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#include <CGAL/Gmpz.h>
#include <CGAL/Extended_homogeneous.h>
#include <CGAL/Nef_polyhedron_3.h>
#include <CGAL/IO/Nef_polyhedron_iostream_3.h>
typedef CGAL::Gmpz NT;
//instead of
//typedef CGAL::Extended_homogeneous<NT> Kernel;
// workaround for VC++
struct Kernel : public CGAL::Extended_homogeneous<NT> {};
typedef CGAL::Nef_polyhedron_3<Kernel> Nef_polyhedron;
typedef Nef_polyhedron::RT RT;
typedef Nef_polyhedron::Point_3 Point_3;
typedef Nef_polyhedron::Plane_3 Plane_3;
typedef Nef_polyhedron::Vertex_const_iterator Vertex_const_iterator;
int main() {
Nef_polyhedron N;
std::cin >> N;
Vertex_const_iterator v;
for(v = N.vertices_begin(); v != N.vertices_end(); ++v) {
Point_3 p(v->point());
if(p.hx().degree() > 0 || p.hy().degree() > 0 || p.hz().degree() > 0)
std::cout << "extended vertex at " << p << std::endl;
else
std::cout << "standard vertex at " << p << std::endl;
if(p == Point_3(RT(0,1), RT(0,1), RT(0,1)))
std::cout << " found vertex (right,back,top) of the infimaximal box"
<< std::endl;
}
return 0;
}
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