Bounding box

A bounding box is a rectangle, or its higher-dimensional counterpart, containing a specified set. For finitely many points, the smallest axis-aligned box is ${\prod }_j[{\min }_i{x}_{ij},{\max }_i{x}_{ij}]$. For $(1,4),(3,-1),(2,2)$ this is $[1,3]\times [-1,4]$. Every coordinate extreme forces the corresponding box endpoint, proving minimality for the chosen axes. Allowing a rotation changes the optimization problem. Disjoint bounding boxes certify disjoint enclosed objects and accelerate geometric searches.