Approximation of convex figures by pairs of rectangles [chapter]

Otfried Schwarzkopf, Ulrich Fuchs, Günter Rote, Emo Welzl
1990 Lecture Notes in Computer Science  
We consider the problem of approximating a convex gure in the plane by a pair (r; R ) of homothetic (that is, similar and parallel) rectangles with r C R. W e 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 P olya and Szeg} o. 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:10.1007/3-540-52282-4_47 fatcat:xq5g37gyu5gv3lge5kvdhtaapi