CGAL::minkowski_sum_2

#include <CGAL/minkowski_sum_2.h>

template<class Kernel, class Container>
Polygon_with_holes_2<Kernel,Container>
	minkowski_sum_2 ( Polygon_2<Kernel,Container> P, Polygon_2<Kernel,Container> Q)
		Computes the Minkowski sum $$P Q of the two given polygons. The function computes the convolution cycles of the two polygons and extract the regions having positive winding number with respect to these cycles. This method work very efficiently, regardless of whether P and Q are convex or non-convex. Note that as the input polygons may not be convex, their Minkowski sum may not be a simple polygon. The result is therefore represented as a polygon with holes. Precondition:  Both P and Q are simple polygons.
template<class Kernel, class Container, class DecompositionStrategy>
Polygon_with_holes_2<Kernel,Container>
	minkowski_sum_2 ( Polygon_2<Kernel,Container> P, Polygon_2<Kernel,Container> Q, DecompositionStrategy decomp)
		Computes the Minkowski sum $$P Q of the two given polygons. If the input polygons P and Q are not convex, the function decomposes them into convex sub-polygons $$P1, ..., Pk and $$Q1, ..., Q and computes the union of pairwise sub-sums (namely $$ i,j(Pi Qj)). The decomposition is performed using the given decomposition strategy decomp, which must be an instance of a class that models the concept PolygonConvexDecomposition. Note that as the input polygons may not be convex, their Minkowski sum may not be a simple polygon. The result is therefore represented as a polygon with holes. Precondition:  Both P and Q are simple polygons.