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**Separating two simple polygons by a sequence of translations.**
*(English)*
Zbl 0646.68052

Let P and Q be two disjoint simple (not necessarily convex) polygons. The authors present an algorithm which determines whether Q can be moved by a sequence of translations to a position sufficiently far from P without colliding with P, and which produces such a motion if it exists. For earlier research on translational separability of planar objects, see G. T. Toussaint, Computational geometry, Mach. Intell. Pattern Recognition 2, 335-375 (1985; Zbl 0588.68053).

Reviewer: E.J.F.Primrose

### MSC:

68Q25 | Analysis of algorithms and problem complexity |

51M20 | Polyhedra and polytopes; regular figures, division of spaces |

52A10 | Convex sets in \(2\) dimensions (including convex curves) |

51M15 | Geometric constructions in real or complex geometry |

### Keywords:

inverse Ackermann function; optimal algorithm; separating polygons. translational separability of planar objects; Computational geometry### Citations:

Zbl 0588.68053
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\textit{R. Pollack} et al., Discrete Comput. Geom. 3, No. 1--2, 123--136 (1988; Zbl 0646.68052)

### References:

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[23] | C. K. Yap, How to Move a Chair Through a Door, Technical Report 238, Computer Science Department, Courant Institute, August 1986. |

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