MPI-INF/SWS Research Reports 1991-2021

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

Smid, Michiel and Janardan, Ravi

March 1994, 14 pages.

Status: available - back from printing

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 {\em 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.

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  AUTHOR = {Smid, Michiel and Janardan, Ravi},
  TITLE = {On the width and roundness of a set of points in the plane},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-94-111},
  MONTH = {March},
  YEAR = {1994},
  ISSN = {0946-011X},