CGAL::intersection() (2D/3D Linear Kernel)

Functions
template<typename Kernel >
cpp11::result_of < Kernel::Intersect_23(Type1, Type2)>::type	CGAL::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. More...
template<typename Kernel >
boost::optional < boost::variant< Point_3, Line_3, Plane_3 > >	CGAL::intersection (const Plane_3< Kernel > &pl1, const Plane_3< Kernel > &pl2, const Plane_3< Kernel > &pl3)
	returns the intersection of 3 planes, which can be a point, a line, a plane, or empty. More...

Function Documentation

template<typename Kernel >

cpp11::result_of<Kernel::Intersect_23(Type1, Type2)>::type CGAL::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.

Here, Intersect_23 means either Intersect_2 or Intersect_3, depending on the arguments.

The following tables give the possible values for Type1 and Type2.

2D intersections

The return type can be obtained through cpp11::result_of<Kernel::Intersect_2(A, B)>::type. It is equivalent to boost::optional< boost::variant< T... > >, the last column in the table providing the template parameter pack.

Type1	Type2	Return Type: T...
Iso_rectangle_2	Iso_rectangle_2	Iso_rectangle_2
Iso_rectangle_2	Line_2	Point_2, or Segment_2
Iso_rectangle_2	Ray_2	Point_2, or Segment_2
Iso_rectangle_2	Segment_2	Point_2, or Segment_2
Iso_rectangle_2	Triangle_2	Point_2, or Segment_2, or Triangle_2, or std::vector<Point_2>
Line_2	Line_2	Point_2, or Line_2
Line_2	Ray_2	Point_2, or Ray_2
Line_2	Segment_2	Point_2, or Segment_2
Line_2	Triangle_2	Point_2, or Segment_2
Ray_2	Ray_2	Point_2, or Segment_2, or Ray_2
Ray_2	Segment_2	Point_2, or Segment_2
Ray_2	Triangle_2	Point_2, or Segment_2
Segment_2	Segment_2	Point_2, or Segment_2
Segment_2	Triangle_2	Point_2, or Segment_2
Triangle_2	Triangle_2	Point_2, or Segment_2, or Triangle_2, or std::vector<Point_2>

3D intersections

The return type can be obtained through cpp11::result_of<Kernel::Intersect_3(A, B)>::type. It is equivalent to boost::optional< boost::variant< T... > >, the last column in the table providing the template parameter pack.

Type1	Type2	Return Type: T...
Line_3	Line_3	Point_3, or Line_3
Line_3	Plane_3	Point_3, or Line_3
Line_3	Ray_3	Point_3, or Ray_3
Line_3	Segment_3	Point_3, or Segment_3
Line_3	Triangle_3	Point_3, or Segment_3
Plane_3	Plane_3	Line_3, or Plane_3
Plane_3	Ray_3	Point_3, or Ray_3
Plane_3	Segment_3	Point_3, or Segment_3
Plane_3	Sphere_3	Point_3, or Circle_3
Plane_3	Triangle_3	Point_3, or Segment_3, or Triangle_3
Ray_3	Ray_3	Point_3, or Ray_3, or Segment_3
Ray_3	Segment_3	Point_3, or Segment_3
Ray_3	Triangle_3 p	Point_3, or Segment_3
Segment_3	Segment_3	Point_3, or Segment_3
Segment_3	Triangle_3	Point_3, or Segment_3
Sphere_3	Sphere_3	Point_3, or Circle_3, or Sphere_3
Triangle_3	Triangle_3	Point_3, or Segment_3, or Triangle_3, or std::vector < Point_3 >

Example

The following example demonstrates the most common use of intersection routines with the 2D and 3D Linear Kernel.

#include <CGAL/intersections.h>

template<typename R>
struct Intersection_visitor {
  typedef void result_type;
  void operator()(const Point_2<R>& p) const 
  { // handle point
  }
  void operator()(const Segment_2<R>& s) const 
  { 
    // handle segment 
  }
};

template <class R>
void foo(const Segment_2<R>& seg, const Line_2<R>& lin)
{
  // with C++11 support
  // auto result = intersection(seg, lin);

  // without C++11
  cpp11::result_of<R::Intersect_2(Segment_2<R>, Line_2<R>)>::type 
    result = intersection(seg, lin);

  if(result) { boost::apply_visitor(Intersection_visitor(), *result); } 
  else { 
    // no intersection 
  }

  // alternatively:
  if(result) {
    if(const Segment_2<R>* s = boost::get<Segment_2>(&*result)) {
      // handle segment
    } else {
      const Point_2<R>* p = boost::get<Point_2>(&*result);
      // handle point
    }
}

Another example showing the use of the intersection function as a plain function call and with Dispatch_output_iterator combined with a standard library algorithm.

File Kernel_23/intersections.cpp

#include <CGAL/Simple_cartesian.h>
#include <CGAL/intersections.h>
#include <CGAL/iterator.h>
#include <CGAL/point_generators_2.h>

#include <boost/bind.hpp>

typedef CGAL::Simple_cartesian<double> K;
typedef K::Point_2                     Point;
typedef K::Segment_2                   Segment;

typedef CGAL::Creator_uniform_2<double,Point>              Pt_creator;
typedef CGAL::Random_points_on_segment_2<Point,Pt_creator> P1;
typedef CGAL::Random_points_on_circle_2<Point,Pt_creator>  P2;
typedef CGAL::Creator_uniform_2< Point, Segment>           Seg_creator;
typedef CGAL::Join_input_iterator_2< P1, P2, Seg_creator>  Seg_iterator;

struct Intersector{
  typedef CGAL::cpp11::result_of<K::Intersect_2(Segment,Segment)>::type result_type;
  const Segment& s;
  K::Intersect_2 intersect;

  Intersector(const Segment& seg): s(seg) {}

  result_type
  operator() ( const Segment& other) const
  {
    return intersect(s, other);
  }
};

int main()
{
  std::vector<Segment> input;

  // Prepare point generator for the horizontal segment, length 200.
  P1 p1( Point(-100,0), Point(100,0));

  // Prepare point generator for random points on circle, radius 250.
  P2 p2( 250);

  // Create segments.
  Seg_iterator g( p1, p2);
  CGAL::cpp11::copy_n( g, 200, std::back_inserter(input));


  // splitting results with Dispatch_output_iterator
  std::vector<Point> points;
  std::vector<Segment> segments;

  typedef CGAL::Dispatch_output_iterator<
    CGAL::cpp11::tuple<Point,Segment>, CGAL::cpp0x::tuple< std::back_insert_iterator<std::vector<Point> >,
                                               std::back_insert_iterator<std::vector<Segment> > > >
    Dispatcher;

  Dispatcher disp = CGAL::dispatch_output<Point,Segment>( std::back_inserter(points),
                                                          std::back_inserter(segments) );

  // intersects the first segment of input with all other segments
  // The resulting points or segments are written in the vectors with the same names
  std::transform( input.begin(), input.end(), disp,
                  Intersector(input.front()) );


  std::cout << "Point intersections: " << points.size() << std::endl;
  std::cout << "Segment intersections: " << segments.size() << std::endl;


  return 0;
}

template<typename Kernel >

boost::optional< boost::variant< Point_3, Line_3, Plane_3 > > CGAL::intersection	(	const Plane_3< Kernel > &	pl1,
		const Plane_3< Kernel > &	pl2,
		const Plane_3< Kernel > &	pl3
	)

returns the intersection of 3 planes, which can be a point, a line, a plane, or empty.