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

This paper describes a method for finding the
rectangle of minimum area in which a given arbitrary 
plane curve can be contained.  The method is of interest
in certain packing and optimum layout problems. 
 It consists of first determining the minimal-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.

CACM July, 1975

Freeman, H.
Shapira, R.

enclosed curve, optimum layout, optimum
packing, minimum-area encasing rectangle

5.19 5.49

CA750705 JB January 9, 1978  10:08 AM

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