### Abstract

An effective and fast algorithm is given for rotational over lap minimization: given an overlapping layout of polygons P_{1},P_{2},P_{3}, ..., P_{k} in a container polygon C_{1} translate and rotate the polygons to a layout that minimizes an overlap measure. A (local) overlap minimum has the property that any perturbation of the polygons increases the chosen measure of overlap. Experiments show that the algorithm works well in practice. It is shown how to apply overlap minimization to create algorithms for other layout tasks: compaction, containment, and minimal enclosure. Compaction: starting with a non-overlapping layout in a rectangular container, plan a non-overlapping motion that minimizes the length or area of the container. Containment: place the polygons into a (possibly non-convex container) without overlapping. Minimal enclosure: find a non-overlapping layout inside a minimum-length, fixed-width rectangle or inside a minimum area rectangle. All of these algorithms have important industrial applications.

Original language | English (US) |
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Pages | 334-343 |

Number of pages | 10 |

State | Published - Jan 1 1997 |

Event | Proceedings of the 1997 13th Annual Symposium on Computational Geometry - Nice, Fr Duration: Jun 4 1997 → Jun 6 1997 |

### Other

Other | Proceedings of the 1997 13th Annual Symposium on Computational Geometry |
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City | Nice, Fr |

Period | 6/4/97 → 6/6/97 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics

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## Cite this

*Rotational polygon overlap minimization*. 334-343. Paper presented at Proceedings of the 1997 13th Annual Symposium on Computational Geometry, Nice, Fr, .