Sphere_3<Kernel>

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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

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 coplanar.

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.

Sphere_3<Kernel> c ( Circle_3<Kernel> c);

introduces a variable c of type Sphere_3<Kernel>. It is initialized to the diametral sphere of the circle.

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)

bool	c.has_on ( Point_3<Kernel> p)
bool	c.has_on ( Circle_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.

CGAL::Sphere_3<Kernel>

Definition

Creation

Access Functions

Predicates

Miscellaneous

See Also