Querying simplexes in quasi-triangulation
- Authors
- Kim, Deok-Soo; Kim, Jae-Kwan; Cho, Youngsong; Kim, Chong-Min
- Issue Date
- Feb-2012
- Publisher
- ELSEVIER SCI LTD
- Keywords
- Voronoi diagram of spheres; Beta-shape; Beta-complex; Quasi-triangulation; Simplex query; Particle proximity; Orthogonal range search
- Citation
- COMPUTER-AIDED DESIGN, v.44, no.2, pp.85 - 98
- Indexed
- SCIE
SCOPUS
- Journal Title
- COMPUTER-AIDED DESIGN
- Volume
- 44
- Number
- 2
- Start Page
- 85
- End Page
- 98
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/166349
- DOI
- 10.1016/j.cad.2011.09.010
- ISSN
- 0010-4485
- Abstract
- Given a quasi-triangulation, the dual structure of the Voronoi diagram of a molecule, querying its simplexes of a particular bounding state for the spherical probe of a given radius occurs frequently. The beta-complex and the beta-shape are such examples with various applications for reasoning the spatial structure of molecules. While such simplexes can be found by linearly scanning all simplexes in the quasi-triangulation, it is desirable to do the query faster. This paper introduces the Q2P-transformation that transforms the simplex query problem in the three-dimensional space to the orthogonal range search problem of points in another three-dimensional space. Based on this observation, we show that the kd-tree data structure suits very well for developing efficient query algorithms for the quasi-triangulation of molecules using the set of sixteen primitive and the set of ten high-level query operators. In particular, the proposed method shows an extremely efficient performance for incremental queries. A subset of the presented observations facilitates efficient simplex queries for any simplicial complexes including the Delaunay and regular triangulations.
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