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Workshop on Algorithms and Data Structures

WADS 1999: Algorithms and Data Structures pp 62–73Cite as

Optimizing Constrained Offset and Scaled Polygonal Annuli

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1663))

Abstract

Aicholzer et al. recently presented a new geometric construct called the straight skeleton of a simple polygon and gave several combinatorial bounds for it. Independently, the current authors defined in companion papers a distance function based on the same offsetting function for convex polygons. In particular, we explored the nearest- and furthest- neighbor Voronoi diagrams of this function and presented algorithms for constructing them. In this paper we give solutions to some constrained annulus placement problems for offset polygons. The goal is to find the smallest annulus region of a polygon containing a set of points. We fix the inner (resp.,outer) polygon of the annulus and minimize the annulus region by minimizing the outer offset (resp., maximizing the inner offset. We also solve a a special case of the first problem: finding the smallest translated offset of a polygon containing an entire point set. We extend our results for the standard polygon scaling function as well

Work on this paper by the first author has been supported by the U.S. ARO under Grant DAAH04-96-1-0013. Work by the second author has been supported by the NSERC of Canada under grant OGP0183877 Work by the third author has been supported by the NSF under Grant CCR-93-1714.

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Author information

Authors and Affiliations

  1. Faculty of Computer Science, The Technion—IIT, Haifa, 32000, Israel

    Gill Barequet

  2. Center for Geometric Computing, Dept. of Computer Science, Johns Hopkins University, Baltimore, MD, 21218-2694

    Prosenjit Bose

  3. School of Computer Science, Carleton University, 1125 Colonel By Dr., Ottawa, Ontario, Canada, K1S 5B6

    Matthew T. Dickerson

Authors
  1. Gill Barequet
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  2. Prosenjit Bose
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  3. Matthew T. Dickerson
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Editor information

Editors and Affiliations

  1. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Canada, K1S 5B6

    Frank Dehne  & Jörg-Rüdiger Sack  & 

  2. School of Computer Science, Simon Fraser University, Burnaby, BC, Canada, V5A 1S6

    Arvind Gupta

  3. Center for Geometric Computing Providence, Brown University, RI, 02912-1910, USA

    Roberto Tamassia

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© 1999 Springer-Verlag Berlin Heidelberg

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Barequet, G., Bose, P., Dickerson, M.T. (1999). Optimizing Constrained Offset and Scaled Polygonal Annuli. In: Dehne, F., Sack, JR., Gupta, A., Tamassia, R. (eds) Algorithms and Data Structures. WADS 1999. Lecture Notes in Computer Science, vol 1663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48447-7_8

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  • DOI: https://doi.org/10.1007/3-540-48447-7_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66279-2

  • Online ISBN: 978-3-540-48447-9

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