### Abstract

Let P = (p_{1},..,p_{n}) and Q = (q_{l},..,q_{m}) be two simple polygons with nonintersecting interiors in the plane specified by their cartesian coordinates in order. Given a direction d we can ask whether P can be translated an arbitrary distance in direction d without colliding with Q. It has been shown that this problem can be solved in time proportional to the number of vertices in P and Q. Here we present a new and efficient algorithm for determining all directions in which such movement is possible. In designing this algorithm a partitioning technique is developed which might find applications when solving other geometric problems. The algorithm utilizes several tools and concepts (e.g. convex hulls, point-location, weakly edge-visible polygons) from the area of computational geometry.

Original language | English (US) |
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Title of host publication | STACS 85 - 2nd Annual Symposium on Theoretical Aspects of Computer Science |

Publisher | Springer-Verlag |

Pages | 310-321 |

Number of pages | 12 |

ISBN (Print) | 9783540139126 |

DOIs | |

State | Published - Jan 1 1985 |

Event | 2nd Annual Symposium on Theoretical Aspects of Computer Science, STACS 1985 - Saarbrucken, Germany Duration: Jan 3 1985 → Jan 5 1985 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 182 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 2nd Annual Symposium on Theoretical Aspects of Computer Science, STACS 1985 |
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Country | Germany |

City | Saarbrucken |

Period | 1/3/85 → 1/5/85 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*STACS 85 - 2nd Annual Symposium on Theoretical Aspects of Computer Science*(pp. 310-321). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 182 LNCS). Springer-Verlag. https://doi.org/10.1007/BFb0024019

**Translating polygons in the plane.** / Sack, Jӧrg R.; Toussaint, Godfried.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*STACS 85 - 2nd Annual Symposium on Theoretical Aspects of Computer Science.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 182 LNCS, Springer-Verlag, pp. 310-321, 2nd Annual Symposium on Theoretical Aspects of Computer Science, STACS 1985, Saarbrucken, Germany, 1/3/85. https://doi.org/10.1007/BFb0024019

}

TY - GEN

T1 - Translating polygons in the plane

AU - Sack, Jӧrg R.

AU - Toussaint, Godfried

PY - 1985/1/1

Y1 - 1985/1/1

N2 - Let P = (p1,..,pn) and Q = (ql,..,qm) be two simple polygons with nonintersecting interiors in the plane specified by their cartesian coordinates in order. Given a direction d we can ask whether P can be translated an arbitrary distance in direction d without colliding with Q. It has been shown that this problem can be solved in time proportional to the number of vertices in P and Q. Here we present a new and efficient algorithm for determining all directions in which such movement is possible. In designing this algorithm a partitioning technique is developed which might find applications when solving other geometric problems. The algorithm utilizes several tools and concepts (e.g. convex hulls, point-location, weakly edge-visible polygons) from the area of computational geometry.

AB - Let P = (p1,..,pn) and Q = (ql,..,qm) be two simple polygons with nonintersecting interiors in the plane specified by their cartesian coordinates in order. Given a direction d we can ask whether P can be translated an arbitrary distance in direction d without colliding with Q. It has been shown that this problem can be solved in time proportional to the number of vertices in P and Q. Here we present a new and efficient algorithm for determining all directions in which such movement is possible. In designing this algorithm a partitioning technique is developed which might find applications when solving other geometric problems. The algorithm utilizes several tools and concepts (e.g. convex hulls, point-location, weakly edge-visible polygons) from the area of computational geometry.

UR - http://www.scopus.com/inward/record.url?scp=84934031999&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84934031999&partnerID=8YFLogxK

U2 - 10.1007/BFb0024019

DO - 10.1007/BFb0024019

M3 - Conference contribution

AN - SCOPUS:84934031999

SN - 9783540139126

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 310

EP - 321

BT - STACS 85 - 2nd Annual Symposium on Theoretical Aspects of Computer Science

PB - Springer-Verlag

ER -