
 
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 $$P: Iff p, q, s are
collinear, COLLINEAR is returned. Iff $$P and the plane
defined by p, q, and s have the same orientation,
POSITIVE is returned; otherwise NEGATIVE is returned. Precondition: p, q, r, and s are coplanar and p, q, and r are not collinear.  

 
If p,q,r are collinear, then COLLINEAR is returned. If not, then p,q,r define a plane $$P. The return value in this case is either POSITIVE or NEGATIVE, but we don't specify it explicitely. However, we guarantee that all calls to this predicate over 3 points in $$P will return a coherent orientation if considered a 2D orientation in $$P. 
CGAL::coplanar
CGAL::coplanar_side_of_bounded_circle
CGAL::orientation