`RegionIntersection`¶

Region common to several regions.

$ wo 'RegionIntersection[Rectangle[{0, 0}, {2, 2}], Rectangle[{1, 1}, {3, 3}]]'
Rectangle[{1, 1}, {2, 2}]

Regions that do not meet give the empty region of the same embedding dimension:

$ wo 'RegionIntersection[Point[{0, 0}], Point[{1, 1}]]'
EmptyRegion[2]

Anything that cannot be combined concretely keeps both regions inside a BooleanRegion:

$ wo 'RegionIntersection[Disk[], Disk[{1, 0}]]'
BooleanRegion[#1 && #2 & , {Disk[{0, 0}], Disk[{1, 0}]}]

RegionIntersection¶