Depending on which CGAL kernel is used, different versions of this global function are available. This is described below.
With the basic 2D and 3D Kernel (see Chapter 7)
#include <CGAL/intersections.h>

 
Two objects obj1 and obj2 intersect if there is a point p that is part of both obj1 and obj2. The intersection region of those two objects is defined as the set of all points p that are part of both obj1 and obj2. Note that for objects like triangles and polygons that enclose a bounded region, this region is considered part of the object. If a segment lies completely inside a triangle, then those two objects intersect and the intersection region is the complete segment. 
The possible value for types Type1 and Type2 and the possible return values wrapped in Object are the following:
type A  type B  return type  

Line_2  Line_2 


Segment_2  Line_2 


Segment_2  Segment_2 


Ray_2  Line_2 


Ray_2  Segment_2 


Ray_2  Ray_2 


Triangle_2  Line_2 


Triangle_2  Segment_2 


Triangle_2  Ray_2 


Triangle_2  Triangle_2 


Iso_rectangle_2  Line_2 


Iso_rectangle_2  Segment_2 


Iso_rectangle_2  Ray_2 


Iso_rectangle_2  Iso_rectangle_2 


Line_3  Line_3 


Plane_3  Line_3 


Plane_3  Ray_3 


Plane_3  Segment_3 


Plane_3  Plane_3 


Plane_3  Sphere_3 


Sphere_3  Sphere_3 

There is also an intersection function between 3 planes.

 
returns the intersection of 3 planes, which can be either a point, a line, a plane, or empty. 
With the 2D Circular Kernel (see Chapter 9)
#include <CGAL/Circular_kernel_intersections.h>
If this kernel is used, in addition to the function and the combination of 2D types described above, another version of the function is provided.
Since both the number of intersections, if any, and their type, depend on the arguments, the function returns an output iterator on Object's, as presented below.
 

 
Copies in the output iterator the intersection elements between the two objects. intersections iterates on elements of type CGAL::Object, in lexicographic order, 
where Type1 and Type2 can both be either
Depending on the types Type1 and Type2, these elements can be assigned to
With the 3D Spherical Kernel (see Chapter 10)
#include <CGAL/Spherical_kernel_intersections.h>
If this kernel is used, in addition to the function and the combination of 3D types described above, two other versions of the function are provided.
Since both the number of intersections, if any, and their type, depend on the arguments, the functions return an output iterator on Object's, as presented below.
The first function is:
 

 
Copies in the output iterator the intersection elements between the two objects. intersections iterates on elements of type CGAL::Object, in lexicographic order, when this ordering is defined on the computed objects, 
where Type1 and Type2 can both be either:
and depending on the types Type1 and Type2, the computed CGAL::Objects can be assigned to
The second function is:
 

 
Copies in the output iterator the intersection elements between the three objects. intersections iterates on elements of type CGAL::Object, in lexicographic order when this ordering is defined on the computed objects 
where Type1, Type2 and Type3 can be either
and depending of these types, the computed CGAL::Objects can be assigned to
The following example demonstrates the most common use of intersection routines with the basic 2D and 3D Kernels.
#include <CGAL/intersections.h> void foo(CGAL::Segment_2<Kernel> seg, CGAL::Line_2<Kernel> line) { CGAL::Object result = CGAL::intersection(seg, line); if (const CGAL::Point_2<Kernel> *ipoint = CGAL::object_cast<CGAL::Point_2<Kernel> >(&result)) {
// handle the point intersection case with *ipoint.
} else if (const CGAL::Segment_2<Kernel> *iseg = CGAL::object_cast<CGAL::Segment_2<Kernel> >(&result)) {
// handle the segment intersection case with *iseg.
} else {
// handle the no intersection case. } }
Examples illustrating the use of this function in the case of the 2D Circular Kernel and the 3D Spherical Kernel are presented respectively in Chapters 9 and 10.