### Abstract

A function f: R → R is unimodal if it increases to a maximum value and then decreases. It is strictly unimodal if the increase and decrease are strict. Unimodality is important for the design of efficient search algorithms because it permits prune-and-search strategies. It also simplifies proofs. An algorithm for R^{3} is presented which has an application to shape matching. Given convex polygon P and Q and a direction in which to translate P, it is easy to find the translation having maximum overlap with Q in linear time.

Original language | English (US) |
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State | Published - Jan 1 1996 |

Event | Proceedings of the 1996 12th Annual Symposium on Computational Geometry - Philadelphia, PA, USA Duration: May 24 1996 → May 26 1996 |

### Other

Other | Proceedings of the 1996 12th Annual Symposium on Computational Geometry |
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City | Philadelphia, PA, USA |

Period | 5/24/96 → 5/26/96 |

### Fingerprint

### ASJC Scopus subject areas

- Chemical Health and Safety
- Software
- Safety, Risk, Reliability and Quality
- Geometry and Topology

### Cite this

*On the sectional area of convex polytopes*. Paper presented at Proceedings of the 1996 12th Annual Symposium on Computational Geometry, Philadelphia, PA, USA, .

**On the sectional area of convex polytopes.** / Avis, David; Bose, Prosenjit; Shermer, Thomas C.; Snoeyink, Jack; Toussaint, Godfried; Zhu, Binhai.

Research output: Contribution to conference › Paper

}

TY - CONF

T1 - On the sectional area of convex polytopes

AU - Avis, David

AU - Bose, Prosenjit

AU - Shermer, Thomas C.

AU - Snoeyink, Jack

AU - Toussaint, Godfried

AU - Zhu, Binhai

PY - 1996/1/1

Y1 - 1996/1/1

N2 - A function f: R → R is unimodal if it increases to a maximum value and then decreases. It is strictly unimodal if the increase and decrease are strict. Unimodality is important for the design of efficient search algorithms because it permits prune-and-search strategies. It also simplifies proofs. An algorithm for R3 is presented which has an application to shape matching. Given convex polygon P and Q and a direction in which to translate P, it is easy to find the translation having maximum overlap with Q in linear time.

AB - A function f: R → R is unimodal if it increases to a maximum value and then decreases. It is strictly unimodal if the increase and decrease are strict. Unimodality is important for the design of efficient search algorithms because it permits prune-and-search strategies. It also simplifies proofs. An algorithm for R3 is presented which has an application to shape matching. Given convex polygon P and Q and a direction in which to translate P, it is easy to find the translation having maximum overlap with Q in linear time.

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UR - http://www.scopus.com/inward/citedby.url?scp=4243882862&partnerID=8YFLogxK

M3 - Paper

ER -