Constructing higher-dimensional convex hulls at logarithmic cost per face
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
On the number of faces in higher-dimensional Voronoi diagrams
SCG '87 Proceedings of the third annual symposium on Computational geometry
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
On computing Voronoi diagrams by divide-prune-and-conquer
Proceedings of the twelfth annual symposium on Computational geometry
On the Radius-Edge Condition in the Control Volume Method
SIAM Journal on Numerical Analysis
Geometry and topology for mesh generation
Geometry and topology for mesh generation
Fast Construction of Nets in Low-Dimensional Metrics and Their Applications
SIAM Journal on Computing
Sparse parallel Delaunay mesh refinement
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Size complexity of volume meshes vs. surface meshes
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Computing Hereditary Convex Structures
Discrete & Computational Geometry - Special Issue: 25th Annual Symposium on Computational Geometry; Guest Editor: John Hershberger
Beating the spread: time-optimal point meshing
Proceedings of the twenty-seventh annual symposium on Computational geometry
Mesh generation and geometric persistent homology
Mesh generation and geometric persistent homology
New Bounds on the Size of Optimal Meshes
Computer Graphics Forum
Delaunay Mesh Generation
A fast algorithm for well-spaced points and approximate delaunay graphs
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We describe a new algorithm for computing the Voronoi diagram of a set of n points in constant-dimensional Euclidean space. The running time of our algorithm is O(f log n log Δ) where f is the output complexity of the Voronoi diagram and Δ is the spread of the input, the ratio of largest to smallest pairwise distances. Despite the simplicity of the algorithm and its analysis, it improves on the state of the art for all inputs with polynomial spread and near-linear output size. The key idea is to first build the Voronoi diagram of a superset of the input points using ideas from Voronoi refinement mesh generation. Then, the extra points are removed in a straightforward way that allows the total work to be bounded in terms of the output complexity, yielding the output sensitive bound. The removal only involves local flips and is inspired by kinetic data structures.