Cutting triangular cycles of lines in space

Boris Aronov; Vladlen Koltun; Micha Sharir

doi:10.1007/s00454-004-1123-5

Cutting triangular cycles of lines in space

Boris Aronov^*
, Vladlen Koltun
, Micha Sharir

^*Corresponding author for this work

School of Computer Science and AI

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We show that n lines in 3-space can be cut into O(n^2-1/69 log^16/69 n) pieces, such that all depth cycles defined by triples of lines are eliminated. This partially resolves a long-standing open problem in computational geometry, motivated by hidden-surface removal in computer graphics.

Original language	English
Pages (from-to)	231-247
Number of pages	17
Journal	Discrete and Computational Geometry
Volume	33
Issue number	2
DOIs	https://doi.org/10.1007/s00454-004-1123-5
State	Published - Feb 2005

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10.1007/s00454-004-1123-5

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abstract = "We show that n lines in 3-space can be cut into O(n2-1/69 log16/69 n) pieces, such that all depth cycles defined by triples of lines are eliminated. This partially resolves a long-standing open problem in computational geometry, motivated by hidden-surface removal in computer graphics.",

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AB - We show that n lines in 3-space can be cut into O(n2-1/69 log16/69 n) pieces, such that all depth cycles defined by triples of lines are eliminated. This partially resolves a long-standing open problem in computational geometry, motivated by hidden-surface removal in computer graphics.

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Cutting triangular cycles of lines in space

Abstract

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