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#include <CGAL/Gmpz.h>
#include <CGAL/Homogeneous.h>
#include <CGAL/Nef_polyhedron_3.h>
#include <CGAL/IO/Nef_polyhedron_iostream_3.h>
typedef CGAL::Homogeneous<CGAL::Gmpz> Kernel;
typedef CGAL::Nef_polyhedron_3<Kernel> Nef_polyhedron;
typedef Nef_polyhedron::Vertex_const_handle Vertex_const_handle;
typedef Nef_polyhedron::Halfedge_const_handle Halfedge_const_handle;
typedef Nef_polyhedron::Halffacet_const_handle Halffacet_const_handle;
typedef Nef_polyhedron::SHalfedge_const_handle SHalfedge_const_handle;
typedef Nef_polyhedron::SHalfloop_const_handle SHalfloop_const_handle;
typedef Nef_polyhedron::SFace_const_handle SFace_const_handle;
typedef Nef_polyhedron::Volume_const_iterator Volume_const_iterator;
typedef Nef_polyhedron::Shell_entry_const_iterator Shell_entry_const_iterator;
typedef Kernel::Point_3 Point_3;
class Shell_explorer {
bool first;
const Nef_polyhedron& N;
Vertex_const_handle v_min;
public:
Shell_explorer(const Nef_polyhedron& N_)
: first(true), N(N_) {}
void visit(Vertex_const_handle v) {
if(first || CGAL::lexicographically_xyz_smaller(v->point(),v_min->point())) {
v_min = v;
first=false;
}
}
void visit(Halfedge_const_handle ) {}
void visit(Halffacet_const_handle ) {}
void visit(SHalfedge_const_handle ) {}
void visit(SHalfloop_const_handle ) {}
void visit(SFace_const_handle ) {}
Vertex_const_handle& minimal_vertex() { return v_min; }
void reset_minimal_vertex() { first = true; }
};
int main() {
Nef_polyhedron N;
std::cin >> N;
int ic = 0;
Volume_const_iterator c;
Shell_explorer SE(N);
CGAL_forall_volumes(c,N) {
std::cout << "Volume " << ic++ << std::endl;
int is = 0;
Shell_entry_const_iterator it;
CGAL_forall_shells_of(it,c) {
SE.reset_minimal_vertex();
N.visit_shell_objects(SFace_const_handle(it),SE);
Point_3 p(SE.minimal_vertex()->point());
std::cout << " minimal vertex of shell " << is++
<< " is at " << p << std::endl;
}
}
}
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