2D Circle (CGAL_Circle_2)

Definition

#include <CGAL/Circle_2.h>

Creation

CGAL_Circle_2<R> circle ( CGAL_Point_2<R> center, R::FT squared_radius, CGAL_Orientation orientation = CGAL_COUNTERCLOCKWISE);
	introduces a variable circle of type CGAL_Circle_2<R>. It is initialized to the circle with center center, squared radius squared_radius and orientation orientation. Precondition: orientation $\ne$ CGAL_COLLINEAR, and further, squared_radius $>=$ 0.
CGAL_Circle_2<R> circle ( CGAL_Point_2<R> p, CGAL_Point_2<R> q, CGAL_Point_2<R> r);
	introduces a variable circle of type CGAL_Circle_2<R>. 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.
CGAL_Circle_2<R> circle ( CGAL_Point_2<R> p, CGAL_Point_2<R> q, CGAL_Orientation orientation = CGAL_COUNTERCLOCKWISE);
	introduces a variable circle of type CGAL_Circle_2<R>. It is initialized to the circle with diameter $\backslash overlinepq$ and orientation orientation. Precondition: orientation $\ne$ CGAL_COLLINEAR.
CGAL_Circle_2<R> circle ( CGAL_Point_2<R> center, CGAL_Orientation orientation = CGAL_COUNTERCLOCKWISE);
	introduces a variable circle of type CGAL_Circle_2<R>. It is initialized to the circle with center center, squared radius zero and orientation orientation. Precondition: orientation $\ne$ CGAL_COLLINEAR. Postcondition: \ccVar.is_degenerate() = true.

Access Functions

CGAL_Point_2<R>	circle.center ()	returns the center of circle.
R::FT	circle.squared_radius ()
		returns the squared radius of circle.
CGAL_orientation	circle.orientation ()
		returns the orientation of circle.

Equality Tests

bool	circle == circle2	returns true, iff circle and circle2 are equal, i.e. if they have the same center, same squared radius and same orientation.
bool	circle != circle2	returns true, iff circle and circle2 are not equal.

Predicates

bool	circle.is_degenerate ()
		returns true, iff circle is degenerate, i.e. if circle has squared radius zero.
CGAL_Oriented_side	circle.oriented_side ( CGAL_Point_2<R> p)
		returns either the constant CGAL_ON_ORIENTED_BOUNDARY, CGAL_ON_POSITIVE_SIDE, or CGAL_ON_NEGATIVE_SIDE, iff p lies on the boundary, properly on the positive side, or properly on the negative side of circle, resp.
CGAL_Bounded_side	circle.bounded_side ( CGAL_Point_2<R> p)
		returns CGAL_ON_BOUNDED_SIDE, CGAL_ON_BOUNDARY, or CGAL_ON_UNBOUNDED_SIDE iff p lies properly inside, on the boundary, or properly outside of circle, resp.
bool	circle.has_on_positive_side ( Point p)
		returns true, iff p lies properly on the positive side of circle.
bool	circle.has_on_negative_side ( Point p)
		returns true, iff p lies properly on the negative side of circle.
bool	circle.has_on_boundary ( Point p)
		returns true, iff p lies on the boundary of circle.
bool	circle.has_on_bounded_side ( Point p)
		returns true, iff p lies properly inside circle.
bool	circle.has_on_unbounded_side ( Point p)
		returns true, iff p lies properly outside of circle.

Miscellaneous

CGAL_Circle_2<R>	circle.opposite ()	returns the circle with the same center and squared radius as circle but with opposite orientation.
CGAL_Circle_2<R>	circle.orthogonal_transform ( CGAL_Aff_transformation_2<R> at)
		returns the circle obtained by applying $at$ on circle. Precondition: at is an orthogonal transformation.
CGAL_Bbox_2	circle.bbox ()	returns a bounding box containing circle.