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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> center, Kernel::FT squared_radius, Orientation 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> p, Point_2<Kernel> q, Point_2<Kernel> 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> p, Point_2<Kernel> q, Orientation 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> center, Orientation 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> 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 == ( circle2) 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 != ( circle2) returns true, iff c and circle2 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_2<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_2<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_2<Kernel> p)
bool c.has_on_negative_side ( Point_2<Kernel> p)
bool c.has_on_boundary ( Point_2<Kernel> p)
bool c.has_on_bounded_side ( Point_2<Kernel> p)
bool c.has_on_unbounded_side ( Point_2<Kernel> p)

Miscellaneous

Circle_2<Kernel> c.opposite () 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> at)
returns the circle obtained by applying at on c.
Precondition: at is an orthogonal transformation.

Bbox_2 c.bbox () returns a bounding box containing c.

See Also

Kernel::Circle_2

Next: Direction_2<Kernel>
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CGAL Open Source Project. Release 3.5. 1 October 2009.