CGAL::Sphere_3<R>

Definition

An object of type Sphere_3<R> is a sphere in the three-dimensional Euclidean space $$ ³. The sphere is oriented, i.e. its boundary has clockwise or counterclockwise orientation. The boundary splits $$ ³ into a positive and a negative side, where the positive side is to the left of the boundary. The boundary further splits $$ ³ into a bounded and an unbounded side. Note that the sphere can be degenerated, i.e. the squared radius may be zero.

Creation

Sphere_3<R> c ( Point_3<R> center, R::FT squared_radius, Orientation orientation = COUNTERCLOCKWISE);
	introduces a variable c of type Sphere_3<R>. It is initialized to the sphere with center center, squared radius squared_radius and orientation orientation. Precondition: orientation $$ COPLANAR, and furthermore, squared_radius $$ 0.
Sphere_3<R> c ( Point_3<R> p, Point_3<R> q, Point_3<R> r, Point_3<R> s);
	introduces a variable c of type Sphere_3<R>. It is initialized to the unique sphere which passes through the points p, q, r and s. The orientation of the sphere is the orientation of the point quadruple p, q, r, s. Precondition: p, q, r, and s are not collinear.
Sphere_3<R> c ( Point_3<R> p, Point_3<R> q, Point_3<R> r, Orientation o = COUNTERCLOCKWISE);
	introduces a variable c of type Sphere_3<R>. It is initialized to the smallest sphere which passes through the points p, q, and r. The orientation of the sphere is o. Precondition: o is not COPLANAR.
Sphere_3<R> c ( Point_3<R> p, Point_3<R> q, Orientation o = COUNTERCLOCKWISE);
	introduces a variable c of type Sphere_3<R>. It is initialized to the smallest sphere which passes through the points p and q. The orientation of the sphere is o. Precondition: o is not COPLANAR.
Sphere_3<R> c ( Point_3<R> center, Orientation orientation = COUNTERCLOCKWISE);
	introduces a variable c of type Sphere_3<R>. It is initialized to the sphere with center center, squared radius zero and orientation orientation. Precondition: orientation $$ COPLANAR. Postcondition: c.is_degenerate() = true.

Access Functions

Point_3<R>	c.center ()	returns the center of c.
R::FT	c.squared_radius ()
		returns the squared radius of c.
orientation	c.orientation ()	returns the orientation of c.

Predicates

bool	c.is_degenerate ()	returns true, iff c is degenerate, i.e. if c has squared radius zero.
Oriented_side	c.oriented_side ( Point_3<R> p)
		returns either the constant ON_ORIENTED_BOUNDARY, ON_POSITIVE_SIDE, or ON_NEGATIVE_SIDE, iff p lies on the boundary, properly on the positive side, or properly on the negative side of c, resp.
Bounded_side	c.bounded_side ( Point_3<R> p)
		returns ON_BOUNDED_SIDE, ON_BOUNDARY, or ON_UNBOUNDED_SIDE iff p lies properly inside, on the boundary, or properly outside of c, resp.
bool	c.has_on_positive_side ( Point_3<R> p)
bool	c.has_on_negative_side ( Point_3<R> p)
bool	c.has_on_boundary ( Point_3<R> p)
bool	c.has_on_bounded_side ( Point_3<R> p)
bool	c.has_on_unbounded_side ( Point_3<R> p)

Miscellaneous

Sphere_3<R>	c.opposite ()	returns the sphere with the same center and squared radius as c but with opposite orientation.
Sphere_3<R>	c.orthogonal_transform ( Aff_transformation_3<R> at)
		returns the sphere obtained by applying $$at on c. Precondition: at is an orthogonal transformation.
Bbox_3	c.bbox ()	returns a bounding box containing c.

See Also

Kernel::Sphere_3