Real Circles ( real_circle )

Definition

An instance C of the data type real_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/real_circle.h >

Types

real_circle::coord_type	the coordinate type (real).
real_circle::point_type	the point type (real_point).

Creation

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

Operations

real_point	C.center()	returns the center of C. Precondition The orientation of C is not 0.
real	C.radius()	returns the radius of C. Precondition The orientation of C is not 0.
real	C.sqr_radius()	returns the squared radius of C. Precondition The orientation of C is not 0.
real_point	C.point1()	returns p1.
real_point	C.point2()	returns p2.
real_point	C.point3()	returns p3.
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.
real_line	C.to_line()	returns line(point1(), point3()).
int	C.orientation()	returns the orientation of C.
int	C.side_of(const real_point& p)
		returns -1, +1, or 0 if p lies right of, left of, or on C respectively.
bool	C.inside(const real_point& p)
		returns true iff p lies inside of C.
bool	C.outside(const real_point& p)
		returns true iff p lies outside of C.
bool	C.contains(const real_point& p)
		returns true iff p lies on C.
real_circle	C.translate(real dx, real dy)
		returns C translated by vector (dx, dy).
real_circle	C.translate(const real_vector& v)
		returns C translated by vector v.
real_circle	C + const real_vector& v	returns C translated by vector v.
real_circle	C - const real_vector& v	returns C translated by vector - v.
real_circle	C.rotate90(const real_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.
real_circle	C.reflect(const real_point& p, const real_point& q)
		returns C reflected across the straight line passing through p and q.
real_circle	C.reflect(const real_point& p)
		returns C reflected across point p.
real_circle	C.reverse()	returns C reversed.
list<real_point>	C.intersection(const real_circle& D)
		returns C $\cap$ D as a list of points.
list<real_point>	C.intersection(const real_line& l)
		returns C $\cap$ l as a list of (zero, one, or two) points sorted along l.
list<real_point>	C.intersection(const real_segment& s)
		returns C $\cap$ s as a list of (zero, one, or two) points sorted along s.
real_segment	C.left_tangent(const real_point& p)
		returns the line segment starting in p tangent to C and left of segment [p,C.center()].
real_segment	C.right_tangent(const real_point& p)
		returns the line segment starting in p tangent to C and right of segment [p,C.center()].
real	C.distance(const real_point& p)
		returns the distance between C and p.
real	C.sqr_dist(const real_point& p)
		returns the squared distance between C and p.
real	C.distance(const real_line& l)
		returns the distance between C and l.
real	C.distance(const real_circle& D)
		returns the distance between C and D.
bool	radical_axis(const real_circle& C1, const real_circle& C2, real_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.