Voronoi Diagrams and Delaunay Triangulations

By Steven J. Fortune. Handbook of Discrete and Computational Geometry, 2nd Ed., 2004

1,058 citations recorded by the source corpus.

Subfields: Building and Construction, Computer Graphics and Computer-Aided Design, Signal Processing

View Paper: https://www.semanticscholar.org/paper/c3c1b4afbd6d79ce37dcafbd3418abbd2d592cc6

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Citations in the corpus

Coverage in wireless ad-hoc sensor networks (2002, methodology): “Delaunay triangulation and Voronoi diagram [4], [5], [6] are widely used in many areas.”
Movement-assisted sensor deployment (2004, background): “TECHNICAL PRELIMINARY: VORONOI DIAGRAM The Voronoi diagram [14], [15] is an important data structure in computational geometry.”
ALEXANDROV'S THEOREM, WEIGHTED DELAUNAY TRIANGULATIONS, AND MIXED VOLUMES (2006, background): “Originally weighted Delaunay triangulations were defined for V ⊂ R2, and M the convex hull of V , see [4], [9], [13].”
Keyframe-based video summarization using Delaunay clustering (2006, background): “Hence, edges of the DT capture spatial proximity [9].”
Coverage control for mobile sensing networks (2002, background): “A. Setting up the coverage control In this section we investigate decentralized control laws that achieve " uniform coverage " of a certain space.”
Coverage control for mobile sensing networks (2002, background): “An overview of Voronoi diagrams is presented in [24], [25], concepts and applications are discussed in [26] and abstract Voronoi diagrams are discussed in [27].”
Predictive Control for Linear and Hybrid Systems (2017, background): “The Delaunay triangulation [109], which has the nice property of minimizing the number of skinny triangles, or those with small angles is a common choice for which incremental update algorithms are well-studied and readily available (i.”
A Survey on Topology Control in Wireless Sensor Networks: Taxonomy, Comparative Study, and Open Issues (2008, methodology): “Voronoi diagrams [5], [29] are used to discover the coverage holes, and three movement-assisted sensor deployment protocols VEC, VOR, and Minimax are proposed, based on the principle of moving sensors from the densely deployed areas to the sparsely deployed areas.”
A Comprehensive Survey and Experimental Comparison of Graph-Based Approximate Nearest Neighbor Search (2021, methodology): “, x,y, z) on the circle at the same time (see [35] for DG’s standard definition).”
Spectral surface reconstruction from noisy point clouds (2004, neutral): “See Fortune [For92] for an introduction.”
Laguerre Voronoi Diagram on the Sphere (2002, background): “The Voronoi diagram is one of the most fundamental concepts in computational geometry, and has been generalized in many directions [5, 8, 10, 17, 19].”
Geometric Approximation Algorithms (2011, background): “The Delaunay triangulation has the property that it maximizes the minimum angle of the triangulation, among all triangulations of the point set [For97].”
A FRAMEWORK FOR MAINTAINING FORMATIONS BASED ON RIGIDITY (2002, background): “(Fortune, 1995) Every polygon with more than three sides has a diagonal.”
A Fully Automated Framework for Control of Linear Systems from Temporal Logic Specifications (2008, background): “polytopes and to [33] and [35] for more information on triangulations.”