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Zonogons: Minkowski Sums of Line Segments in 2D
Zonogons: Minkowski Sums of Line Segments in 2D
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 line segments with an endpoint at the origin. The line segments joining the origin to all possible sums of the endpoints are also shown.
The Minkowski sum of two line segments is a parallelogram. With more segments, the resulting figure is called a zonogon, which, like a parallelogram, has opposite sides equal and parallel.
In 3D (not shown here), a zonohedron is again the Minkowski sum of such line segments. Its opposite faces are zonogons that are equal, parallel, and symmetric about the center of the zonohedron.