Minkowski sum

The Minkowski sum is a way to combine two sets of points in the plane (or in space) by adding every point in one set to every point in the other set. If $A$ and $B$ are two sets of points, their Minkowski sum $A + B$ is the set of all points you can get by adding a point from $A$ to a point from $B$.

Important properties

• If $A$ and $B$ are both convex, then $A + B$ is also convex.

• The Minkowski sum is commutative: $A + B = B + A$.

• The Minkowski sum is associative: $(A + B) + C = A + (B + C)$.

• If $A$ and $B$ are polygons, $A + B$ is also a polygon.