Max-Planck-Institut für Informatik
max planck institut
informatik
mpii logo Minerva of the Max Planck Society
 

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:

To download this research report, please select the type of document that fits best your needs.Attachement Size(s):
94-111.pdf94-111.pdfMPI-I-94-110.dvi.Z40 KBytes; 161 KBytes
Please note: If you don't have a viewer for PostScript on your platform, try to install GhostScript and GhostView
URL to this document: http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1994-111
Hide details for BibTeXBibTeX
@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},
}