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Approximation of convex figures by pairs of rectangles

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STACS 90 (STACS 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 415))

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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⊂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(log3 n).

This research was supported by the Deutsche Forschungsgemeinschaft under Grant Al 253/1-1, Schwerpunktprogramm “Datenstrukturen und effiziente Algorithmen”

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References

  1. Helmut Alt, Rudolf Fleischmer, Kurt Mehlhorn, Günter Rote, Emo Welzl, and Chee Yap. On certificates for polygon containment and shape approximation. (manuscript).

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Author notes

  1. Günter Rote

    Present address: Institut für Mathematik, Technische Universität Graz, Kopernikusgasse 24, A-8010, Graz, Austria

Authors and Affiliations

  1. Institut für Informatik, FB Mathematik, Freie Universität Berlin, Arnimalle 2-6, D-1000, Berlin 33, West Germany

    Otfried Schwarzkopf, Ulrich Fuchs, Günter Rote & Emo Welzl

Authors
  1. Otfried Schwarzkopf
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  2. Ulrich Fuchs
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  3. Günter Rote
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  4. Emo Welzl
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Christian Choffrut Thomas Lengauer

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© 1990 Springer-Verlag Berlin Heidelberg

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Schwarzkopf, O., Fuchs, U., Rote, G., Welzl, E. (1990). Approximation of convex figures by pairs of rectangles. In: Choffrut, C., Lengauer, T. (eds) STACS 90. STACS 1990. Lecture Notes in Computer Science, vol 415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52282-4_47

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  • DOI: https://doi.org/10.1007/3-540-52282-4_47

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52282-9

  • Online ISBN: 978-3-540-46945-2

  • eBook Packages: Springer Book Archive

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