In
geometry, the Minkowski sum (also known as
dilation
Dilation (or dilatation) may refer to:
Physiology or medicine
* Cervical dilation, the widening of the cervix in childbirth, miscarriage etc.
* Coronary dilation, or coronary reflex
* Dilation and curettage, the opening of the cervix and surgi ...
) of two
sets of
position vectors ''A'' and ''B'' in
Euclidean space
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidea ...
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 using the
complement operation as
:
In general
. For instance, in a one-dimensional case