313 lines
7.9 KiB
C
313 lines
7.9 KiB
C
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// Copyright (c) 2000
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// Utrecht University (The Netherlands),
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// ETH Zurich (Switzerland),
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// INRIA Sophia-Antipolis (France),
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// Max-Planck-Institute Saarbruecken (Germany),
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// and Tel-Aviv University (Israel). All rights reserved.
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//
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// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public License as
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// published by the Free Software Foundation; either version 3 of the License,
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// or (at your option) any later version.
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//
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// Licensees holding a valid commercial license may use this file in
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// accordance with the commercial license agreement provided with the software.
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//
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// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
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// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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//
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// $URL$
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// $Id$
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// SPDX-License-Identifier: LGPL-3.0+
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//
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//
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// Author(s) : Andreas Fabri
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#ifndef CGAL_CARTESIAN_PLANE_3_H
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#define CGAL_CARTESIAN_PLANE_3_H
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#include <CGAL/array.h>
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#include <CGAL/Handle_for.h>
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#include <CGAL/Cartesian/solve_3.h>
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#include <CGAL/Cartesian/plane_constructions_3.h>
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namespace CGAL {
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template <class R_>
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class PlaneC3
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{
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typedef typename R_::FT FT;
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typedef typename R_::Point_2 Point_2;
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typedef typename R_::Point_3 Point_3;
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typedef typename R_::Vector_3 Vector_3;
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typedef typename R_::Direction_3 Direction_3;
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typedef typename R_::Line_3 Line_3;
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typedef typename R_::Ray_3 Ray_3;
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typedef typename R_::Segment_3 Segment_3;
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typedef typename R_::Plane_3 Plane_3;
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typedef typename R_::Circle_3 Circle_3;
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typedef typename R_::Construct_point_3 Construct_point_3;
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typedef typename R_::Construct_point_2 Construct_point_2;
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typedef cpp11::array<FT, 4> Rep;
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typedef typename R_::template Handle<Rep>::type Base;
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Base base;
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public:
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typedef R_ R;
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PlaneC3() {}
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PlaneC3(const Point_3 &p, const Point_3 &q, const Point_3 &r)
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{ *this = plane_from_points<R>(p, q, r); }
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PlaneC3(const Point_3 &p, const Direction_3 &d)
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{ *this = plane_from_point_direction<R>(p, d); }
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PlaneC3(const Point_3 &p, const Vector_3 &v)
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{ *this = plane_from_point_direction<R>(p, v.direction()); }
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PlaneC3(const FT &a, const FT &b, const FT &c, const FT &d)
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: base(CGAL::make_array(a, b, c, d)) {}
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PlaneC3(const Line_3 &l, const Point_3 &p)
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{ *this = plane_from_points<R>(l.point(),
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l.point()+l.direction().to_vector(),
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p); }
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PlaneC3(const Segment_3 &s, const Point_3 &p)
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{ *this = plane_from_points<R>(s.start(), s.end(), p); }
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PlaneC3(const Ray_3 &r, const Point_3 &p)
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{ *this = plane_from_points<R>(r.start(), r.second_point(), p); }
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typename R::Boolean operator==(const PlaneC3 &p) const;
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typename R::Boolean operator!=(const PlaneC3 &p) const;
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const FT & a() const
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{
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return get_pointee_or_identity(base)[0];
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}
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const FT & b() const
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{
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return get_pointee_or_identity(base)[1];
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}
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const FT & c() const
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{
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return get_pointee_or_identity(base)[2];
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}
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const FT & d() const
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{
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return get_pointee_or_identity(base)[3];
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}
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Line_3 perpendicular_line(const Point_3 &p) const;
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Plane_3 opposite() const;
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Point_3 point() const;
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Point_3 projection(const Point_3 &p) const;
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Vector_3 orthogonal_vector() const;
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Direction_3 orthogonal_direction() const;
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Vector_3 base1() const;
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Vector_3 base2() const;
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Point_3 to_plane_basis(const Point_3 &p) const;
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Point_2 to_2d(const Point_3 &p) const;
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Point_3 to_3d(const Point_2 &p) const;
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typename R::Oriented_side oriented_side(const Point_3 &p) const;
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typename R::Boolean has_on_positive_side(const Point_3 &l) const;
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typename R::Boolean has_on_negative_side(const Point_3 &l) const;
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typename R::Boolean has_on(const Point_3 &p) const
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{
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return oriented_side(p) == ON_ORIENTED_BOUNDARY;
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}
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typename R::Boolean has_on(const Line_3 &l) const
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{
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return has_on(l.point())
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&& has_on(l.point() + l.direction().to_vector());
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}
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typename R::Boolean has_on(const Circle_3 &circle) const
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{
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if(circle.squared_radius() != FT(0)) {
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const Plane_3& p = circle.supporting_plane();
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if(is_zero(a())) {
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if(!is_zero(p.a())) return false;
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if(is_zero(b())) {
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if(!is_zero(p.b())) return false;
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return c() * p.d() == d() * p.c();
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}
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return (p.c() * b() == c() * p.b()) &&
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(p.d() * b() == d() * p.b());
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}
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return (p.b() * a() == b() * p.a()) &&
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(p.c() * a() == c() * p.a()) &&
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(p.d() * a() == d() * p.a());
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} else return has_on(circle.center());
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}
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typename R::Boolean is_degenerate() const;
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};
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template < class R >
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CGAL_KERNEL_INLINE
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typename R::Boolean
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PlaneC3<R>::operator==(const PlaneC3<R> &p) const
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{
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if (CGAL::identical(base, p.base))
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return true;
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return equal_plane(*this, p);
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}
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template < class R >
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inline
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typename R::Boolean
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PlaneC3<R>::operator!=(const PlaneC3<R> &p) const
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{
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return !(*this == p);
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}
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template < class R >
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inline
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typename PlaneC3<R>::Point_3
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PlaneC3<R>::point() const
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{
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return point_on_plane(*this);
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}
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template < class R >
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inline
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typename PlaneC3<R>::Point_3
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PlaneC3<R>::
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projection(const typename PlaneC3<R>::Point_3 &p) const
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{
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return projection_plane(p, *this);
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}
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template < class R >
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inline
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typename PlaneC3<R>::Vector_3
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PlaneC3<R>::orthogonal_vector() const
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{
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return R().construct_orthogonal_vector_3_object()(*this);
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}
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template < class R >
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inline
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typename PlaneC3<R>::Direction_3
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PlaneC3<R>::orthogonal_direction() const
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{
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return Direction_3(a(), b(), c());
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}
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template < class R >
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typename PlaneC3<R>::Vector_3
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PlaneC3<R>::base1() const
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{
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return R().construct_base_vector_3_object()(*this, 1);
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}
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template < class R >
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typename PlaneC3<R>::Vector_3
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PlaneC3<R>::base2() const
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{
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return R().construct_base_vector_3_object()(*this, 2);
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}
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template < class R >
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typename PlaneC3<R>::Point_3
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PlaneC3<R>::
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to_plane_basis(const typename PlaneC3<R>::Point_3 &p) const
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{
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FT alpha, beta, gamma;
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Construct_point_3 construct_point_3;
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Cartesian_internal::solve(base1(), base2(), orthogonal_vector(), p - point(),
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alpha, beta, gamma);
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return construct_point_3(alpha, beta, gamma);
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}
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template < class R >
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typename PlaneC3<R>::Point_2
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PlaneC3<R>::
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to_2d(const typename PlaneC3<R>::Point_3 &p) const
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{
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FT alpha, beta, gamma;
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Construct_point_2 construct_point_2;
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Cartesian_internal::solve(base1(), base2(), orthogonal_vector(), p - point(),
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alpha, beta, gamma);
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return construct_point_2(alpha, beta);
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}
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template < class R >
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inline
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typename PlaneC3<R>::Point_3
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PlaneC3<R>::
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to_3d(const typename PlaneC3<R>::Point_2 &p) const
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{
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return R().construct_lifted_point_3_object()(*this, p);
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}
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template < class R >
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inline
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typename PlaneC3<R>::Line_3
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PlaneC3<R>::
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perpendicular_line(const typename PlaneC3<R>::Point_3 &p) const
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{
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return Line_3(p, orthogonal_direction());
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}
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template < class R >
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inline
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typename PlaneC3<R>::Plane_3
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PlaneC3<R>::opposite() const
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{
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return PlaneC3<R>(-a(), -b(), -c(), -d());
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}
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template < class R >
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inline
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typename R::Oriented_side
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PlaneC3<R>::
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oriented_side(const typename PlaneC3<R>::Point_3 &p) const
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{
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return side_of_oriented_plane(*this, p);
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}
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template < class R >
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inline
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typename R::Boolean
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PlaneC3<R>::
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has_on_positive_side(const typename PlaneC3<R>::Point_3 &p) const
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{
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return oriented_side(p) == ON_POSITIVE_SIDE;
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}
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template < class R >
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inline
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typename R::Boolean
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PlaneC3<R>::
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has_on_negative_side(const typename PlaneC3<R>::Point_3 &p) const
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{
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return oriented_side(p) == ON_NEGATIVE_SIDE;
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}
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template < class R >
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inline
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typename R::Boolean
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PlaneC3<R>::
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is_degenerate() const
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{ // FIXME : predicate
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return CGAL_NTS is_zero(a()) && CGAL_NTS is_zero(b()) &&
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CGAL_NTS is_zero(c());
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}
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} //namespace CGAL
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#endif // CGAL_CARTESIAN_PLANE_3_H
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