Revisit of Minimum-area Enclosing Rectangle of a Convex Polygon

摘要

The problem of minimum-area enclosing rectangle of a convex polygon was first studied in [1] in 1975. We revis it this problem by providing a new complete proof via the elementary calculus and the method of rotating calipers [4], [5], [7] with transparent existence condition not revealed explicitly in [1] mainly based on geometric reasoning. The existence of minimum-area enclosing rectangle is mathematically due to monotonicy of area of enclosing rectangle with respect to the rotation angle defining its configuration relative to an initial enclosing rectangle.