CGAL::Circle_3< Kernel > Class Template Reference

#include <CGAL/Circle_3.h>

Definition

template<typename Kernel>
class CGAL::Circle_3< Kernel >

An object c of type Circle_3 is a circle in the three-dimensional Euclidean space \( \E^3\).

Note that the circle can be degenerate, i.e. the squared radius may be zero.

Is model of

Kernel::Circle_3

Related Functions
(Note that these are not member functions.)
bool	operator== (const Circle_3< Kernel > &c1, Circle_3< Kernel > const &c2)
	returns true, iff c1 and c2 are equal, i.e. if they have the same center, the same squared radius and the same supporting plane.
bool	operator!= (const Circle_3< Kernel > &c1, Circle_3< Kernel > const &c2)

Creation
	Circle_3 (const Point_3< Kernel > &center, const Kernel::FT &sq_r, const Plane_3< Kernel > &plane)
	introduces a variable c of type Circle_3.
	Circle_3 (const Point_3< Kernel > &center, const Kernel::FT &sq_r, const Vector_3< Kernel > &n)
	introduces a variable c of type Circle_3.
	Circle_3 (const Point_3< Kernel > &p, const Point_3< Kernel > &q, const Point_3< Kernel > &r)
	introduces a variable c of type Circle_3.
	Circle_3 (const Sphere_3< Kernel > &sphere1, const Sphere_3< Kernel > &sphere2)
	introduces a variable c of type Circle_3.
	Circle_3 (const Sphere_3< Kernel > &sphere, const Plane_3< Kernel > &plane)
	introduces a variable c of type Circle_3.
	Circle_3 (const Plane_3< Kernel > &plane, const Sphere_3< Kernel > &sphere)
	introduces a variable c of type Circle_3.

Access Functions
const Point_3< Kernel > &	center () const
	returns the center of c.
const Kernel::FT &	squared_radius () const
	returns the squared radius of c.
const Plane_3< Kernel > &	supporting_plane () const
	returns the supporting plane of c.
const Sphere_3< Kernel > &	diametral_sphere () const
	returns the diametral sphere of c.
Kernel::FT const &	area_divided_by_pi () const
	returns the area of c, divided by \( \pi\).
double	approximate_area () const
	returns an approximation of the area of c.
Kernel::FT	squared_length_divided_by_pi_square () const
	returns the squared length of c, divided by \( \pi^2\).
double	approximate_squared_length () const
	returns an approximation of the squared length (i.e. perimeter) of c.

Predicates
bool	has_on (const Point_3< Kernel > &p) const

Operations
Bbox_3	bbox () const
	returns a bounding box containing c.

Constructor & Destructor Documentation

Circle_3() [1/6]

template<typename Kernel >

CGAL::Circle_3< Kernel >::Circle_3	(	const Point_3< Kernel > &	center,
		const Kernel::FT &	sq_r,
		const Plane_3< Kernel > &	plane
	)

introduces a variable c of type Circle_3.

It is initialized to the circle of center center and squared radius sq_r in plane plane.

Precondition

center lies in plane and sq_r >= 0.

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

Circle_3() [2/6]

template<typename Kernel >

CGAL::Circle_3< Kernel >::Circle_3	(	const Point_3< Kernel > &	center,
		const Kernel::FT &	sq_r,
		const Vector_3< Kernel > &	n
	)

introduces a variable c of type Circle_3.

It is initialized to the circle of center center and squared radius sq_r in a plane normal to the vector n.

Precondition

sq_r >= 0.

Circle_3() [3/6]

template<typename Kernel >

CGAL::Circle_3< Kernel >::Circle_3	(	const Point_3< Kernel > &	p,
		const Point_3< Kernel > &	q,
		const Point_3< Kernel > &	r
	)

introduces a variable c of type Circle_3.

It is initialized to the circle passing through the three points.

Precondition

The three points are not collinear.

Circle_3() [4/6]

template<typename Kernel >

CGAL::Circle_3< Kernel >::Circle_3	(	const Sphere_3< Kernel > &	sphere1,
		const Sphere_3< Kernel > &	sphere2
	)

introduces a variable c of type Circle_3.

It is initialized to the circle along which the two spheres intersect.

Precondition

The two spheres intersect along a circle.

Circle_3() [5/6]

template<typename Kernel >

CGAL::Circle_3< Kernel >::Circle_3	(	const Sphere_3< Kernel > &	sphere,
		const Plane_3< Kernel > &	plane
	)

introduces a variable c of type Circle_3.

It is initialized to the circle along which the sphere and the plane intersect.

Precondition

The sphere and the plane intersect along a circle.

Circle_3() [6/6]

template<typename Kernel >

CGAL::Circle_3< Kernel >::Circle_3	(	const Plane_3< Kernel > &	plane,
		const Sphere_3< Kernel > &	sphere
	)

introduces a variable c of type Circle_3.

It is initialized to the circle along which the sphere and the plane intersect.

Precondition

The sphere and the plane intersect along a circle.

Member Function Documentation

center()

template<typename Kernel >

const Point_3< Kernel > & CGAL::Circle_3< Kernel >::center

(

)

const

returns the center of c.

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

diametral_sphere()

template<typename Kernel >

const Sphere_3< Kernel > & CGAL::Circle_3< Kernel >::diametral_sphere

(

)

const

returns the diametral sphere of c.

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

squared_radius()

template<typename Kernel >

const Kernel::FT & CGAL::Circle_3< Kernel >::squared_radius

(

)

const

returns the squared radius of c.

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

supporting_plane()

template<typename Kernel >

const Plane_3< Kernel > & CGAL::Circle_3< Kernel >::supporting_plane

(

)

const

returns the supporting plane of c.

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.