Quasi-worlds and quasi-operators on quasi-triangulations
- Authors
- Kim, Deok-Soo; Cho, Youngsong; Sugihara, Kokichi
- Issue Date
- Oct-2010
- Publisher
- ELSEVIER SCI LTD
- Keywords
- Voronoi diagram of spheres; Quasi-triangulation; Quasi-world; Topology; Extended inter-world data structure; Simplex; Complex
- Citation
- COMPUTER-AIDED DESIGN, v.42, no.10, pp.874 - 888
- Indexed
- SCIE
SCOPUS
- Journal Title
- COMPUTER-AIDED DESIGN
- Volume
- 42
- Number
- 10
- Start Page
- 874
- End Page
- 888
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/173640
- DOI
- 10.1016/j.cad.2010.06.002
- ISSN
- 0010-4485
- Abstract
- Quasi-triangulation is the dual structure of the Voronoi diagram of spheres, and it has been used as a convenient and powerful geometric construct for representing the proximity among spherical particles with different radii. In this paper, we present the formalism of the quasi-triangulation based on a quasi-world model and define primitive query operators called quasi-operators for correct and efficient topology traversal on the quasi-triangulation. Algorithms for the quasi-operators are also presented based on the extended inter-world data structure. The proposed quasi-operators have the potential to be a fundamental platform on which efficient algorithms for application problems on quasi-triangulation can be correctly and easily developed. The recently announced powerful constructs of the beta-complex and the beta-shape are such examples.
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