Paper Info
Title
Querying simplexes in quasi-triangulation
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 @b-complex and the @b-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.
Year
DOI
Venue
2012
10.1016/j.cad.2011.09.010
Computer-Aided Design
Keywords
Field
DocType
kd-tree data structure suit,high-level query operator,incremental query,simplex query problem,observations facilitates efficient simplex,efficient query algorithm,querying simplex,efficient performance,three-dimensional space,spatial structure,dual structure
Discrete mathematics,Data structure,Mathematical optimization,Algorithm,Simplex,Operator (computer programming),Voronoi diagram,Search problem,Quasi-triangulation,Mathematics,Delaunay triangulation,Bounding overwatch
Journal
Volume
Issue
ISSN
44
2
0010-4485
Citations 
PageRank 
References 
9
0.58
17
Authors
4
Name
Order
Citations
PageRank
Deok-Soo Kim163359.12
Jaekwan Kim2555.70
Youngsong Cho325022.15
Chong-Min Kim490.58