\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL - 3D Fast Intersection and Distance Computation (AABB Tree)
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// Author(s): Camille Wormser, Pierre Alliez
// An example of an AABB tree constructed with custom point and triangle types.
#include <iostream>
#include <list>
#include <CGAL/Simple_cartesian.h>
#include <CGAL/AABB_tree.h>
#include <CGAL/AABB_traits.h>
// custom point type
struct My_point {
double m_x;
double m_y;
double m_z;
My_point(const double x,
const double y,
const double z)
: m_x(x), m_y(y), m_z(z) {}
// custom triangle type with
// three pointers to points
struct My_triangle {
My_point *m_pa;
My_point *m_pb;
My_point *m_pc;
My_triangle(My_point *pa,
My_point *pb,
My_point *pc)
: m_pa(pa), m_pb(pb), m_pc(pc) {}
// the custom triangles are stored into a vector
typedef std::vector<My_triangle>::const_iterator Iterator;
// The following primitive provides the conversion facilities between
// the custom triangle and point types and the CGAL ones
struct My_triangle_primitive {
// this is the type of data that the queries returns. For this example
// we imagine that, for some reasons, we do not want to store the iterators
// of the vector, but raw pointers. This is to show that the Id type
// does not have to be the same as the one of the input parameter of the
// constructor.
typedef const My_triangle* Id;
// CGAL types returned
typedef K::Point_3 Point; // CGAL 3D point type
typedef K::Triangle_3 Datum; // CGAL 3D triangle type
Id m_pt; // this is what the AABB tree stores internally
My_triangle_primitive() {} // default constructor needed
// the following constructor is the one that receives the iterators from the
// iterator range given as input to the AABB_tree
My_triangle_primitive(Iterator it)
: m_pt(&(*it)) {}
const Id& id() const { return m_pt; }
// utility function to convert a custom
// point type to CGAL point type.
Point convert(const My_point *p) const
return Point(p->m_x,p->m_y,p->m_z);
// on the fly conversion from the internal data to the CGAL types
Datum datum() const
return Datum(convert(m_pt->m_pa),
// returns a reference point which must be on the primitive
Point reference_point() const
{ return convert(m_pt->m_pa); }
int main()
My_point a(1.0, 0.0, 0.0);
My_point b(0.0, 1.0, 0.0);
My_point c(0.0, 0.0, 1.0);
My_point d(0.0, 0.0, 0.0);
std::vector<My_triangle> triangles;
// constructs AABB tree
Tree tree(triangles.begin(),triangles.end());
// counts #intersections
K::Ray_3 ray_query(K::Point_3(1.0, 0.0, 0.0), K::Point_3(0.0, 1.0, 0.0));
std::cout << tree.number_of_intersected_primitives(ray_query)
<< " intersections(s) with ray query" << std::endl;
// computes closest point
K::Point_3 point_query(2.0, 2.0, 2.0);
K::Point_3 closest_point = tree.closest_point(point_query);
std::cerr << "closest point is: " << closest_point << std::endl;