CGAL::intersection

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 11)

#include <CGAL/intersections.h>

Object intersection ( Type1<Kernel> obj1, Type2<Kernel> obj2)
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
Point_2
Line_2
Segment_2 Line_2
Point_2
Segment_2
Segment_2 Segment_2
Point_2
Segment_2
Ray_2 Line_2
Point_2
Ray_2
Ray_2 Segment_2
Point_2
Segment_2
Ray_2 Ray_2
Point_2
Segment_2
Ray_2
Triangle_2 Line_2
Point_2
Segment_2
Triangle_2 Segment_2
Point_2
Segment_2
Triangle_2 Ray_2
Point_2
Segment_2
Triangle_2 Triangle_2
Point_2
Segment_2
Triangle_2
std::vector<Point_2>
Iso_rectangle_2 Line_2
Point_2
Segment_2
Iso_rectangle_2 Segment_2
Point_2
Segment_2
Iso_rectangle_2 Ray_2
Point_2
Segment_2
Iso_rectangle_2 Iso_rectangle_2
Iso_rectangle_2
Line_3 Line_3
Point_3
Line_3
Line_3 Plane_3
Point_3
Line_3
Line_3 Ray_3
Point_3
Ray_3
Line_3 Segment_3
Point_3
Segment_3
Line_3 Triangle_3
Point_3
Segment_3
Plane_3 Plane_3
Line_3
Plane_3
Plane_3 Ray_3
Point_3
Ray_3
Plane_3 Segment_3
Point_3
Segment_3
Plane_3 Sphere_3
Point_3
Circle_3
Plane_3 Triangle_3
Point_3
Segment_3
Triangle_3
Ray_3 Ray_3
Point_3
Ray_3
Segment_3
Ray_3 Segment_3
Point_3
Segment_3
Ray_3 Triangle_3
Point_3
Segment_3
Segment_3 Segment_3
Point_3
Segment_3
Segment_3 Triangle_3
Point_3
Segment_3
Sphere_3 Sphere_3
Point_3
Circle_3
Sphere_3
Triangle_3 Triangle_3
Point_3
Segment_3
Triangle_3
std::vector < Point_3 >

There is also an intersection function between 3 planes.

Object intersection ( Plane_3<Kernel> pl1, Plane_3<Kernel> pl2, Plane_3<Kernel> pl3)
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 13)

#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.

template < class OutputIterator >
OutputIterator intersection ( Type1 obj1, Type2 obj2, OutputIterator intersections)
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 14)

#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:

template < class OutputIterator >
OutputIterator intersection ( Type1 obj1, Type2 obj2, OutputIterator intersections)
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:

template < class OutputIterator >
OutputIterator intersection ( Type1 obj1, Type2 obj2, Type3 obj3, OutputIterator intersections)
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

Example

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 13 and 14.

See Also

CGAL::do_intersect
CGAL::Object