Version 5.0 The LEDA User Manual

14.14 Rational Circles ( rat circle )
1. Definition
An instance C of data type rat circle is an oriented circle in the plane. A circle is
defined by three points p 1 , p 2 , p 3 with rational coordinates (rat points). The orientation
of C is equal to the orientation of the three defining points, i.e., orientation(p 1 , p 2 , p 3 ).
Positive orientation corresponds to counterclockwise orientation and negative orientation
corresponds to clockwise orientation.
Some triples of points are unsuitable for defining a circle. A triple is admissable if
|{p 1 , p 2 , p 3 }| ≠ 2. Assume now that p 1 , p 2 , p 3 are admissable. If |{p 1 , p 2 , p 3 }| = 1 they
define the circle with center p 1 and radius zero. If p 1 , p 2 , and 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.
If p 1 , p 2 , and p 3 are not collinear, C is the circle passing through them.
#include < LEDA/geo/rat circle.h >
2. Types
rat circle :: coord type
rat circle :: point type
rat circle :: float type
the coordinate type (rational).
the point type (rat point).
the corresponding floatin-point type (circle).
3. Creation
rat circle C(const rat point& a, const rat point& b, const rat point& c);
rat circle C(const rat point& a, const rat point& b);
rat circle C(const rat point& a);
introduces a variable C of type rat circle. C is initialized to
the circle through points a, b, and c.
Precondition: a, b, and c are admissable.
introduces a variable C of type circle. C is initialized to
the counter-clockwise oriented circle with center a passing
through b.
introduces a variable C of type circle. C is initialized to the
trivial circle with center a.
rat circle C;
introduces a variable C of type rat circle. C is initialized to
the trivial circle centered at (0, 0).