Advertisement

Approximation of convex figures by pairs of rectangles

  • Otfried Schwarzkopf
  • Ulrich Fuchs
  • Günter Rote
  • Emo Welzl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 415)

Abstract

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⊂CR. 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).

Keywords

Convex Hull Convex Body Convex Polygon Binary Search Expansion Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AFM*]
    Helmut Alt, Rudolf Fleischmer, Kurt Mehlhorn, Günter Rote, Emo Welzl, and Chee Yap. On certificates for polygon containment and shape approximation. (manuscript).Google Scholar
  2. [Joh48]
    F. John. Extremum problems with inequalities as subsidiary conditions. In Courant Anniversary Volume, pages 187–204, New York, 1948.Google Scholar
  3. [Las89]
    Marek Lassak. Approximation of plane convex bodies by centrally symmetric bodies. 1989. To appear in J. London Math. Soc. Google Scholar
  4. [Lei59]
    K. Leichtweiß. Über die affine Exzentrizität konvexer Körper. Arch. Math., 10:187–199, 1959.CrossRefGoogle Scholar
  5. [PS51]
    G. Pólya and G. Szegö. Isoperimetric inequalities in mathematical physics. Ann. Math. Stud. Princeton, 27, 1951.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Otfried Schwarzkopf
    • 1
  • Ulrich Fuchs
    • 1
  • Günter Rote
    • 1
  • Emo Welzl
    • 1
  1. 1.Institut für Informatik, FB MathematikFreie Universität BerlinBerlin 33West Germany

Personalised recommendations