Version 5.0 The LEDA User Manual

14.21 Real Circles ( real circle )
1. Definition
An instance C of the data type real 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/real circle.h >
2. Types
real circle :: coord type
real circle :: point type
the coordinate type (real).
the point type (real point).
3. 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);
real circle C(const real point& a);
introduces a variable C of type real circle. C is initialized
to the counter-clockwise oriented circle with center a passing
through b.
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);
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 c and radius r with positive (i.e.
counter-clockwise) orientation.
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.