Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
ACM Computing Surveys (CSUR)
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
A Revised Simplex Search Procedure for Stochastic Simulation Response Surface Optimization
INFORMS Journal on Computing
An efficient algorithm for three-dimensional β-complex and β-shape via a quasi-triangulation
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Molecular surfaces on proteins via beta shapes
Computer-Aided Design
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Expert Systems with Applications: An International Journal
Euclidean Voronoi diagram of 3D balls and its computation via tracing edges
Computer-Aided Design
Quasi-worlds and quasi-operators on quasi-triangulations
Computer-Aided Design
Three-dimensional beta-shapes and beta-complexes via quasi-triangulation
Computer-Aided Design
Fast Discovery of Voronoi Vertices in the Construction of Voronoi Diagram of 3D Balls
ISVD '10 Proceedings of the 2010 International Symposium on Voronoi Diagrams in Science and Engineering
Searching Simplexes in Quasi-triangulation
ISVD '10 Proceedings of the 2010 International Symposium on Voronoi Diagrams in Science and Engineering
Reduction of the search space in the edge-tracing algorithm for the voronoi diagram of 3d balls
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
QTF: Quasi-triangulation file format
Computer-Aided Design
Technical Section: Efficient construction of the Čech complex
Computers and Graphics
Anomalies in quasi-triangulations and beta-complexes of spherical atoms in molecules
Computer-Aided Design
Protein structure optimization by side-chain positioning via beta-complex
Journal of Global Optimization
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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.