WOLFRAM|DEMONSTRATIONS PROJECT

The Minkowski Sum of a Disk and a Polygon

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radius
0.1
The Minkowski sum of two subsets in the plane,
A
and
B
, is the set of all sums
a+b
, where
a∈A
and
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
A+B
is as the set of translates of
A
by all of the elements of
B
. A translate of a set
A
by a vector
b
is the set of all sums
a+b
, where
a∈A
. 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.
If the polygon is convex, so is its sum with a disk.