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#include <CGAL/Gmpz.h>
#include <CGAL/Homogeneous.h>
#include <CGAL/Nef_polyhedron_S2.h>
typedef CGAL::Gmpz RT;
typedef CGAL::Homogeneous<RT> Kernel;
typedef CGAL::Nef_polyhedron_S2<Kernel> Nef_polyhedron;
typedef Nef_polyhedron::Sphere_point Sphere_point;
typedef Nef_polyhedron::Sphere_segment Sphere_segment;
typedef Nef_polyhedron::Sphere_circle Sphere_circle;
int main() {
Nef_polyhedron N1(Nef_polyhedron::COMPLETE);
Sphere_circle c(1,1,1); // c : x + y + z = 0
Nef_polyhedron N2(c, Nef_polyhedron::INCLUDED);
Nef_polyhedron N3(N2.complement());
CGAL_assertion(N1 == N2.join(N3));
Sphere_point p1(1,0,0), p2(0,1,0), p3(0,0,1);
Sphere_segment s1(p1,p2), s2(p2,p3), s3(p3,p1);
Sphere_segment triangle[3] = { s1, s2, s3 };
Nef_polyhedron N4(triangle, triangle+3);
Nef_polyhedron N5;
N5 += N2;
N5 = N5.intersection(N4);
CGAL_assertion(N5 <= N2 && N5 != N4);
return 0;
}
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