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 $$.
double	c.approximate_area ()	returns an approximation of the area of c.
Kernel::FT	c.squared_length_divided_by_pi_square ()
		returns the squared length of c, divided by $$2.
double	c.approximate_squared_length ()	returns an approximation of the squared length (i.e. perimeter) of c.

Predicates

Operations

See Also

Kernel::Circle_3