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

CGAL 4.8 - Convex Decomposition of Polyhedra

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Convex_decomposition_3/list_of_convex_parts.cpp
#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
#include <CGAL/Polyhedron_3.h>
#include <CGAL/Nef_polyhedron_3.h>
#include <CGAL/IO/Nef_polyhedron_iostream_3.h>
#include <CGAL/Nef_3/SNC_indexed_items.h>
#include <CGAL/convex_decomposition_3.h>
#include <list>
typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
typedef CGAL::Polyhedron_3<Kernel> Polyhedron_3;
typedef CGAL::Nef_polyhedron_3<Kernel, CGAL::SNC_indexed_items> Nef_polyhedron_3;
typedef Nef_polyhedron_3::Volume_const_iterator Volume_const_iterator;
int main() {
Nef_polyhedron_3 N;
std::cin >> N;
CGAL::convex_decomposition_3(N);
std::list<Polyhedron_3> convex_parts;
// the first volume is the outer volume, which is
// ignored in the decomposition
Volume_const_iterator ci = ++N.volumes_begin();
for( ; ci != N.volumes_end(); ++ci) {
if(ci->mark()) {
Polyhedron_3 P;
N.convert_inner_shell_to_polyhedron(ci->shells_begin(), P);
convex_parts.push_back(P);
}
}
std::cout << "decomposition into " << convex_parts.size() << " convex parts " << std::endl;
}