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

CGAL 4.3 - 3D Boolean Operations on Nef Polyhedra

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Nef_3/transformation.cpp
#include <CGAL/Gmpz.h>
#include <CGAL/Extended_homogeneous.h>
#include <CGAL/Nef_polyhedron_3.h>
#include <CGAL/IO/Nef_polyhedron_iostream_3.h>
//instead of
//typedef CGAL::Extended_homogeneous<CGAL::Gmpz> Kernel;
// workaround for VC++
struct Kernel : public CGAL::Extended_homogeneous<CGAL::Gmpz> {};
typedef CGAL::Nef_polyhedron_3<Kernel> Nef_polyhedron;
typedef Nef_polyhedron::Plane_3 Plane_3;
typedef Nef_polyhedron::Vector_3 Vector_3;
typedef Nef_polyhedron::Aff_transformation_3 Aff_transformation_3;
int main() {
Nef_polyhedron N(Plane_3(0,1,0,0));
Aff_transformation_3 transl(CGAL::TRANSLATION, Vector_3(5, 7, 9));
Aff_transformation_3 rotx90(1,0,0,
0,0,-1,
0,1,0,
1);
Aff_transformation_3 scale(3,0,0,
0,3,0,
0,0,3,
2);
N.transform(transl);
CGAL_assertion(N == Nef_polyhedron(Plane_3(0,1,0,-7)));
N.transform(rotx90);
CGAL_assertion(N == Nef_polyhedron(Plane_3(0,0,1,-7)));
N.transform(scale);
CGAL_assertion(N == Nef_polyhedron(Plane_3(0,0,2,-21)));
return 0;
}