Approximation of convex figures by pairs of rectangles
We consider the problem of approximating a convex figure in the plane by a pair (τ, R) of homothetic (i.e. similar and parallel) rectangles with τ⊂C⊂R. We show the existence of such pairs where the sides of the outer rectangle have length at most double the length of the inner rectangle, thereby solving a problem posed by Pólya and Szegő.
If the n vertices of a convex polygon C are given as a sorted array, such an approximating pair of rectangles can be computed in time O(log3n).
KeywordsConvex Hull Convex Body Convex Polygon Binary Search Expansion Factor
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