Circle_3<Kernel>

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CGAL::Circle_3<Kernel>

Definition

An object of type Circle_3<Kernel> is a circle in the three-dimensional Euclidean space ³. Note that the circle can be degenerate, i.e. the squared radius may be zero.

Creation

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

introduces a variable c of type Circle_3<Kernel>. 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.

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

introduces a variable c of type Circle_3<Kernel>. 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<Kernel> c ( Point_3<Kernel> const& p, Point_3<Kernel> const& q, Point_3<Kernel> const& r);

introduces a variable c of type Circle_3<Kernel>. It is initialized to the circle passing through the three points.

Precondition:

The three points are not collinear.

Circle_3<Kernel> c ( Sphere_3<Kernel> const& sphere1, Sphere_3<Kernel> const& sphere2);

introduces a variable c of type Circle_3<Kernel>. It is initialized to the circle along which the two spheres intersect.

Precondition:

The two spheres intersect along a circle.

Circle_3<Kernel> c ( Sphere_3<Kernel> const& sphere, Plane_3<Kernel> const& plane);

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

introduces a variable c of type Circle_3<Kernel>. It is initialized to the circle along which the sphere and the plane intersect.

Precondition:

The sphere and the plane intersect along a circle.

Access Functions

Point_3<Kernel> const&	c.center () const	returns the center of c.
Kernel::FT const&	c.squared_radius () const	returns the squared radius of c.
Plane_3<Kernel> const&	c.supporting_plane () const	returns the supporting plane of c.
Sphere_3<Kernel> const&	c.diametral_sphere () const	returns the diametral sphere of c.

Kernel::FT const&	c.area_divided_by_pi () const	returns the area of c, divided by π.
double const&	c.approximate_area () const	returns an approximation of the area of c.
Kernel::FT const&	c.squared_length_divided_by_pi_square () const
		returns the squared length of c, divided by π².
double const&	c.approximate_squared_length () const
		returns an approximation of the squared length (i.e. perimeter) of c.

Predicates

bool

c.has_on ( Point_3<Kernel> const& p) const

Operations

bool	operator == ( const& c1, 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& c1, const& c2)

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

CGAL::Circle_3<Kernel>

Definition

Creation

Access Functions

Predicates

Operations

See Also