relationship between Minkowski addition and the trajectory of a numerical controle machine?

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This is a very naive question about the Minkowski addition. I hope not to be off-topic.

I read in the Wikipedia's article dedicated to it :

In numerical control machining, the programming of the NC tool exploits the fact that the Minkowski sum of the cutting piece with its trajectory gives the shape of the cut in the material.

I don't understand the relationship "cutting piece + trajectory = the shape of the cut in the material" .

By example, if I look at the first image of the article (blue+green = red) enter image description here

... I don't get it : where would be the cutting piece ? what about the trajectory ?

Any help would be appreciated !