CGAL 5.1.3  2D and 3D Linear Geometry Kernel

AdaptableFunctor
(with five arguments)CGAL::side_of_oriented_sphere()
Operations  
Oriented_side  operator() (const Kernel::Point_3 &p, const Kernel::Point_3 &q, const Kernel::Point_3 &r, const Kernel::Point_3 &s, const Kernel::Point_3 &t) 
returns the relative position of point t to the oriented sphere defined by p , q , r and s . More...  
Oriented_side Kernel::SideOfOrientedSphere_3::operator()  (  const Kernel::Point_3 &  p, 
const Kernel::Point_3 &  q,  
const Kernel::Point_3 &  r,  
const Kernel::Point_3 &  s,  
const Kernel::Point_3 &  t  
) 
returns the relative position of point t
to the oriented sphere defined by p
, q
, r
and s
.
The order of the points p
, q
, r
, and s
is important, since it determines the orientation of the implicitly constructed sphere. If the points p
, q
, r
and s
are positive oriented, positive side is the bounded interior of the sphere.
In case of degeneracies, CGAL::ON_ORIENTED_BOUNDARY is returned if all points are coplanar. Otherwise, there is a cyclic permutation of the five points that puts four non coplanar points first, it is used to answer the predicate: e.g. side_of_oriented_sphere(q, r, s, t, p)
is returned if q
, r
, s
, and t
are non coplanar.