Version 5.0 The LEDA User Manual

14.15 Rational Triangles ( rat triangle )
1. Definition
An instance t of the data type rat triangle is an oriented triangle in the two-dimensional
plane with rational coordinates. A rat triangle t splits the plane into one bounded and
one unbounded region. If t is positively oriented, the bounded region is to the left of it, if
it is negatively oriented, the unbounded region is to the left of it. t is called degenerate,
if the 3 vertices of t are collinear.
#include < LEDA/geo/rat triangle.h >
2. Types
rat triangle :: coord type
rat triangle :: point type
the coordinate type (rational).
the point type (rat point).
3. Creation
rat triangle t;
introduces a variable t of type rat triangle. t is initialized to
the empty triangle.
rat triangle t(const rat point& p, const rat point& q, const rat point& r);
introduces a variable t of type rat triangle. t is initialized to
the triangle [p, q, r].
rat triangle t(const rational& x1 , const rational& y1 , const rational& x2 ,
const rational& y2 , const rational& x3 , const rational& y3 );
introduces a variable t of type rat triangle. t is initialized to
the triangle [(x1, y1), (x2, y2), (x3, y3)].
rat triangle t(const triangle& t, int prec = rat point :: default precision);
4. Operations
introduces a variable t of type rat triangle. t is initialized
to the triangle obtained by approximating the three defining
points of t.
void t.normalize( ) simplifies the homogenous representation by calling
p.normalize( ) for every vertex of t.
rat point t.point1( ) returns the first vertex of triangle t.
rat point t.point2( ) returns the second vertex of triangle t.
rat point t.point3( ) returns the third vertex of triangle t.