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Minkowski sum


In geometry, the Minkowski sum (also known as dilation) of two sets of position vectors A and B in Euclidean space is formed by adding each vector in A to each vector in B, i.e., the set

Analogously, the Minkowski difference (or geometric difference) is defined as

It is important to note that in general . For instance, in a one-dimensional case and the Minkowski difference , whereas The correct formula connecting Minkowski sum and difference is as follows (here stands for the complement of ):


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