CGAL 5.3 - 2D and 3D Linear Geometry Kernel
Kernel::CoplanarOrientation_3 Concept Reference

## Definition

Refines:
AdaptableFunctor (with four arguments)
See also
CGAL::coplanar_orientation()

## Operations

A model of this concept must provide:

Orientation operator() (const Kernel::Point_3 &p, const Kernel::Point_3 &q, const Kernel::Point_3 &r, const Kernel::Point_3 &s)
If p, q, and s are collinear, then CGAL::COLLINEAR is returned. More...

Orientation operator() (const Kernel::Point_3 &p, const Kernel::Point_3 &q, const Kernel::Point_3 &r)
If p, q, and r are collinear, then CGAL::COLLINEAR is returned. More...

## ◆ operator()() [1/2]

 Orientation Kernel::CoplanarOrientation_3::operator() ( const Kernel::Point_3 & p, const Kernel::Point_3 & q, const Kernel::Point_3 & r, const Kernel::Point_3 & s )

If p, q, and s are collinear, then CGAL::COLLINEAR is returned.

If not, let P be the plane defined by the points p, q, and r. Note that the order defines the orientation of P. If P and the plane defined by p, q, and s have the same orientation, then CGAL::POSITIVE is returned; otherwise CGAL::NEGATIVE is returned.

Precondition
p, q, r, and s are coplanar and p, q, and r are not collinear.

## ◆ operator()() [2/2]

 Orientation Kernel::CoplanarOrientation_3::operator() ( const Kernel::Point_3 & p, const Kernel::Point_3 & q, const Kernel::Point_3 & r )

If p, q, and r are collinear, then CGAL::COLLINEAR is returned.

If not, let P be the plane defined by the points p, q, and r. 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 as a 2D orientation in P.