On the multimodality of distances in convex polygons

David Avis, Godfried T. Toussaint, Binay K. Bhattacharya

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)153-156
Number of pages4
JournalComputers and Mathematics with Applications
Issue number2
StatePublished - 1982

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics


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