### Abstract

For the first time it is shown how to reduce the cost of performing specific geometric constructions by using rounded arithmetic instead of exact arithmetic. By exploiting a property of floating-point arithmetic called monotonicity, a technique called double-precision geometry can replace exact arithmetic with rounded arithmetic in any efficient algorithm for computing the set of intersections of a set of lines or line segments. The technique reduces the complexity of any such line or segment arrangement algorithm by a constant factor. In addition, double-precision geometry reduces by a factor of N the complexity of rendering segment arrangements on a 2^{N} × 2^{N} integer grid such that output segments have grid points as endpoints.

Original language | English (US) |
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Title of host publication | Annual Symposium on Foundations of Computer Science (Proceedings) |

Publisher | Publ by IEEE |

Pages | 500-505 |

Number of pages | 6 |

ISBN (Print) | 0818619821, 9780818619823 |

DOIs | |

State | Published - Jan 1 1989 |

Externally published | Yes |

Event | 30th Annual Symposium on Foundations of Computer Science - Research Triangle Park, NC, USA Duration: Oct 30 1989 → Nov 1 1989 |

### Publication series

Name | Annual Symposium on Foundations of Computer Science (Proceedings) |
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ISSN (Print) | 0272-5428 |

### Other

Other | 30th Annual Symposium on Foundations of Computer Science |
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City | Research Triangle Park, NC, USA |

Period | 10/30/89 → 11/1/89 |

### ASJC Scopus subject areas

- Hardware and Architecture

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## Cite this

*Annual Symposium on Foundations of Computer Science (Proceedings)*(pp. 500-505). (Annual Symposium on Foundations of Computer Science (Proceedings)). Publ by IEEE. https://doi.org/10.1109/sfcs.1989.63525