Ingeometry, the distance set of a collection of points is the setofdistances between distinct pairs of points. Thus, it can be seen as the generalization of a difference set, the set of distances (and their negations) in collections of numbers.
Several problems and results in geometry concern distance sets, usually based on the principle that a large collection of points must have a large distance set (for varying definitions of "large"):
Distance sets have also been used as a shape descriptorincomputer vision.[10]