### Abstract

A (not necessarily convex) object C in the plane is κ-curved for some constant κ, κ<1, if it has constant description complexity, and for each point p on the boundary of C, one can place a disk B whose boundary passes through p, its radius is κ·diam(C) and it is contained in C. We prove that the combinatorial complexity of the boundary of the union of a set C of n κ-curved objects (e.g., fat ellipses or rounded heart-shaped objects) is O(λ_{s}(n)log n), for some constant s.

Original language | English (US) |
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Pages | 206-213 |

Number of pages | 8 |

DOIs | |

State | Published - Jan 1 1998 |

Externally published | Yes |

Event | Proceedings of the 1998 14th Annual Symposium on Computational Geometry - Minneapolis, MN, USA Duration: Jun 7 1998 → Jun 10 1998 |

### Other

Other | Proceedings of the 1998 14th Annual Symposium on Computational Geometry |
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City | Minneapolis, MN, USA |

Period | 6/7/98 → 6/10/98 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics

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## Cite this

Efrat, A., & Katz, M. J. (1998).

*On the union of κ-curved objects*. 206-213. Paper presented at Proceedings of the 1998 14th Annual Symposium on Computational Geometry, Minneapolis, MN, USA, . https://doi.org/10.1145/276884.276908