A randomized algorithm for closest-point queries
SIAM Journal on Computing
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
A Delaunay refinement algorithm for quality 2-dimensional mesh generation
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
A Lower Bound to Finding Convex Hulls
Journal of the ACM (JACM)
On the Radius-Edge Condition in the Control Volume Method
SIAM Journal on Numerical Analysis
Quality Mesh Generation in Higher Dimensions
SIAM Journal on Computing
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
Lectures on Discrete Geometry
A time-optimal delaunay refinement algorithm in two dimensions
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Fast Construction of Nets in Low-Dimensional Metrics and Their Applications
SIAM Journal on Computing
Curve and Surface Reconstruction: Algorithms with Mathematical Analysis (Cambridge Monographs on Applied and Computational Mathematics)
Sparse parallel Delaunay mesh refinement
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Topological inference via meshing
Proceedings of the twenty-sixth annual symposium on Computational geometry
New Bounds on the Size of Optimal Meshes
Computer Graphics Forum
A new approach to output-sensitive voronoi diagrams and delaunay triangulations
Proceedings of the twenty-ninth annual symposium on Computational geometry
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 present NetMesh, a new algorithm that produces a conforming Delaunay mesh for point sets in any fixed dimension with guaranteed optimal mesh size and quality. Our comparison-based algorithm runs in O(n log n + m) time, where n is the input size and m is the output size, and with constants depending only on the dimension and the desired element quality. It can terminate early in O(n log n) time returning a O(n) size Voronoi diagram of a superset of P, which again matches the known lower bounds. The previous best results in the comparison model depended on the log of the spread of the input, the ratio of the largest to smallest pairwise distance. We reduce this dependence to O(log n) by using a sequence of ε-nets to determine input insertion order into a incremental Voronoi diagram. We generate a hierarchy of well-spaced meshes and use these to show that the complexity of the Voronoi diagram stays linear in the number of points throughout the construction.