### Abstract

We present here an algorithm for the curve arrangement problem: determine how a set of planar curves subdivides the plane. This algorithm uses rounded arithmetic and generates an approximate result. It can be applied to a broad class of planar curves, and it is based on a new definition of approximate curve arrangements. This result is an important step towards the creation of practical computer programs for reasoning about algebraic curves of high degree.

Original language | English (US) |
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Title of host publication | Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989 |

Publisher | Association for Computing Machinery |

Pages | 197-207 |

Number of pages | 11 |

Volume | Part F130124 |

ISBN (Electronic) | 0897913183 |

DOIs | |

State | Published - Jun 5 1989 |

Externally published | Yes |

Event | 5th Annual Symposium on Computational Geometry, SCG 1989 - Saarbruchen, Germany Duration: Jun 5 1989 → Jun 7 1989 |

### Other

Other | 5th Annual Symposium on Computational Geometry, SCG 1989 |
---|---|

Country | Germany |

City | Saarbruchen |

Period | 6/5/89 → 6/7/89 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics

### Cite this

*Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989*(Vol. Part F130124, pp. 197-207). Association for Computing Machinery. https://doi.org/10.1145/73833.73856

**Calculating approximate curve arrangements using rounded arithmetic.** / Milenkovic, Victor.

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

*Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989.*vol. Part F130124, Association for Computing Machinery, pp. 197-207, 5th Annual Symposium on Computational Geometry, SCG 1989, Saarbruchen, Germany, 6/5/89. https://doi.org/10.1145/73833.73856

}

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T1 - Calculating approximate curve arrangements using rounded arithmetic

AU - Milenkovic, Victor

PY - 1989/6/5

Y1 - 1989/6/5

N2 - We present here an algorithm for the curve arrangement problem: determine how a set of planar curves subdivides the plane. This algorithm uses rounded arithmetic and generates an approximate result. It can be applied to a broad class of planar curves, and it is based on a new definition of approximate curve arrangements. This result is an important step towards the creation of practical computer programs for reasoning about algebraic curves of high degree.

AB - We present here an algorithm for the curve arrangement problem: determine how a set of planar curves subdivides the plane. This algorithm uses rounded arithmetic and generates an approximate result. It can be applied to a broad class of planar curves, and it is based on a new definition of approximate curve arrangements. This result is an important step towards the creation of practical computer programs for reasoning about algebraic curves of high degree.

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U2 - 10.1145/73833.73856

DO - 10.1145/73833.73856

M3 - Conference contribution

VL - Part F130124

SP - 197

EP - 207

BT - Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989

PB - Association for Computing Machinery

ER -