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#### On the Width and Roundness of a Set of Points in the Plane

##### Fulltext (public)

94-111.pdf

(Any fulltext), 162KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Smid, M., & Janardan, R.(1994). *On the Width and Roundness
of a Set of Points in the Plane* (MPI-I-94-111). Saarbrücken: Max-Planck-Institut für Informatik.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-B78A-7

##### Abstract

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.