### 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 |

State | Published - Nov 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 |

### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Hardware and Architecture

### Cite this

*Annual Symposium on Foundations of Computer Science (Proceedings)*(pp. 500-505). Publ by IEEE.

**Double precision geometry : A general technique for calculating line and segment intersections using rounded arithmetic.** / Milenkovic, Victor.

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

*Annual Symposium on Foundations of Computer Science (Proceedings).*Publ by IEEE, pp. 500-505, 30th Annual Symposium on Foundations of Computer Science, Research Triangle Park, NC, USA, 10/30/89.

}

TY - GEN

T1 - Double precision geometry

T2 - A general technique for calculating line and segment intersections using rounded arithmetic

AU - Milenkovic, Victor

PY - 1989/11

Y1 - 1989/11

N2 - 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 2N × 2N integer grid such that output segments have grid points as endpoints.

AB - 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 2N × 2N integer grid such that output segments have grid points as endpoints.

UR - http://www.scopus.com/inward/record.url?scp=0024765832&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024765832&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0024765832

SN - 0818619821

SP - 500

EP - 505

BT - Annual Symposium on Foundations of Computer Science (Proceedings)

PB - Publ by IEEE

ER -