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

CGAL 4.8 - 2D Boolean Operations on Nef Polygons

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Nef_2/nef_2_construction.cpp
#include <CGAL/Exact_integer.h>
#include <CGAL/Filtered_extended_homogeneous.h>
#include <CGAL/Nef_polyhedron_2.h>
typedef CGAL::Exact_integer RT;
typedef CGAL::Filtered_extended_homogeneous<RT> Extended_kernel;
typedef CGAL::Nef_polyhedron_2<Extended_kernel> Nef_polyhedron;
typedef Nef_polyhedron::Point Point;
typedef Nef_polyhedron::Line Line;
int main() {
Nef_polyhedron N1(Nef_polyhedron::COMPLETE);
Line l(2,4,2); // l : 2x + 4y + 2 = 0
Nef_polyhedron N2(l,Nef_polyhedron::INCLUDED);
Nef_polyhedron N3 = N2.complement();
CGAL_assertion(N1 == N2.join(N3));
Point p1(0,0), p2(10,10), p3(-20,15);
Point triangle[3] = { p1, p2, p3 };
Nef_polyhedron N4(triangle, triangle+3);
Nef_polyhedron N5 = N2.intersection(N4);
CGAL_assertion(N5 <= N2 && N5 <= N4);
return 0;
}