Fast discovery of Voronoi vertices in the construction of Voronoi diagram of 3D balls

ISVD 2010 - 7th International Symposium on Voronoi Diagrams in Science and Engineering

Volumn , Issue , 2010, Pages 95-104

  Maňák, Martin ^a   Kolingerová, Ivana ^a  

^a UNIVERSITY OF WEST BOHEMIA   (Czech Republic)

Author keywords

Computational geometry; ; Edge tracing; Feasible regions; Voronoi diagram of spheres

Indexed keywords

DELAUNAY TRIANGULATION; EDGE TRACING; FEASIBLE REGIONS; GEOMETRICAL PROBLEMS; NEW APPROACHES; PROTEIN DATA; QUADRATIC TIME; SPATIAL FILTERS; VORONOI DIAGRAMS; VORONOI VERTICES;

CASCADES (FLUID MECHANICS); GRAPHIC METHODS; SPHERES; THREE DIMENSIONAL;

COMPUTATIONAL GEOMETRY;

EID: 77955694898     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ISVD.2010.22     Document Type: Conference Paper

References (17)

1. A. Bondi, "van der Waals Volumes and Radii," Journal of Physical Chemistry, vol.68, no.3, pp. 441-451, March 1964.
2. P. Medek, P. Beneš, and J. Sochor, "Computation of tunnels in protein molecules using Delaunay triangulation," Journal of WSCG, vol.15, no.1-3, pp. 107-114, January 2007.
3. D.-S. Kim, "A beta-complex solves all geometry problems in a molecule," in The 6th International Symposium on Voronoi Diagrams in Science and Engineering, 2009, pp. 254-260.
4. D.-S. Kim, D. Kim, Y. Cho, and K. Sugihara, "Quasitriangulation and interworld data structure in three dimensions," Computer-Aided Design, vol.38, no.7, 2006.
5. D.-S. Kim, D. Kim, and Y. Cho, "Euclidean Voronoi diagrams of 3d spheres: Their construction and related problems from biochemistry," in IMA Conference on the Mathematics of Surfaces, 2005, pp. 255-271.
6. D.-S. Kim, Y. Cho, and D. Kim, "Euclidean Voronoi diagram of 3d balls and its computation via tracing edges," Computer-Aided Design, vol.37, pp. 1412-1424, 2005.
7. N. N. Medvedev, V. P. Voloshin, V. A. Luchnikov, and M. L. Gavrilova, "An algorithm for three-dimensional Voronoi S-network," Journal of Computational Chemistry, vol.27, no.14, pp. 1676-1692, 2006.
8. D. Kim and D.-S. Kim, "Region-expansion for the Voronoi diagram of 3d spheres," Computer-Aided Design, vol.38, pp. 417-430, 2006.
9. M. Gavrilova, "A reliable algorithm for computing the generalized Voronoi diagram for a set of spheres in the euclidean d-dimensional space."
10. J.-D. Boissonnat and C. Delage, "Convex hull and Voronoi diagram of additively weighted points," in ESA, 2005.
11. Y. Cho, D. Kim, H.-C. Lee, J. Y. Park, and D.-S. Kim, "Reduction of the search space in the edge-tracing algorithm for the Voronoi diagram of 3d balls," in ICCSA (1), 2006.
12. "CGAL, Computational Geometry Algorithms Library," http://www.cgal.org.
13. M. Tanemura, T. Ogawa, and N. Ogita, "A new algorithm for three-dimensional Voronoi tessellation," Journal of Computational Physics, vol.51, no.2, pp. 191-207, 1983.
14. E. Yaffe and D. Halperin, "Approximating the pathway axis and the persistence diagram of a collection of balls in 3-space," in SCG '08: Proceedings of the twenty-fourth annual symposium on Computational geometry. New York, NY, USA: ACM, 2008, pp. 260-269.
15. "RCSB PDB," http://www.rcsb.org.
16. M. Zemek and I. Kolingerova, "A library for the construction of a dynamic regular and Delaunay tetrahedronization," 2009, http://www.kiv.zcu.cz/en/research/software/detail.html?id=39.
17. "QuteMol," http://qutemol.sourceforge.net.