### Abstract

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 n^{2}/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 language | English (US) |
---|---|

Pages (from-to) | 153-156 |

Number of pages | 4 |

Journal | Computers and Mathematics with Applications |

Volume | 8 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1982 |

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### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Modeling and Simulation

### Cite this

*Computers and Mathematics with Applications*,

*8*(2), 153-156. https://doi.org/10.1016/0898-1221(82)90054-2

**On the multimodality of distances in convex polygons.** / Avis, David; Toussaint, Godfried; Bhattacharya, Binay K.

Research output: Contribution to journal › Article

*Computers and Mathematics with Applications*, vol. 8, no. 2, pp. 153-156. https://doi.org/10.1016/0898-1221(82)90054-2

}

TY - JOUR

T1 - On the multimodality of distances in convex polygons

AU - Avis, David

AU - Toussaint, Godfried

AU - Bhattacharya, Binay K.

PY - 1982/1/1

Y1 - 1982/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=49049144884&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49049144884&partnerID=8YFLogxK

U2 - 10.1016/0898-1221(82)90054-2

DO - 10.1016/0898-1221(82)90054-2

M3 - Article

AN - SCOPUS:49049144884

VL - 8

SP - 153

EP - 156

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 2

ER -