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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/Plane_3.h $ // $Id: include/CGAL/Cartesian/Plane_3.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Andreas Fabri #ifndef CGAL_CARTESIAN_PLANE_3_H #define CGAL_CARTESIAN_PLANE_3_H #include #include #include #include namespace CGAL { template class PlaneC3 { typedef typename R_::FT FT; typedef typename R_::Point_2 Point_2; typedef typename R_::Point_3 Point_3; typedef typename R_::Vector_3 Vector_3; typedef typename R_::Direction_3 Direction_3; typedef typename R_::Line_3 Line_3; typedef typename R_::Ray_3 Ray_3; typedef typename R_::Segment_3 Segment_3; typedef typename R_::Plane_3 Plane_3; typedef typename R_::Circle_3 Circle_3; typedef typename R_::Construct_point_3 Construct_point_3; typedef typename R_::Construct_point_2 Construct_point_2; typedef std::array Rep; typedef typename R_::template Handle::type Base; Base base; public: typedef R_ R; PlaneC3() {} PlaneC3(const Point_3 &p, const Point_3 &q, const Point_3 &r) { *this = plane_from_points(p, q, r); } PlaneC3(const Point_3 &p, const Direction_3 &d) { *this = plane_from_point_direction(p, d); } PlaneC3(const Point_3 &p, const Vector_3 &v) { *this = plane_from_point_direction(p, v.direction()); } PlaneC3(Origin o, const Vector_3 &v) { *this = plane_from_point_direction(o, v.direction()); } PlaneC3(const FT &a, const FT &b, const FT &c, const FT &d) : base{a, b, c, d} {} PlaneC3(const Line_3 &l, const Point_3 &p) { *this = plane_from_points(l.point(), l.point()+l.direction().to_vector(), p); } PlaneC3(const Segment_3 &s, const Point_3 &p) { *this = plane_from_points(s.start(), s.end(), p); } PlaneC3(const Ray_3 &r, const Point_3 &p) { *this = plane_from_points(r.start(), r.second_point(), p); } typename R::Boolean operator==(const PlaneC3 &p) const; typename R::Boolean operator!=(const PlaneC3 &p) const; const FT & a() const { return get_pointee_or_identity(base)[0]; } const FT & b() const { return get_pointee_or_identity(base)[1]; } const FT & c() const { return get_pointee_or_identity(base)[2]; } const FT & d() const { return get_pointee_or_identity(base)[3]; } Line_3 perpendicular_line(const Point_3 &p) const; Plane_3 opposite() const; Point_3 point() const; Point_3 projection(const Point_3 &p) const; Vector_3 orthogonal_vector() const; Direction_3 orthogonal_direction() const; Vector_3 base1() const; Vector_3 base2() const; Point_3 to_plane_basis(const Point_3 &p) const; Point_2 to_2d(const Point_3 &p) const; Point_3 to_3d(const Point_2 &p) const; typename R::Oriented_side oriented_side(const Point_3 &p) const; typename R::Boolean has_on_positive_side(const Point_3 &l) const; typename R::Boolean has_on_negative_side(const Point_3 &l) const; typename R::Boolean has_on(const Point_3 &p) const { return oriented_side(p) == ON_ORIENTED_BOUNDARY; } typename R::Boolean has_on(const Line_3 &l) const { return has_on(l.point()) && has_on(l.point() + l.direction().to_vector()); } typename R::Boolean has_on(const Circle_3 &circle) const { if(circle.squared_radius() != FT(0)) { const Plane_3& p = circle.supporting_plane(); if(is_zero(a())) { if(!is_zero(p.a())) return false; if(is_zero(b())) { if(!is_zero(p.b())) return false; return c() * p.d() == d() * p.c(); } return (p.c() * b() == c() * p.b()) && (p.d() * b() == d() * p.b()); } return (p.b() * a() == b() * p.a()) && (p.c() * a() == c() * p.a()) && (p.d() * a() == d() * p.a()); } else return has_on(circle.center()); } typename R::Boolean is_degenerate() const; }; template < class R > CGAL_KERNEL_INLINE typename R::Boolean PlaneC3::operator==(const PlaneC3 &p) const { if (CGAL::identical(base, p.base)) return true; return equal_plane(*this, p); } template < class R > inline typename R::Boolean PlaneC3::operator!=(const PlaneC3 &p) const { return !(*this == p); } template < class R > inline typename PlaneC3::Point_3 PlaneC3::point() const { FT x, y, z; point_on_planeC3(a(), b(), c(), d(), x, y, z); return R().construct_point_3_object()(x, y, z); } template < class R > inline typename PlaneC3::Point_3 PlaneC3:: projection(const typename PlaneC3::Point_3 &p) const { FT x, y, z; projection_planeC3(a(), b(), c(), d(), R().compute_x_3_object()(p), R().compute_y_3_object()(p), R().compute_z_3_object()(p), x, y, z); return R().construct_point_3_object()(x, y, z); } template < class R > inline typename PlaneC3::Vector_3 PlaneC3::orthogonal_vector() const { return R().construct_orthogonal_vector_3_object()(*this); } template < class R > inline typename PlaneC3::Direction_3 PlaneC3::orthogonal_direction() const { return Direction_3(a(), b(), c()); } template < class R > typename PlaneC3::Vector_3 PlaneC3::base1() const { return R().construct_base_vector_3_object()(*this, 1); } template < class R > typename PlaneC3::Vector_3 PlaneC3::base2() const { return R().construct_base_vector_3_object()(*this, 2); } template < class R > typename PlaneC3::Point_3 PlaneC3:: to_plane_basis(const typename PlaneC3::Point_3 &p) const { FT alpha, beta, gamma; Construct_point_3 construct_point_3; Cartesian_internal::solve(base1(), base2(), orthogonal_vector(), p - point(), alpha, beta, gamma); return construct_point_3(alpha, beta, gamma); } template < class R > typename PlaneC3::Point_2 PlaneC3:: to_2d(const typename PlaneC3::Point_3 &p) const { FT alpha, beta, gamma; Construct_point_2 construct_point_2; Cartesian_internal::solve(base1(), base2(), orthogonal_vector(), p - point(), alpha, beta, gamma); return construct_point_2(alpha, beta); } template < class R > inline typename PlaneC3::Point_3 PlaneC3:: to_3d(const typename PlaneC3::Point_2 &p) const { return R().construct_lifted_point_3_object()(*this, p); } template < class R > inline typename PlaneC3::Line_3 PlaneC3:: perpendicular_line(const typename PlaneC3::Point_3 &p) const { return Line_3(p, orthogonal_direction()); } template < class R > inline typename PlaneC3::Plane_3 PlaneC3::opposite() const { return PlaneC3(-a(), -b(), -c(), -d()); } template < class R > inline typename R::Oriented_side PlaneC3:: oriented_side(const typename PlaneC3::Point_3 &p) const { return side_of_oriented_plane(*this, p); } template < class R > inline typename R::Boolean PlaneC3:: has_on_positive_side(const typename PlaneC3::Point_3 &p) const { return oriented_side(p) == ON_POSITIVE_SIDE; } template < class R > inline typename R::Boolean PlaneC3:: has_on_negative_side(const typename PlaneC3::Point_3 &p) const { return oriented_side(p) == ON_NEGATIVE_SIDE; } template < class R > inline typename R::Boolean PlaneC3:: is_degenerate() const { // FIXME : predicate return CGAL_NTS is_zero(a()) && CGAL_NTS is_zero(b()) && CGAL_NTS is_zero(c()); } } //namespace CGAL #endif // CGAL_CARTESIAN_PLANE_3_H