Example
For example, if we have two sets A and B, each consisting of three position vectors (informally, three points), representing the vertices of two (triangles) in, with coordinates
- A = {(1, 0), (0, 1), (0, −1)}
and
- B = {(0, 0), (1, 1), (1, −1)} ,
then the Minkowski sum is
A + B = {(1, 0), (2, 1), (2, −1), (0, 1), (1, 2), (1, 0), (0, −1), (1, 0), (1, −2)} , which looks like a hexagon, with three 'repeated' points at (1, 0).
For Minkowski addition, the zero set {0}, containing only the zero vector 0, is an identity element: For every subset S, of a vector space
- S + {0} = S;
The empty set is important in Minkowski addition, because the empty set annihilates every other subset: for every subset, S, of a vector space, its sum with the empty set is empty: S + = .
Read more about this topic: Minkowski Addition
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—Marcel Proust (1871–1922)