A minimum bounding box of a bounded set is a rectangular box of smallest volume that contains the set, where the box is allowed to rotate. In the plane it is a minimum-area bounding rectangle. The term is sometimes used instead for an axis-aligned bounding box, so the permitted orientations must be stated.
The minimum bounding box of a finite point set is unchanged when the set is replaced by its convex hull. In the plane, at least one side of a minimum-area rectangle is collinear with an edge of the convex hull. This observation leads to a rotating-calipers algorithm after the convex hull has been computed. The three-dimensional problem requires considering orientations determined by features of the convex hull and is not obtained by independently minimizing three coordinate ranges.
