Querying simplexes in quasi-triangulation
- Title
- Querying simplexes in quasi-triangulation
- Author
- 김덕수
- Keywords
- Voronoi diagram of spheres; Beta-shape; Beta-complex; Quasi-triangulation; Simplex query; Particle proximity; Orthogonal range search
- Issue Date
- 2012-02
- Publisher
- Elsevier Science B.V., Amsterdam.
- Citation
- Computer-Aided Design, Vol.44, No.2 [2012], p85-98
- 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.
- URI
- http://www.sciencedirect.com/science/article/pii/S0010448511002430?via%3Dihubhttp://hdl.handle.net/20.500.11754/67395
- ISSN
- 0010-4485
- DOI
- 10.1016/j.cad.2011.09.010
- Appears in Collections:
- COLLEGE OF ENGINEERING[S](공과대학) > MECHANICAL ENGINEERING(기계공학부) > Articles
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