Cutting Triangular Cycles of Lines in Space

Authors:
Boris Aronov;Vladlen Koltun;Micha Sharir
Affiliations:
Department of Computer and Information Science, Polytechnic University, Brooklyn, NY 11201-3840, USA;Computer Science Division, University of California, Berkeley, CA 94720-1776, USA;School of Computer Science, Tel Aviv University, Tel-Aviv 69978, Israel and Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
Venue:
Discrete & Computational Geometry
Year:
2005

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Cutting cycles of rods in space: hardness and approximation

Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms

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Abstract

We show that n lines in 3-space can be cut into O(n2-1/69log16/69n) 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.