### Abstract

The cutting triangular cycles of lines in space were investigated. It was shown that a collection of lines in 3-space can be cut into a subquadratic number of pieces, such that all depth cycles defined by triples of lines are eliminated. A long-standing open problem in computational geometry, motivated by hidden-surface removal in computer graphics, was solved.

Original language | English (US) |
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Title of host publication | Conference Proceedings of the Annual ACM Symposium on Theory of Computing |

Pages | 547-555 |

Number of pages | 9 |

State | Published - 2003 |

Event | 35th Annual ACM Symposium on Theory of Computing - San Diego, CA, United States Duration: Jun 9 2003 → Jun 11 2003 |

### Other

Other | 35th Annual ACM Symposium on Theory of Computing |
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Country | United States |

City | San Diego, CA |

Period | 6/9/03 → 6/11/03 |

### Fingerprint

### Keywords

- Cycles
- Hidden-surface removal
- Lines in space
- Weavings

### ASJC Scopus subject areas

- Software

### Cite this

*Conference Proceedings of the Annual ACM Symposium on Theory of Computing*(pp. 547-555)

**Cutting triangular cycles of lines in space.** / Aronov, Boris; Koltun, Vladlen; Sharir, Micha.

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

*Conference Proceedings of the Annual ACM Symposium on Theory of Computing.*pp. 547-555, 35th Annual ACM Symposium on Theory of Computing, San Diego, CA, United States, 6/9/03.

}

TY - GEN

T1 - Cutting triangular cycles of lines in space

AU - Aronov, Boris

AU - Koltun, Vladlen

AU - Sharir, Micha

PY - 2003

Y1 - 2003

N2 - The cutting triangular cycles of lines in space were investigated. It was shown that a collection of lines in 3-space can be cut into a subquadratic number of pieces, such that all depth cycles defined by triples of lines are eliminated. A long-standing open problem in computational geometry, motivated by hidden-surface removal in computer graphics, was solved.

AB - The cutting triangular cycles of lines in space were investigated. It was shown that a collection of lines in 3-space can be cut into a subquadratic number of pieces, such that all depth cycles defined by triples of lines are eliminated. A long-standing open problem in computational geometry, motivated by hidden-surface removal in computer graphics, was solved.

KW - Cycles

KW - Hidden-surface removal

KW - Lines in space

KW - Weavings

UR - http://www.scopus.com/inward/record.url?scp=0038784528&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038784528&partnerID=8YFLogxK

M3 - Conference contribution

SP - 547

EP - 555

BT - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

ER -