### Abstract

Let P and Q be two disjoint simple polygons having n sides each. We present an algorithm which determines whether Q can be moved by a single translation to a position sufficiently far from P, and which produces all such motions if they exist. The algorithm runs in time O(t(n)) where t(n) is the time needed to triangulate an n-sided polygon. Since Tarjan and Van Wyk have recently shown that t(n)=O(n log log n) this improves the previous best result for this problem which was O(n log n) even after triangulation.

Original language | English (US) |
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Pages (from-to) | 265-278 |

Number of pages | 14 |

Journal | Discrete & Computational Geometry |

Volume | 4 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 1989 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

### Cite this

**On separating two simple polygons by a single translation.** / Toussaint, Godfried.

Research output: Contribution to journal › Article

*Discrete & Computational Geometry*, vol. 4, no. 1, pp. 265-278. https://doi.org/10.1007/BF02187729

}

TY - JOUR

T1 - On separating two simple polygons by a single translation

AU - Toussaint, Godfried

PY - 1989/12/1

Y1 - 1989/12/1

N2 - Let P and Q be two disjoint simple polygons having n sides each. We present an algorithm which determines whether Q can be moved by a single translation to a position sufficiently far from P, and which produces all such motions if they exist. The algorithm runs in time O(t(n)) where t(n) is the time needed to triangulate an n-sided polygon. Since Tarjan and Van Wyk have recently shown that t(n)=O(n log log n) this improves the previous best result for this problem which was O(n log n) even after triangulation.

AB - Let P and Q be two disjoint simple polygons having n sides each. We present an algorithm which determines whether Q can be moved by a single translation to a position sufficiently far from P, and which produces all such motions if they exist. The algorithm runs in time O(t(n)) where t(n) is the time needed to triangulate an n-sided polygon. Since Tarjan and Van Wyk have recently shown that t(n)=O(n log log n) this improves the previous best result for this problem which was O(n log n) even after triangulation.

UR - http://www.scopus.com/inward/record.url?scp=0347829329&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347829329&partnerID=8YFLogxK

U2 - 10.1007/BF02187729

DO - 10.1007/BF02187729

M3 - Article

AN - SCOPUS:0347829329

VL - 4

SP - 265

EP - 278

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 1

ER -