Approximation of convex figures by pairs of rectangles

Otfried Schwarzkopf, Ulrich Fuchs, Günter Rote, Emo Welzl
1998 Computational geometry  
We consider the problem of approximating a convex figure in the plane by a pair (r, R) of homothetic (that is, similar and parallel) rectangles with r C_ C C_ R. We show the existence of such a pair where the sides of the outer rectangle are at most twice as long as the sides of the inner rectangle, thereby solving a problem posed by P61ya and Szeg6. 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(log 2 n).
doi:10.1016/s0925-7721(96)00019-3 fatcat:pl7yk2imw5ccrl6w6renpx4l4a