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

CGAL 4.3 - 2D Minkowski Sums

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Minkowski_sum_2/sum_triangles.cpp
// Computing the Minkowski sum of two triangles.
#include "ms_rational_nt.h"
#include <CGAL/Cartesian.h>
#include <CGAL/minkowski_sum_2.h>
#include <iostream>
#include "print_utils.h"
typedef CGAL::Cartesian<Number_type> Kernel;
typedef Kernel::Point_2 Point_2;
typedef CGAL::Polygon_2<Kernel> Polygon_2;
typedef CGAL::Polygon_with_holes_2<Kernel> Polygon_with_holes_2;
int main ()
{
// Construct the first polygon (a triangle).
Polygon_2 P;
P.push_back (Point_2 (0, 0));
P.push_back (Point_2 (6, 0));
P.push_back (Point_2 (3, 5));
// Construct the second polygon (a triangle).
Polygon_2 Q;
Q.push_back (Point_2 (0, 0));
Q.push_back (Point_2 (2, -2));
Q.push_back (Point_2 (2, 2));
// Compute the Minkowski sum.
Polygon_with_holes_2 sum = minkowski_sum_2 (P, Q);
CGAL_assertion (sum.number_of_holes() == 0);
std::cout << "P = "; print_polygon (P);
std::cout << "Q = "; print_polygon (Q);
std::cout << "P (+) Q = "; print_polygon (sum.outer_boundary());
return (0);
}