mirror of https://github.com/CGAL/cgal
385 lines
10 KiB
C++
385 lines
10 KiB
C++
// 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.
|
|
//
|
|
// $Source$
|
|
// $Revision$ $Date$
|
|
// $Name$
|
|
//
|
|
// Author(s) : Herve Bronnimann
|
|
|
|
#ifndef CGAL_CARTESIAN_SPHERE_3_H
|
|
#define CGAL_CARTESIAN_SPHERE_3_H
|
|
|
|
#include <CGAL/utility.h>
|
|
#include <CGAL/Interval_arithmetic.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_::Aff_transformation_3 Aff_transformation_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 ¢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 = 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 ¢er,
|
|
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;
|
|
}
|
|
|
|
Sphere_3 orthogonal_transform(const Aff_transformation_3 &t) const
|
|
{
|
|
// FIXME: precond: t.is_orthogonal() (*UNDEFINED*)
|
|
Vector_3 vec(FT(1), FT(0)); // unit vector
|
|
vec = vec.transform(t); // transformed
|
|
FT sq_scale = vec.squared_length(); // squared scaling factor
|
|
|
|
return SphereC3(t.transform(center()),
|
|
sq_scale * squared_radius(),
|
|
t.is_even() ? orientation()
|
|
: CGAL::opposite(orientation()));
|
|
}
|
|
|
|
// 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_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;
|
|
|
|
Bbox_3 bbox() 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_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()) );
|
|
}
|
|
|
|
template < class R >
|
|
CGAL_KERNEL_INLINE
|
|
Bbox_3
|
|
SphereC3<R>::bbox() const
|
|
{
|
|
typename R::Construct_bbox_3 construct_bbox_3;
|
|
Bbox_3 b = construct_bbox_3(center());
|
|
|
|
Interval_nt<> x (b.xmin(), b.xmax());
|
|
Interval_nt<> y (b.ymin(), b.ymax());
|
|
Interval_nt<> z (b.zmin(), b.zmax());
|
|
|
|
Interval_nt<> sqr = CGAL_NTS to_interval(squared_radius());
|
|
Interval_nt<> r = CGAL::sqrt(sqr);
|
|
Interval_nt<> minx = x-r;
|
|
Interval_nt<> maxx = x+r;
|
|
Interval_nt<> miny = y-r;
|
|
Interval_nt<> maxy = y+r;
|
|
Interval_nt<> minz = z-r;
|
|
Interval_nt<> maxz = z+r;
|
|
|
|
return Bbox_3(minx.inf(), miny.inf(), minz.inf(),
|
|
maxx.sup(), maxy.sup(), maxz.sup());
|
|
}
|
|
|
|
/*
|
|
template < class R >
|
|
inline
|
|
EllipseC3<SphereC3<R>::FT> SphereC3<R>::i
|
|
transform(const Aff_transformationC3<SphereC3<R>::FT> &t) const
|
|
{
|
|
return SphereC3<R>(t.transform(center()),
|
|
squared_radius(),
|
|
orientation());
|
|
}
|
|
*/
|
|
|
|
#ifndef CGAL_NO_OSTREAM_INSERT_SPHEREC3
|
|
template < class R >
|
|
CGAL_KERNEL_INLINE
|
|
std::ostream &
|
|
operator<<(std::ostream &os, const SphereC3<R> &c)
|
|
{
|
|
switch(os.iword(IO::mode)) {
|
|
case IO::ASCII :
|
|
os << c.center() << ' ' << c.squared_radius() << ' '
|
|
<< static_cast<int>(c.orientation());
|
|
break;
|
|
case IO::BINARY :
|
|
os << c.center();
|
|
write(os, c.squared_radius());
|
|
write(os, static_cast<int>(c.orientation()));
|
|
break;
|
|
default:
|
|
os << "SphereC3(" << c.center() << ", " << c.squared_radius();
|
|
switch (c.orientation()) {
|
|
case CLOCKWISE:
|
|
os << ", clockwise)";
|
|
break;
|
|
case COUNTERCLOCKWISE:
|
|
os << ", counterclockwise)";
|
|
break;
|
|
default:
|
|
os << ", collinear)";
|
|
break;
|
|
}
|
|
break;
|
|
}
|
|
return os;
|
|
}
|
|
#endif // CGAL_NO_OSTREAM_INSERT_SPHEREC3
|
|
|
|
#ifndef CGAL_NO_ISTREAM_EXTRACT_SPHEREC3
|
|
template < class R >
|
|
CGAL_KERNEL_INLINE
|
|
std::istream &
|
|
operator>>(std::istream &is, SphereC3<R> &c)
|
|
{
|
|
typename R::Point_3 center;
|
|
typename R::FT squared_radius;
|
|
int o;
|
|
switch(is.iword(IO::mode)) {
|
|
case IO::ASCII :
|
|
is >> center >> squared_radius >> o;
|
|
break;
|
|
case IO::BINARY :
|
|
is >> center;
|
|
read(is, squared_radius);
|
|
is >> o;
|
|
break;
|
|
default:
|
|
std::cerr << "" << std::endl;
|
|
std::cerr << "Stream must be in ascii or binary mode" << std::endl;
|
|
break;
|
|
}
|
|
if (is)
|
|
c = SphereC3<R>(center, squared_radius,
|
|
static_cast<Orientation>(o));
|
|
return is;
|
|
}
|
|
#endif // CGAL_NO_ISTREAM_EXTRACT_SPHEREC3
|
|
|
|
CGAL_END_NAMESPACE
|
|
|
|
#endif // CGAL_CARTESIAN_SPHERE_3_H
|