Cutting triangular cycles of lines in space

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.

• Type: Conference
• Year: 2003
• Where: STOC
• Authors: Boris Aronov, Vladlen Koltun, Micha Sharir
• Keywords: Algorithms, Depth Cycles, Long-standing Open Problem, STOC 2003