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 2N × 2N integer grid such that output segments have grid points as endpoints.
| Original language | English (US) |
|---|---|
| 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 |
|---|---|
| City | Research Triangle Park, NC, USA |
| Period | 10/30/89 → 11/1/89 |
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ASJC Scopus subject areas
- Hardware and Architecture
Cite this
Double precision geometry : A general technique for calculating line and segment intersections using rounded arithmetic. / Milenkovic, Victor.
Annual Symposium on Foundations of Computer Science (Proceedings). Publ by IEEE, 1989. p. 500-505.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
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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.
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M3 - Conference contribution
SN - 0818619821
SP - 500
EP - 505
BT - Annual Symposium on Foundations of Computer Science (Proceedings)
PB - Publ by IEEE
ER -