/usr/include/CGAL/Cartesian/Circle_3.h is in libcgal-dev 4.7-4.
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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) : Monique Teillaud, Pedro Machado, Sebastien Loriot
#ifndef CGAL_CARTESIAN_CIRCLEC3_H
#define CGAL_CARTESIAN_CIRCLEC3_H
#include <CGAL/Interval_nt.h>
namespace CGAL {
template <class R_ >
class CircleC3 {
typedef typename R_::Sphere_3 Sphere_3;
typedef typename R_::Plane_3 Plane_3;
typedef typename R_::Point_3 Point_3;
typedef typename R_::Vector_3 Vector_3;
typedef typename R_::Direction_3 Direction_3;
typedef typename R_::FT FT;
typedef std::pair<Sphere_3, Plane_3> Rep;
typedef typename R_::template Handle<Rep>::type Base;
Base base;
public:
typedef R_ R;
CircleC3() {}
CircleC3(const Point_3& center, const FT& squared_r, const Direction_3& d)
{
CGAL_kernel_assertion(squared_r >= FT(0));
// non-degenerated Direction
CGAL_kernel_assertion((d.dx() != FT(0)) || (d.dy() != FT(0)) || (d.dz() != FT(0)));
base = Rep(Sphere_3(center,squared_r),
plane_from_point_direction(center, d));
}
CircleC3(const Point_3& center, const FT& squared_r, const Vector_3& normal)
{
CGAL_kernel_assertion(squared_r >= FT(0));
// non-degenerated Vector
CGAL_kernel_assertion((normal.x() != FT(0)) ||
(normal.y() != FT(0)) ||
(normal.z() != FT(0)));
base = Rep(Sphere_3(center,squared_r),
Plane_3(center, normal.direction()));
}
CircleC3(const Point_3& center, const FT& squared_r, const Plane_3& p)
{
// the plane contains the center and it is not degenerate
CGAL_kernel_assertion(!R().is_degenerate_3_object()(p));
CGAL_kernel_assertion((p.a() * center.x() +
p.b() * center.y() +
p.c() * center.z() +
p.d()) == CGAL::ZERO);
CGAL_kernel_assertion(squared_r >= FT(0));
base = Rep(Sphere_3(center,squared_r), p);
}
CircleC3(const Sphere_3 &s1, const Sphere_3 &s2) {
Object obj = R().intersect_3_object()(s1, s2);
// s1,s2 must intersect
CGAL_kernel_precondition(!(obj.is_empty()));
const typename R::Circle_3* circle_ptr=object_cast<typename R::Circle_3>(&obj);
if(circle_ptr!=NULL)
base = Rep(circle_ptr->diametral_sphere(), circle_ptr->supporting_plane());
else {
const typename R::Point_3* point=object_cast<typename R::Point_3>(&obj);
CGAL_kernel_precondition(point!=NULL);
CircleC3 circle = CircleC3(*point, FT(0), Vector_3(FT(1),FT(0),FT(0)));
base = Rep(circle.diametral_sphere(), circle.supporting_plane());
}
}
CircleC3(const Plane_3 &p, const Sphere_3 &s, int) : base(s, p) {}
CircleC3(const Plane_3 &p, const Sphere_3 &s) {
Object obj = R().intersect_3_object()(p, s);
// s1,s2 must intersect
CGAL_kernel_precondition(!(obj.is_empty()));
const typename R::Circle_3* circle_ptr=object_cast<typename R::Circle_3>(&obj);
if(circle_ptr!=NULL)
base = Rep(circle_ptr->diametral_sphere(), circle_ptr->supporting_plane());
else {
const typename R::Point_3* point=object_cast<typename R::Point_3>(&obj);
CGAL_kernel_precondition(point!=NULL);
CircleC3 circle = CircleC3(*point, FT(0), Vector_3(FT(1),FT(0),FT(0)));
base = Rep(circle.diametral_sphere(), circle.supporting_plane());
}
}
CircleC3(const Point_3 &p, const Point_3 &q, const Point_3 &r) {
// p, q, r are not collinear
CGAL_kernel_precondition(!R().collinear_3_object()(p, q, r));
Plane_3 p1 = R().construct_plane_3_object()(p, q, r);
Plane_3 p2 = R().construct_bisector_3_object()(p, q);
Plane_3 p3 = R().construct_bisector_3_object()(p, r);
Object obj = R().intersect_3_object()(p1, p2, p3);
// must be a point, otherwise they are collinear
const Point_3& center=*object_cast<Point_3>(&obj);
FT sqr = R().compute_squared_distance_3_object()(center, r);
Sphere_3 s = R().construct_sphere_3_object()(center, sqr);
base = Rep(s, p1);
}
const Plane_3& supporting_plane() const
{
return get_pointee_or_identity(base).second;
}
const Sphere_3& supporting_sphere() const
{
return diametral_sphere();
}
Point_3 center() const
{
return diametral_sphere().center();
}
FT squared_radius() const
{
return diametral_sphere().squared_radius();
}
const Sphere_3& diametral_sphere() const
{
return get_pointee_or_identity(base).first;
}
double approximate_area() const
{
return CGAL_PI * to_double(squared_radius());
}
double approximate_squared_length() const
{
return CGAL_PI * CGAL_PI * 4.0 * to_double(squared_radius());
}
FT area_divided_by_pi() const
{
return squared_radius();
}
FT squared_length_divided_by_pi_square() const
{
return 4 * squared_radius();
}
// this bbox function
// can be optimize by doing different cases
// for each variable = 0 (cases with is_zero)
CGAL::Bbox_3 bbox() const
{
typedef CGAL::Interval_nt<false> Interval;
CGAL::Interval_nt<false>::Protector ip;
const Sphere_3 &s = diametral_sphere();
const FT &sq_r = s.squared_radius();
const Point_3 &p = s.center();
if(sq_r == FT(0)) return p.bbox();
const Plane_3 &plane = supporting_plane();
const Interval a = CGAL::to_interval(plane.a());
const Interval b = CGAL::to_interval(plane.b());
const Interval c = CGAL::to_interval(plane.c());
const Interval x = CGAL::to_interval(p.x());
const Interval y = CGAL::to_interval(p.y());
const Interval z = CGAL::to_interval(p.z());
const Interval r2 = CGAL::to_interval(sq_r);
const Interval r = CGAL::sqrt(r2); // maybe we can work with r2
// in order to save this operation
// but if the coefficients are to high
// the multiplication would lead to inf
// results
const Interval a2 = CGAL::square(a);
const Interval b2 = CGAL::square(b);
const Interval c2 = CGAL::square(c);
const Interval sqr_sum = a2 + b2 + c2;
const Interval mx = r * CGAL::sqrt((sqr_sum - a2)/sqr_sum);
const Interval my = r * CGAL::sqrt((sqr_sum - b2)/sqr_sum);
const Interval mz = r * CGAL::sqrt((sqr_sum - c2)/sqr_sum);
return CGAL::Bbox_3((x-mx).inf(),(y-my).inf(),(z-mz).inf(),
(x+mx).sup(),(y+my).sup(),(z+mz).sup());
}
bool operator==(const CircleC3 &) const;
bool operator!=(const CircleC3 &) const;
bool has_on(const Point_3 &p) const;
bool has_on_bounded_side(const Point_3 &p) const;
bool has_on_unbounded_side(const Point_3 &p) const;
Bounded_side bounded_side(const Point_3 &p) const;
bool is_degenerate() const
{
return diametral_sphere().is_degenerate();
}
};
template < class R >
inline
bool
CircleC3<R>::
has_on(const typename CircleC3<R>::Point_3 &p) const
{
return R().has_on_3_object()(diametral_sphere(),p) &&
R().has_on_3_object()(supporting_plane(),p);
}
template < class R >
inline
bool
CircleC3<R>::
has_on_bounded_side(const typename CircleC3<R>::Point_3 &p) const
{
CGAL_kernel_precondition(R().has_on_3_object()(supporting_plane(), p));
return squared_distance(center(),p) < squared_radius();
}
template < class R >
inline
bool
CircleC3<R>::
has_on_unbounded_side(const typename CircleC3<R>::Point_3 &p) const
{
CGAL_kernel_precondition(R().has_on_3_object()(supporting_plane(), p));
return squared_distance(center(),p) > squared_radius();
}
template < class R >
CGAL_KERNEL_INLINE
Bounded_side
CircleC3<R>::
bounded_side(const typename CircleC3<R>::Point_3 &p) const
{
CGAL_kernel_precondition(is_degenerate() || R().has_on_3_object()(supporting_plane(), p));
return diametral_sphere().bounded_side(p);
}
template < class R >
CGAL_KERNEL_INLINE
bool
CircleC3<R>::operator==(const CircleC3<R> &t) const
{
if (CGAL::identical(base, t.base))
return true;
if(!(center() == t.center() &&
squared_radius() == t.squared_radius())) return false;
const typename R::Plane_3 p1 = supporting_plane();
const typename R::Plane_3 p2 = t.supporting_plane();
if(is_zero(p1.a())) {
if(!is_zero(p2.a())) return false;
if(is_zero(p1.b())) {
if(!is_zero(p2.b())) return false;
return p1.c() * p2.d() == p1.d() * p2.c();
}
return (p2.c() * p1.b() == p1.c() * p2.b()) &&
(p2.d() * p1.b() == p1.d() * p2.b());
}
return (p2.b() * p1.a() == p1.b() * p2.a()) &&
(p2.c() * p1.a() == p1.c() * p2.a()) &&
(p2.d() * p1.a() == p1.d() * p2.a());
}
template < class R >
CGAL_KERNEL_INLINE
bool
CircleC3<R>::operator!=(const CircleC3<R> &t) const
{
return !(*this == t);
}
} //namespace CGAL
#endif // CGAL_CARTESIAN_CIRCLEC3_H
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