Version 5.0 The LEDA User Manual

14.5 Circles ( circle )
1. 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 |{p 1 , p 2 , p 3 }|= 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.
#include < LEDA/geo/circle.h >
2. Types
circle :: coord type
circle :: point type
the coordinate type (double).
the point type (point).
3. Creation
circle C(const point& a, const point& b, const point& c);
circle C(const point& a, const point& b);
introduces a variable C of type circle. C is initialized to the
oriented circle through points a, b, and c.
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);
circle C(double x, double y, 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. counterclockwise)
orientation.
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.