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// Copyright (c) 2000 // Utrecht University (The Netherlands), // ETH Zurich (Switzerland), // INRIA Sophia-Antipolis (France), // Max-Planck-Institute Saarbruecken (Germany), // and Tel-Aviv University (Israel). All rights reserved. // // This file is part of CGAL (www.cgal.org) // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Cartesian_kernel/include/CGAL/Cartesian/Sphere_3.h $ // $Id: include/CGAL/Cartesian/Sphere_3.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Herve Bronnimann #ifndef CGAL_CARTESIAN_SPHERE_3_H #define CGAL_CARTESIAN_SPHERE_3_H #include #include #include #include namespace CGAL { template class SphereC3 { typedef typename R_::Boolean Boolean; typedef typename R_::Bounded_side Bounded_side; typedef typename R_::FT FT; // https://doc.cgal.org/latest/Manual/devman_code_format.html#secprogramming_conventions typedef typename R_::Point_3 Point_3_; typedef typename R_::Vector_3 Vector_3; typedef typename R_::Sphere_3 Sphere_3; typedef typename R_::Circle_3 Circle_3; typedef boost::tuple Rep; typedef typename R_::template Handle::type Base; Base base; public: typedef R_ R; SphereC3() {} SphereC3(const Point_3_ ¢er, const FT &squared_radius, const Orientation &o = COUNTERCLOCKWISE) { CGAL_kernel_precondition( (squared_radius >= FT(0)) & (o != COLLINEAR) ); base = Rep(center, squared_radius, o); } // Sphere passing through and oriented by p,q,r,s SphereC3(const Point_3_ &p, const Point_3_ &q, const Point_3_ &r, const Point_3_ &s) { Orientation orient = make_certain(CGAL::orientation(p, q, r, s)); Point_3_ center = CGAL::circumcenter(p, q, r, s); FT squared_radius = squared_distance(p, center); base = Rep(center, squared_radius, orient); } // Sphere with great circle passing through p,q,r, oriented by o SphereC3(const Point_3_ &p, const Point_3_ &q, const Point_3_ &r, const Orientation &o = COUNTERCLOCKWISE) { CGAL_kernel_precondition(o != COLLINEAR); Point_3_ center = CGAL::circumcenter(p, q, r); FT squared_radius = squared_distance(p, center); base = Rep(center, squared_radius, o); } // Sphere with diameter pq and orientation o SphereC3(const Point_3_ &p, const Point_3_ &q, const Orientation &o = COUNTERCLOCKWISE) { CGAL_kernel_precondition(o != COLLINEAR); Point_3_ center = midpoint(p, q); FT squared_radius = squared_distance(p, center); base = Rep(center, squared_radius, o); } explicit SphereC3(const Point_3_ ¢er, const Orientation& o = COUNTERCLOCKWISE) { CGAL_kernel_precondition(o != COLLINEAR); base = Rep(center, FT(0), o); } typename R::Boolean operator==(const SphereC3 &) const; typename R::Boolean operator!=(const SphereC3 &) const; const Point_3_ & center() const { return get_pointee_or_identity(base).template get<0>(); } const FT & squared_radius() const { // Returns the square of the radius (instead of the radius itself, // which would require square roots) return get_pointee_or_identity(base).template get<1>(); } Orientation orientation() const { return get_pointee_or_identity(base).template get<2>(); } // A circle is degenerate if its (squared) radius is null or negative typename R::Boolean is_degenerate() const; // Returns a circle with opposite orientation Sphere_3 opposite() const; typename R_::Oriented_side oriented_side(const Point_3_ &p) const; //! precond: ! x.is_degenerate() (when available) // Returns R::ON_POSITIVE_SIDE, R::ON_ORIENTED_BOUNDARY or // R::ON_NEGATIVE_SIDE Boolean has_on(const Circle_3 &p) const; Boolean has_on(const Point_3_ &p) const; Boolean has_on_boundary(const Point_3_ &p) const; Boolean has_on_positive_side(const Point_3_ &p) const; Boolean has_on_negative_side(const Point_3_ &p) const; Bounded_side bounded_side(const Point_3_ &p) const; //! precond: ! x.is_degenerate() (when available) // Returns R::ON_BOUNDED_SIDE, R::ON_BOUNDARY or R::ON_UNBOUNDED_SIDE Boolean has_on_bounded_side(const Point_3_ &p) const; Boolean has_on_unbounded_side(const Point_3_ &p) const; }; template < class R > CGAL_KERNEL_INLINE typename R::Boolean SphereC3::operator==(const SphereC3 &t) const { if (CGAL::identical(base, t.base)) return true; return center() == t.center() && squared_radius() == t.squared_radius() && orientation() == t.orientation(); } template < class R > inline typename R::Boolean SphereC3::operator!=(const SphereC3 &t) const { return !(*this == t); } template < class R > CGAL_KERNEL_MEDIUM_INLINE typename R::Oriented_side SphereC3:: oriented_side(const typename SphereC3::Point_3_ &p) const { typedef typename R::Oriented_side Oriented_side; return enum_cast(bounded_side(p)) * orientation(); } template < class R > CGAL_KERNEL_INLINE typename R::Bounded_side SphereC3:: bounded_side(const typename SphereC3::Point_3_ &p) const { typedef typename R::Bounded_side Bounded_side; return enum_cast(compare(squared_radius(), squared_distance(center(), p))); } template < class R > inline typename R::Boolean SphereC3:: has_on(const typename SphereC3::Circle_3 &c) const { typedef typename SphereC3::Point_3_ Point_3_; typedef typename SphereC3::FT FT; Point_3_ proj = c.supporting_plane().projection(center()); if(!(proj == c.center())) return false; const FT d2 = squared_distance(center(),c.center()); return ((squared_radius() - d2) == c.squared_radius()); } template < class R > inline typename R::Boolean SphereC3:: has_on(const typename SphereC3::Point_3_ &p) const { return has_on_boundary(p); } template < class R > inline typename R::Boolean SphereC3:: has_on_boundary(const typename SphereC3::Point_3_ &p) const { // FIXME: it's a predicate... return squared_distance(center(),p) == squared_radius(); // NB: J'ai aussi trouve ailleurs : // return oriented_side(p)==ON_ORIENTED_BOUNDARY; // a voir... } template < class R > CGAL_KERNEL_INLINE typename R::Boolean SphereC3:: has_on_negative_side(const typename SphereC3::Point_3_ &p) const { if (orientation() == COUNTERCLOCKWISE) return has_on_unbounded_side(p); return has_on_bounded_side(p); // NB: J'ai aussi trouve ailleurs : // return oriented_side(p)==ON_NEGATIVE_SIDE; } template < class R > CGAL_KERNEL_INLINE typename R::Boolean SphereC3:: has_on_positive_side(const typename SphereC3::Point_3_ &p) const { if (orientation() == COUNTERCLOCKWISE) return has_on_bounded_side(p); return has_on_unbounded_side(p); // NB: J'ai aussi trouve ailleurs : // return oriented_side(p)==ON_POSITIVE_SIDE; } template < class R > inline typename R::Boolean SphereC3:: has_on_bounded_side(const typename SphereC3::Point_3_ &p) const { // FIXME: it's a predicate... return squared_distance(center(),p) < squared_radius(); // NB: J'ai aussi trouve ailleurs : // return bounded_side(p)==ON_BOUNDED_SIDE; } template < class R > inline typename R::Boolean SphereC3:: has_on_unbounded_side(const typename SphereC3::Point_3_ &p) const { // FIXME: it's a predicate... return squared_distance(center(),p) > squared_radius(); // NB: J'ai aussi trouve ailleurs : // return bounded_side(p)==ON_UNBOUNDED_SIDE; } template < class R > inline typename R::Boolean SphereC3:: is_degenerate() const { // FIXME: it's a predicate (?) return CGAL_NTS is_zero(squared_radius()); } template < class R > inline typename SphereC3::Sphere_3 SphereC3::opposite() const { return SphereC3(center(), squared_radius(), CGAL::opposite(orientation()) ); } } //namespace CGAL #endif // CGAL_CARTESIAN_SPHERE_3_H