Topology-Oriented Incremental Algorithm for the Robust Construction of the Voronoi Diagrams of Disks
- Authors
- Lee, Mokwon; Sugihara, Kokichi; Kim, Deok-Soo
- Issue Date
- Sep-2016
- Publisher
- ASSOC COMPUTING MACHINERY
- Keywords
- Algorithms; Theory; Additively-weighted Voronoi diagram; disks; quasi-triangulation; betacomplex; simplex; simplicial complex; topology
- Citation
- ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, v.43, no.2, pp.1 - 23
- Indexed
- SCIE
SCOPUS
- Journal Title
- ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
- Volume
- 43
- Number
- 2
- Start Page
- 1
- End Page
- 23
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/2521
- DOI
- 10.1145/2939366
- ISSN
- 0098-3500
- Abstract
- Voronoi diagrams are useful for spatial reasoning, and the robust and efficient construction of the ordinary Voronoi diagram of points is well known. However, its counterpart for circular disks in R-2 and spherical balls in R-3 remains a challenge. In this article, we propose a topology-oriented incremental algorithm which robustly and efficiently computes a Voronoi diagram by incrementing a new disk generator to an existing one. The key idea is to enforce the convexity of the Voronoi cell corresponding to the incrementing disk so that a simple variation of the algorithm for points proposed by Sugihara in 1992 can be applied. A benchmark using both random and degenerate disks shows that the proposed algorithm is superior to CGAL in both computational efficiency and algorithmic robustness.
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