Robust construction of the additively-weighted voronoi diagram via topology-oriented incremental algorithm
- Authors
- Lee, M.; Sugihara, K.; Kim, D.-S.
- Issue Date
- 2016
- Publisher
- Springer Verlag
- Keywords
- Additively-weighted; Algorithm; Circle; Disk; Robustness; Topology-oriented; Voronoi diagram
- Citation
- Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), v.9725, pp.514 - 521
- Indexed
- SCOPUS
- Journal Title
- Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
- Volume
- 9725
- Start Page
- 514
- End Page
- 521
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/24750
- DOI
- 10.1007/978-3-319-42432-3_66
- ISSN
- 0302-9743
- Abstract
- Voronoi diagrams tessellate the space where each cell corresponds to an associated generator under an a priori defined distance and have been extensively used to solve geometric problems of various disciplines. Additively-weighted Voronoi diagrams, also called the Voronoi diagram of disks and spheres, have many critical applications and a few algorithms are known. However, algorithmic robustness remains a major hurdle to use these Voronoi diagrams in practice. There are two important yet different approaches to design robust algorithms: the exact-computation and topology-oriented approaches. The former uses high-precision arithmetic and guarantees the correctness mathematically with the cost of a significant use of computational resources. The latter focuses on topological properties to keep consistency using logical computation rather than numerical computation. In this paper, we present a robust and efficient algorithm for computing the Voronoi diagram of disks using a topology-oriented incremental method. The algorithm is rather simple as it primarily checks topological changes only during each disk is incrementally inserted into a previously constructed Voronoi diagram of some other disks.
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