Voronoi diagrams and arrangements
Discrete & Computational Geometry
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Davenport-Schinzel sequences and their geometric applications
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The bisector surface of rational space curves
ACM Transactions on Graphics (TOG)
Voronoi diagrams and Delaunay triangulations
Handbook of discrete and computational geometry
Voronoi diagrams of lines in 3-space under polyhedral convex distance functions
Journal of Algorithms - Special issue on SODA '95 papers
A tight bound for the complexity of voroni diagrams under polyhedral convex distance functions in 3D
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
ACM SIGACT News
Polyhedral Voronoi diagrams of polyhedra in three dimensions
Proceedings of the eighteenth annual symposium on Computational geometry
Almost Tight Upper Bounds for Vertical Decompositions in Four Dimensions
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Polyhedral Voronoi diagrams of polyhedra in three dimensions
Proceedings of the eighteenth annual symposium on Computational geometry
3D hyperbolic Voronoi diagrams
Computer-Aided Design
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part V
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(MATH) We show that the combinatorial complexity of the Euclidean Voronoi diagram of n lines in $\reals3 that have at most c distinct orientations, is O(c 4 n 2+&egr;), for any &egr;0. This result is a step towards proving the long-standing conjecture that the Euclidean Voronoi diagram of lines in three dimensions has near-quadratic complexity. It provides the first natural instance in which this conjecture is shown to hold. In a broader context, our result adds a natural instance to the (rather small) pool of instances of general 3-dimensional Voronoi diagrams for which near-quadratic complexity bounds are known.