CGAL 5.0.3 - 2D and 3D Linear Geometry Kernel
Functions
CGAL::intersection() (2D/3D Linear Kernel)
2D and 3D Linear Geometry Kernel Reference » Global Kernel Functions » CGAL::intersection()
template<typename Kernel >
cpp11::result_of<Kernel::Intersect_23(Type1, Type2)>::type CGAL::intersection(Type1< Kernel > obj1, Type2< Kernel > obj2 )#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.
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 CGAL::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.
Type1Type2Return Type: T...Iso_rectangle_2Iso_rectangle_2Iso_rectangle_2
Iso_rectangle_2Line_2Point_2, or Segment_2Iso_rectangle_2Ray_2Point_2, or Segment_2Iso_rectangle_2Segment_2Point_2, or Segment_2Iso_rectangle_2Triangle_2Point_2, or Segment_2, or Triangle_2, or std::vector<Point_2>Line_2Line_2Point_2, or Line_2Line_2Ray_2Point_2, or Ray_2Line_2Segment_2Point_2, or Segment_2Line_2Triangle_2Point_2, or Segment_2Ray_2Ray_2Point_2, or Segment_2, or Ray_2Ray_2Segment_2Point_2, or Segment_2Ray_2Triangle_2Point_2, or Segment_2Segment_2Segment_2Point_2, or Segment_2Segment_2Triangle_2Point_2, or Segment_2Triangle_2Triangle_2Point_2, or Segment_2, or Triangle_2, or std::vector<Point_2>
Additional overloads are provided for the type Point_2 combined with any other type with the result type being boost::optional< boost::variant< Point_2 > >.
3D Intersections
The return type can be obtained through CGAL::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.
Type1Type2Return Type: T...Line_3Line_3Point_3, or Line_3Line_3Plane_3Point_3, or Line_3Line_3Ray_3Point_3, or Ray_3Line_3Segment_3Point_3, or Segment_3Line_3Triangle_3Point_3, or Segment_3Plane_3Plane_3Line_3, or Plane_3Plane_3Ray_3Point_3, or Ray_3Plane_3Segment_3Point_3, or Segment_3Plane_3Sphere_3Point_3, or Circle_3Plane_3Triangle_3Point_3, or Segment_3, or Triangle_3Ray_3Ray_3Point_3, or Ray_3, or Segment_3Ray_3Segment_3Point_3, or Segment_3Ray_3Triangle_3 pPoint_3, or Segment_3Segment_3Segment_3Point_3, or Segment_3Segment_3Triangle_3Point_3, or Segment_3Sphere_3Sphere_3Point_3, or Circle_3, or Sphere_3Triangle_3Triangle_3Point_3, or Segment_3, or Triangle_3, or std::vector < Point_3 >Additional overloads are provided for the type Point_3 combined with any other type with the result type being boost::optional< boost::variant< Point_3 > >.
Examples
The following examples demonstrate the most common use of intersection() functions with the 2D and 3D Linear Kernel.
In the first two examples we intersect a segment and a line. The result type can be obtained with CGAL::cpp11::result_of. It looks simpler if you use a C++ compiler which supports auto, but you must anyways know that the result type is a boost::optional<boost::variant<..> >, in order to unpack the point or segment.
boost::optional comes in as there might be no intersection. boost::variant comes in as, if there is an intersection, it is either a point or a segment.
As explained in the boost manual pages for boost::variant, there are two ways to access the variants. The first examples uses boost::get.
File Kernel_23/intersection_get.cpp
#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
#include <CGAL/intersections.h>
typedef CGAL::Exact_predicates_exact_constructions_kernel K;
typedef K::Point_2 Point_2;
typedef K::Segment_2 Segment_2;
typedef K::Line_2 Line_2;
typedef K::Intersect_2 Intersect_2;
int main()
{
Segment_2 seg(Point_2(0,0), Point_2(2,2));
Line_2 lin(1,-1,0);
CGAL::cpp11::result_of<Intersect_2(Segment_2, Line_2)>::type
result = intersection(seg, lin);
if (result) {
if (const Segment_2* s = boost::get<Segment_2>(&*result)) {
std::cout << *s << std::endl;
} else {
const Point_2* p = boost::get<Point_2 >(&*result);
std::cout << *p << std::endl;
}
}
return 0;
}
The second example uses boost::apply_visitor.
File Kernel_23/intersection_visitor.cpp
#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
#include <CGAL/intersections.h>
typedef CGAL::Exact_predicates_exact_constructions_kernel K;
typedef K::Point_2 Point_2;
typedef K::Segment_2 Segment_2;
typedef K::Line_2 Line_2;
typedef K::Intersect_2 Intersect_2;
struct Intersection_visitor {
typedef void result_type;
void operator()(const Point_2& p) const
{
std::cout << p << std::endl;
}
void operator()(const Segment_2& s) const
{
std::cout << s << std::endl;
}
};
int main()
{
Segment_2 seg(Point_2(0,0), Point_2(1,1));
Line_2 lin(1,-1,0);
// with C++11 support
// auto result = intersection(seg, lin);
// without C++11
CGAL::cpp11::result_of<Intersect_2(Segment_2, Line_2)>::type
result = intersection(seg, lin);
if (result) {
boost::apply_visitor(Intersection_visitor(), *result);
} else {
// no intersection
}
return 0;
}
A third example shows 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/Exact_predicates_exact_constructions_kernel.h>
#include <CGAL/iterator.h>
#include <CGAL/point_generators_2.h>
#include <boost/bind.hpp>
typedef CGAL::Exact_predicates_exact_constructions_kernel 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);
std::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<
std::tuple<Point,Segment>, std::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;
}
https://doc.cgal.org/latest/Kernel_23/group__intersection__linear__grp.html
