t(sin(lon), -cos(lon), c0);
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}
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}
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}
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template <typename Point>
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void compute_point(CalculationType const& a, Point& p)
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{
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CalculationType const c1 = 1;
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// Axis-Angle rotation
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// see: https://en.wikipedia.org/wiki/Axis-angle_representation
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CalculationType const cos_a = cos(a);
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CalculationType const sin_a = sin(a);
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// cos_a * v
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point3d_t s1 = m_xyz0;
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geometry::multiply_value(s1, cos_a);
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// sin_a * (n x v)
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point3d_t s2 = geometry::cross_product(m_axis, m_xyz0);
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geometry::multiply_value(s2, sin_a);
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// (1 - cos_a)(n.v) * n
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point3d_t s3 = m_axis;
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geometry::multiply_value(s3, (c1 - cos_a) *
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geometry::dot_product(m_axis, m_xyz0));
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// v_rot = cos_a * v + sin_a * (n x v) + (1 - cos_a)(n.v) * e
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point3d_t v_rot = s1;
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geometry::add_point(v_rot, s2);
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geometry::add_point(v_rot, s3);
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p = formula::cart3d_to_sph<Point>(v_rot);
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}
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private :
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point3d_t m_xyz0;
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point3d_t m_xyz1;
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point3d_t m_axis;
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};
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}}} // namespace boost::geometry::formula
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#endif // BOOST_GEOMETRY_FORMULAS_INTERPOLATE_POINT_SPHERICAL_HPP
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