\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 3D Fast Intersection and Distance Computation (AABB Tree)

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AABB_tree/AABB_polyhedron_facet_intersection_example.cpp
// Author(s) : Camille Wormser, Pierre Alliez
#include <iostream>
#include <list>
#include <CGAL/Simple_cartesian.h>
#include <CGAL/AABB_tree.h>
#include <CGAL/AABB_traits.h>
#include <CGAL/Polyhedron_3.h>
#include <CGAL/boost/graph/graph_traits_Polyhedron_3.h>
#include <CGAL/AABB_face_graph_triangle_primitive.h>
typedef CGAL::Simple_cartesian<double> K;
typedef K::Point_3 Point;
typedef K::Plane_3 Plane;
typedef K::Vector_3 Vector;
typedef K::Segment_3 Segment;
typedef CGAL::Polyhedron_3<K> Polyhedron;
typedef CGAL::AABB_face_graph_triangle_primitive<Polyhedron> Primitive;
typedef CGAL::AABB_traits<K, Primitive> Traits;
typedef CGAL::AABB_tree<Traits> Tree;
typedef boost::optional< Tree::Intersection_and_primitive_id<Segment>::Type > Segment_intersection;
typedef boost::optional< Tree::Intersection_and_primitive_id<Plane>::Type > Plane_intersection;
typedef Tree::Primitive_id Primitive_id;
int main()
{
Point p(1.0, 0.0, 0.0);
Point q(0.0, 1.0, 0.0);
Point r(0.0, 0.0, 1.0);
Point s(0.0, 0.0, 0.0);
Polyhedron polyhedron;
polyhedron.make_tetrahedron(p, q, r, s);
// constructs AABB tree
Tree tree(faces(polyhedron).first, faces(polyhedron).second, polyhedron);
// constructs segment query
Point a(-0.2, 0.2, -0.2);
Point b(1.3, 0.2, 1.3);
Segment segment_query(a,b);
// tests intersections with segment query
if(tree.do_intersect(segment_query))
std::cout << "intersection(s)" << std::endl;
else
std::cout << "no intersection" << std::endl;
// computes #intersections with segment query
std::cout << tree.number_of_intersected_primitives(segment_query)
<< " intersection(s)" << std::endl;
// computes first encountered intersection with segment query
// (generally a point)
Segment_intersection intersection =
tree.any_intersection(segment_query);
if(intersection)
{
// gets intersection object
if(boost::get<Point>(&(intersection->first)))
std::cout << "intersection object is a point" << std::endl;
}
// computes all intersections with segment query (as pairs object - primitive_id)
std::list<Segment_intersection> intersections;
tree.all_intersections(segment_query, std::back_inserter(intersections));
// computes all intersected primitives with segment query as primitive ids
std::list<Primitive_id> primitives;
tree.all_intersected_primitives(segment_query, std::back_inserter(primitives));
// constructs plane query
Vector vec(0.0,0.0,1.0);
Plane plane_query(a,vec);
// computes first encountered intersection with plane query
// (generally a segment)
Plane_intersection plane_intersection = tree.any_intersection(plane_query);
if(plane_intersection)
{
if(boost::get<Segment>(&(plane_intersection->first)))
std::cout << "intersection object is a segment" << std::endl;
}
return EXIT_SUCCESS;
}