CGAL 5.1 - 2D and 3D Linear Geometry Kernel: CGAL::Circle_3< Kernel > Class Template Reference

CGAL 5.1 - 2D and 3D Linear Geometry Kernel

#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. More...

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`. More...

	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`. More...

	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`. More...

	Circle_3 (const Sphere_3< Kernel > &sphere1, const Sphere_3< Kernel > &sphere2)
	introduces a variable `c` of type `Circle_3`. More...

	Circle_3 (constSphere_3< Kernel > &sphere, const Plane_3< Kernel > &plane)
	introduces a variable `c` of type `Circle_3`. More...

	Circle_3 (const Plane_3< Kernel > &plane, const Sphere_3< Kernel > &sphere)
	introduces a variable `c` of type `Circle_3`. More...

Access Functions
const Point_3< Kernel > &	center () const
	returns the center of `c`. More...

const Kernel::FT &	squared_radius () const
	returns the squared radius of `c`. More...

const Plane_3< Kernel > &	supporting_plane () const
	returns the supporting plane of `c`. More...

const Sphere_3< Kernel > &	diametral_sphere () const
	returns the diametral sphere of `c`. More...

Kernel::FT const &	area_divided_by_pi () const
	returns the area of `c`, divided by \( \pi\). More...

double	approximate_area () const
	returns an approximation of the area of `c`. More...

Kernel::FT	squared_length_divided_by_pi_square () const
	returns the squared length of `c`, divided by \( \pi^2\). More...

double	approximate_squared_length () const
	returns an approximation of the squared length (i.e. perimeter) of `c`. More...

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

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

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 \( \geq\) 0.

◆ 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 \( \geq\) 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	(	constSphere_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

◆ approximate_area()

template<typename Kernel >

double CGAL::Circle_3< Kernel >::approximate_area ( ) const

returns an approximation of the area of c.

◆ approximate_squared_length()

template<typename Kernel >

double CGAL::Circle_3< Kernel >::approximate_squared_length ( ) const

returns an approximation of the squared length (i.e. perimeter) of c.

◆ area_divided_by_pi()

template<typename Kernel >

Kernel::FT const& CGAL::Circle_3< Kernel >::area_divided_by_pi ( ) const

returns the area of c, divided by \( \pi\).

◆ bbox()

template<typename Kernel >

Bbox_3 CGAL::Circle_3< Kernel >::bbox ( ) const

returns a bounding box containing c.

◆ center()

template<typename Kernel >

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

returns the center of c.

◆ diametral_sphere()

template<typename Kernel >

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

returns the diametral sphere of c.

◆ has_on()

template<typename Kernel >

bool CGAL::Circle_3< Kernel >::has_on ( const Point_3< Kernel > & p ) const

◆ squared_length_divided_by_pi_square()

template<typename Kernel >

Kernel::FT CGAL::Circle_3< Kernel >::squared_length_divided_by_pi_square ( ) const

returns the squared length of c, divided by \( \pi^2\).

◆ squared_radius()

template<typename Kernel >

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

returns the squared radius of c.

◆ supporting_plane()

template<typename Kernel >

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

returns the supporting plane of c.

Friends And Related Function Documentation

◆ operator!=()

template<typename Kernel >

bool operator!=	(	const Circle_3< Kernel > &	c1,
		Circle_3< Kernel > const &	c2
	)

related

◆ operator==()

template<typename Kernel >

bool operator==	(	const Circle_3< Kernel > &	c1,
		Circle_3< Kernel > const &	c2
	)

related

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.