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
The cost of balancing generalized quadtrees
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
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
Quality Mesh Generation in Higher Dimensions
SIAM Journal on Computing
Journal of the ACM (JACM)
Nice point sets can have nasty Delaunay triangulations
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Generating well-shaped d-dimensional Delaunay meshes
Theoretical Computer Science - Computing and combinatorics
Quality Meshing with Weighted Delaunay Refinement
SIAM Journal on Computing
Dense Point Sets Have Sparse Delaunay Triangulations or “... But Not Too Nasty”
Discrete & Computational Geometry
Variational tetrahedral meshing
ACM SIGGRAPH 2005 Papers
Topology guaranteeing manifold reconstruction using distance function to noisy data
Proceedings of the twenty-second annual symposium on Computational geometry
Size complexity of volume meshes vs. surface meshes
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Topological inference via meshing
Proceedings of the twenty-sixth annual symposium on Computational geometry
HOT: Hodge-optimized triangulations
ACM SIGGRAPH 2011 papers
Beating the spread: time-optimal point meshing
Proceedings of the twenty-seventh annual symposium on Computational geometry
Geometric Inference for Probability Measures
Foundations of Computational Mathematics
Mesh generation and geometric persistent homology
Mesh generation and geometric persistent homology
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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The theory of optimal size meshes gives a method for analyzing the output size (number of simplices) of a Delaunay refinement mesh in terms of the integral of a sizing function over the input domain. The input points define a maximal such sizing function called the feature size. This paper presents a way to bound the feature size integral in terms of an easy to compute property of a suitable ordering of the point set. The key idea is to consider the pacing of an ordered point set, a measure of the rate of change in the feature size as points are added one at a time. In previous work, Miller et al. showed that if an ordered point set has pacing ϕ, then the number of vertices in an optimal mesh will be O(ϕdn), where d is the input dimension. We give a new analysis of this integral showing that the output size is only θ(n+nlogϕ). The new analysis tightens bounds from several previous results and provides matching lower bounds. Moreover, it precisely characterizes inputs that yield outputs of size O(n). © 2012 Wiley Periodicals, Inc. (This work was partially supported by the National Science Foundation under grant number CCF-1065106, by GIGA grant ANR-09-BLAN-0331-01, and by the European project CG-Learning No. 255827.)