Circles (circle)

Definition

An instance C of the data type circle is an oriented circle in the plane passing through three points p_1, p_2, p_3. The orientation of C is equal to the orientation of the three defining points, i.e. orientation(p_1,p_2,p_3). If $\vert\,\{p_1,p_2,p_3\}\,\vert$ = 1 C is the empty circle with center p_1. If p_1,p_2,p_3 are collinear C is a straight line passing through p_1, p_2 and p_3 in this order and the center of C is undefined.

Creation

circle	C(point a, point b, point c);
		introduces a variable C of type circle. C is initialized to the oriented circle through points a, b, and c.
circle	C(point a, 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(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(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.

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 p_1.
point	C.point2()	returns p_2.
point	C.point3()	returns p_3.
point	C.point_on_circle(double alpha, double=0)
		returns a point p on C with angle of alpha.
bool	C.is_degenerate()	returns true if the defining points are collinear.
bool	C.is_trivial()	returns true if C has radius zero.
int	C.orientation()	returns the orientation of C.
int	C.side_of(point p)	returns -1, +1, or 0 if p lies right of, left of, or on C respectively.
bool	C.inside(point p)	returns true if p lies inside of C, false otherwise.
bool	C.outside(point p)	returns !C.inside(p).
bool	C.contains(point p)	returns true if p lies on C, false otherwise.
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(vector v)	returns C translated by vector v.
circle	C + vector v	returns C translated by vector v.
circle	C - vector v	returns C translated by vector -v.
circle	C.rotate(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(point q)	returns C rotated about q by an angle of 90 degrees.
circle	C.reflect(point p, point q)
		returns C reflected across the straight line passing through p and q.
circle	C.reflect(point p)	returns C reflected across point p.
circle	C.reverse()	returns C reversed.
list<point>	C.intersection(circle D)	returns C <intersection> D as a list of points.
list<point>	C.intersection(line l)	returns C <intersection> l as a list of (zero, one, or two) points sorted along l.
list<point>	C.intersection(segment s)	returns C <intersection> s as a list of (zero, one, or two) points sorted along s.
segment	C.left_tangent(point p)	returns the line segment starting in p tangent to C and left of segment [p,C.center()].
segment	C.right_tangent(point p)	returns the line segment starting in p tangent to C and right of segment [p,C.center()].
double	C.distance(point p)	returns the distance between C and p.
double	C.sqr_dist(point p)	returns the squared distance between C and p.
double	C.distance(line l)	returns the distance between C and l.
double	C.distance(circle D)	returns the distance between C and D.