✦ LIBER ✦

On the multimodality of distances in convex polygons

✍ Scribed by David Avis; Godfried T. Toussaint; Binay K. Bhattacharya

Publisher: Elsevier Science
Year: 1982
Tongue: English
Weight: 264 KB
Volume: 8
Category: Article
ISSN: 0898-1221
DOI: 10.1016/0898-1221(82)90054-2

No coin nor oath required. For personal study only.

✦ Synopsis

Examples are given of n vertex convex polygons for which the distances between a fixed vertex and the remaining vertices, visited in order, form a multi-modal function. We show that this function may have as many as n/2 modes, or local maxima. Further examples are given of n vertex convex polygons in which n2/8 pairs of vertices are local maxima of their corresponding distance functions. These results are used to construct an example that shows that a general algorithm of Dobkin and Snyder may not, in fact, be used to find the diameter of a convex polygon.

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