## CGAL::Sphere_3<Kernel>

### Definition

An object of type Sphere_3<Kernel> 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 also 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<Kernel> c ( | Point_3<Kernel> center, Kernel::FT squared_radius, Orientation orientation = COUNTERCLOCKWISE);

| introduces a variable c of type Sphere_3<Kernel>. 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<Kernel> c ( | Point_3<Kernel> p, Point_3<Kernel> q, Point_3<Kernel> r, Point_3<Kernel> s);

| introduces a variable c of type Sphere_3<Kernel>. 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<Kernel> c ( | Point_3<Kernel> p, Point_3<Kernel> q, Point_3<Kernel> r, Orientation o = COUNTERCLOCKWISE);

| introduces a variable c of type Sphere_3<Kernel>. 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<Kernel> c ( | Point_3<Kernel> p, Point_3<Kernel> q, Orientation o = COUNTERCLOCKWISE);

| introduces a variable c of type Sphere_3<Kernel>. 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<Kernel> c ( | Point_3<Kernel> center, Orientation orientation = COUNTERCLOCKWISE);

| introduces a variable c of type Sphere_3<Kernel>. 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<Kernel> | c.center () | returns the center of c.
Kernel::FT | c.squared_radius ()
|  | returns the squared radius of c.
orientation | c.orientation () | returns the orientation of c.
bool | c.operator == ( sphere2)
|  | returns true, iff c and sphere2 are equal, i.e. if they have the same center, same squared radius and same orientation.
bool | c.operator != ( sphere2)
|  | returns true, iff c and sphere2 are not equal.

### 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<Kernel> 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<Kernel> 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<Kernel> p)
bool | c.has_on_negative_side ( Point_3<Kernel> p)
bool | c.has_on_boundary ( Point_3<Kernel> p)
bool | c.has_on_bounded_side ( Point_3<Kernel> p)
bool | c.has_on_unbounded_side ( Point_3<Kernel> p)

### Miscellaneous

Sphere_3<Kernel> | c.opposite () | returns the sphere with the same center and squared radius as c but with opposite orientation.

Sphere_3<Kernel>

c.orthogonal_transform ( | Aff_transformation_3<Kernel> 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