Dynamic Voronoi Diagram for Moving Disksopen access
- Authors
- Song, Chanyoung; Cha, Jehyun; Lee, Mokwon; Kim, Deok-Soo
- Issue Date
- Jun-2021
- Publisher
- IEEE COMPUTER SOC
- Keywords
- Unmanned vehicles; moving vehicles; path planning; collision avoidance; topology event; weighted Voronoi diagram
- Citation
- IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, v.27, no.6, pp.2923 - 2940
- Indexed
- SCIE
SCOPUS
- Journal Title
- IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
- Volume
- 27
- Number
- 6
- Start Page
- 2923
- End Page
- 2940
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/1108
- DOI
- 10.1109/TVCG.2019.2959321
- ISSN
- 1077-2626
- 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(infinity)) . 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)nlog n) time with O(nlog n) preprocessing time and O(n + k(F) + k(C)) memory for n disk generators, k(F) edge flips, and k(C) disk collisions during the time horizon. Given an event history, the Voronoi diagram of an arbitrary moment t* < t(infinity )can be constructed in O(k* + n) time where k* represents the number of events in [0, t*) . An example of the collision avoidance problem among moving disks is given by predicting future conjunctions among the disks using the proposed algorithm. Dynamic Voronoi diagrams will be very useful as a platform for the planning and management of the traffics of unmanned vehicles such as cars on street, vessels on surface, drones and airplanes in air, and satellites in geospace.
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