/usr/include/CGAL/Cartesian/Plane_3.h is in libcgal-dev 4.7-4.
This file is owned by root:root, with mode 0o644.
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// 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); you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 3 of the License,
// or (at your option) any later version.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL$
// $Id$
//
//
// Author(s) : Andreas Fabri
#ifndef CGAL_CARTESIAN_PLANE_3_H
#define CGAL_CARTESIAN_PLANE_3_H
#include <CGAL/array.h>
#include <CGAL/Handle_for.h>
#include <CGAL/Cartesian/solve_3.h>
#include <CGAL/Cartesian/plane_constructions_3.h>
namespace CGAL {
template <class R_>
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 cpp11::array<FT, 4> Rep;
typedef typename R_::template Handle<Rep>::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<R>(p, q, r); }
PlaneC3(const Point_3 &p, const Direction_3 &d)
{ *this = plane_from_point_direction<R>(p, d); }
PlaneC3(const Point_3 &p, const Vector_3 &v)
{ *this = plane_from_point_direction<R>(p, v.direction()); }
PlaneC3(const FT &a, const FT &b, const FT &c, const FT &d)
: base(CGAL::make_array(a, b, c, d)) {}
PlaneC3(const Line_3 &l, const Point_3 &p)
{ *this = plane_from_points<R>(l.point(),
l.point()+l.direction().to_vector(),
p); }
PlaneC3(const Segment_3 &s, const Point_3 &p)
{ *this = plane_from_points<R>(s.start(), s.end(), p); }
PlaneC3(const Ray_3 &r, const Point_3 &p)
{ *this = plane_from_points<R>(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<R>::operator==(const PlaneC3<R> &p) const
{
if (CGAL::identical(base, p.base))
return true;
return equal_plane(*this, p);
}
template < class R >
inline
typename R::Boolean
PlaneC3<R>::operator!=(const PlaneC3<R> &p) const
{
return !(*this == p);
}
template < class R >
inline
typename PlaneC3<R>::Point_3
PlaneC3<R>::point() const
{
return point_on_plane(*this);
}
template < class R >
inline
typename PlaneC3<R>::Point_3
PlaneC3<R>::
projection(const typename PlaneC3<R>::Point_3 &p) const
{
return projection_plane(p, *this);
}
template < class R >
inline
typename PlaneC3<R>::Vector_3
PlaneC3<R>::orthogonal_vector() const
{
return R().construct_orthogonal_vector_3_object()(*this);
}
template < class R >
inline
typename PlaneC3<R>::Direction_3
PlaneC3<R>::orthogonal_direction() const
{
return Direction_3(a(), b(), c());
}
template < class R >
typename PlaneC3<R>::Vector_3
PlaneC3<R>::base1() const
{
return R().construct_base_vector_3_object()(*this, 1);
}
template < class R >
typename PlaneC3<R>::Vector_3
PlaneC3<R>::base2() const
{
return R().construct_base_vector_3_object()(*this, 2);
}
template < class R >
typename PlaneC3<R>::Point_3
PlaneC3<R>::
to_plane_basis(const typename PlaneC3<R>::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<R>::Point_2
PlaneC3<R>::
to_2d(const typename PlaneC3<R>::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<R>::Point_3
PlaneC3<R>::
to_3d(const typename PlaneC3<R>::Point_2 &p) const
{
return R().construct_lifted_point_3_object()(*this, p);
}
template < class R >
inline
typename PlaneC3<R>::Line_3
PlaneC3<R>::
perpendicular_line(const typename PlaneC3<R>::Point_3 &p) const
{
return Line_3(p, orthogonal_direction());
}
template < class R >
inline
typename PlaneC3<R>::Plane_3
PlaneC3<R>::opposite() const
{
return PlaneC3<R>(-a(), -b(), -c(), -d());
}
template < class R >
inline
typename R::Oriented_side
PlaneC3<R>::
oriented_side(const typename PlaneC3<R>::Point_3 &p) const
{
return side_of_oriented_plane(*this, p);
}
template < class R >
inline
typename R::Boolean
PlaneC3<R>::
has_on_positive_side(const typename PlaneC3<R>::Point_3 &p) const
{
return oriented_side(p) == ON_POSITIVE_SIDE;
}
template < class R >
inline
typename R::Boolean
PlaneC3<R>::
has_on_negative_side(const typename PlaneC3<R>::Point_3 &p) const
{
return oriented_side(p) == ON_NEGATIVE_SIDE;
}
template < class R >
inline
typename R::Boolean
PlaneC3<R>::
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
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