Anomaly occurrences in quasi-triangulations and Beta-complexes
- Authors
- Kim, Donguk; Cho, Youngsong; Kim, Deok-Soo
- Issue Date
- Jul-2013
- Publisher
- IEEE Computer Society
- Keywords
- anomaly; beta-complex; quasi-triangulation; Voronoi diagram of spheres
- Citation
- ISVD 2013 - 10th International Symposium on Voronoi Diagrams in Science and Engineering, pp.82 - 88
- Indexed
- SCOPUS
- Journal Title
- ISVD 2013 - 10th International Symposium on Voronoi Diagrams in Science and Engineering
- Start Page
- 82
- End Page
- 88
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/162355
- DOI
- 10.1109/ISVD.2013.18
- Abstract
- Voronoi diagrams, quasi-triangulations, and beta-complexes are powerful for solving spatial problems among spherical particles with different radii. However, a quasi-triangulation, and thus a beta-complex as well, can be a non-simplicial complex due to an anomaly condition. While a beta-complex is straightforward to use when it is a simplicial complex, it may not seem obvious if it is not. In this paper, we report the experimental statistics of showing the frequency of anomaly case occurrences in both quasi-triangulations and beta-complexes of molecular structures and randomly generated models in three-dimension. The experiment was based on 100 molecular structures from the protein data bank (PDB) and four random sets where each set consists of 100 models of three-dimensional spheres. Anomalies extremely rarely occur in molecular structures and rarely occur even in random sphere sets.
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