# MPI-I-94-111

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

### Smid, Michiel and Janardan, Ravi

**MPI-I-94-111**. March** **1994, 14 pages. | Status:** **available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:

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.

Acknowledgement:** **

References to related material:

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**URL to this document: **http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1994-111

**BibTeX**
`@TECHREPORT{``SmidRavi94``,`

` 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},`

`}`