Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Toward the simulation of spatial mental images using the Voronoi¨ model
Representation and processing of spatial expressions
Kinetic data structures: a state of the art report
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Data structures for mobile data
Journal of Algorithms
Box-trees and R-trees with near-optimal query time
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Dense point sets have sparse Delaunay triangulations: or "…but not too nasty"
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Proximity and applications in general metrics
Proximity and applications in general metrics
A compact piecewise-linear Voronoi diagram for convex sites in the plane
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Data Structures for Efficient Dynamic Processing in 3-D
International Journal of Robotics Research
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In this paper, we give the definition for the voronoi diagram and its dual graph - Delaunay triangulation for 3D cuboids. We prove properties of the 3D Delaunay triangulation, and provide algorithms to construct and update the Delaunay triangulation. The Delaunay triangulation data structure is used to perform proximity searches for both static and kinetic cases. We describe experimental results that show how the Delaunay triangulation is used on a mobile robot to model, understand and reason about the spatial information of the environment.