### Abstract

An (α, β)-covered object is a simply connected planar region c with the property that for each point p ∈ ∂c there exists a triangle contained in c and having p as a vertex, such that all its angles are at least α > 0 and all its edges are at least β.diam(c)-long. This notion extends that of fat convex objects. We show that the combinatorial complexity of the union of n (α, β)-covered objects of "constant description complexity" is O(λ _{s+2}(n) log ^{2} n log log n), where s is the maximum number of intersections between the boundaries of any pair of given objects, and λ _{s} (n) denotes the maximum length of an (n, s)-Davenport-Schinzel sequence. Our result extends and improves previous results concerning convex α-fat objects.

Original language | English (US) |
---|---|

Pages (from-to) | 775-787 |

Number of pages | 13 |

Journal | SIAM Journal on Computing |

Volume | 34 |

Issue number | 4 |

DOIs | |

State | Published - Sep 13 2005 |

### Fingerprint

### Keywords

- Fat objects
- Motion planning
- Realistic input models

### ASJC Scopus subject areas

- Computer Science(all)
- Mathematics(all)