CGAL 5.5  2D and 3D Linear Geometry Kernel

Functions  
template<typename Kernel >  
Orientation  CGAL::coplanar_orientation (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s) 
Let P be the plane defined by the points p , q , and r . More...  
template<typename Kernel >  
Orientation  CGAL::coplanar_orientation (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r) 
If p,q,r are collinear, then CGAL::COLLINEAR is returned. More...  
Orientation CGAL::coplanar_orientation  (  const CGAL::Point_3< Kernel > &  p, 
const CGAL::Point_3< Kernel > &  q,  
const CGAL::Point_3< Kernel > &  r,  
const CGAL::Point_3< Kernel > &  s  
) 
#include <CGAL/Kernel/global_functions.h>
Let P
be the plane defined by the points p
, q
, and r
.
Note that the order defines the orientation of P
. The function computes the orientation of points p
, q
, and s
in P
: Iff p
, q
, s
are collinear, CGAL::COLLINEAR
is returned. Iff P
and the plane defined by p
, q
, and s
have the same orientation, CGAL::POSITIVE
is returned; otherwise CGAL::NEGATIVE
is returned.
p
, q
, r
, and s
are coplanar and p
, q
, and r
are not collinear. Orientation CGAL::coplanar_orientation  (  const CGAL::Point_3< Kernel > &  p, 
const CGAL::Point_3< Kernel > &  q,  
const CGAL::Point_3< Kernel > &  r  
) 
#include <CGAL/Kernel/global_functions.h>
If p,q,r
are collinear, then CGAL::COLLINEAR
is returned.
If not, then p,q,r
define a plane p
. The return value in this case is either CGAL::POSITIVE
or CGAL::NEGATIVE
, but we don't specify it explicitly. However, we guarantee that all calls to this predicate over 3 points in p
will return a coherent orientation if considered a 2D orientation in p
.