Circle_2<Kernel>

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CGAL::Circle_2<Kernel>

Definition

An object of type Circle_2<Kernel> is a circle in the two-dimensional Euclidean plane ². The circle is oriented, i.e. its boundary has clockwise or counterclockwise orientation . The boundary splits ² into a positive and a negative side, where the positive side is to the left of the boundary. The boundary also splits ² into a bounded and an unbounded side. Note that the circle can be degenerated, i.e. the squared radius may be zero.

Creation

Circle_2<Kernel> c ( Point_2<Kernel> const& center, Kernel::FT const& squared_radius, Orientation const& ori = COUNTERCLOCKWISE);

introduces a variable c of type Circle_2<Kernel>. It is initialized to the circle with center center, squared radius squared_radius and orientation ori.

Precondition:

ori ≠ COLLINEAR, and further, squared_radius ≥ 0.

Circle_2<Kernel> c ( Point_2<Kernel> const& p, Point_2<Kernel> const& q, Point_2<Kernel> const& r);

introduces a variable c of type Circle_2<Kernel>. It is initialized to the unique circle which passes through the points p, q and r. The orientation of the circle is the orientation of the point triple p, q, r.

Precondition:

p, q, and r are not collinear.

Circle_2<Kernel> c ( Point_2<Kernel> const& p, Point_2<Kernel> const& q, Orientation const& ori = COUNTERCLOCKWISE);

introduces a variable c of type Circle_2<Kernel>. It is initialized to the circle with diameter pq and orientation ori.

Precondition:

ori ≠ COLLINEAR.

Circle_2<Kernel> c ( Point_2<Kernel> const& center, Orientation const& ori = COUNTERCLOCKWISE);

introduces a variable c of type Circle_2<Kernel>. It is initialized to the circle with center center, squared radius zero and orientation ori.

Precondition:

ori ≠ COLLINEAR.

Postcondition:

c.is_degenerate() = true.

Access Functions

Point_2<Kernel> const&	c.center () const	returns the center of c.
Kernel::FT const&	c.squared_radius () const	returns the squared radius of c.
Orientation const&	c.orientation () const	returns the orientation of c.

bool	c.operator == ( const& circle2) const
		returns true, iff c and circle2 are equal, i.e. if they have the same center, same squared radius and same orientation .

bool	c.operator != ( const& circle2) const
		returns true, iff c and circle2 are not equal.

Predicates

bool	c.is_degenerate () const	returns true, iff c is degenerate, i.e. if c has squared radius zero.

Oriented_side	c.oriented_side ( Point_2<Kernel> const& p) const
		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_2<Kernel> const& p) const
		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_2<Kernel> p) const
bool	c.has_on_negative_side ( Point_2<Kernel> p) const
bool	c.has_on_boundary ( Point_2<Kernel> p) const
bool	c.has_on_bounded_side ( Point_2<Kernel> p) const
bool	c.has_on_unbounded_side ( Point_2<Kernel> p) const

Miscellaneous

Circle_2<Kernel>

c.opposite () const

returns the circle with the same center and squared radius as c but with opposite orientation .

Circle_2<Kernel>

c.orthogonal_transform ( Aff_transformation_2<Kernel> const& at) const

returns the circle obtained by applying at on c.

Precondition:

at is an orthogonal transformation.

Bbox_2

c.bbox () const

returns a bounding box containing c.

CGAL::Circle_2<Kernel>

Definition

Creation

Access Functions

Predicates

Miscellaneous

See Also