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// Copyright (c) 1997, 2012, 2019 INRIA Sophia-Antipolis (France). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Triangulation_on_sphere_2/include/CGAL/Geographical_coordinates_traits_2.h $ // $Id: include/CGAL/Geographical_coordinates_traits_2.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // Author(s) : Mael Rouxel-Labbé #ifndef CGAL_TRIANGULATION_ON_SPHERE_GEOGRAPHICAL_COORDINATES_TRAITS_2_H #define CGAL_TRIANGULATION_ON_SPHERE_GEOGRAPHICAL_COORDINATES_TRAITS_2_H #include #include #include #include #include #include #include // @todo // Note: this is currently undocumented because it uses a conversion to // the Cartesian domain R^3 to perform predicates and constructions, // losing the benefit of the exact representation on the way. // It can be useful on its own (especially since it contains code // to handle generic convex domains), but hidden points are possible // and are not handled properly. namespace CGAL { template struct Geographical_coordinates { typedef typename LK::FT FT; typedef FT Latitude; typedef FT Longitude; Geographical_coordinates() : _la(360), _lo(360) { } Geographical_coordinates(const FT la, const FT lo) : _la(la), _lo(lo) { } Latitude latitude() const { return _la; } Longitude longitude() const { return _lo; } friend std::ostream& operator<<(std::ostream& os, const Geographical_coordinates& l) { os << l._la << " " << l._lo; return os; } private: FT _la; FT _lo; }; namespace internal { template struct Construct_geographical_coordinates : public CGAL::cpp98::unary_function > { typedef typename LK::FT FT; typedef typename LK::Point_3 Point_3; typedef CGAL::Geographical_coordinates result_type; Construct_geographical_coordinates(const Point_3& center, const FT radius) : _center(center), _radius(radius) { } result_type operator()(const Point_3& pt) const { CGAL_assertion(pt != _center); const FT la = 180. * std::asin((pt.z() - _center.z()) / _radius) / CGAL_PI; const FT lo = 180. * std::atan2((pt.y() - _center.y()), (pt.x() - _center.x())) / CGAL_PI; return result_type(la, lo); } private: const Point_3& _center; const FT _radius; }; template struct Construct_Cartesian_coordinates : public CGAL::cpp98::unary_function > { typedef typename LK::FT FT; typedef typename LK::Point_3 Point_3; typedef CGAL::Geographical_coordinates Coordinates; Construct_Cartesian_coordinates(const Point_3& center, const FT radius) : _center(center), _radius(radius) { } Point_3 operator()(const Coordinates& l) const { #if 1 const FT rla = CGAL_PI * l.latitude() / 180.; const FT rlo = CGAL_PI * l.longitude() / 180.; const FT x = _center.x() + _radius * std::cos(rla) * std::cos(rlo); const FT y = _center.y() + _radius * std::cos(rla) * std::sin(rlo); const FT z = _center.z() + _radius * std::sin(rla); #else const FT rla = CGAL_PI * l.latitude() / 180.; const FT rlo = CGAL_PI * l.longitude() / 180.; // Quoting wikipedia: // - The Earth's equatorial radius a, or semi-major axis, is the distance from its center // to the equator and equals 6,378.1370 km (3,963.1906 mi) // - The Earth's polar radius b, or semi-minor axis, is the distance from its center to the North // and South Poles, and equals 6,356.7523 km (3,949.9028 mi). const FT equ_radius = 6378.1370; const FT pol_radius = 6356.7523; FT radius_ratio = equ_radius / pol_radius; const FT a2 = square(_radius * radius_ratio); const FT b2 = square(_radius); // Using https://en.wikipedia.org/wiki/Geographic_coordinate_conversion#From_geodetic_to_ECEF_coordinates const FT N = a2 / sqrt(a2 * square(std::cos(rla)) + b2 * square(std::sin(rla))); const FT h = 0; const FT x = _center.x() + (N + h) * std::cos(rla) * std::cos(rlo); const FT y = _center.y() + (N + h) * std::cos(rla) * std::sin(rlo); const FT z = _center.z() + (b2 * N / a2 + h) * std::sin(rla); #endif return Point_3(x, y, z); } private: const Point_3& _center; const FT _radius; }; template struct Construct_circumcenter_on_geo_sphere_2 { public: typedef typename LK::FT FT; typedef typename LK::Point_3 Point_3; typedef typename LK::Vector_3 Vector_3; typedef Geographical_coordinates Point_on_sphere_2; typedef Geographical_coordinates result_type; Construct_circumcenter_on_geo_sphere_2( const Base_functor_ f, const Point_3& center, const FT radius) : _center(center), _radius(radius), _f(f) { } result_type operator()(const Point_on_sphere_2& p, const Point_on_sphere_2& q, const Point_on_sphere_2& r) const { Construct_Cartesian_coordinates to_P3(_center, _radius); Construct_geographical_coordinates to_PoS2(_center, _radius); return to_PoS2(_f(to_P3(p), to_P3(q), to_P3(r))); } private: const Base_functor_ _f; const Point_3& _center; const FT _radius; }; // Adaptor for calling the functors with the points projected on the sphere template class Functor_geo_projection_adaptor : public Functor_ { typedef Functor_ Functor; typedef Functor_ Base; typedef typename LK::FT FT; typedef typename LK::Point_3 Point_3; typedef Geographical_coordinates Point; typedef Construct_Cartesian_coordinates To_Point_3; public: Functor_geo_projection_adaptor(const Functor& f, const Point_3& center, const FT radius) : Base(f), to_p3(center, radius) { } public: using Base::operator(); decltype(auto) operator()(const Point& p0, const Point& p1) { return Base::operator()(to_p3(p0), to_p3(p1)); } decltype(auto) operator()(const Point& p0, const Point& p1, const Point& p2) { return Base::operator()(to_p3(p0), to_p3(p1), to_p3(p2)); } decltype(auto) operator ()(const Point& p0, const Point& p1, const Point& p2, const Point& p3) { return Base::operator()(to_p3(p0), to_p3(p1), to_p3(p2), to_p3(p3)); } decltype(auto) operator()(const Point& p0, const Point& p1, const Point& p2, const Point& p3, const Point& p4) { return Base::operator()(to_p3(p0), to_p3(p1), to_p3(p2), to_p3(p3), to_p3(p4)); } private: const To_Point_3 to_p3; }; } // namespace internal template class Geographical_coordinates_traits_2 : public Delaunay_triangulation_on_sphere_traits_2 { protected: typedef Delaunay_triangulation_on_sphere_traits_2 Base; typedef Geographical_coordinates_traits_2 Self; public: typedef typename LK::FT FT; typedef typename LK::Point_3 Point_3; typedef Geographical_coordinates Point_on_sphere_2; // predicates typedef internal::Functor_geo_projection_adaptor Collinear_are_strictly_ordered_on_great_circle_2; typedef internal::Functor_geo_projection_adaptor Compare_on_sphere_2; typedef internal::Functor_geo_projection_adaptor Equal_on_sphere_2; typedef internal::Functor_geo_projection_adaptor Orientation_on_sphere_2; typedef internal::Functor_geo_projection_adaptor Side_of_oriented_circle_on_sphere_2; // constructions typedef internal::Construct_geographical_coordinates Construct_point_on_sphere_2; typedef internal::Construct_Cartesian_coordinates Construct_point_3; typedef internal::Functor_geo_projection_adaptor Construct_segment_3; typedef internal::Functor_geo_projection_adaptor Construct_triangle_3; typedef internal::Functor_geo_projection_adaptor Construct_arc_on_sphere_2; typedef internal::Construct_circumcenter_on_geo_sphere_2 Construct_circumcenter_on_sphere_2; public: Geographical_coordinates_traits_2(const Point_3& sphere = CGAL::ORIGIN, const FT radius = 1, const LK& lk = LK()) : Base(sphere, radius, lk) { } // predicates public: Collinear_are_strictly_ordered_on_great_circle_2 collinear_are_strictly_ordered_on_great_circle_2_object() const { return Collinear_are_strictly_ordered_on_great_circle_2( Base::collinear_are_strictly_ordered_on_great_circle_2_object(), Base::center(), Base::radius()); } Compare_on_sphere_2 compare_on_sphere_2_object() const { return Compare_on_sphere_2(Base::compare_on_sphere_2_object(), Base::center(), Base::radius()); } Equal_on_sphere_2 equal_on_sphere_2_object() const { return Equal_on_sphere_2(Base::equal_on_sphere_2_object(), Base::center(), Base::radius()); } Orientation_on_sphere_2 orientation_on_sphere_2_object() const { return Orientation_on_sphere_2(Base::orientation_on_sphere_2_object(), Base::center(), Base::radius()); } Side_of_oriented_circle_on_sphere_2 side_of_oriented_circle_on_sphere_2_object() const { return Side_of_oriented_circle_on_sphere_2(Base::side_of_oriented_circle_on_sphere_2_object(), Base::center(), Base::radius()); } // constructions public: Construct_point_on_sphere_2 construct_point_on_sphere_2_object() const { return Construct_point_on_sphere_2(Base::center(), Base::radius()); } Construct_point_3 construct_point_3_object() const { return Construct_point_3(Base::center(), Base::radius()); } Construct_arc_on_sphere_2 construct_arc_on_sphere_2_object() const { return Construct_arc_on_sphere_2(Base::construct_arc_on_sphere_2_object(), Base::center(), Base::radius()); } Construct_circumcenter_on_sphere_2 construct_circumcenter_on_sphere_2_object() const { return Construct_circumcenter_on_sphere_2(Base::construct_circumcenter_on_sphere_2_object(), Base::center(), Base::radius()); } public: bool is_on_sphere(const Point_on_sphere_2& /*p*/) const { return true; } bool are_points_too_close(const Point_on_sphere_2& p, const Point_on_sphere_2& q) const { return Base::are_points_too_close(construct_point_3_object()(p), construct_point_3_object()(q)); } }; } // namespace CGAL #endif // CGAL_TRIANGULATION_ON_SPHERE_GEOGRAPHICAL_COORDINATES_TRAITS_2_H