On embedding a graph in the grid with the minimum number of bends
SIAM Journal on Computing
Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
A simple output-sensitive algorithm for hidden surface removal
ACM Transactions on Graphics (TOG)
Counting and cutting cycles of lines and rods in space
Computational Geometry: Theory and Applications
Efficient hidden surface removal for objects with small union size
Computational Geometry: Theory and Applications
Computing and Verifying Depth Orders
SIAM Journal on Computing
Cutting cylces of rods in space
Proceedings of the fourteenth annual symposium on Computational geometry
Computational Geometry: Theory and Applications
Divide-and-conquer approximation algorithms via spreading metrics
Journal of the ACM (JACM)
Ray Shooting, Depth Orders and Hidden Surface Removal
Ray Shooting, Depth Orders and Hidden Surface Removal
4-edge-coloring graphs of maximum degree 3 in linear time
Information Processing Letters
Cutting Triangular Cycles of Lines in Space
Discrete & Computational Geometry
Vertical ray shooting and computing depth orders for fat objects
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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We study the problem of cutting a set of rods (line segments in ℝ3) into fragments, using a minimum number of cuts, so that the resulting set of fragments admits a depth order. We prove that this problem is NP-complete, even when the rods have only three distinct orientations. We also give a polynomial-time approximation algorithm with no restriction on rod orientation that computes a solution of size O(τ log τ log log τ), where τ is the size of an optimal solution.