### Abstract

Given a two dimensional, non-overlapping layout of convex and non-convex polygons, compaction can be thought of as simulating the motion of the polygons as a result of applied 'forces.' Compaction can be modeled as a motion of the polygons that reduces the value of some linear functional on their positions. Optimal compaction, planning a motion that finds the global minimum reachable value, is shown to be NP-complete. We give a compaction algorithm that finds a local minimum by direct calculation of the new polygon positions via linear programming. We also consider the related problem of separating overlapping polygons using a minimal amount of motion and show it to be NP-complete. A locally optimum version of this problem is solved using a slight modification of the compaction algorithm. The compaction algorithm and the separation algorithm have been applied to marker making: the task of packing polygonal pieces on a sheet of cloth of fixed width so that total length is minimized. The compaction algorithm has improved cloth utilization of human generated pants markers. The separation algorithm together with a database of human-generated markers can be used to automatically generate markers that are close to human performance.

Original language | English (US) |
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Title of host publication | Proceedings of the 9th Annual Symposium on Computational Geometry |

Editors | Anon |

Publisher | Publ by ACM |

Pages | 153-162 |

Number of pages | 10 |

ISBN (Print) | 0897915828 |

State | Published - Dec 1 1993 |

Externally published | Yes |

Event | Proceedings of the 9th Annual Symposium on Computational Geometry - San Diego, CA, USA Duration: May 19 1993 → May 21 1993 |

### Publication series

Name | Proceedings of the 9th Annual Symposium on Computational Geometry |
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### Other

Other | Proceedings of the 9th Annual Symposium on Computational Geometry |
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City | San Diego, CA, USA |

Period | 5/19/93 → 5/21/93 |

### ASJC Scopus subject areas

- Engineering(all)

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## Cite this

*Proceedings of the 9th Annual Symposium on Computational Geometry*(pp. 153-162). (Proceedings of the 9th Annual Symposium on Computational Geometry). Publ by ACM.