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Circle Type (Circle)

Definition

An object of the class Circle is a circle in two-dimensional Euclidean plane 2. Its boundary splits the plane into a bounded and an unbounded side. By definition, an empty Circle has no boundary and no bounded side, i.e. its unbounded side equals the whole plane 2. A Circle containing exactly one point p has no bounded side, its boundary is {p}, and its unbounded side equals 2 \ {p}.

Types

Circle::Point
Point type.

The following type is only needed, if the member function is_valid of Min_circle_2 is used.

Circle::Distance
Distance type. The function squared_radius (see below) returns an object of this type.

Creation

void circle.set () sets circle to the empty circle.

void circle.set ( Point p) sets circle to the circle containing exactly {p}.

void circle.set ( Point p, Point q) sets circle to the circle with diameter equal to the segment connecting p and q. The algorithm guarantees that set is never called with two equal points.

void circle.set ( Point p, Point q, Point r)
sets circle to the circle through p,q,r. The algorithm guarantees that set is never called with three collinear points.

Predicates

bool circle.has_on_unbounded_side ( Point p)
returns true, iff p lies properly outside of circle.

Each of the following predicates is only needed, if the corresponding predicate of Min_circle_2 is used.

CGAL::Bounded_side circle.bounded_side ( Point 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_bounded_side ( Point p)
returns true, iff p lies properly inside circle.

bool circle.has_on_boundary ( Point p)
returns true, iff p lies on the boundary of circle.

bool circle.is_empty () returns true, iff circle is empty (this implies degeneracy).

bool circle.is_degenerate () returns true, iff circle is degenerate, i.e. if circle is empty or equal to a single point.

Additional Operations for Checking

The following operations are only needed, if the member function is_valid of Min_circle_2 is used.

bool circle == circle2 returns true, iff circle and circle2 are equal.

Point circle.center () returns the center of circle.

Distance circle.squared_radius () returns the squared radius of circle.

I/O

The following I/O operator is only needed, if the corresponding I/O operator of Min_circle_2 is used.

std::ostream& std::ostream& os << circle writes circle to output stream os.

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CGAL Open Source Project. Release 3.5. 1 October 2009.