# The Minkowski Sum of a Disk and a Polygon

The Minkowski Sum of a Disk and a Polygon

The Minkowski sum of two subsets in the plane, and , is the set of all sums , where and .

A

B

a+b

a∈A

b∈B

This Demonstration shows the Minkowski sum of a disk and a polygon. Adding the disk pushes out the sides and vertices of the polygon by the radius of the circle.

Another way of thinking of the Minkowski sum is as the set of translates of by all of the elements of . A translate of a set by a vector is the set of all sums , where . Geometrically, adding a disk to a polygon translates copies of the disk to every point of the polygon. Or, vice versa: translate copies of the polygon to every point of the disk.

A+B

A

B

A

b

a+b

a∈A

If the polygon is convex, so is its sum with a disk.