Constructing higher-dimensional convex hulls at logarithmic cost per face
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
A probabilistic algorithm for the post office problem
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
A randomized algorithm for closest-point queries
SIAM Journal on Computing
Coordinate representation of order types requires exponential storage
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Higher-dimensional Voronoi diagrams in linear expected time
Discrete & Computational Geometry
Euclidean minimum spanning trees and bichromatic closest pairs
Discrete & Computational Geometry
Deferred data structure for the nearest neighbor problem
Information Processing Letters
Convex independent sets and 7-holes in restricted planar point sets
Discrete & Computational Geometry
Cutting hyperplanes for divide-and-conquer
Discrete & Computational Geometry
Computing and Verifying Depth Orders
SIAM Journal on Computing
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
A Delaunay based numerical method for three dimensions: generation, formulation, and partition
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Separators for sphere-packings and nearest neighbor graphs
Journal of the ACM (JACM)
Realistic input models for geometric algorithms
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Tetrahedral mesh generation by Delaunay refinement
Proceedings of the fourteenth annual symposium on Computational geometry
A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Geometric pattern matching: a performance study
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Optimal coarsening of unstructured meshes
Journal of Algorithms
Geometric matching under noise: combinatorial bounds and algorithms
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Smoothing and cleaning up slivers
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A simple algorithm for homeomorphic surface reconstruction
Proceedings of the sixteenth annual symposium on Computational geometry
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Proceedings of the sixteenth annual symposium on Computational geometry
Voronoi-based interpolation with higher continuity
Proceedings of the sixteenth annual symposium on Computational geometry
Space-Time Tradeoffs for Emptiness Queries
SIAM Journal on Computing
Generating well-shaped Delaunay meshed in 3D
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Nice point sets can have nasty Delaunay triangulations
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Geometry and topology for mesh generation
Geometry and topology for mesh generation
Ray Shooting, Depth Orders and Hidden Surface Removal
Ray Shooting, Depth Orders and Hidden Surface Removal
Smooth-surface reconstruction in near-linear time
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Computing Hierarchies of Clusters from the Euclidean Minimum Spanning Tree in Linear Time
Proceedings of the 15th Conference on Foundations of Software Technology and Theoretical Computer Science
CG '91 Proceedings of the International Workshop on Computational Geometry - Methods, Algorithms and Applications
Pattern Matching for Spatial Point Sets
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
The power crust, unions of balls, and the medial axis transform
Computational Geometry: Theory and Applications
Collision detection for deforming necklaces
Proceedings of the eighteenth annual symposium on Computational geometry
The Delaunay tetrahedralization from Delaunay triangulated surfaces
Proceedings of the eighteenth annual symposium on Computational geometry
A linear bound on the complexity of the delaunay triangulation of points on polyhedral surfaces
Proceedings of the seventh ACM symposium on Solid modeling and applications
Modified DAG Location for Delaunay Triangulation
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Complexity of the delaunay triangulation of points on surfaces the smooth case
Proceedings of the nineteenth annual symposium on Computational geometry
Well-separated pair decomposition for the unit-disk graph metric and its applications
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
An empirical comparison of techniques for updating Delaunay triangulations
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Deformable spanners and applications
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Collision detection for deforming necklaces
Computational Geometry: Theory and Applications - Special issue on the 18th annual symposium on computational geometrySoCG2002
Deformable spanners and applications
Computational Geometry: Theory and Applications
Deformable spanners and applications
Computational Geometry: Theory and Applications
Efficient proximity search for 3-D cuboids
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Contour-Based terrain model reconstruction using distance information
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part III
The emergence of sparse spanners and greedy well-separated pair decomposition
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
A pseudopolynomial time O(log n)-approximation algorithm for art gallery problems
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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The spread of a finite set of points is the ratio between the longest and shortest pairwise distances. We prove that the Delaunay triangulation of any set of n points in IR3 with spread Δ has complexity O(Δ3). This bound is tight in the worst case for all Δ = O(√n). In particular, the Delaunay triangulation of any dense point set has linear complexity. On the other hand, for any n and Δ = O(n), we construct a regular triangulation of complexity Ω(nΔ) whose n vertices have spread Δ.