### 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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Title of host publication | Proceedings of the Annual Symposium on Computational Geometry |

Publisher | ACM |

Pages | 206-213 |

Number of pages | 8 |

State | Published - 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 |

### Fingerprint

### ASJC Scopus subject areas

- Chemical Health and Safety
- Software
- Safety, Risk, Reliability and Quality
- Geometry and Topology

### Cite this

*Proceedings of the Annual Symposium on Computational Geometry*(pp. 206-213). ACM.

**On the union of κ-curved objects.** / Efrat, Alon; Katz, Matthew J.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Annual Symposium on Computational Geometry.*ACM, pp. 206-213, Proceedings of the 1998 14th Annual Symposium on Computational Geometry, Minneapolis, MN, USA, 6/7/98.

}

TY - GEN

T1 - On the union of κ-curved objects

AU - Efrat, Alon

AU - Katz, Matthew J.

PY - 1998

Y1 - 1998

N2 - 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(λs(n)log n), for some constant s.

AB - 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(λs(n)log n), for some constant s.

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UR - http://www.scopus.com/inward/citedby.url?scp=0031643499&partnerID=8YFLogxK

M3 - Conference contribution

SP - 206

EP - 213

BT - Proceedings of the Annual Symposium on Computational Geometry

PB - ACM

ER -