Determining the Minimum-Area Encasing Rectangle for an Arbitrary Closed Curve.

This report describes a method for finding the rectangle of minimum-area in which a given arbitrary plan cure can be contained. The method is of interest in certain packing and optimum layout problems. It consists of first determining the minimla-perimeter convex polygon that encloses the given curve and then selecting the rectangle of minimum area capable of containing this polygon. Three theorems are introduced to show that one side of the minimum-area rectangle must be colinear with an edge of the enclosed polygon and that the minimum-area encasing rectangle for the convex polygon is also the minimum-area rectangle for the curve.