Voronoi diagrams and arrangements
Discrete & Computational Geometry
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Randomized incremental construction of abstract Voronoi diagrams
Computational Geometry: Theory and Applications
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Intersections with random geometric object
Computational Geometry: Theory and Applications
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Computational Geometry: Theory and Applications
The C++ Programming Language, Third Edition
The C++ Programming Language, Third Edition
Discrete Applied Mathematics
How to Compute the Voronoi Diagram of Line Segments: Theoretical and Experimental Results
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
The Clarkson–Shor Technique Revisited and Extended
Combinatorics, Probability and Computing
Robust, generic and efficient construction of envelopes of surfaces in three-dimensional spaces
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Exact and efficient 2D-arrangements of arbitrary algebraic curves
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Exact arrangements on tori and Dupin cyclides
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Arrangements of geodesic arcs on the sphere
Proceedings of the twenty-fourth annual symposium on Computational geometry
SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science
Divide-and-conquer for Voronoi diagrams revisited
Proceedings of the twenty-fifth annual symposium on Computational geometry
The predicates of the Apollonius diagram: Algorithmic analysis and implementation
Computational Geometry: Theory and Applications - Special issue on robust geometric algorithms and their implementations
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part V
Computational Geometry: Theory and Applications
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We present a general framework for computing Voronoi diagrams of different classes of sites under various distance functions in R2. Most diagrams mentioned in the paper are in the plane. However, the framework is sufficiently general to support diagrams embedded on a family of two-dimensional parametric surfaces in three-dimensions. The computation of the diagrams is carried out through the construction of envelopes of surfaces in 3-space provided by Cgal (the Computational Geometry Algorithm Library). The construction of the envelopes follows a divide-and-conquer approach. A straightforward application of the divide-and-conquer approach for Voronoi diagrams yields algorithms that are inefficient in the worst case. We prove that through randomization, the expected running time becomes near-optimal in the worst case. We also show how to apply the new framework and other existing tools from Cgal to compute minimum-width annuli of sets of disks, which requires the computation of two Voronoi diagrams of different types, and of the overlay of the two diagrams. We do not assume general position. Namely, we handle degenerate input, and produce exact results.