2021
DOI: 10.1109/tvcg.2019.2959321
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Dynamic Voronoi Diagram for Moving Disks

Abstract: Voronoi diagrams are powerful for understanding spatial properties. However, few reports have been made for moving generators despite their important applications. We present a topology-oriented event-increment (TOI-E) algorithm for constructing a Voronoi diagram of moving circular disks in the plane over the time horizon [0,t ∞ ). The proposed TOI-E algorithm computes the event history of the Voronoi diagram over the entire time horizon in O(k F log n + k C n log n) time with O(n log n) preprocessing time and… Show more

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Cited by 7 publications
(4 citation statements)
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“…A novel 3D visibility graph is proposed in [4] and applied in motion and control. Song [5] introduced dynamic Voronoi diagrams for moving disks. Debnath [6] compared the visibility graphs with the navigation meshes and Voronoi diagrams.…”
Section: Related Workmentioning
confidence: 99%
“…A novel 3D visibility graph is proposed in [4] and applied in motion and control. Song [5] introduced dynamic Voronoi diagrams for moving disks. Debnath [6] compared the visibility graphs with the navigation meshes and Voronoi diagrams.…”
Section: Related Workmentioning
confidence: 99%
“…e Voronoi diagram was proposed with the famous structure of computational geometry. It is widely used in many fields such as geometry, architecture, and geography [35][36][37][38]. Voronoi diagrams can partition data into set spaces and are effective in the study of local neighborhoods for each partition [39].…”
Section: Related Workmentioning
confidence: 99%
“…Wenzheng Chi et al [9] have presented a generalized-Voronoi-diagram (GVD)-based heuristic pathplanning algorithm to generate a heuristic path, guide the sampling process of RRTs, and further improve the motion-planning efficiency of RRTs. To solve the problems in dynamic environments, Chanyoung Song et al [10] have presented a data structure and algorithm to construct a Voronoi diagram composed of moving circular disks (dynamic Voronoi diagram of moving disks) in the plane.…”
Section: Introductionmentioning
confidence: 99%