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 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 language | English (US) |
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Pages (from-to) | 97-108 |
Number of pages | 12 |
Journal | International Journal of Computational Geometry and Applications |
Volume | 9 |
Issue number | 1 |
DOIs | |
State | Published - Feb 1999 |
Externally published | Yes |
Keywords
- Roundness
- Voronoi diagram
- Width