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

CGAL 4.8 - 3D Boolean Operations on Nef Polyhedra

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Nef_3/point_set_operations.cpp
#include <CGAL/Exact_integer.h>
#include <CGAL/Extended_homogeneous.h>
#include <CGAL/Nef_polyhedron_3.h>
typedef CGAL::Extended_homogeneous<CGAL::Exact_integer> Kernel;
typedef CGAL::Nef_polyhedron_3<Kernel> Nef_polyhedron;
typedef Kernel::Plane_3 Plane_3;
int main() {
Nef_polyhedron N1(Plane_3( 1, 0, 0,-1));
Nef_polyhedron N2(Plane_3(-1, 0, 0,-1));
Nef_polyhedron N3(Plane_3( 0, 1, 0,-1));
Nef_polyhedron N4(Plane_3( 0,-1, 0,-1));
Nef_polyhedron N5(Plane_3( 0, 0, 1,-1));
Nef_polyhedron N6(Plane_3( 0, 0,-1,-1));
Nef_polyhedron I1(!N1 + !N2); // open slice in yz-plane
Nef_polyhedron I2(N3 - !N4); // closed slice in xz-plane
Nef_polyhedron I3(N5 ^ N6); // open slice in yz-plane
Nef_polyhedron Cube1(I2 * !I1);
Cube1 *= !I3;
Nef_polyhedron Cube2 = N1 * N2 * N3 * N4 * N5 * N6;
CGAL_assertion(Cube1 == Cube2); // both are closed cube
CGAL_assertion(Cube1 == Cube1.closure());
CGAL_assertion(Cube1 == Cube1.regularization());
CGAL_assertion((N1 - N1.boundary()) == N1.interior());
CGAL_assertion(I1.closure() == I1.complement().interior().complement());
CGAL_assertion(I1.regularization() == I1.interior().closure());
return 0;
}