BIT Numerical Mathematics

, Volume 23, Issue 4, pp 456–471 | Cite as

On the X-Y convex hull of a set of X-Y polygons

  • T. M. Nicholl
  • D. T. Lee
  • Y. Z. Liao
  • C. K. Wong
Part I Computer Science


We study the class of rectilinear polygons, calledX – Y polygons, with horizontal and vertical edges, which are frequently used as building blocks for very large-scale integrated (VLSI) circuit layout and wiring. In the paper we introduce the notion of convexity within the class ofX – Y polygons and present efficient algorithms for computing theX – Y convex hulls of anX – Y polygon and of a set ofX – Y polygons under various conditions. Unlike convex hulls in the Euclidean plane, theX – Y convex hull of a set ofX – Y polygons may not exist. The condition under which theX – Y convex hull exists is given and an algorithm for testing if the given set ofX – Y polygons satisfies the condition is also presented.


Analysis of algorithms convexity rectilinear polygons 


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Copyright information

© BIT Foundations 1983

Authors and Affiliations

  • T. M. Nicholl
    • 1
  • D. T. Lee
    • 1
  • Y. Z. Liao
    • 2
  • C. K. Wong
    • 2
  1. 1.Department of Electrical Engineering and Computer ScienceNorthwestern UniversityEvanstonUSA
  2. 2.IBM T. J. Watson Research CenterYorktown HeightsUSA

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