Circles ( circle )

Definition

An instance C of the data type circle is an oriented circle in the plane passing through three points p₁, p₂, p₃. The orientation of C is equal to the orientation of the three defining points, i.e. orientation(p₁, p₂, p₃). If |   {p₁, p₂, p₃}   |= 1 C is the empty circle with center p₁. If p₁, p₂, p₃ are collinear C is a straight line passing through p₁, p₂ and p₃ in this order and the center of C is undefined.

#include < LEDA/geo/circle.h >

Types

circle::coord_type	the coordinate type (double).
circle::point_type	the point type (point).

Creation

circle	C(const point& a, const point& b, const point& c)
		introduces a variable C of type circle. C is initialized to the oriented circle through points a, b, and c.
circle	C(const point& a, const point& b)
		introduces a variable C of type circle. C is initialized to the counter-clockwise oriented circle with center a passing through b.
circle	C(const point& a)	introduces a variable C of type circle. C is initialized to the trivial circle with center a.
circle	C	introduces a variable C of type circle. C is initialized to the trivial circle with center (0, 0).
circle	C(const point& c, double r)
		introduces a variable C of type circle. C is initialized to the circle with center c and radius r with positive (i.e. counter-clockwise) orientation.
circle	C(double x, double y, double r)
		introduces a variable C of type circle. C is initialized to the circle with center (x, y) and radius r with positive (i.e. counter-clockwise) orientation.
circle	C(const circle& c, int)	introduces a variable C of type circle. C is initialized to a copy of c. The second argument is for compatability with rat_circle.

Operations

point	C.center()	returns the center of C. Precondition The orientation of C is not 0.
double	C.radius()	returns the radius of C. Precondition The orientation of C is not 0.
double	C.sqr_radius()	returns the squared radius of C. Precondition The orientation of C is not 0.
point	C.point1()	returns p1.
point	C.point2()	returns p2.
point	C.point3()	returns p3.
point	C.point_on_circle(double alpha, double=0)
		returns a point p on C with angle of alpha. The second argument is for compatability with rat_circle.
bool	C.is_degenerate()	returns true if the defining points are collinear.
bool	C.is_trivial()	returns true if C has radius zero.
bool	C.is_line()	returns true if C is a line.
line	C.to_line()	returns line(point1(), point3()).
int	C.orientation()	returns the orientation of C.
int	C.side_of(const point& p)	returns -1, +1, or 0 if p lies right of, left of, or on C respectively.
bool	C.inside(const point& p)	returns true iff p lies inside of C.
bool	C.outside(const point& p)	returns true iff p lies outside of C.
bool	C.contains(const point& p)
		returns true iff p lies on C.
circle	C.translate_by_angle(double a, double d)
		returns C translated in direction a by distance d.
circle	C.translate(double dx, double dy)
		returns C translated by vector (dx, dy).
circle	C.translate(const vector& v)
		returns C translated by vector v.
circle	C + const vector& v	returns C translated by vector v.
circle	C - const vector& v	returns C translated by vector - v.
circle	C.rotate(const point& q, double a)
		returns C rotated about point q by angle a.
circle	C.rotate(double a)	returns C rotated about the origin by angle a.
circle	C.rotate90(const point& q, int i=1)
		returns C rotated about q by an angle of i x 90 degrees. If i > 0 the rotation is counter-clockwise otherwise it is clockwise.
circle	C.reflect(const point& p, const point& q)
		returns C reflected across the straight line passing through p and q.
circle	C.reflect(const point& p)	returns C reflected across point p.
circle	C.reverse()	returns C reversed.
list<point>	C.intersection(const circle& D)
		returns C $\cap$ D as a list of points.
list<point>	C.intersection(const line& l)
		returns C $\cap$ l as a list of (zero, one, or two) points sorted along l.
list<point>	C.intersection(const segment& s)
		returns C $\cap$ s as a list of (zero, one, or two) points sorted along s.
segment	C.left_tangent(const point& p)
		returns the line segment starting in p tangent to C and left of segment [p, C.center()].
segment	C.right_tangent(const point& p)
		returns the line segment starting in p tangent to C and right of segment [p, C.center()].
double	C.distance(const point& p)
		returns the distance between C and p.
double	C.sqr_dist(const point& p)
		returns the squared distance between C and p.
double	C.distance(const line& l)	returns the distance between C and l.
double	C.distance(const circle& D)
		returns the distance between C and D.
bool	radical_axis(const circle& C1, const circle& C2, line& rad_axis)
		if the radical axis for C1 and C2 exists, it is assigned to rad_axis and true is returned; otherwise the result is false.