Version 5.0 The LEDA User Manual

16.8 Rational Points in 3D-Space ( d3 rat point )
1. Definition
An instance of data type d3 rat point is a point with rational coordinates in the threedimensional
space. A point with cartesian coordinates (a, b, c) is represented by homogeneous
coordinates (x, y, z, w) of arbitrary length integers (see 5.1) such that a = x/w,
b = y/w, c = z/w and w > 0.
#include < LEDA/geo/d3 rat point.h >
2. Creation
d3 rat point p;
introduces a variable p of type d3 rat point initialized to the point
(0, 0, 0).
d3 rat point p(const rational& a, const rational& b, const rational& c);
introduces a variable p of type d3 rat point initialized to the point
(a, b, c).
d3 rat point p(integer a, integer b, integer c);
introduces a variable p of type d3 rat point initialized to the point
(a, b, c).
d3 rat point p(integer x, integer y, integer z, integer w);
d3 rat point p(const rat vector& v);
introduces a variable p of type d3 rat point initialized to the point
with homogeneous coordinates (x, y, z, w) if w > 0 and to point
(−x, −y, −z, −w) if w < 0.
Precondition: w ≠ 0.
introduces a variable p of type d3 rat point initialized to the point
(v[0], v[1], v[2]).
Precondition: : v.dim( ) = 3.
3. Operations
d3 point p.to float( ) returns a floating point approximation of p.
rat vector p.to vector( ) returns the vector extending from the origin to p.
integer p.X( ) returns the first homogeneous coordinate of p.
integer p.Y( ) returns the second homogeneous coordinate of p.
integer p.Z( ) returns the third homogeneous coordinate of p.