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

CGAL 4.8 - 3D Spherical Geometry Kernel

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Circular_kernel_3/intersecting_spheres.cpp
#include <CGAL/Exact_spherical_kernel_3.h>
#include <CGAL/Random.h>
typedef CGAL::Exact_spherical_kernel_3 Spherical_k;
typedef CGAL::Point_3<Spherical_k> Point_3;
typedef CGAL::Sphere_3<Spherical_k> Sphere_3;
int main() {
CGAL::Random generatorOfgenerator;
int random_seed = generatorOfgenerator.get_int(0, 123456);
CGAL::Random theRandom(random_seed);
int count = 0;
std::cout << "We will compute the approximate probability that 3 spheres wit"
<< "h radius 1 intersect on a 5x5x5 box, it might take some time." << std::endl;
for(int i=0; i<10000; i++) {
double x1 = theRandom.get_double(0.0,5.0);
double y1 = theRandom.get_double(0.0,5.0);
double z1 = theRandom.get_double(0.0,5.0);
double r = 1.0;
double x2 = theRandom.get_double(0.0,5.0);
double y2 = theRandom.get_double(0.0,5.0);
double z2 = theRandom.get_double(0.0,5.0);
double x3 = theRandom.get_double(0.0,5.0);
double y3 = theRandom.get_double(0.0,5.0);
double z3 = theRandom.get_double(0.0,5.0);
Sphere_3 s1 = Sphere_3(Point_3(x1,y1,z1), r);
Sphere_3 s2 = Sphere_3(Point_3(x2,y2,z2), r);
Sphere_3 s3 = Sphere_3(Point_3(x3,y3,z3), r);
std::vector< CGAL::Object > intersecs;
CGAL::intersection(s1, s2, s3, std::back_inserter(intersecs));
if(intersecs.size() > 0) count++;
}
std::cout << "The approximate probability that 3 spheres with radius 1"
<< std::endl;
std::cout << "choosen (uniformly) randomly on a 5x5x5 box intersect is: "
<< ((double)count)/((double)(10000)) << std::endl;
return 0;
}