### Abstract

A translation lattice packing of k polygons P_{1}, P_{2}, P_{3}, ..., P_{k} is a (non-overlapping) packing of the k polygons which can be replicated without overlap at each point of a lattice i_{0}v_{0}+i_{1}v_{1}, where v_{0} and v_{1} are vectors generating the lattice and i_{0} and i_{1} range over all integers. A densest translational lattice packing is one which minimizes the area |v_{0}×v_{1}| of the fundamental parallelogram. An algorithm and implementation is given for densest translation lattice packing. This algorithm has useful applications in industry, particularly clothing manufacture.

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

Publisher | ACM |

Pages | 280-289 |

Number of pages | 10 |

State | Published - 2000 |

Event | 16th Annual Symposium on Computational Geometry - Hong Kong, Hong Kong Duration: Jun 12 2000 → Jun 14 2000 |

### Other

Other | 16th Annual Symposium on Computational Geometry |
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City | Hong Kong, Hong Kong |

Period | 6/12/00 → 6/14/00 |

### 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. 280-289). ACM.

**Densest translational lattice packing of non-convex polygons.** / Milenkovic, Victor.

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

*Proceedings of the Annual Symposium on Computational Geometry.*ACM, pp. 280-289, 16th Annual Symposium on Computational Geometry, Hong Kong, Hong Kong, 6/12/00.

}

TY - GEN

T1 - Densest translational lattice packing of non-convex polygons

AU - Milenkovic, Victor

PY - 2000

Y1 - 2000

N2 - A translation lattice packing of k polygons P1, P2, P3, ..., Pk is a (non-overlapping) packing of the k polygons which can be replicated without overlap at each point of a lattice i0v0+i1v1, where v0 and v1 are vectors generating the lattice and i0 and i1 range over all integers. A densest translational lattice packing is one which minimizes the area |v0×v1| of the fundamental parallelogram. An algorithm and implementation is given for densest translation lattice packing. This algorithm has useful applications in industry, particularly clothing manufacture.

AB - A translation lattice packing of k polygons P1, P2, P3, ..., Pk is a (non-overlapping) packing of the k polygons which can be replicated without overlap at each point of a lattice i0v0+i1v1, where v0 and v1 are vectors generating the lattice and i0 and i1 range over all integers. A densest translational lattice packing is one which minimizes the area |v0×v1| of the fundamental parallelogram. An algorithm and implementation is given for densest translation lattice packing. This algorithm has useful applications in industry, particularly clothing manufacture.

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M3 - Conference contribution

SP - 280

EP - 289

BT - Proceedings of the Annual Symposium on Computational Geometry

PB - ACM

ER -