### Abstract

We study the motion of a rod (line segment) in the plane in the presence of polygonal obstacles, under an optimality criterion based on minimizing the orbit length of a fixed but arbitrary point (called the focus) on the rod. Our central result is that this problem is NP-hard when the focus is in the relative interior of the rod. Other results include a local characterization of this so-called d_{1}-optimal motion, and an efficient approximation algorithm.

Original language | English (US) |
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Title of host publication | Proceedings of the Annual Symposium on Computational Geometry |

Publisher | ACM |

Pages | 252-263 |

Number of pages | 12 |

State | Published - 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

*Proceedings of the Annual Symposium on Computational Geometry*(pp. 252-263). ACM.

**d1-optimal motion for a rod.** / Asano, Tetsuo; Kirkpatrick, David; Yap, Chee.

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

*Proceedings of the Annual Symposium on Computational Geometry.*ACM, pp. 252-263, Proceedings of the 1996 12th Annual Symposium on Computational Geometry, Philadelphia, PA, USA, 5/24/96.

}

TY - GEN

T1 - d1-optimal motion for a rod

AU - Asano, Tetsuo

AU - Kirkpatrick, David

AU - Yap, Chee

PY - 1996

Y1 - 1996

N2 - We study the motion of a rod (line segment) in the plane in the presence of polygonal obstacles, under an optimality criterion based on minimizing the orbit length of a fixed but arbitrary point (called the focus) on the rod. Our central result is that this problem is NP-hard when the focus is in the relative interior of the rod. Other results include a local characterization of this so-called d1-optimal motion, and an efficient approximation algorithm.

AB - We study the motion of a rod (line segment) in the plane in the presence of polygonal obstacles, under an optimality criterion based on minimizing the orbit length of a fixed but arbitrary point (called the focus) on the rod. Our central result is that this problem is NP-hard when the focus is in the relative interior of the rod. Other results include a local characterization of this so-called d1-optimal motion, and an efficient approximation algorithm.

UR - http://www.scopus.com/inward/record.url?scp=0029703026&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029703026&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0029703026

SP - 252

EP - 263

BT - Proceedings of the Annual Symposium on Computational Geometry

PB - ACM

ER -