2D Circle (Circle_2)

Definition

An object of type Circle_2<R> 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 further splits $$ ² into a bounded and an unbounded side. Note that the circle can be degenerated, i.e. the squared radius may be zero.

#include <CGAL/Circle_2.h>

Creation

Circle_2<R> circle ( Point_2<R> center, R::FT squared_radius, Orientation orientation = COUNTERCLOCKWISE);
	introduces a variable circle of type Circle_2<R>. It is initialized to the circle with center center, squared radius squared_radius and orientation orientation. Precondition: orientation $$ COLLINEAR, and further, squared_radius $$ 0.
Circle_2<R> circle ( Point_2<R> p, Point_2<R> q, Point_2<R> r);
	introduces a variable circle of type 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.
Circle_2<R> circle ( Point_2<R> p, Point_2<R> q, Orientation orientation = COUNTERCLOCKWISE);
	introduces a variable circle of type Circle_2<R>. It is initialized to the circle with diameter $$pq and orientation orientation. Precondition: orientation $$ COLLINEAR.
Circle_2<R> circle ( Point_2<R> center, Orientation orientation = COUNTERCLOCKWISE);
	introduces a variable circle of type Circle_2<R>. It is initialized to the circle with center center, squared radius zero and orientation orientation. Precondition: orientation $$ COLLINEAR. Postcondition: circle.is_degenerate() = true.

Access Functions

Point_2<R>	circle.center ()	returns the center of circle.
R::FT	circle.squared_radius ()
		returns the squared radius of circle.
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.
Oriented_side	circle.oriented_side ( Point_2<R> 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 circle, resp.
Bounded_side	circle.bounded_side ( Point_2<R> p)
		returns ON_BOUNDED_SIDE, ON_BOUNDARY, or ON_UNBOUNDED_SIDE iff p lies properly inside, on the boundary, or properly outside of circle, resp.
bool	circle.has_on_positive_side ( Point_2<R> p)
bool	circle.has_on_negative_side ( Point_2<R> p)
bool	circle.has_on_boundary ( Point_2<R> p)
bool	circle.has_on_bounded_side ( Point_2<R> p)
bool	circle.has_on_unbounded_side ( Point_2<R> p)

Miscellaneous

Circle_2<R>	circle.opposite ()	returns the circle with the same center and squared radius as circle but with opposite orientation.
Circle_2<R>	circle.orthogonal_transform ( Aff_transformation_2<R> at)
		returns the circle obtained by applying $$at on circle. Precondition: at is an orthogonal transformation.
Bbox_2	circle.bbox ()	returns a bounding box containing circle.