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

CGAL 4.8 - 2D Minkowski Sums

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Minkowski_sum_2/sum_by_decomposition.cpp
// Computing the Minkowski sum of two non-convex polygons read from a file
// using the small-side angle-bisector decomposition strategy.
#include <fstream>
#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
#include <CGAL/minkowski_sum_2.h>
#include <CGAL/Small_side_angle_bisector_decomposition_2.h>
#include "pgn_print.h"
typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
typedef Kernel::Point_2 Point;
typedef CGAL::Polygon_2<Kernel> Polygon_2;
typedef CGAL::Polygon_with_holes_2<Kernel> Polygon_with_holes_2;
int main(int argc, char* argv[])
{
// Open the input file and read two polygons from it.
const char* filename = (argc > 1) ? argv[1] : "rooms_star.dat";
std::ifstream in_file(filename);
if (! in_file.is_open()) {
std::cerr << "Failed to open the input file." << std::endl;
return -1;
}
Polygon_2 P, Q;
in_file >> P >> Q;
in_file.close();
// Compute the Minkowski sum using the decomposition approach.
CGAL::Small_side_angle_bisector_decomposition_2<Kernel> ssab_decomp;
Polygon_with_holes_2 sum = CGAL::minkowski_sum_2(P, Q, ssab_decomp);
std::cout << "P (+) Q = "; print_polygon_with_holes(sum);
return 0;
}