Voronoi diagrams and arrangements
Discrete & Computational Geometry
Improved incremental randomized Delaunay triangulation
Proceedings of the fourteenth annual symposium on Computational geometry
Modern computer algebra
3-Dimensional Euclidean Voronoi Diagrams of Lines with a Fixed Number of Orientations
SIAM Journal on Computing
Dynamic Additively Weighted Voronoi Diagrams in 2D
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Exact computation of the medial axis of a polyhedron
Computer Aided Geometric Design
Expected time analysis for Delaunay point location
Computational Geometry: Theory and Applications
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
The predicates for the Voronoi diagram of ellipses
Proceedings of the twenty-second annual symposium on Computational geometry
Effective Computational Geometry for Curves and Surfaces (Mathematics and Visualization)
Effective Computational Geometry for Curves and Surfaces (Mathematics and Visualization)
The visibility-Voronoi complex and its applications
Computational Geometry: Theory and Applications - Special issue on the 21st European workshop on computational geometry (EWCG 2005)
The voronoi diagram of three lines
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Approximating the pathway axis and the persistence diagram of a collection of balls in 3-space
Proceedings of the twenty-fourth annual symposium on Computational geometry
A fast planar partition algorithm. I
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
An experimental study of point location in planar arrangements in CGAL
Journal of Experimental Algorithmics (JEA)
Computing the Voronoi cells of planes, spheres and cylinders in R3
Computer Aided Geometric Design
The predicates of the Apollonius diagram: Algorithmic analysis and implementation
Computational Geometry: Theory and Applications - Special issue on robust geometric algorithms and their implementations
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Constructing two-dimensional Voronoi diagrams via divide-and-conquer of envelopes in space
Transactions on computational science IX
Convex hull and voronoi diagram of additively weighted points
ESA'05 Proceedings of the 13th annual European conference on Algorithms
A generic algebraic kernel for non-linear geometric applications
Proceedings of the twenty-seventh annual symposium on Computational geometry
On soft predicates in subdivision motion planning
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We introduce a new, efficient, and complete algorithm, and its exact implementation, to compute the Voronoi diagram of lines in space. This is a major milestone towards the robust construction of the Voronoi diagram of polyhedra. As we follow the exact geometric-computation paradigm, it is guaranteed that we always compute the mathematically correct result. The algorithm is complete in the sense that it can handle all configurations, in particular all degenerate ones. The algorithm requires O(n3+ε) time and space, where n is the number of lines. The Voronoi diagram is represented by a data structure that permits answering point-location queries in O(log2 n) expected time. The implementation employs the Cgal packages for constructing arrangements and lower envelopes together with advanced algebraic tools.