On the width and roundness of a set of points in the plane

Michiel Smid, Ravi Janardan

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Let S be a set of points in the plane. The width (resp. roundness) of S is defined as the minimum width of any slab (resp. annulus) that contains all points of S. We give a new characterization of the width of a point set. Also, we give a rigorous proof of the fact that either the roundness of S is equal to the width of S, or the center of the minimum-width annulus is a vertex of the closest-point Voronoi diagram of S, the furthest-point Voronoi diagram of S, or an intersection point of these two diagrams. This proof corrects the characterization of roundness used extensively in the literature.

Original languageEnglish (US)
Pages (from-to)97-108
Number of pages12
JournalInternational Journal of Computational Geometry and Applications
Issue number1
StatePublished - Feb 1999


  • Roundness
  • Voronoi diagram
  • Width


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