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

CGAL 4.8 - 2D Minkowski Sums

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Minkowski_sum_2/sum_triangle_square.cpp
// Computing the Minkowski sum of a triangle and a square.
#include <CGAL/basic.h>
#include <CGAL/minkowski_sum_2.h>
#include "bops_linear.h"
int main()
{
// Construct the triangle.
Polygon_2 P;
P.push_back(Point_2(-1, -1)); P.push_back(Point_2(1, -1));
P.push_back(Point_2(0, 1));
std::cout << "P = " << P << std::endl;
// Construct the square.
Polygon_2 Q;
Q.push_back(Point_2(3, -1)); Q.push_back(Point_2(5, -1));
Q.push_back(Point_2(5, 1)); Q.push_back(Point_2(3, 1));
std::cout << "Q = " << Q << std::endl;
// Compute the Minkowski sum.
Polygon_with_holes_2 sum = CGAL::minkowski_sum_2(P, Q);
CGAL_assertion(sum.number_of_holes() == 0);
std::cout << "P (+) Q = " << sum.outer_boundary() << std::endl;
return 0;
}