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template<class Kernel, class Container>
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Polygon_with_holes_2<Kernel,Container>
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minkowski_sum_2 ( Polygon_2<Kernel,Container> P, Polygon_2<Kernel,Container> Q)
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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. |
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template<class Kernel, class Container, class DecompositionStrategy>
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Polygon_with_holes_2<Kernel,Container>
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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, … , Qℓ 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. |
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