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cgal/Cartesian_kernel/include/CGAL/Cartesian/Sphere_3.h

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// Copyright (c) 2000 Utrecht University (The Netherlands),
// ETH Zurich (Switzerland), Freie Universitaet Berlin (Germany),
// INRIA Sophia-Antipolis (France), Martin-Luther-University Halle-Wittenberg
// (Germany), Max-Planck-Institute Saarbruecken (Germany), RISC Linz (Austria),
// 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; version 2.1 of the License.
// See the file LICENSE.LGPL distributed with CGAL.
//
// 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) : Herve Bronnimann
#ifndef CGAL_CARTESIAN_SPHERE_3_H
#define CGAL_CARTESIAN_SPHERE_3_H
#include <CGAL/utility.h>
#include <CGAL/Handle_for.h>
#include <CGAL/Interval_nt.h>
CGAL_BEGIN_NAMESPACE
template <class R_>
class SphereC3
{
typedef typename R_::FT FT;
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 Triple<Point_3, FT, Orientation> Rep;
typedef typename R_::template Handle<Rep>::type Base;
Base base;
public:
typedef R_ R;
SphereC3() {}
SphereC3(const Point_3 &center, 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 = CGAL::orientation(p, q, r, s);
Point_3 center = 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 = 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);
}
SphereC3(const Point_3 &center,
const Orientation& o = COUNTERCLOCKWISE)
{
CGAL_kernel_precondition(o != COLLINEAR);
base = Rep(center, FT(0), o);
}
bool operator==(const SphereC3 &) const;
bool operator!=(const SphereC3 &) const;
const Point_3 & center() const
{
return get(base).first;
}
const FT & squared_radius() const
{
// Returns the square of the radius (instead of the radius itself,
// which would require square roots)
return get(base).second;
}
Orientation orientation() const
{
return get(base).third;
}
// A circle is degenerate if its (squared) radius is null or negative
bool is_degenerate() const;
// Returns a circle with opposite orientation
Sphere_3 opposite() const;
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
bool has_on(const Circle_3 &p) const;
bool has_on_boundary(const Point_3 &p) const;
bool has_on_positive_side(const Point_3 &p) const;
bool 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
bool has_on_bounded_side(const Point_3 &p) const;
bool has_on_unbounded_side(const Point_3 &p) const;
};
template < class R >
CGAL_KERNEL_INLINE
bool
SphereC3<R>::operator==(const SphereC3<R> &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
bool
SphereC3<R>::operator!=(const SphereC3<R> &t) const
{
return !(*this == t);
}
template < class R >
CGAL_KERNEL_MEDIUM_INLINE
Oriented_side
SphereC3<R>::
oriented_side(const typename SphereC3<R>::Point_3 &p) const
{
return Oriented_side(bounded_side(p) * orientation());
}
template < class R >
CGAL_KERNEL_INLINE
Bounded_side
SphereC3<R>::
bounded_side(const typename SphereC3<R>::Point_3 &p) const
{
// FIXME: it's a predicate...
return Bounded_side((Comparison_result)
CGAL_NTS compare(squared_radius(),
squared_distance(center(),p)));
}
template < class R >
inline
bool
SphereC3<R>::
has_on(const typename SphereC3<R>::Circle_3 &c) const
{
typedef typename SphereC3<R>::Point_3 Point_3;
typedef typename SphereC3<R>::FT FT;
Point_3 proj = c.supporting_plane().projection(center());
if(!(proj == c.center())) return false;
const FT d2 = CGAL::square(center().x() - c.center().x()) +
CGAL::square(center().y() - c.center().y()) +
CGAL::square(center().z() - c.center().z());
return ((squared_radius() - d2) == c.squared_radius());
}
template < class R >
inline
bool
SphereC3<R>::
has_on_boundary(const typename SphereC3<R>::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
bool
SphereC3<R>::
has_on_negative_side(const typename SphereC3<R>::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
bool
SphereC3<R>::
has_on_positive_side(const typename SphereC3<R>::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
bool
SphereC3<R>::
has_on_bounded_side(const typename SphereC3<R>::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
bool
SphereC3<R>::
has_on_unbounded_side(const typename SphereC3<R>::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
bool
SphereC3<R>::
is_degenerate() const
{
// FIXME: it's a predicate (?)
return CGAL_NTS is_zero(squared_radius());
}
template < class R >
inline
typename SphereC3<R>::Sphere_3
SphereC3<R>::opposite() const
{
return SphereC3<R>(center(), squared_radius(),
CGAL::opposite(orientation()) );
}
CGAL_END_NAMESPACE
#endif // CGAL_CARTESIAN_SPHERE_3_H
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