A single beta-complex solves all geometry problems in a molecule

6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009

Volumn , Issue , 2009, Pages 254-260

  Kim, Deok Soo ^a  

^a Hanyang University   (South Korea)

Author keywords

Beta complex; Beta shape; Molecular geometry; Molecular structure; Quasi triangulation; Voronoi diagram

Indexed keywords

BETA-COMPLEX; BETA-SHAPE; GEOMETRY PROBLEMS; MOLECULAR GEOMETRIES; POWER DIAGRAMS; SHAPE ANALYSIS; VORONOI DIAGRAMS;

ATOMS; MOLECULAR STRUCTURE; MOLECULES; TRIANGULATION;

COMPUTATIONAL GEOMETRY;

EID: 77951429103     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ISVD.2009.41     Document Type: Conference Paper

References (27)

1. P. G. Mezey, Shape in Chemistry: An Introduction to Molecular Shape and Topology, VCH Publishers, 1993, iSBN: 0-89573-727-2.
2. A. Okabe, B. Boots, K. Sugihara, S. N. Chiu, Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, 2nd Edition, John Wiley & Sons, Chichester, 1999.
3. F. M. Richards, The interpretation of protein structures: Total volume, group volume distributions and packing density, Journal of Molecular Biology 82 (1974) 1-14.
4. J. D. Bernal, J. L. Finney, Random close-packed hard-sphere model ii. Geometry of random packing of hard spheres, Discussions of the Faraday Society 43 (1967) 62-69.
5. N. N. Medvedev, The algorithm for three-dimensional Voronoi polyhedra, Journal of Compuataional Physics 67 (1986) 223-229.
6. Y. I. Naberukhin, V. P. Voloshin, N. N. Medvedev, Geometrical analysis of the structure of simple liquids: Percolation approach, Molecular Physics 73 (1991) 917-936.
7. V. A. Luchnikov, N. N. Medvedev, L. Oger, J.-P. Troadec, Voronoi-Delaunay analysis of voids in systems of nonspherical particles, Physical Review E 59 (6) (1999) 7205-7212.
8. V. A. Luchnikov, N. Medvedev, Y. I. Naberukhin, H. R. Schober, Voronoi-Delaunay analysis of normal modes in a simple model glass, Physical Review B 62 (2000) 3181-3189.
9. N. N. Medvedev, V. P. Voloshin, V. A. Luchnikov, M. L. Gavrilova, An algorithm for three-dimensional Voronoi S-network, Journal of Computational Chemistry 27 (14) (2006) 1676-1692.
10. G. F. Voronoi, Novelles applications des paramètres continus à la thèorie des formes audratiques, Journal fur die Reine und Angewandte Mthematik 134 (1908) 198-287.
11. F. Aurenhammer, Voronoi diagrams - a survey of a fundamental geometric data structure, ACM Computing Surveys 23 (3) (1991) 345-405.
12. F. Aurenhammer, Power diagrams: Properties, algorithms and applications, SIAM Journal on Computing 16 (1987) 78-96
13. M. Sanner, Modelling and applications of molecular surfaces, Ph.D. thesis, Université de Haute-Alsace, France (1992).
14. D. Halperin, M. H. Overmars, Spheres, molecules, and hidden surface removal, in: Proceedings of the 10th ACM Symposium on Computational Geometry, 1994, pp. 113-122.
15. A. Varshney, W. V. W. Brooks, Jr., Computing smooth molecular surfaces, IEEE Computer Graphics and Applications 14 (1994) 19-25.
16. J.-D. Boissonnat, M. Yvinec, Algorithmic Geometry, Cambridge University Press, Cambridge, 1998.
17. D.-S. Kim, Y. Cho, D. Kim, Euclidean Voronoi diagram of 3D balls and its computation via tracing edges, Computer-Aided Design 37 (13) (2005) 1412-1424.
18. D. Kim, D.-S. Kim, Region-expansion for the Voronoi diagram of 3D spheres, Computer-Aided Design 38 (5) (2006) 417-430.
19. H.-M. Will, Computation of additively weighted Voronoi cells for applications in molecular biology, Ph.D. thesis, Swiss Federal Institute of Technology, Zurich (1999).
20. T. Nishida, K. Sugihara, Precision necessary for d-dimensional sphere voronoi diagrams, in: Proceedings of the 5th International Symposium on Voronoi diagrams in Science and Engineering, 2008, pp. 22-28.
21. D.-S. Kim, D. Kim, Y. Cho, K. Sugihara, Quasi-triangulation and interworld data structure in three dimensions, Computer-Aided Design 38 (7) (2006) 808-819.
22. J. Liang, H. Edelsbrunner, C. Woodward, Anatomy of protein pockets and cavities: Measurement of binding site geometry and implications for ligand design, Protein Science 7 (1998) 1884-1897.
23. A. Goede, R. Preissner, C. Frömmel, Voronoi cell: New method for allocation of space among atoms: Elimination of avoidable errors in calculation of atomic volume, Journal of Computational Chemistry 18 (9) (1997) 1113-1123.
24. A. Poupon, Voronoi and Voronoi-related tessellations in studies of protein structure and interaction, Current Opinion in Structural Biology 14 (2004) 233-241.
25. A. J. Hopfinger, Conformational Properties of Macromolecules, Academic Press, 1973.
26. R. PDB, Rcsb pdb 2008 annual report, Tech. rep., RCSB PDB (2008).
27. RCSB Protein Data Bank Homepage, http://www.rcsb.org/pdb/ (2009).