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> center, Kernel::FT sq_r, Plane_3<Kernel> 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> center, Kernel::FT sq_r, Vector_3<Kernel> 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> p, Point_3<Kernel> q, Point_3<Kernel> 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> sphere1, Sphere_3<Kernel> 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> sphere, Plane_3<Kernel> 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> plane, Sphere_3<Kernel> 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>	c.center ()	returns the center of c.
Kernel::FT	c.squared_radius ()	returns the squared radius of c.
Plane_3<Kernel>	c.supporting_plane ()	returns the supporting plane of c.
Sphere_3<Kernel>	c.diametral_sphere ()	returns the diametral sphere of c.

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

Predicates

bool

c.has_on ( Point_3<Kernel> p)

Operations

bool	operator == ( c1, 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 != ( c1, c2)

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

CGAL::Circle_3<Kernel>

Definition

Creation

Access Functions

Predicates

Operations

See Also