Version 5.0 The LEDA User Manual

14.10 Rational Points ( rat point )
1. Definition
An instance of data type rat point is a point with rational coordinates in the twodimensional
plane. A point with cartesian coordinates (a, b) is represented by homogeneous
coordinates (x, y, w) of arbitrary length integers (see 5.1) such that a = x/w and
b = y/w and w > 0.
#include < LEDA/geo/rat point.h >
2. Types
rat point :: coord type
rat point :: point type
rat point :: float type
the coordinate type (rational).
the point type (rat point).
the corresponding floating-point type (point).
3. Creation
rat point p;
introduces a variable p of type rat point initialized to the point
(0, 0).
rat point p(const rational& a, const rational& b);
introduces a variable p of type rat point initialized to the point
(a, b).
rat point p(integer a, integer b);
introduces a variable p of type rat point initialized to the point
(a, b).
rat point p(integer x, integer y, integer w);
introduces a variable p of type rat point initialized to the point
with homogeneous coordinates (x, y, w) if w > 0 and to point
(−x, −y, −w) if w < 0.
Precondition: w ≠ 0.
rat point p(const rat vector& v);
introduces a variable p of type rat point initialized to the point
(v[0], v[1]).
Precondition: : v.dim( ) = 2.